Chapter One:

Supply, Demand, and Equilibrium

General Discussion

Even after a course in principles, many students are confused about the fundamentalsof supply and demand. The most frequent sources of difficulty are:

1) The distinction between demand and quantity demanded. The text places consid-erable emphasis on this. I always tell my students that a failure to grasp this distinctionresults in the ability to make arguments that sound very logical but are in fact incorrect;problem 4 at the end of the chapter provides a good example. I have occasionally madeit a semester-long assignment to collect examples of such fallacies from the popular press;students with subscriptions to the New York Times or the Wall Street Journal have ampleraw material to work from.

2) A failure to understand that the equilibrating process does not affect the supplyand demand curves. The story that we tell about price adjustment following a tempo-rary disequilibrium does not involve any changes in the quantities that people desire toexchange.

3) A failure to understand the role of price adjustment from a point of disequilibriumin the supply and demand model. It is important for students to understand that in thissimple model we always assume that all markets are in equilibrium. We do tell storiesabout what we think would happen out of equilibrium (demanders bidding up prices thatare too low or suppliers bidding down prices that are too high), but the purpose of thesestories is only to motivate the assumption that disequilibrium does not occur. Studentssometimes come away with the false impression that the details of price adjustment are anintegral part of the model and that the model attempts to describe the path to equilibrium.It is important to be on guard against this.

4) An incorrect approach to comparative statics. Ask students what will happen tothe price of bread following a rise in the price of butter. Some will respond that bread isnow less desirable, so that people want less of it, which causes the price to be bid down.Others may respond that in that case, less bread will be produced, and this fall in quantitywill lead to a higher price. This in turn calls more bread into the market, which causesthe price to be bid down, which causes... It is distressingly common for students to beginreasoning in such a circle, stop at an arbitrary point, and think that they have reacheda correct conclusion. I stress to my students that when you are asked how the price ofbread will react in a given circumstance, it is never correct to begin by thinking aboutthe price of bread. One must begin by thinking about the effects on supply and demand(in this case, demand is down and supply is unchanged) and only then infer the effect onprice (in this case, price is down).

Many students are bothered by two aspects of this analysis. First, it will seem tothem (correctly) that each step in the earlier, convoluted analysis is an important oneand that all of these counteracting effects need to be taken into account. They believe(incorrectly) that the supply and demand analysis fails to do this. Second, they simplywill not see any reason why the supply and demand analysis should be preferred to themore naive approach.

To address these questions, I sometimes ask students to volunteer the various directand indirect ways in which the price of bread is affected by an increase in the price ofbutter. (In fact, this works even better if you use a slightly more complicated examplein which both supply and demand change simultaneously.) I list them on the blackboard

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(1: lower demand leads to lower price; 2: less bread produced causes price to be bid up,etc.) When the list is long enough, I point out that no one could possibly sort out all ofthese countervailing effects and come to a conclusion without some additional device. Ithen point out that supply and demand analysis is such a device. The key (and for manystudents, this must really be stressed) is that in the single shift of the demand curve,we really do take account of all of these effects simultaneously. The fact that all of theeffects are important is exactly what makes it both correct and necessary to resort tocurve-shifting.

Teaching Suggestions

1) Regarding the seat belt example on pp. 9-10: Someone (I think Armen Alchian)has suggested that the best way to prevent highway deaths might be to require thatevery car have a spear mounted on the steering wheel aimed directly at the driver’s heart.Surely this would reduce the number of accidents. This observation always gets a laughand makes the point.

2) For another example of how people react to prices in non-market situations: Thereis apparently a psychology experiment in which subjects are given cups of coffee and toldthat they can keep the cups. They are not warned that the cups are extremely hot. Whenthe cup is clearly inexpensive, subjects usually drop it; when it is made of fine china, theymanage to hang on. I wanted to include this example in the book but was not able totrack down a reference on time.

3) Along the same lines, you can cite the paper of Viscusi in the 1984 AmericanEconomic Review : Apparently when child safety caps on medicines are made more difficultto remove, sufficiently many people stop using the caps at all that there is an increase inthe number of accidental poisonings.

4) For some students it might be necessary to stress that equilibrium can occur atany price and quantity, and that unusually high or low prices do not imply disequilibrium.For example, if wages are very low and few people are working, some students want tojump to the conclusion that there is disequilibrium in the labor market.

Point out to them that a low demand curve for labor explains the same phenomenon.

5) To drive home the inverse relationship between price and quantity demanded,you might mention that in August, 1990, East German taxicab drivers went on strike todemand lower fares.

6) Here is a slightly different way to present the material in Exhibit 1–10 (the economicincidence of a tax is independent of its legal incidence). Begin by drawing a graph showingjust the original supply and demand curves. Note that ultimately the suppliers must beon their supply curve and the demanders must be on their demand curve; otherwise priceswill adjust.

Now note that a 5 cent tax, regardless of its legal nature, drives a 5 cent “wedge”between the suppliers’ price and the demanders’ price. Take a piece of chalk, hold itvertically, and say that its length is “5 cents.” Then hold the chalk vertically between thesupply and demand curves near the price axis, and slowly move it rightward until its topand bottom just touch the demand and supply curves. Conclude that you have found thepost-tax equilibrium. Now note that in order to find this equilibrium, you never had toask what sort of tax was being imposed; thus such information must be irrelevant.

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Additional Problems

1. Proctor and Gamble will soon market a product called Olestra, which can be used inplace of fat in cooking, but is very low in calories. Thus it will be possible to makelow-calorie hamburgers, french fries, milkshakes, and so forth. True or False: Theaverage American will weigh less after this product appears on the market.

2. True or False: If a frost wipes out half the Florida orange crop, then some peoplewho want to buy oranges will not be able to.

3. True or False: If we observe a reduction in the number of cars being purchased, thenwe should expect this change in demand to lead to a fall in price.

4. True or False: A sharp rise in the price of eggs would be unlikely to last very long;after all, the rise in price would lead to a fall in demand, and this fall in demandwould then cause the price to fall.

5. True or False: According to the laws of supply and demand, when the price of a goodrises, less of that good will be sold.

6. True or False: In the cities, there are more medical services provided than there arein rural areas. Nevertheless, the price of medical services is higher in the cities. Thisindicates that our simple “supply and demand” story does not apply to markets forthings like medical care.

7. True or False : If both the quantity consumed and the price of medical services haverisen in the last fifteen years, then the demand curve for medical services must haveshifted.

8. Ice cream is more expensive in New York than in Iowa, but nevertheless New Yorkerseat more ice cream than Iowans do.True or False: This is contrary to what a simple “supply and demand” analysis wouldpredict.

9. If the price of ice cream is higher in New York than in Iowa, it must be because thedemand for ice cream is higher in New York.

10. If the demand curve for avocados is horizontal, then an excise tax on avocados willbe passed on entirely to demanders.

11. If the supply curve for corn is perfectly horizontal, how will an excise tax affect themareket price of corn? What about a sales tax?

12. If the supply curve for corn is perfectly vertical, how will an excise tax affect themareket price of corn? What about a sales tax?

13. True or False: Some cities raise revenue by levying a tax on employers equal to acertain number of dollars per employee per year. This is a good thing for workers,because workers are not taxed.

14. Coconino County raises revenue through a tax on workers: everybody who has a jobin Coconino County must pay a tax of $25 per year. It has been proposed that thistax be abolished and replaced by a tax on businesses equal to $25 per employee peryear. True or False: Although this change sounds like a good thing for workers, itmight actually turn out to be bad for them, since the number of jobs would go down.

15. Coconino County raises revenue through a tax on workers: everybody who has a jobin Coconino County must pay a tax of $25 per year. It has been proposed that thistax be abolished and replaced by a tax on businesses equal to $25 per employee per

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year. True or False: Although this change sounds like a good thing for workers, itmight actually turn out to be bad for them, since it could cause wages to fall.

16. The government of Fredonia wants to increase employment and is deciding betweentwo plans. Plan I is to encourage hiring by giving employers $1 for each hour of laborthat they hire. Plan II is to encourage entry into the labor market by giving workers$1 (in addition to their salary) for every hour that they work.a) Show separately how each plan affects the demand for labor, the supply of labor,

and the equilibrium wage rate.b) Which plan is better for workers? Which plan is better for employers?c) Referring to your graphs from part a), carefully explain how you were able to

draw the conclusion in part b).

17. The government of Coconino County wants to encourage firms to hire more workers.To accomplish this, each firm receives a government subsidy of $100 per year for eachworker on the payroll. To raise the funds for this program, everybody who has ajob in Coconino County must pay a $100 per year “employment tax”. Recently, acity councilman has proposed abolishing the entire program (eliminating both thesubsidies to firms and the tax on workers). True or False: If the councilman has hisway, there will be fewer jobs in Coconino County.Justify your answer carefully, by looking at the effects on both the supply and demandfor labor.

18. Suppose that for some reason, Canadian companies want to sell exactly 100 widgetsper year in the U.S., regardless of the price. American widget producers like toproduce more widgets when the price goes up.a) In the U.S. widget market, draw the Canadian companies’ supply curve and the

overall supply curve.Now suppose that the U.S. government wants to improve the fortunes of U.S. widget-makers, and is considering two plans to accomplish this. Under Plan A, all Canadianimports will be banned. Under Plan B, the U.S. government will purchase 100 widgetsper year from American manufacturers at whatever is the going price.b) Use supply and demand diagrams to illustrate the effects of these two plans.

Which is better for the widget-makers? How do you know?

19. Suppose that the only way to reach a certain restuarant is by train, and the trainfare is $3. One day a law is passed requiring the restaurant owner to provide freetransportation to his restaurant, which he does by making an arrangement with therailroad whereby his customers ride free and he pays the $3 fare per customer directlyto the railroad.a) What does this do to the supply curve for restaurant meals?b) What does this do the demand curve for restaurant meals (Hint: It does not

stay fixed.)c) What does this do to the price and quantity served of restaurant meals?d) Of the following, who benefits and who loses as a result of this law: The restau-

rant owner, the restaurant customers, the railroad?

20. Apples are currently subject to a sales tax of 10 cents per apple. They sell for 25cents apiece (that is, to buy an apple, the consumer must pay 25 cents plus 10 centssales tax).a) Suppose the sales tax is eliminated. How much can you say about the new price

of apples?b) Suppose the sales tax is replaced by an excise tax of 10 cents per apple. How

much can you say about the new price of apples?

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21. The following diagram shows the demand and supply for widgets:

a) Suppose the government imposes a sales tax of $5 per widget. What is the newprice of widgets, and how many are sold? Briefly explain how you got youranswer.

b) Suppose instead that the government imposes an excise tax of $5 per widget.What is the new price of widgets, and how many are sold?

c) Which tax is better for consumers? Explain your answer in one sentence, basedon your answers to parts a) and b).

22. The market for yachts is in equilibrium at a quantity of 500 per year; all 500 arebought by private citizens. Suppose the U.S. government announces that henceforthit will buy 150 yachts per year (regardless of the price).a) What happens to the demand for yachts?b) Now how many yachts are bought by private citizens? (Hint: The number bought

by private citizens is equal to the total number bought minus the the numberbought by the government.) If it is possible to answer this question with anexact number, do so. Otherwise, give a range of numbers (like “between 1,000and 2,000”). Explain how you got your answer.

23. Suppose that a sales tax would cause the price of an apple to fall by 3 cents. Whatwould be the effect of an excise tax of 10 cents per apple? (Remember that “price”means the pre-tax price.)

24. Suppose that a 40 cent excise tax on apples would lead to a 35 cent increase in themarket price of apples. How would a 40 cent sales tax affect the market price ofapples?(The “market price” means the price paid by the buyer to the seller, not including

any taxes paid by the buyer.)

25. True or False: If the demand curve for rabbit fur is perfectly horizontal, then anexcise tax on rabbit fur would be passed on entirely to demanders.

26. Two presidential candidates have offered different economic platforms. Paul Simon,a Democrat, proposes to help the working class by giving each worker an income tax

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reduction of $1 for each hour that he works. Art Garfunkel, a Republican, proposesto encourage employment by giving every firm a subsidy of $1 for each hour of laborthat it hires.a) Illustrate the effects of the Simon plan on the demand and supply curves for

labor.b) Illustrate the effects of the Garfunkel plan on the demand and supply curves for

labor.c) True or False: Workers might actually prefer the Garfunkel plan because it

encourages firms to offer more jobs at higher wages. Justify your answer carefully.

27. The government is considering an economic plan under which consumers will pay anew sales tax of 50 cents per gallon of gasoline. The revenue will be used to paysubsidies to gas station owners, who will receive 50 cents from the government forevery gallon of gas that they sell.a) How does this plan affect the demand curve for gasoline?b) How does this plan affect the supply curve for gasoline?c) True or False: Although this plan looks like a good thing for gas station owners,

it might actually hurt them because demanders will buy less gasoline.

28. Suppose that it costs car manufacturers $1,000 to install an air bag in a car, and thateach customer values an air bag at $500. A new law requires every car to have an airbag.a) Show how the new law affects the demand and supply curves for cars.b) What happens to the price of a car after the law is passed? Does it go up or

down? Does it change by more or less than $500? Does it change by more orless than $1,000?

c) Are consumers made better or worse off by this law? Justify your answer.

29. Suppose that wheat is purchased only by poor people, whose demand for wheat isgiven by the following chart:

Price Quantity$1 8 bushels2 73 64 5

In the spirit of Christmas, a coalition of rich people has decided to buy wheat at thegoing market price (whatever that price happens to be) and resell it to poor peopleat half that price. Moreover, they will buy and resell as much wheat as poor peoplecare to purchase.a) List the coordinates of four points on the new demand curve (that is, the rich

people’s demand curve) for wheat.b) Suppose that the supply curve for wheat is vertical at a quantity of 7. Do the

poor benefit from the generosity of the rich?c) Suppose instead that the supply curve for wheat is horizontal at a price of $2.

Do the poor benefit from the generosity of the rich?

30. Apples currently sell for 20 cents apiece. Label each of the following statementscertainly true, possibly true or certainly false and justify your answers:a) A 10 cent sales tax would cause the price to fall to 15 cents, and a 10 cent excise

tax would cause the price to rise to 25 cents.b) A 10 cent sales tax would cause the price to fall to 14 cents, and a 10 cent excise

tax would cause the price to rise to 26 cents.

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c) A 10 cent sales tax would cause the price to fall to 11 cents and a 10 cent excisetax would cause the price to rise to 21 cents.

d) Neither tax would affect the price.

31. Cars currently sell for $1500 apiece, plus $500 sales tax.a) If the sales tax is eliminated, what can you say about the new price of cars?b) If the sales tax is eliminated and replaced by a $500 excise tax, what can you

say about the new price of cars?c) If the sales tax is eliminated and replaced by a $1000 excise tax, what can you

say about the new price of cars?

32. Suppose a new law requires students to give each of their professors a $100 tip at theend of the semester.a) What happens to the demand for college courses?b) What happens to the supply of college courses?c) Are students made better or worse off as a result of this law? What about

professors? Justify your answer.

33. Apples currently sell for 50 cents apiece. The government is considering three differentplans. Plan A is to subsidize apple purchases; every time you buy an apple, you geta dime back from the government. Plan B is to subsidize apple sales; every time yousell an apple, you get a dime back from the government. Plan C is to tax apple sales:Every time you sell an apple, you pay a dime to the government. When Plan A isinstituted, the price of apples rises to 57 cents.a) What would have happened to the price of apples if the government had insti-

tuted Plan B instead of Plan A?b) What would have happened to the price of apples if the government had in-

stituted Plans A and C simultaneously instead of Plan A alone? Justify youranswer.

34. Suppose a new law requires every college professor in your city to wear a specialuniform while teaching. These uniforms must be rented from the mayor’s brother ata cost of $1 per hour. With the law in effect, universities pay professors $5.40 perhour.a) If the law were repealed, how much would professors get paid?b) If the law were replaced by a new law requiring the universities to pay for the

uniforms (at the same $1 per hour), how much would professors get paid?For each part your answer should be an exact number if possible, or a range of numbersotherwise. (Hint: Remember that the professors are the suppliers of teaching servicesand universities are the demanders.)

35. The federal government wants to improve the fortunes of domestic car manufacturersand is considering two plans to accomplish this. Under Plan A, every purchaser of adomestic car would receive a $100 rebate from the government. Under Plan B, carmanufacturers would receive a $100 rebate from the government for every car theysell.a) How does Plan A affect the demand for cars?b) How does Plan B affect the supply of cars?c) Compare and contrast the effects of the two plans.

36. A new law requires each firm to provide its workers with free parking spaces. Thesespaces are worth $200 a year to the workers and cost firms $500 a year to provide. Isthis law good for workers? Is it good for firms? Justify your answers.

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 1

1. False, in the sense of “not necessarily true.” A fuel-efficient car reduces theprice of “miles driven,” so people choose to drive more miles. More driving withgreater fuel efficiency could lead to either an increase or a decrease in the amountof gasoline consumed.

If the demand curve for “miles driven” is particularly steep, do Americansincrease or decrease their use of gasoline? What if it is particularly shallow?

1. False (in the sense of: not necessarily true). The existence of the new birthcontrol method lowers the “price” of those activities that are capable of producingunwanted babies, and so leads to greater participation in those activities. Sincemore sexual encounters take place, but each encounter has a lowered probability ofleading to an unwanted birth, the number of unwanted births could go either upor down.

To put it another way: after the discovery, there are two sorts of occasionson which people will use the new method of birth control. First there are thoseoccasions when they would have otherwise used a less effective method. Second,there are those occasions on which they would otherwise have refrained from sexaltogether. On the first sort of occasion, the new method leads to fewer unwantedpregnancies than previously, but on the second sort of occasion it leads to more.

The example is analogous to the “reckless driving” example in the text. Some-times students attempt to carry the analogy too far by asserting that the numberof unwanted babies must stay about the same (just as, after safety equipment wasintroduced, the number of driver deaths stayed about the same). But there is noreason why this needs to be true. We have one reason to believe that unwantedpregnancies will decrease (better birth control) and another to believe that theywill increase (more people taking chances). Either effect could be bigger than theother, or they might just happen to cancel each other out, as appears to have beenthe case with auto safety.

Sometimes students attempt to argue that the new method might have noeffect since some people will refuse to use it, for reasons of religion or aesthetics.But this is not a good answer, since the fact that some people will not use themethod doesn’t prove anything. In order to draw any conclusions from this sort ofargument, it would be necessary to maintain that nobody will use the new method,and this seems implausible.

2. False, in the sense of “not necessarily true.” A fuel-efficient car reduces theprice of “miles driven,” so people choose to drive more miles. More driving withgreater fuel efficiency could lead to either an increase or a decrease in the amountof gasoline consumed.

If the demand curve for “miles driven” is particularly steep, do Americansincrease or decrease their use of gasoline? What if it is particularly shallow?

3. Some other “goods” may be sexual relations, clean air, warm weather or marriage.

4. False. A change in price cannot affect demand. It’s true that when demand falls,price falls. It’s not true that the fall in price causes demand to go back up.

5. False. The demand curve for apartments shifts downward; therefore the pricefalls.

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6. The demand curve for cigarettes shifts rightward by 10 cigarettes per year. Theequilibrium quantity of cigarettes increases by less than 10 per year. The numberof cigarettes smoked by others is equal to the new equilibrium quantity minus theten that are thrown away. Thus Nosmo is correct in believing that he reduces thenumber of cigarettes that other people smoke, but incorrect in believing that hereduces that number by 10 per year.

7. False, the fall in demand would reduce the equilibrium price which would in turnreduce the quantity supplied. As a result, there will not be an additional pound ofmeat for someone else to eat.

8. No. The supply curve for homes has shifted leftward, leading to a higher priceand lower quantity. This doesn’t violate anything.

9. False. We are told only that the quantity has fallen. This might equally well becaused by a decrease in demand (in which case price must fall) or by an decreasein supply (in which case the price must rise.)

10. The demand for American beef fell. Therefore the price and quantity of Americanbeef must have fallen. Because the relevant market is the world market, this meansthat worldwide, less American beef was consumed (in fact about 15% less). To seewhat happened to quantity consumed in the U.S. , you need to look at the Americandemand curve. The curve shifts left (due to the mad cow scare) and the price falls(due to what’s happened in the world market). The new quantity could, in theory,be either left or right of the old; in fact it was to the right.

11. P= $ 2.00 and Q= 7 lbs.

12.a) $.50 $2.00. 4 pounds.b) $2.50, $.50. 4 pounds.c) In either case you would not care.

12.a) $9.b) $5.

13.a) $2b) $8

14.a) Supply falls so price rises and quantity falls.b) Demand rises so price rises and quantity rises.c) Demand and supply both fall. Quantity falls and price could go either way.d) As farm workers move to the city to earn the higher wages, the supply of corn falls.

Price rises and quantity falls. Sometimes students argue that wealthier industrialworkers will demand more corn and therefore the demand curve shifts out as well.This is a commendable insight, but it overlooks the fact that those higher wagesare paid by employers, who might now reduce their demand for corn, offsetting theadditional demand by the workers. Therefore, unless we know more about whywages went up, we need not expect the market demand curve to shift.

15.a) Demand falls, price falls and quantity falls.b) Supply increases, price falls and quantity rises.c) Demand increases, price increases and quantity increases.d) Demand increases, price increases and quantity increases.e) Supply increases, price falls and quantity rises.

16. A sales tax has no effect on the price; an excise tax is passed on entirely to theconsumer. So, for example, an excise tax of $1 per head of lettuce causes the priceto rise by $1.

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Regarding the excise tax, students commonly reach the correct answer whileoffering a reason that is quite mistaken. Their (incorrect) argument is this: A ver-tical demand curve indicates that demanders will pay any price at all for avocados;therefore suppliers are able to pass the tax on completely without losing any sales.The argument is incorrect because it overlooks the fact that suppliers compete witheach other. Any given supplier will indeed lose sales if he fails to match the goingmarket price.

Indeed, to see that the argument cannot possibly be correct, ask yourself whysuppliers don’t raise their prices prior to the tax increase. If suppliers charge $1originally and $1.25 after the imposition of a $.25 tax, why don’t they charge $1.25(or more) even before the tax is imposed? The reason is that price is determinednot by individual suppliers, but by the intersection of supply and demand.

17. False. This is true if “high” is replaced with steep and “low” is replaced with flat.

18. The supply curve of compact cars is perfectly horizontal. Therefore an excise taxcauses the price to rise by the full amount of the tax, so true.

19. False. The Upper Slobbovian demand curve is steeper, so quantity falls by less inUpper Slobbovia.

20. False. The supply of housing shifts rightward by 1000, so the equilibrium quantityof housing shifts rightward by less than 1000.

21. a) and e) are possibly true. b) and d) are certainly false because a sales tax cannotcause a price increase. c) is certainly false because an excise tax cannot cause aprice decrease.

22. The price would fall to 13 cents apiece.

23. The sales tax causes the demand curve to drop vertically by 10 cents per gallon.The excise subsidy causes the supply curve to drop vertically by 10 cents per gallon.Because both curves have dropped the same distance vertically, it is as if the entiregraph has moved down a distance 10 cents; therefore the new equilibrium pointis 10 cents directly below the old one. In other words, the price drops 10 cents.Demanders now pay a price that is lower by 10 cents, but they have to pay 10 centstax; therefore they are neither helped nor hurt. Suppliers now collect a price thatis lower by 10 cents, but they also receive a 10 cent excise subsidy; therefore theyare neither hurt nor helped.

24.a) The price of hamburgers rises from $5 to $7.b) The price of hamburgers falls from $5 to $2.c) Each plan is equally good for buyers; each plan is equally good for sellers.

22. The price of apples would rise to 27 cents.

23.a) It will be between $1500 and $2000.b) It will be exactly $2000.c) It will be between $2000 and $2500.

25.a) It means that everyone will have exactly the same take-home pay regardless ofwhich plan is chosen. Also, employers will have exactly the same labor costs re-gardless of which plan is chosen. For example, if a tax on workers causes wagesto rise to $6 per hour, then a tax on employers will cause wages to fall to $5 perhour; either way, workers receive a take-home (after-tax) pay of $5 per hour andemployers spend $6 per hour to hire labor.

b You should draw the demand and supply curves for labor.A tax on workers causes the supply curve to rise vertically by $1 and a tax on

employers causes the demand curve to fall vertically by $1. The resulting prices to

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suppliers and demanders can be shown to be independent of the choice of tax viareasoning as in Exhibit 1-10.

26.a) Demand shifts down by $500. Supply shifts vertically down by $200.b) The annual wage goes down by more than $200 but less than $500.c It is bad for firms, who pay $500 per worker for parking spaces but reduce wages

by less than $500. It is bad for workers, who receive parking spaces worth $200but also receive pay cuts of more than $200.

Answers to Numerical Exercises

27.a) The graph is as shown:

230

Price Price

Quantity QuantityTUESDAY WEDNESDAY

b) The equilibrium quantity on Wednesday is 180.c) The distance between the two darkened points on the Tuesday graph is 50. The

distance between the two darkened points on the Wednesday graph is 50. Thusthe two pairs of points must be identical. On the Wednesday graph, the rightmostpoint is at 230 (because it is the same as on the Tuesday graph); the leftmost pointis therefore at 230− 50 = 180.

N1. P = $1, Q = 800 oranges/day.N2. Supply: Q = 800 · P − 400;

Demand: Q = −200 · P + 1, 000.P = $1.40, Q = 720 oranges/day. $ .90.

N3. Supply: Q = 800 · P ;Demand: Q = −200 · P + 900. P=$.90,Q = 720 oranges/day. $ .90.

N4. Supply: Q = 800 · P − 160;Demand: Q = −200 · P + 940.P = $1.10, Q = 720 oranges/day. $ .90.

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Chapter Two:

Prices, Costs, and the Gains from Trade

General Discussion and Teaching Suggestions

1. Following the “quality of oranges” example in Section 2.1, I often assign aproblem that probably originated with Dee McCloskey: Since Prohibition raisedthe cost of producing and selling whiskey, the average quality of whiskey soldduring Prohibition would have been lower than at other times (True or False).The most naive “Trues” come from students who didn’t understand the orangesexample; there are thankfully few of these. The somewhat naive “Falses” comefrom students who blindly apply the logic of the example, substituting good andbad liquor for good and bad oranges, and the cost of hiding the still for the costof the orange’s train ticket. The brightest students see this argument, but alsorecognize that the cost of hiding a still in your bathtub is not the same as the costof hiding the Jack Daniels distillery, leaving the conclusion uncertain.

2. The carpenter-electrician example is cooked up to come out neatly, so thatthere are gains from trade when the two tasks are exchanged at a relative price ofone for one. Some ambitious students will try it with other numbers and will bedistressed to find that things don’t work out so well. Refer them to the numericalexercise at the end of the chapter for a full explanation.

3. A majority of students find the carpenter-electrician example surprising butclear. A few will argue vehemently against the conclusion. Often their argumentswill revolve around the possibility of one agent’s “paying” the other to perform atask. (For example, the electrician, who has become wealthy through his superiorskills, pays the carpenter to do all of the work while he goes to the Riviera; or, thecarpenter, who is such a bumbler, pays the electrician to get all of the jobs doneright.) The correct response is that “payment” must consist of the delivery of somegood. For simplicity, we have assumed that the only two goods in the world arerewiring jobs and paneling jobs. If the student insists on introducing another goodto be used as a medium of exchange—say, bananas—then we must add anotherrow to the tables in Exhibit 2–2, for “growing bananas” (in addition to panelingand rewiring). This will complicate the example, but will not change the essentialconclusion.

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Additional Problems

1. Comment briefly on the merits of the proposal in the following letter to theeditor of the Des Moines Register :

One of the reasons Iowa farmers are suffering economically is because weare buying too much food which has been processed in other places while weare selling our raw products, i.e., corn, soybeans and livestock, for whatever“the market” dictates.

The solution is for groups of agreeable Iowans, including women andolder teenagers, to incorporate and start producing a finished food, i.e.,specials breads or pastries, canned or frozen foods or vegetables, corn meal,tofu, etc.

Sell these at farmer’s markets, for school lunches, for food stamps, per-haps the World Trade Center, eventually!

—Mildred Conley

2. True or False: A rational society will use its most fertile land for agriculture.

3. West Publishing Company owns its own printing presses. The Dryden Pressrents time on presses belonging to other firms. True or False: This gives Westa comparative advantage over Dryden, because it can produce books morecheaply.

4. True or False: If Americans produce both industrial and agricultural productsmore cheaply than Mexicans can, then there can be no benefit to Americansfrom trading with Mexico.

5. True or False: Consumers pay higher prices in retail markets than they wouldif they could buy directly from wholesalers, because they have to pay enoughto cover two profit margins.

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 2

1. The relative price of tea decreased. The relative price of Civics increased.2. You may conclude that he is confused. If the relative price of widgets in terms of

gadgets has risen, then the relative price of gadgets in terms of widgets must havefallen.

3. The difference will be smaller.4. There will be a greater percentage of childless couples at the cheap movie. For a

childless couple, a show might cost 10 times as much as a movie; add the cost of ababysitter and the show now costs less than ten times as much. So for a childlesscouple, the show is more expensive relative to the movie (and the movie is cheaperrelative to the show) than it is for a couple with children.

5. The logic of the “good and bad oranges” example (at the end of Section 2.1)suggests that the average quality of liquor should have risen. But that logic neednot apply. It costs about the same to ship a good orange or a bad orange. It doesnot cost about the same to hide the Jack Daniels distillery and a bathtub full ofgin. So: Not necessarily true.

6. False. The gains from trade arise from comparative advantages, not absoluteadvantages.

7.a) 400 bushels of corn. 300 bushels of corn. Oklahoma.b) Iowa.c) In Iowa 7.6 acres must be used while in Oklahoma 22 acres must be used.d) Iowa has .4 extra acres and Oklahoma has 2 extra acres.

8. False. If Dell buys hard drives from other manufacturers, it is because that’scheaper than making its own hard drives. The cost to Dell of making hard driveswould be the forgone opportunity to do the things that Dell is good at.

9. False, in the sense of “not necessarily true.” The statement of the problem omitsthe key information that Mary is a highly skilled neurosurgeon, whereas Georgecan do nothing except type. Mary’s greater typing speed does not imply that shehas a comparative advantage at typing.

Some students argue that if you are an employer who only wants to hire atypist, and if George and Mary are available at the same wage rate, then yes, itmakes more sense to hire Mary as a typist than to hire George. But even thisstrained interpretation does not lead to the alleged conclusion. If you can reallyhire Mary at typist’s wages, then you should set her to performing brain surgery,collect her fees as revenue to your firm, and use a small part of that revenue to hireGeorge to do the typing.

10. False. Suppose that the going wage for child labor on farms is $5 per hour. Thenthe farmer without children must pay $5 to employ someone else’s children; thefarmer with children must forgo $5 per hour (which he could earn by renting hischildren out to neighboring farmers) to employ his own children. Both face thesame cost of $5 per hour.

Some students argue that the farmer with children incurs the costs of feeding,housing, and education. However, it is not correct to count these among the costs

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of putting the children to work, since they must be paid whether the children workor not.

Other students argue that the farmer with children is wealthier at the end ofthe year since he makes no cash payments to hire labor. Whether or not this istrue, it is irrelevant to the question. The question does not ask which farmer iswealthier; it asks only which farmer has higher costs of harvesting. The answer isthat both have the same costs.

11. False. The students with the most talent for medicine need not have a comparativeadvantage in medicine.

12. False, in the sense of not necessarily (or even probably) true. If the people ofthe country are desperate for food, they ought to engage in that activity whichwill produce the most food. That activity might be growing food, or it might beproducing decorative jewelry and trading it for food.

13. False. Except in the hairline case in which each country has the same costs forall activities, the country must have a comparative advantage in something (seeExhibit 2.2).

14. False. This puts the Winkies at a comparative disadvantage in producing auto-mobiles but a comparative advantage in producing other goods. Thus, the gainsfrom trade makes both the Winkies and the Munchkins better off.

15. It goes wrong exactly where it says that in each case there are the same costs forproducing, shipping, and marketing the clothes. If a professional middleman canperform some of these tasks more cheaply than Anderson-Little can, then BrandX might be able to pay the middleman more than enough to cover his costs andstill deliver the clothes more cheaply than Anderson-Little.

16. False. People trade for two reasons, one of which is different tastes. Some peoplewill choose inferior housing in order to have better cars, or more books, or fanciervacations.

One student answered this question by saying “False, because there are somepeople who, no matter how high their incomes, would still choose to live in themost disgusting, degrading, infested, and putrid environments imaginable.” Anasterisk pointed to a footnote at the bottom of the exam paper which read, “Forexample, my uncle.”

Answers to Numerical Exercises

N1.a)Rewiring Paneling

Electrician 1/2 Paneling 2 RewiringsCarpenter 2/3 Panelings 3/2 Rewirings

b) The electrician. The carpenter.

c)Without Trade With Trade

Electrician 15 hours 10 hoursCarpenter 25 hours 30 hours

The electrician benefits from this trade, but the carpenter does not.

d)

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Without Trade With Trade

Electrician 15 hours 12 hoursCarpenter 25 hours 24 hours

Both gain from this trade.

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Chapter Three:

The Behavior of Consumers

General Discussion and Teaching Suggestions

1) Although the text stresses that opportunities and constraints are determinedentirely independently, the point can never be overstressed.

2) My own teaching strategy has been to cover the basics (Sections 3.1 and 3.2)and then to assign some challenging problems that force students to think aboutthe meaning of it all. Since many students have no idea where to begin, I have themwork in groups of 4 or 5, with about a week to turn in their solutions. I then go overthe solutions in class, and work some additional challenging problems. Studentsare much better able to follow the additional problems after having worked a fewon their own.

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Additional Problems

1. Herman buys 10 turnips each year. True or False: If the price of turnips risesby 10 cents apiece, and if Herman’s tastes and income remain unchanged, thenhe will have $1 a year less to spend on other things.

2. It is possible for a community to have too little crime. (Hint: What is the costof crime prevention?)

3. Writing in the New York Times, radio commentator Ira Eisenberg describedthe innovative voucher program recently initiated in Berkeley, California:

Instead of shunning street beggars, or grudgingly handing them cash,Berkeley residents can now offer panhandlers vouchers purchased from localmerchants. The vouchers are as good as real money for buying food, laundryservices, bus fares, even hot showers. They can’t be exchanged for alcoholor cigarettes, let alone illegal drugs.

What do you think of Berkeley’s voucher plan, and of Mr. Eisenberg’s analysis?

4. Assuming that you like to drive, but dislike breathing polluted air, draw yourindifference curves between car rides and air pollution. Assuming that youhave to breathe one unit of polluted air for each ten miles that you drive,draw the appropriate constraint. What is the optimal amount of pollution foryou to breathe? Under what circumstances would it be zero?

5. Draw a typical set of indifference curves between “Smoking” and “Lung Dam-age” for a person who likes to smoke. Draw the relevant budget constraint.Now suppose that a new cigarette is invented that is identical to currentlyavailable cigarettes in every way except that it causes less lung damage percigarette. Show the new budget line and the new optimum. Could this in-vention lead to an increase in the number of people who get lung cancer fromsmoking?

6. Suppose you like driving fast but you hate getting injured.a) Draw a graph with “speed” on the horizontal axis and “probability of in-

jury” on the vertical. Do your indifference curves slope upward or down-ward? Why?

b) Suppose you drive to work every day 40 miles per hour (mph) and havea 5% annual chance of being injured. You are aware that in generalyour chance of being injured (measured in percent) is always equal to1/8 of your driving speed (measured in mph). Draw the relevant budgetconstraint, and draw a set of indifference curves that could have led toyour decision to drive at 40mph.

c) In order for your chosen speed to be an optimum, what must be trueabout the shape of your indifference curves? Must they be concave orconvex?

d) Suppose that because of a new kind of safety device, the probability ofinjury falls to 1/10 of your driving speed. Draw the new budget constraintand the new optimum. Can you determine whether the device causes afall in your probability of being injured? Can you determine whether thedevice makes you happier?

7. Suppose you have an income of $10 and are offered the opportunity to purchasedog collars at $1 apiece. However, if you buy at least 5 dog collars at thatprice, then you can buy any number of additional collars at 50 cents a piece.Draw your budget constraint between dog collars and all other goods.

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8. Huey consumes only two goods, X and Y . His indifference curves have theusual (convex) shape. He prefers basket (1, 3) to basket (2, 2).a) Is it possible to tell whether Huey prefers (1, 3) to (3, 1)?b) Is it possible to tell whether Huey prefers (2, 2) to (3, 1)?

9. Dewey consumes only two goods, X and Y . His indifference curves have theusual (convex) shape. He prefers basket (1, 3) to basket (3, 1).a) Is it possible to tell whether Dewey prefers (1, 3) to (2, 2)?b) Is it possible to tell whether Dewey prefers (3, 1) to (2, 2)?

10. Louie consumes only two goods, X and Y . His indifference curves have theusual (convex) shape. He prefers basket (2, 2) to basket (1, 3).a) Is it possible to tell whether Louie prefers (2, 2) to (3, 1)?b) Is it possible to tell whether Louie prefers (1, 3) to (3, 1)?

11. Donald consumes only two goods, X and Y . His indifference curves have theusual (convex) shape. He is exactly indifferent between baskets (1, 3) and(2, 2). Which does he prefer between (2, 2) and (3, 1)?

12. Suppose that you have an income of $10, and are offered the opportunity topurchase dog collars at $1 apiece. However, if you buy at least 5 dog collars atthat price, you may purchase any number of additional collars at $.50 apiece.Draw your budget constraint between dog collars and all other goods.

13. a) Suppose that the carnival and the circus have both come to town, and areboth offering free admission. You have 6 free hours to kill. Draw your “budgetconstraint” between hours at the carnival and hours at the circus.b) Now suppose that the carnival institutes an admission fee of $2 per hourand the circus institutes an admission fee of $4 per hour. You still have only6 hours to kill, and you also have only $16 to spend. Draw your new budgetconstraint.

14. Herman has an income of $12. In Year 1, when buttons and bows each soldfor $1 apiece, he bought 4 buttons and 8 bows. In Year 2, when buttons cost$.50 apiece and bows cost $4 apiece, he bought 8 buttons and 2 bows. Trueor False: It is not possible to tell from this information in which year Hermanwas better off.

15. Recently the price of cheese has risen from $4 per pound to $6 per pound,the price of meat has fallen from $5 per pound to $2 per pound, and Susan’sincome has stayed fixed at $22 per week. Since the price changes, Susan hasbeen buying 3 pounds of cheese and 2 pounds of meat every week. Is Susanhappier now than she was before?

16. Suppose the only goods you buy are bread and circus tickets. When breadsells for $1 a loaf and circus tickets sell for $1 apiece, you buy 7 loaves of breadand 3 circus tickets to exhaust your income of $10. One day the price of breadfalls to 50 cents a loaf while the price of circus tickets rises to $2 apiece andyour income remains unchanged. Is it possible to say with certainty whetheryou are better off? Why or why not?

17. Dizzyland Amusement Park has begun sellling a VIP pass that costs $20 andentitles the bearer to a discount price on rides. Mickey Duck, as Dizzylandpatron, has decided he is definitely happier buying a VIP pass than not buyingone.a) In a diagram with “Rides” on the horizontal axis and “All Other Goods”

on the vertical axis, illustrate the shift in Mickey’s budget line when he

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buys the pass.b) True or False: Mickey will certainly go on more rides now that he has a

VIP pass.

18. Kramden’s Grocery advertises “We randomly chose 10 of our customers andcalculated how much they’d have paid for their market baskets at Norton’sSupermarket. At Norton’s they were an average of 6% higher.” Does thisconvince you that wise shoppers will shop at Kramden’s? Why or why not?

19. Suppose that the only items you consume are bread and wine. One day theprice of wine increases, and simultaneously your income increases. You noticethat you are exactly as happy as you were before either change took place.a) What happens to the quantity of wine that you consume? To the quantity

of bread?b) Can you still afford your original market basket if you want it?

Illustrate your answer with indifference curves.(Note: After Chapter Four has been covered, this problem is much easier.Assigning it now forces the students to develop for themselves some skills thatwill be useful in Chapter Four. It does appear in the textbook at the end ofChapter Four.)

20. Suppose that the only goods you consume are apples and peaches. One day theprice of apples goes up, and the price of peaches goes down, and you find thatyou can still just afford to buy the same combination of apples and peachesthat you were buying all along. True or False: The price changes leave youneither better nor worse off.

21. True or False: It makes no sense to say that an hour of your time is worthexactly $10, since you engage in many different activities, and the value of anhour devoted to one of them might be quite different than the value of an hourdevoted to another.

22. Consider the baskets A = (1, 3), B = (2, 2) and C = (3, 1). Notice that thesebaskets lie along a straight line. Jack is indifferent between baskets A and B.Jill is indifferent between baskets B and C. Is it possible that Jack and Jillcould have identical tastes? Justify your answer. (You should assume thatindifference curves have the usual shape.)

23. Basket A contains 1 X and 5 Y’s. Basket B contains 5 X’s and 1 Y. BasketC contains 3 X’s and 3 Y’s. On Monday you are offered a choice betweenBasket A and Basket C, and you choose A. On Tuesday, you are offered achoice between Basket B and Basket C, and you choose B. True or False: Wemay infer that your tastes changed overnight.

24. Suppose the basket of goods you buy in 1999 costs more, at 1998 prices, thanthe basket you bought in 1998 would cost at those prices. Can you say forcertain in which year you are better off?

25. Suppose the basket of goods you buy in 1999 would have cost more, at 1998prices, than the basket which you bought in 1998 cost at those prices. Canyou say for certain in which year you are better off?

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26. The Pullman Company has a lot of pull in the town of Pullman, Illinois.Everybody in town is identical, and they all work for the company, which paysthem each $10 a day. Their favorite food is apples, which they get from a mailorder catalogue for $1 apiece.a) Draw the typical resident’s budget line between “apples” and “all other

goods” (measured in dollars). Draw in the optimum point.b) Pullman plans to lower the wage rate to $8 a day. Draw the new budget

line.c) Pullman has discovered that if residents are less happy than they were

at $10 a day, they will all leave town. To prevent this, Pullman hasoffered to subsidize everyone’s apple purchases: From now on, if you area Pullmanite who buys an apple, you will pay only a fraction of the costand the company will pay the rest. Pullman plans to choose a fractionwhich is just large enough to keep people from leaving town. Draw thenew budget line. Indicate the new budget point. Label the correspondingquantity of apples A.

d) Use your graph to illustrate the amount that Pullman spends on the applesubsidy. (Hint: How much of your $8 income do you have left over afterbuying A apples? How much of your $8 income would you have left overif you bought A apples at the unsubsidized price of $1 apiece? Where isthe difference coming from?

e) True or False: Pullman could end up spending just as much on the applesubsidy as it saves by lowering wages.

27. The Pullman Company has a lot of pull in the town of Pullman, Illinois.Everybody in town is identical, and they all work for the company, whichpays them each $10 a day. The company runs the government, pocketing alltax revenue for itself. Residents eat apples, which they purchase from a mailorder company for $1 apiece. But the company imposes a 100% sales tax, soresidents actually pay $2 apiece for apples.a) Draw the typical resident’s budget line between “apples” and “all other

goods” (measured in dollars). Draw in the optimum point. Label thecorresponding quantity of apples A.

b) Use your graph to illustrate the amount of revenue that Pullman derivesfrom the apple tax. (Hint: How much income do you have left after buyingA apples? How much income would you have left if you had bought thesame number of apples at the untaxed price of $1 apiece? Where is thedifference going?

c) Pullman wants to lower the wage rate to $8 a day. Unfortunately, if resi-dents become any less happy, they will all leave town. However, Pullmanhas calculated that eliminating the apple tax would be just enough toconvince people to stay in town at a wage of $8 a day. Assuming thatPullman lowers the wage and eliminates the tax, draw the new budgetline.

d) True or False: The combined changes described in part (c) leave Pullmanneither better nor worse off than before.

Warning to instructors: The following three problems are considerably morediffcult than the preceding two, although all have more or less the same flavor.

28. The Pullman Company has a lot of pull in the town of Pullman, Illinois.Everybody in town is identical, and they all work for the company, which pays

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them each $10 a day. Their favorite food is apples, which they get from amail order catalogue for $1 apiece. However, the company subsidizes applepurchases, so that every time you pay $1 for an apple, you get back 50 centsfrom the company.a) Draw the typical resident’s budget line between apples and dollars.b) Pullman has decided to eliminate the apple subsidy. But to avoid discon-

tent among the workers, it plans to simultaneously raise the wage rate byjust enough to keep workers exactly as happy as they have always been.Draw the typical worker’s new budget line.

c) On your graph, illustrate the amount that Pullman spends per worker inthe original situation (be sure to count the wage plus the amount spenton the subsidy!). Illustrate the amount Pullman spends per worker afterthe subsidy is cut and the wage is raised. Was Pullman wise to institutethese changes?

29. The Pullman Company has a lot of pull in the town of Pullman, Illinois.Everybody in town is identical, and they all work for the company, which paysthem each $10 a day. Their favorite food is apples, which they get from a mailorder catalogue for $1 apiece.a) Draw the typical resident’s budget line between apples and dollars.b) Pullman has decided to institute a sales tax of $1 per apple. But to prevent

dissatisfied workers from leaving town, Pullman must simultaneously raisewages so that workers are just as happy as before. Draw the new budgetline.

c) Use your graph to illustrate Pullman’s new net expense per worker (thatis, the amount paid to the worker minus the amount collected back insales tax).

d) Was Pullman wise to institute the sales tax?

30. The Pullman Company has a lot of pull in the town of Pullman, Illinois.Everybody in town is identical, and they all work for the company, which paysthem each $10 a day. Their favorite food is apples, which they buy at thecompany-owned grocery store for $1 apiece. The company buys its apples for$1 apiece and therefore earns no profit at the grocery store.a) Draw the typical resident’s budget line between apples and dollars.b) Pullman has decided to raise the price of apples to $2 apiece. But to pre-

vent dissatisfied workers from leaving town, Pullman must simultaneouslyraise wages so that workers are just as happy as before. Draw the newbudget line.

c) True or False: Although Pullman is now paying higher wages, it is alsoearning profits at the grocery store. Thus increasing the price of applesmight or might not have been a wise move.

31. Suppose you have 30 years of life which can be allocated between leisure andworking at a wage of $10,000 per year.a) Draw your budget constraint between “leisure” and “lifetime income”.b) Suppose now that you are given the option to attend college, in which

case you will have only 26 years available for leisure and working, butyour wage will be higher than $10,000 a year. Suppose also that you areexactly indifferent between attending college and not attending college.Illustrate this situation with budget lines and indifference curves.

c) True or False: If you attend college, you will definitely spend more timeworking than if you do not attend college. Justify your answer.

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32. John buys shoes for $1 a pair and socks for $1 a pair. His total income is $20.a) Draw John’s budget line.b) Now suppose the government institutes two new programs: First they tax

shoes, so that shoes now cost John $2 a pair. Second, they give John acash gift of $10. Draw his new budget line.

c) Suppose that after the new government programs are instituted, Johnchooses to buy 10 pairs of shoes and 10 pairs of socks. Has the pair ofgovernment programs made John better off, worse off, or neither? Justifyyour answer.

33. Suppose you have an income of $15 per month and can buy meat for $1 perpound.a) Draw your budget constraint between meat and dollars.b) Now suppose the government imposes a sales tax that raises the (after-

tax) price of meat to $1.50 per pound. After the tax is imposed, you buy4 pounds of meat per month. Draw your new budget line and your newoptimum point.

c) Now suppose that, while continung to collect the sales tax, the governmentgives you a cash gift of $2 per month. Draw your new budget line andthe new optimum.

d) In part c), the combination of the sales tax and the cash gift leaves youjust as happy as you were to begin with.

34. Your income is $50 a week and you can buy meat at $10 a pound.a) Draw your budget line between “meat” on the horizontal axis and “dol-

lars” on the vertical.b) Suppose that the government starts a new program that will allow you

to buy as much meat as you want to, with the government paying half ofthe cost. Draw your new budget line and your new optimum point. Callit A.

c) Now suppose that the government cancels the program but replaces it bya new program, under which you are given just enough cash each week sothat you can just afford to buy basket A. Draw your new budget line.

d) Which government program do you like better, the one where they payfor half your meat or the one where they give you the cash? Use yourgraph to justify your answer.

The next two problems are somewhat more difficult. They can be made easierby replacing the phrase “Show the location of your new optimum point” with“Explain why your new optimum point must occur at the intersection betweenyour old and new budget lines.”

35. Suppose the government imposes a sales tax on food and simultaneously givesyou a cash gift every year. Suppose the amount collected in tax is exactlyequal to the size of the gift.a) Use a graph showing how this combined program affects your budget line

between “food” and “all other goods” (measured in dollars). Show thelocation of your new optimum point.

b) True or False: The combined program leaves you neither better nor worseoff than before it was instituted.

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36. Suppose the government imposes an annual head tax and simultaneously be-gins subsidizing food purchases. Suppose the amount collected in tax is exactlyequal to the size of the subsidy.a) Use a graph showing how this combined program affects your budget line

between “food” and “all other goods” (measured in dollars). Show thelocation of your new optimum point.

b) True or False: The combined program leaves you neither better nor worseoff than before it was instituted.

37. Suppose you have a choice between attending two colleges. At Eli College,you pay $100 per credit hour, and can take as many or as few credit hours asyou like. At Leland College, you pay $500 per year and are required to takeexactly 10 credit hours.a) Assuming you have $2,000 to spend, draw your budget constraint between

credit hours and dollars. (Hint: The constraint includes all those pointsyou can reach by attending Eli and all those points you can reach byattending Leland.)

b) Suppose you choose to attend Leland College. True or False: If Eli lowersits price to $50 per credit hour, you will surely transfer to Eli. (Assumethat both colleges are identical except for the price, and that it costs younothing to transfer.)

38. You have an income of $120 per week and own a car that costs $2 per mile todrive. You choose to drive 50 miles per week.a) Draw your budget constraint between “miles driven” and “all other goods”,

with “all other goods” measured in dollars. Show your optimum point.b) Suppose you are offered the opportunity to purchase for $60 a car that

costs 50 cents a mile to drive. If you do this, you’ll throw your old caraway. Draw the budget constraint that results if you buy the new car.Note that the two budget constraints cross at (40, 40).

c) Would you buy the new car? Defend your answer using indifference curves.

39. Suppose you get rid of your old gas-guzzler and buy an new, fuel efficient car.Driving is now cheaper, but on the other hand, you have to make monthly carpayments. You find that on balance, you are exactly as happy as you werebefore. Illustrate this situation using indifference curves between “car rides”and “all other goods”. Are you driving more or less than you did before?

40. Suppose that eggs sell for $1 a dozen, wine sells for $1 a bottle, and yourincome is $12.

a Draw your budget line.b Suppose that the government imposes a sales tax on eggs, causing the price

(to demanders) to rise to $2 a dozen. At the same time, the governmentsends everybody in America a check for $4. You now choose to buy 4dozen eggs and 8 bottles of wine. Draw your new budget line and yournew optimum point.

c How much does the sales tax add to the cost of the basket (4, 8)?d True or False: Because you get $4 back from the government, you end

up just as happy as you were to begin with. Use your diagram to justifyyour answer.

41. Suppose that the government issues $100 worth of food stamps to everybodyin your city. These food stamps are coupons that can be exchanged for $100worth of food at the grocery store, but they can be used only by the person

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to whom they are issued.a) Draw your budget constraint between food and all other goods both before

and after the food stamps are issued. In doing so, measure food in unitssuch that 1 unit of food sells for $1, and assume that your income beforethe food stamps were issued was $500.

b) Suppose that you find that you would prefer to sell some of your foodstamps for their dollar value, if only you were allowed to. What can weconclude about the marginal value of food?

42. Suppose that you have 16 waking hours per day, which you can allocate be-tween working for a wage of $1 per hour and relaxing. Draw your budgetconstraint between “dollars” and “hours of relaxation.” Now suppose thatyou invent a pill that enables you to get by on 4 hours sleep per night, andtherefore have 20 waking hours per day. Draw your new constraint. Is itpossible that you will now choose to work fewer hours than you did before?

Now suppose that at the same time, the pill stops working (so that you’reback to 16 hours a day) and your wage goes up to $1.50 per hour. Drawyour new budget constraint. Suppose you find that the wage increase makesit possible for you to attain the same combination of dollars and relaxationthat you chose when you had the pill. How much will you work after the wageincrease, compared with how much you worked when you had the pill?

43. (Warning: This is a hard problem.) Suppose that you have available 16 work-ing hours per day, which you can allocate between growing apples and relaxing.Show how you decide on your allocation. Now the government decides to in-stitute a tax whereby x% of your apples are taken away and discarded. Showyour new allocation of time. Suppose that the government wants to acquireexactly A apples through this tax. How will they choose x? Now supposethat a change in your metabolism causes you to have 20 waking hours per dayinstead of 16. The government wishes to change the tax rate x so as to stillcollect A apples from you. How do they choose the new x, and where is yournew optimum?Could you be worse off at your new 20 hour a day optimum than at your old16 hour a day optimum?

44. Suppose you expect to earn $10 this year and $10 next year. Each dollar youearn this year can be be either spent, or saved at an interest rate of 10%. Ifyou want to spend more than $10 this year, you can borrow money at 10%interest and repay it next year. Next year, you plan to pay off your debts (ifany), then spend all your earnings and all your savings (if any).a) Draw your budget line between “dollars spent this year” and “dollars

spent next year”.b) Suppose the government imposes a 50% income tax on all your earnings

this year and next year (not including your interest earnings). Draw yournew budget line.

c) Suppose the government imposes a 50% sales tax on everything you buythis year and next year. Draw your new budget line.

d) Suppose the government imposes a 50% income tax on all your earningsthis year and next year, including your interest earnings. Draw your newbudget line.

d) True or False: If interest earnings are not subject to income tax, thenan income tax and a sales tax will lead you to spend exactly the sameamount both this year and next year.

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45. Mr. Smith has a very low income and Mr. Jones has a very high income. Theyboth purchase education from the same private school.a) In a single diagram, draw budget lines between “education” and “all other

goods” for both Mr. Smith and Mr. Jones.b) Now suppose the government offers a certain quantity of free education

with the proviso that if you acept the offer, you must consume exactlythat quantity, no more and no less. Draw Mr. Smith’s new budget con-straint and Mr. Jones’s new budget constraint. (Hint: Mr. Smith’s newbudget constraint is no longer a line, but a line and a point; likewise forMr. Jones.)

c) Suppose Mr. Smith accepts the government’s offer and Mr. Jones rejectsit. Is it possible that Mr. Smith and Mr. Jones have identical tastes?

46. Suppose you are a government policymaker and your goal is to make poorpeople happier. You can do so by subidizing their food, education and medicalcare, or you can do so by giving them cash.a) On the basis of your answer to Problem 22 in the textbook, make an

argument in favor of giving cash.b) On the basis of your answer to the preceding problem in this manual,

make an argument for subsidizing education instead of giving cash. (Hint:Suppose you want to help only the poor, but it’s difficult for you to tellwho’s poor and who’s rich, and you are worried that rich people will tryto claim a share of the cash giveaways.)

c) Can you think of a reason why governments would want deliberately tolimit the quantity or quality of education available at public schools?

47. Mr. Jones can purcahse varying quantities of education from private schoolsat a going price. One day there opens in Mr.Jones’s neighborhood a publicschool that he may attend for free if he wants to. However, if he attends thepublic school, he must accept the amount of education that it offers. He can nolonger take any private school classes because the public and private schoolsare in session at the same time.a) Draw Mr. Jones’s old and new budget constraints.b) Draw a set of indifference curves that implies Mr. Jones will increase his

consumption of education when the public school opens. Draw a set thatimplies his consumption of education will not change. Draw a set thatimplies he will decrease his consumption of education. Call these theindifference curves of Mr. A. Jones, Mr. B. Jones and Mr. C. Jones. Canyou rank Mr. A., Mr. B., and Mr. C. in terms of how much they seem tolike education?

c) True or False: If most people are reasonably but not fanatically fond ofeducation, then an offer of free public education could reduce the quantityof education consumed.

3–10

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 3

1. False. This statement confuses a change in opportunities with a change in tastes.2. The indifference curves are L-shaped, with corners at (1, 1), (2, 2), etc.3. The indifference curves are parallel lines with slope −1/2 (assuming you’ve put

nickels on the horizontal axis). The marginal value of a nickel is 1/2 dime.4.

CATS CATS DOGS

DOGS FISH FISH

In each case, the arrows point in the "upward" direction.

5.a) Because typing and filing are not “goods,” we need to rethink the shape of theindifference curves. First, notice that for a given basket A, baskets to the southwestof A are preferred to A and baskets to the northeast of A are inferior to A. Thusno such baskets can be on the same indifference curve as A. The only baskets thatcan be on the same indifference curve as A are to the northwest and southeast ofA; it follows that the indifference curves slope downward.

b) The slope of the indifference curve is −2, indicating that you’d be willing to trade1 hour of typing for 2 hours of filing. If you hated typing even more, you’d bewilling to trade 1 hour of typing for even more hours of filing; thus the indifferencecurve would be steeper (with a slope, for example, of −3 or −4).

c) When you’re doing a lot of typing, you’re likely to be willing to make bigger sac-rifices to avoid yet another hour of it. Thus the indfference curve is steeper nearbaskets with a lot of typing and little filing, and shallower near baskets with lesstyping and much filing. In other words, they bow outward from the origin.

d) The line has slope −1 and intersects both axes at 8 hours.e) At (3, 5), the indifference curve is steeper than the budget line. Thus your optimum

point—the tangency of an indifference curve with the budget line—must occurbelow and to the right of (3, 5). In other words, you will now type more than 3hours per day.

6. Drawing an indifference curve through both (1,3) and (2,2), you will find that itmust pass above (3,1). Therefore Huey prefers both (1,3) and (2,2) to (3,1).

7.

3–11

X

Y

a) Filbert’s and Lychee’s indifference curves cross; therefore they have different tastes.b) Filbert and Lychee’s budget lines have different slopes; therefore they pay different

prices.8. True: With nonconvex indifference curves you always specialize in the consump-

tion of either X or Y. A small price change might or might not induce you to switchspecializations. If you are specialized in Y and remain specialized in Y, then yourconsumption of X is left unchanged. If you are specialized in Y and switch tobeing specialized in X, then your consumption of X changes dramatically. A thirdpossibility is that you are specialized in X and remain specialized in X, in whichcase your consumption of X will change by a small amount.

9. Both budget lines pass through the point (6,4), and there is an indifference curvethrough the 2006 budget line at that point. The 2007 budget line is steeper, whichrequires its tangency with an indifference curve to lie above and to the left of (6,4);moreover this indifference curve must lie above the curve through (6,4). Therefore2007 is the year in which you eat more pizza and the year in which you are happier.

10. After the changes, you can still just afford your original basket, so your newbudget line cuts through your old tangency. Therefore you are better off after thechanges.

11.

SHOES

SOCKS

(DIAGRAM IS NOT TO SCALE!)In 2002, you choose the marked tangency at(12,6). In 2003, you choose a point on thedarkened part of the the flatter budget line.The entire darkened portion lies to the rightof the crossing at (10,10). Therefore youdefinitely buy more than 10 pairs of shoesin 2003. But the darkened portion lies partlyto the left of the tangency at (12,6).Therefore you might buy either more orfewer than 12 pairs of shoes in 2003.

3–12

12. NOTE TO INSTRUCTORS: The first paragraph of this problem should read asfollows: Audrey buys only apples and peaches. In June, apples sell for $2 each andpeaches sell for $1 each. In July, apples sell for $1 each and peaches sell for $2each. Audrey’s income is $20 in June and $20 in July. In one early printing of thebook, the first “$1” is misprinted as “$2”. This makes the problem much easier(or perhaps much harder, as students will need enough confidence to recognizethat with the misprint, most of the information given in later parts of the problembecomes irrelevant). If you assign this problem, you’ll want to make sure studentshave the correct version.

a)

Apples

Peaches

June July

a) If Audrey is equally happy in both months,a single indifference curve must be tangent to bothbudget lines as shown. She therefore definitelyeats more apples in July, i.e. TRUE.

b,c)

Apples

Peaches

June July

b) If Audrey eats exactly 8 apples in June,the picture looks like this. Her Julytangency must lie on a higher indifferencecurve (like the dashed one), so TRUE.

c) The dashed indifference curve could infact be tangent to the July line slightly LEFT of the quantity 8, (as inidicated by the arrow) soFALSE.

8

In case any of your students receive the incorrect version of the problem, here’s theanswer to that:

Apples

Peaches

June July

a) Audrey CANNOT be equally happy in both months; theJuly indifference curve must be higher than the June curve.

b) We already know Audrey is happier in July. The extrainformation that she eats 8 apples in June doesn't changethis.

c) The dashed indifference curve could in fact be tangent tothe July line slightly LEFT of the quantity 8, (as inidicated bythe arrow) so FALSE.

8

13.

3–13

COFFEE

TEA 4

2 4

2

COFFEE

TEA 4

2 4

2

COFFEE

TEA 4

2 4

2

COFFEE

TEA 4

2 4

2

The pictures show four possible configurations. In the first of the four,Amanda and Bernard have crossing indifference curves, and hence differenttastes. In the last of the four, Amanda and Bernard share an indifferencecurve, but this doesn't prove they share all their indifference curves;hence they might or might not have different tastes. In the other twopictures, Amanda and Bernard might or might not have different tastesfor multiple reasons: first, we can't tell whether the pictured indifferencecurves cross after they are extended further, and second, even ifthe pictured curves don't cross, we can't infer anything about all theunpictured curves. So reviewing the four pictures, we see that theanswer to the "same tastes" question is: Maybe no, or maybe maybe, ormaybe maybe, or maybe maybe. Which adds up to maybe.

14. Drawing the picture, you should see that Chris’s indifference curve through (2, 1)crosses David’s indifference curve through (1, 2). Therefore their tastes must differ.

15. Evelyn and Frederick could have identical preferences.16. Of course not. The information given concerns opportunities, not tastes.17.

W

T

APPLES

BANANAS

False, or at least not necessarily true. It is possible that at Wegman's, she buysbasketW , which would be more expensive at Tops. However, at Tops shewould buy basketT and be happier.

18. John’s original budget line passes through (20,0) and (0,20). After the changes,his budget is steeper, passing through (15,0) and (0,30). The tangency to the newline is at (10,10) where the two lines cross. His old tangency must be on a higherindifference curve, so the government program has made him worse off.

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19.

Eggs

Other goods

6A

B

When the price of eggs doubles, Freddy moves from Ato B. If he'd lost six dollars, he could just have afforded B.Therefore, the "lost six dollars" budget line (shown dashed)passes through B, and there must be a tangency somewherebetween B and C. This tangency would be on a higherindifference curve than the one passing through B, soFreddy prefers losing $6.

C

20. The old tangency is marked in black; the new tangency can be anywhwere onthe blackened part of the new budget line. You might choose either more or lessleisure than before, hence either less or more time spent working.

INCOME

LEISURE16 20

160

$200

21. Workers are initially at point O. The sales tax causes the budget line to pivot inand the raise causes the budget line to shift out parallel to itself. The new optimumis at X. The size of the raise is the vertical distance from X to Z. The amount ofsales tax collected is the vertical distance from W to X and the raise is the verticaldistance from W to Z. The raise exceeds the tax revenue, so Pullman is unwise toinstitute the tax.

AOG

APPLES 10

10 X

O

W

Z

22.a) Herman’s new budget line goes through the points (20, $0) and (0, $10). Hisoptimum is at the point P = (8, $6).

b) Herman’s new budget line goes through (14, $0) and (0, $14). It goes through pointP .

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c) Both programs are equally expensive for the government (each costs $4). Hermanprefers the second program, which allows him to reach a higher indifference curve.

23.a) The broken line L is your budget line.

14.50

24

L

14

7.50

L

M

M

LEISURE

$

b) Your new budget line is M , and your new tangency must be northwest of the oldone, so you work more hours. Therefore tax revenue increases.

c) The new one as it allows you to attain a higher indifference curve.24.

a) If you work not at all, you get 24 leisure hours and a $6 gift from the government.If you work constantly, you get 0 leisure hours and $18 (earnings of $24, minus $12income tax, plus $6 gift). By working different numbers of hours, you can achieveany point on the line connecting these two options; that is, your budget line is theline labeled NEW in the picture.

24 LEISURE

$

OLD

NEW

24

18

b) If the average citizen got back more or less than he paid in, the government wouldbe paying out more or less than the total tax revenue.

c) The new optimum must be at a tangency to the NEW budget line. It also mustlie on the ORIGINAL budget line, since you getting back as gift exactly the sameamount that you are paying in tax. Thus the NEW optimum is at point P in thepicture, at the intersection of the two budget lines.

Caution: We are not claiming that you would deliberately choose a pointwhere the two budget lines cross. You are only interested in choosing a point oftangency with the NEW budget line. That point might be above, below, or onthe ORIGINAL line. However, if the optimum is above the ORIGINAL line, youmust be receiving more from the government than you are paying in, which causesthe government to reduce the size of the gift and causes the NEW budget line tomove down. The opposite happens if the optimum is below the NEW budget line.The government continues this adjustment process until it finds a NEW budget

3–16

line such that the new optimum P lies on the ORIGINAL line.d) Your ORIGINAL optimum was at Q. Comparing P with Q, we see that you are

now working less hard (P is to the right of Q), and that you are less happy (P ison a lower indifference curve than Q).

Answers to Numerical Exercises

N1.a) Pairs of Wax Lips Packs of Candy Cigarettes

0 201 182 163 144 125 106 87 68 49 210 0

b)

Fred chooses thebasket (5, 10).

c)Pairs of Wax Lips Packs of Candy Cigarettes MV

0 201 18 ∞2 16 163 14 74 12 45 10 2 1/26 8 1 3/57 6 18 4 4/79 2 1/410 0 1/9

Fred chooses the basket for which the MV of a pair of wax lips is equal toits relative price, which is 2. Thus he takes either the basket (5,10) or the basket(6,8); this is consistent with our answer to (b).

Actually, the apparent ambiguity in the answer to this question results fromthe fact that we have only allowed Fred to count candy cigarettes and wax lips inwhole number quantities. If we had allowed fractional quantities, we would argueas follows: suppose that Fred now has w pairs of wax lips and p packs of candycigarettes. Now we reduce his wax lip holdings by h pairs (where h is a very smallfraction), and then increase his candy cigarette holdings by m packs, where m ischosen to keep Fred just as happy as he was before. Thus we have

w · p = (w − h) · (p + m).

Solving this givesm ≈ p

w· h.

(We ignore the term h ·m, which is small.It follows that the marginal value of wax lips is m = (p/w) · h packs of candy

cigarettes per h pairs of wax lips, or p/w packs of candy cigarettes per pair of

3–17

wax lips. With this, we can replace the approximations in the table above by thefollowing exact figures:

Pairs of Wax Lips Packs of Candy Cigarettes MV

0 20 ∞1 18 182 16 83 14 4 2/34 12 35 10 26 8 1 1/37 6 6/78 4 1/29 2 2/910 0 0

Now we can see that with 5 pairs of wax lips and 10 packs of candy cigarettes,For Fred, the MV of a pair of wax lips is exactly 2 packs of candy cigarettes, sothat this is the basket he will choose.

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Chapter Four:

Consumers in the Marketplace

General Discussion and Teaching Suggestions

1) To give students an idea of where we’re going, it can be helpful to pointout that in Chapter Three we studied the behavior of a consumer with a givenbudget line, while in Chapter Four we will study how that consumer’s behaviorchanges when his budget line changes. In the solved problems in Section 3.3 andthe problems at the end of Chapter Three, we have already seen a lot of examplesof changing budget lines; in this chapter we will systematize that knowledge andtry to make some general statements about the directions of changes.

2) The text discusses only the Hicksian version of the compensated demandcurve (holding utility fixed) and the corresponding decomposition into substitutionand income effects. Good students can be challenged to work out the details ofthe Slutsky compensation (holding fixed a Laspeyres index of the price level) andthe corresponding Slutsky decomposition. For the right students, you can makeadditional assignments such as: define a “Hicksian” decomposition that consists ofan income effect followed by a substitution effect (as opposed to the substitutioneffect followed by income effect that is traditional), illustrate its geometry, andsay whatever else you can about it. Or: do the same thing with a “Slutsky-style”decomposition. Although I’ve never tried it, it seems a worthwhile experimentto assign such problems as topics for short papers. With several variants of theproblem available, the threat of collusion is substantially reduced.

Alternatively, the “mix and match” problems beginning on page 4-6 of thismanual lead the students through every possible variation of such problems, withenough coaching so they can be used as exam problems rather than short papertopics.

3) Students will want to know why we study the compensated demand curve.One response is that it allows us to isolate the substitution effect and to demon-strate that its direction is unambiguous; this allows us to draw the non-obviousconclusion that all Giffen goods are inferior, and in fact that the Giffen phenomenonrequires in some sense a “large” income effect in order to occur.

A second response is that there are other theoretical applications of the com-pensated demand curve, for example to the theory of consumers’ surplus in ChapterEight. But this will not be very satisfying to students at this point in the course.

Yet a third response invokes the notion of the representative agent (withoutthe need to introduce that piece of jargon). It is true that many consumers ofapples experience no change in their money income when the price of apples goesup. If you want to know how many apples such a consumer will buy at a given price,you must look along his uncompensated demand curve. However, there are somesituations in which it is reasonable to expect people to be income- compensatedfor a price change. Suppose, for example, that you own an apple orchard. In thatcase, whenever the price of apples goes up, your income goes up as well. However,this is still not a good justification for studying the compensated demand curve,because it is unlikely that your income will go up by exactly enough to compensateyou for the higher price of apples. Indeed, if your income is derived primarily fromyour orchard, then you are likely to be considerably overcompensated for any pricechange.

In general, a rise in the price of apples is helpful to apple sellers and harmful to

4–1

apple buyers. How does it affect people on average? The complete answer dependson the exact meaning that we attach to the phrase “on average”, but one way tothink about it is this: Since the total number of apples bought must equal the totalnumber of apples sold, the gains to sellers must in some sense just balance the gainsto buyers. Therefore, on average, people are made neither better nor worse off bya change in the price of apples, which is to say that on average, people are income–compensated for the price change.

Thus if we are attempting to model the behavior of an individual consumer orof a small part of the economy, the uncompensated demand curve is the right oneto use. But in certain models that attempt to take account of all of the activitiesof everyone in the economy (you might even want to introduce the phrase “generalequilibrium”, or to mention that such models are increasingly important in macroe-conomics), the compensated demand curve provides the appropriate description ofconsumer behavior on average.

4–2

Additional Problems

1. True or False: For a rich man and a poor man, a Mercedes-Benz is equallyexpensive.

2. The only good Hiram ever buys is potatos; he would never consider buyingany other good.a) True or False: Potatos cannot possibly be an inferior good for Hiram.b) What is the shape of Hiram’s Engel curve for potatos?

3. The only good Hiram ever buys is potatos; he would never consider buyingany other good.a) True or False: Potatos cannot possibly be a Giffen good for Hiram.b) What is the shape of Hiram’s demand curve for potatos?

4. You buy only beer and pizza. One day the price of beer goes down, the priceof pizza goes up, and you discover that you can just exactly afford to continuebuying the basket you were buying all along. Do these changes leave youhappier, less happy, or equally happy? Illustrate your answer with indifferencecurves.

5. Suppose that the federal government issues $100 worth of food stamps toeveryone in your city. These food stamps are coupons that can be exchangedfor $100 worth of food at the grocery store, but can only be used by the personto whom they are issued.a) Draw your budget constraint between “Food” and “All Other Goods”

both before and after the food stamps are issued.b) True or False: If food is a normal (as opposed to inferior) good, then the

food stamps will surely lead to more food being eaten.c) Suppose that you lose your $100 worth of food stamps but at the same

time, your income increases by $200. True or False: If food is a normal(as opposed to inferior) good, this will surely lead to an increase in yourfood consumption.

6. Suppose that Hiram buys potatos and only potatos; he would never considerbuying any other good. True or False: Potatos cannot possibly be an inferiorgood for Hiram.

7. Suppose that Hiram buys potatos and only potatos; he would never considerbuying any other good. True or False: Potatos cannot possibly be a Giffengood for Hiram.

8. True or False: All Giffen goods are inferior goods, but not all inferior goodsare Giffen goods.

9. Homer consumes beer and donuts. Beer is an inferior good. One day theprice of donuts falls. Use a graph to show what happens to Homer’s beerconsumption. Does Homer end up drinking more or less beer than before?Justify your answer carefully.

10. The only two goods you consume are X and Y. Y is an inferior good. Supposethat the price of X goes down.a) Illustrate the substitution and income effects.b) True or False: Your consumption of Y must go down. Justify your answer

in terms of the effects you illustrated in part a).

11. The only two goods you consume are X and Y. X is a Giffen good. Supposethat the price of X goes up.

4–3

a) Illustrate the substitution and income effects.b) True or False: Your consumption of Y must go down. Justify your answer.

12. On Monday, apples and peaches sell for $1 each. Your income is $10, withwhich you buy 2 apples and 8 peaches. On Tuesday, the price of apples risesto $2 and the price of peaches falls to 50 cents (and your income remains $10).a) Draw your Monday and Tuesday budget lines and show your Monday

optimum point. Label it M .b) Suppose your optimum point on Tuesday is to the right of M . Are apples

a normal good? Use your diagram to fully justify your answer.

13. Suppose you allocate all your wealth to “housing” and “savings”. Housingcosts $40 per square foot. You have $100,000 in wealth and have elected tobuild a 1000 square foot house.a) Draw your budget line between housing (on the horizontal axis) and sav-

ings (on the vertical). Draw the indifference curve you are on.b) Now suppose the price of housing falls to $30 per square foot. Draw your

new budget line. (Hint: You can keep your existing house if you want to.)c) True or False: The fall in housing prices makes you happier.d) Assume that housing is an inferior good and illustrate the substitution

and income effects from a fall in housing prices.e) True or False: If housing is an inferior good, then in this problem the

substitution effect must be larger than the income effect.

14. Homer consumes only donuts and coffee. One day the price of donuts falls,and Homer responds by increasing his coffee consumption.a) Show how the fall in the price of donuts affects Homer’s budget line.b) Show Homer’s old and new optimum, and label them A and B. How does

your graph illustrate the fact that Homer now consumes more coffee?c) Shortly after the price of donuts falls, Homer is informed that his salary

has been cut. He finds that he is now exactly as happy as he was beforeany of the changes took place. Show his new budget line and his newoptimum point. Label it C.

d) Use your graph to determine whether coffee is an inferior good. Justifyyour answer in terms of the relative locations of points A, B and C. Becareful to note that although the price of donuts has changed, the questionasks whether coffee is inferior.

e) Is it possible to tell whether coffee is a Giffen good? Why or why not?

15. William consumes meat and potatos. When the price of meat goes up, Williamcontinues to consume exactly the same number of potatos as before.a) Draw a picture showing William’s budget lines before and after the price

of meat goes up. Show his optimum points on both budget lines. Howdoes your picture reflect the fact that Wiliam’s potato consumption isunchanged?

b) Draw a compensated budget line and indicate the substitution and incomeeffects of the price change.

c) Can you tell whether potatos are a normal or an inferior good for William?Justify your answer thoroughly.

d) Can you tell whether potatos are a Giffen good for William? Justify youranswer thoroughly.

16. In each of the following pictures, the black dots represent tangencies withindifference curves. In which pictures is X normal? In which pictures is Y

4–4

normal? In which pictures is X Giffen? In which pictures is Y Giffen?

X

Y

X

Y

X

Y

X

Y

X

Y

B

17. Suppose you consume only cakes and ale. You currently have 5 cakes and 7pints of ale. Now someone starts giving you additional cakes, while your aleconsumption remains unchanged. You find that each additional cake has alower marginal value than the previous one.a) True or False: Ale must be a normal good.b) True or False: Cakes must be a normal good.

18. Bugs consumes only carrots and lettuce, both of which are normal goods forBugs. One day the price of carrots goes up.a) Illustrate Bugs’ old and new optimum points, and show the substitution

and income effects. How does your graph reflect the fact that carrots area normal good? How does it reflect the fact that lettuce is a normal good?

b) Can you say for certain whether the substitution effect causes Bugs tobuy more or less lettuce than before? If so, use your graph to explainwhy. If not, explain on what your answer would depend. (Warning: Thequestion asks about quantities of lettuce, not of carrots.)

c) Can you say for certain whether the income effect causes Bugs to buymore or less lettuce than before? If so, use your graph to explain why. Ifnot, explain on what your answer would depend.

d) When the price of carrots goes up, can you say for certain whether Bugswould buy more or less lettuce than before? If so, justify your answer; ifnot, explain on what the answer would depend.

e) Suppose that almost all of Bugs’s income is spent on lettuce. Now whenthe price of carrots goes up, do you expect him to buy more or less lettucethan before? Carefully justify your answer in terms of the substitutionand income effects.

4–5

19. Can a good be simultaneously inferior and non-Giffen? Justify your answerusing a diagram that illustrates the income and substitution effects of a priceincrease.

20. Suppose you consume only X and Y . Both goods are normal. When the priceof X goes up, which of the following is true?

i) Your consumption of Y definitely goes up.ii) Your consumption of Y definitely goes down.iii) Your consumption of Y could go either up or down.If you answered (i) or (ii), give a complete justification for your answer. If youanswered (iii), state what additional piece of information you would need todetermine what happens to your consumption of Y . In any case, your answershould be in terms of substitution and income effects.

21. Sam consumes only green eggs and ham.a) Draw a diagram with green eggs on the horizontal axis and ham on the

vertical. Illustrate how Sam’s budget line is affected by a rise in the priceof ham.

b) Show the indifference curve that Sam was on before the price change, anddraw in a compensated budget line.

c) Suppose that green eggs are an inferior good for Sam, and show Sam’snew optimum point. How does your graph reflect the fact that green eggsare an inferior good?

d) In terms of your graph, identify the substitution and the income effects.e) True or False: If green eggs are an inferior good, then when the price

of ham goes up, Sam consumes more green eggs. Carefully justify youranswer in terms of the substitution effect and the income effect.

22. The only goods you consume are X and Y. Assume that both X and Y arenormal goods. One day the price of X goes down.a) Illustrate your old and new budget lines and your old and new consump-

tion points. Illustrate the substitution and income effects from the fall inthe price of X. Make sure I can tell what’s what on your graph, eitherwith labels or with explanation nearby.

b) Can you say for certain whether the substitution effect causes you to con-sume more Y or less Y? If so, use your graph to explain why. If not, explainwhat the answer would depend on. (Please take note that although theprice of X has fallen, the question asks about your consumption of Y , notof X.)

c) Can you say for certain whether the income effect causes you to consumemore Y or less Y? If so, use your graph to explain why. If not, explainwhat the answer would depend on.

d) When the price of X goes down, can you say for certain whether you buymore Y or less Y? If so, carefully justify your answer. If not, explain whatthe answer would depend on.

e) Suppose that almost all of your income is spent on Y. Now when the priceof X goes up, do you expect to buy more Y or less Y? Carefully justifyyour answer in terms of income and substitution effects.

23. Suppose that there are two kinds of cars: cheap cars that get lousy gas mileageand expensive cars that get good mileage.a) Considering that you get to decide which kind of car to own, draw your

budget constraint between “miles driven” and “all other goods”.b) Suppose that the price of gasoline goes up, and you respond by increasing

4–6

your purchases of gasoline. True or False: This means that gasoline is aGiffen good for you.

24. Freddie’s income is $20 a month. In June, cookies cost $1 apiece, crackerscost $1 apiece, and Freddie buys 5 cookies and 15 crackers. In July, cookiescost $1.50 apiece, crackers cost $.50 apiece, and Freddie buys 9 cookies and 13crackers. Can you determine whether cookies are a normal or an inferior goodfor Freddie? What about crackers? Fully justify your answers.

25. You consume only beer and pizza. Beer is a normal good. One day the priceof beer goes down and the price of pizza goes up. Must you consume morebeer? Justify your answer with indifference curves.

26. Herman Munster eats ten cheese sandwiches every day for lunch, and he wouldcontinue eating ten cheese sandwiches every day even if the price of cheesedoubled. Can you determine whether cheese sandwiches are an inferior goodfor Herman? Justify your answer.

27. Your income is $100 a month. You sign up for a telephone plan that costs $10a month plus 10 cents per call.a) Once you’ve signed up for the phone plan, draw your budget constraint

between phone calls and “all other goods”, with “all other goods” mea-sured in dollars.

b) Now suppose the phone company offers an alternative plan that costs $20a month plus 5 cents per phone call. You like this plan better so youswitch; after switching, you make fewer calls per month. Illustrate thissitutation with indifference curves.

c) True or False: Given the information in part b), phone calls must be aGiffen good for you.

d) True or False: Given the information in part b), phone calls must be aninferior good for you.

28. Suppose apples are an ordinary (non-Giffen) inferior good and oranges are aGiffen good. Which do you expect to have the steeper Engel curve, apples ororanges? Explain why.

29. If your indifference curves between X and Y are shaped as in Exhibit 3-10,what is your income elasticity of demand for X? What is your price elasticityof demand for X?

30. Herman’s demand curve for chocolate bars has the same elasticity at all points.True or False: That elasticity must be equal to 1. (Note: This problem ishard.)

31. Suppose that your price elasticity of demand for carrots is -2 and the price ofcarrots goes up 1%. What happens to your total expenditure on carrots?

32. When the price of carrots goes up, Maeve’s total expenditure on carrots goesdown. What can you conclude about her price elasticity of demand for carrots?

33. True or False: For a normal good, the price elasticity of demand must begreater in absolute value than the income elasticity of demand. Hint: Imaginea 1% change in price, and think about income and substitution effects. Whichof these effects is reflected in the income elasticity of demand? Which in theprice elasticity of demand?

34. In August, 1990, East German taxicab drivers were on strike demanding lowercab fares. What must the drivers have believed about the price elasticity of

4–7

demand for taxicab rides?Mix and Match Problems

The following “mix and match” procedure produces 192 variations on problems9 and 10 in the textbook. At the end of this section (beginning on page 4-10) I givesome illustrations of the problems you can create via the mix and match procedure.

STEP I: Choose an “opening” from among choices A − L below. (Twelvechoices.)

STEP II: Each of the twelve openings contains contains the phrase “just ashappy as”. Either leave this phrase unchanged, or replace it with “just able toafford the same basket that you bought”. (Two choices.)

STEP III: Choose a “closing” from among choices P − S below. (Fourchoices.)

STEP IV: Either do or do not interchange X’s and Y ’s throughout the prob-lem. (Two choices.)

For example, the following set of choices essentially reproduces problem 9 fromthe text. I: Opening A; II: Leave phrase unchanged; III: Closing P ; IV: Do notinterchange X and Y .

Likewise, the following set of choices essentially reproduces problem 10 fromthe text. I: Opening H; II: Replace the phrase; III: Closing S; IV: Do interchangeX and Y .

The following sets of choices essentially ask students to reproduce the argu-ments in the main body of the textbook. I: Opening H; II: Don’t replace the phrase;III: Closing P or Q; IV: Do not interchange X and Y . In this case, you shoulddelete the part of closing P or Q that asks the student to produce an argumentdifferent from the one in the text.

NOTE: If in Step IV, you elect to switch X’s and Y ’s, I think it’s a goodidea to include a “don’t get confused” warning. For example, in problem 10 in thetextbook, I have changed “the price of Y goes up” to “the price of Y (not X! )goes up”.

The Openings

A. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X goes up (while

your income and the price of Y remain fixed). Draw a diagram, with X onthe horizontal axis and Y on the vertical, to illustrate how your budget linemoves. Illustrate your optimum points on the two budget lines, labelingMonday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, the price of X returns to its Mondaylevel, but at the same moment your income falls by just enough so thatyou are just as happy on Wednesday as on Tuesday. Draw your newbudget line and your new optimum point. Label the optimum W .

B. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X falls (while

your income and the price of Y remain fixed). Draw a diagram, withX on the horizontal axis and Y on the vertical, to illustrate how yourbudget line moves. Illustrate your optimum points on the two budgetlines, labeling Monday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, the prices of X and Y remain at theirTuesday levels, but at the same moment your income falls by just enough

4–8

so that you are just as happy on Wednesday as on Monday. Draw yournew budget line and your new optimum point. Label the optimum W .

C. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, your income falls (while the

prices of X and Y remain fixed). Draw a diagram, with X on the horizon-tal axis and Y on the vertical, to illustrate how your budget line moves.Illustrate your optimum points on the two budget lines, labeling Monday’soptimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, your income returns to its Mondaylevel, while the price of X rises by enough so that you are just as happyon Wednesday as on Tuesday. Draw your new budget line and your newoptimum point. Label the optimum W .

D. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, your income rises (while

the prices of X and Y remain fixed). Draw a diagram, with X on thehorizontal axis and Y on the vertical, to illustrate how your budget linemoves. Illustrate your optimum points on the two budget lines, labelingMonday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, your income remains at its Tuesdaylevel, while the price of X rises by enough so that you are just as happyon Wednesday as on Monday. Draw your new budget line and your newoptimum point. Label the optimum W .

E. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, your income rises (while

the prices of X and Y remain fixed). Draw a diagram, with X on thehorizontal axis and Y on the vertical, to illustrate how your budget linemoves. Illustrate your optimum points on the two budget lines, labelingMonday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, your income returns to its Mondaylevel, while the price of X falls by enough so that you are just as happyon Wednesday as on Tuesday. Draw your new budget line and your newoptimum point. Label the optimum W .

F. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, your income falls (while the

prices of X and Y remain fixed). Draw a diagram, with X on the horizon-tal axis and Y on the vertical, to illustrate how your budget line moves.Illustrate your optimum points on the two budget lines, labeling Monday’soptimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, your income remains at its Tuesdaylevel, while the price of X falls by enough so that you are just as happyon Wednesday as on Monday. Draw your new budget line and your newoptimum point. Label the optimum W .

G. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X falls (while

your income and the price of Y remain fixed). Draw a diagram, withX on the horizontal axis and Y on the vertical, to illustrate how yourbudget line moves. Illustrate your optimum points on the two budgetlines, labeling Monday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, the price of X returns to its Monday

4–9

level, while your income increases by enough so that you are just as happyon Wednesday as on Tuesday. Draw your new budget line and your newoptimum point. Label the optimum W .

H. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X rises (while

your income and the price of Y remain fixed). Draw a diagram, withX on the horizontal axis and Y on the vertical, to illustrate how yourbudget line moves. Illustrate your optimum points on the two budgetlines, labeling Monday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, the price of X remains at its Tuesdaylevel, while your income increases by enough so that you are just as happyon Wednesday as on Monday. Draw your new budget line and your newoptimum point. Label the optimum W .

I. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X falls and the

price of Y rises. You find that on Tuesday you are just as happy ason Monday. Draw a diagram, with X on the horizontal axis and Y onthe vertical, to illustrate how your budget line moves. Illustrate youroptimum points on the two budget lines, labeling Monday’s optimum Mand Tuesday’s optimum T .

b) Now suppose that on Wednesday, the Tuesday prices remain in effect, butyour income increases. In fact, Wednesday’s percentage increase in yourincome is equal to Tuesday’s percentage increase in the price of Y . Drawyour new budget line and your new optimum point. Label the optimumW .

J. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X rises and

the price of Y falls. You find that on Tuesday you are just as happyas on Monday. Draw a diagram, with X on the horizontal axis and Yon the vertical, to illustrate how your budget line moves. Illustrate youroptimum points on the two budget lines, labeling Monday’s optimum Mand Tuesday’s optimum T .

b) Now suppose that on Wednesday, the price of X falls by just enough sothat the relative price of X in terms of Y is the same on Wednesday ason Monday. Draw your new budget line and your new optimum point.Label the optimum W .

K. Suppose the only goods you buy are X and Y .a) Suppose that between Monday and Tuesday, the price of X rises and

the price of Y falls. You find that on Tuesday you are just as happyas on Monday. Draw a diagram, with X on the horizontal axis and Yon the vertical, to illustrate how your budget line moves. Illustrate youroptimum points on the two budget lines, labeling Monday’s optimum Mand Tuesday’s optimum T .

b) Now suppose that on Wednesday, the Tuesday prices remain in effect,but your income falls. In fact, Wednesday’s percentage decrease in yourincome is equal to Tuesday’s percentage decrease in the price of Y . Drawyour new budget line and your new optimum point. Label the optimumW .

L. Suppose the only goods you buy are X and Y .

4–10

a) Suppose that between Monday and Tuesday, the price of X falls and theprice of Y rises. You find that on Tuesday you are just as happy ason Monday. Draw a diagram, with X on the horizontal axis and Y onthe vertical, to illustrate how your budget line moves. Illustrate youroptimum points on the two budget lines, labeling Monday’s optimum Mand Tuesday’s optimum T .

b) Now suppose that on Wednesday, the price of X rises by just enough sothat the relative price of X in terms of Y is the same on Wednesday ason Monday. Draw your new budget line and your new optimum point.Label the optimum W .

The Closings

P. In each of parts (c), (d) and (e), determine whether the statement is (1) truealways, (2) false always, (3) true if X is an inferior good, but otherwise false,(4) false if X is an inferior good but otherwise true, (5) true if X is a Giffengood, but otherwise false, or (6) false if X is a Giffen good but otherwise true:

c) M is to the left of T .d) T is to the left of W .e) M is to the left of W .

f) True or False: Every Giffen good is an inferior good. Justify your answerby using the earlier parts of this problem, not by using the argumentgiven in the text.

Note to instructors: For a slight variation on closing P , change “Every Giffen goodis an inferior good” to “A normal good cannot be Giffen” in part f). This is ofcourse logically equivalent, but to a certain class of students it will appear to be avery different problem.

Q. Answer the following questions:

c) In terms of the locations of points M , T , and W , what does it mean forX to be an inferior good?

d) In terms of the locations of points M , T , and W , what does it mean forX to be a Giffen good?

e) Which of the following statements is always true and why: M is to theleft of T ; M is to the right of T ; M is to the left of W ; M is to the rightof W ; T is to the left of W ; T is to the right of W .

f) True or False: Every Giffen good is an inferior good. Justify your answerby using the earlier parts of this problem, not by using the argumentgiven in class.

Note to instructors: As with closing P , closing Q has another slight variation:change “Every Giffen good is an inferior good” to “A normal good cannot beGiffen” in part f). This is of course logically equivalent, but to a certain class ofstudents it will appear to be a very different problem.

R. Answer the following questions:

c) In terms of the locations of points M , T , and W , what does it mean forX to be a normal (as opposed to inferior) good? What does it mean forY to be a normal good?

d) Y is called a Figgen good if it is true that “when the price of X goesdown, the quantity demanded of Y goes up” (or equivalently, “when the

4–11

price of X goes up, the quantity of Y demanded goes down”). In termsof points M , T and W , what would it mean for Y to be a Figgen good?(Be careful to keep your X’s and Y ’s straight!)

e) True or False: Every Figgen good is a normal good. Give a completejustification for your answer.

f) True or False: A Figgen good cannot be Giffen. Give a complete justifi-cation for your answer.

Note to instructors: For a further variation on closing R, change “Every Figgengood is a normal good” to “An inferior good cannot be Figgen” in part e).

S. Answer the following questions:

c) In terms of the locations of points M , T , and W , what does it mean forX to be a normal (as opposed to inferior) good? What does it mean forY to be a normal good?

d) Y is called a Neffig good if it is true that “when the price of X goes up,the quantity demanded of Y goes up” (or equivalently, “when the priceof X goes down, the quantity demanded of Y goes down”). In terms ofpoints M , T and W , what would it mean for X to be a Neffig good?

e) True or False: Every inferior good is a Neffig good. Fully justify youranswer.

f) True or False: Every Giffen good is a Neffig good. Fully justify youranswer.

IllustrationsThe following problems illustrate the results of the mix-and-match procedure.

In some cases I have changed X and Y to, e.g. wine and roses, just for variety.1. (STEP I: F. STEP II: no switch. STEP III: P. STEP IV: no switch)

Suppose that the only goods you buy are wine and roses.a) Suppose that between Monday and Tuesday, your income falls (while the

prices of wine and roses remain fixed). Draw a diagram, with wine on thehorizontal axis and roses on the vertical, to illustrate how your budget linemoves. Illustrate your optimum points on the two budget lines, labelingMonday’s optimum M and Tuesday’s optimum T .

b) Now suppose that on Wednesday, your income remains at its Tuesdaylevel, but the price of wine falls. In fact, it happens to fall by just enoughso that you are equally as happy on Wednesday as on Monday. Draw yournew budget line and your new optimum. Label it W .

In each of parts (c), (d) and (e), determine whether the statement is (1) truealways, (2) false always, (3) true if wine is an inferior good, but otherwisefalse, (4) false if wine is an inferior good but otherwise true, (5) true if wineis a Giffen good, but otherwise false, or (6) false if wine is a Giffen good butotherwise true:

c) M is to the left of T .d) T is to the left of W .e) M is to the left of W .

f) True or False: Every Giffen good is an inferior good. Justify your an-swer by using the earlier parts of this problem, not by using otherarguments we gave in class.

2. (STEP I: E; STEP II: no switch; STEP III P (variant); STEP IV: no switch)

4–12

Suppose the only goods you buy are bread and circus tickets.a) Suppose that between Monday and Tuesday, your income rises (while the

prices of both bread and circus tickets remain fixed). Draw a diagram,with bread on the horizontal axis and circus tickets on the vertical, toillustrate how your budget line moves. Illustrate your optimum pointson the two budget lines, labeling Monday’s optimum M and Tuesday’soptimum T .

b) Now suppose that on Wednesday, your income returns to its Mondaylevel, but at the same moment the price of bread falls by exactly enoughso that you are just as happy on Wednesday as on Tuesday. Draw yournew budget line and your new optimum.

In each of parts (c), (d) and (e), determine whether the statement is (1) truealways, (2) false always, (3) true if bread is an inferior good, but otherwisefalse, (4) false if bread is an inferior good but otherwise true, (5) true if breadis a Giffen good, but otherwise false, or (6) false if bread is a Giffen good butotherwise true:

c) M is to the left of T .d) T is to the left of W .e) M is to the left of W .

f) True or False: A normal good cannot be Giffen. Justify your answer byusing the earlier parts of this problem, not by using other argumentswe gave in class.

3. (STEP I: D; STEP II: no switch; STEP III: Q; STEP IV: no switch)You consume two goods, X and Y . From Monday to Tuesday, your incomerises. On Wednesday, your income remains at its Tuesday level, but the priceof X rises. On Wednesday you are exactly as happy as on Monday.a) Draw your budget lines for all three days. Be sure to label which is which.

Label the three days’ optimum points M , T and W (for Monday, Tuesdayand Wednesday).

b) In terms of the locations of M , T and W , what does it mean for X to beinferior?

c) In terms of the locations of M , T and W , what does it mean for X to beGiffen?

d) Which of the following is always true, and why?: M is to the left of T ;M is to the right of T ; M is to the left of W ; M is to the right of W ; Tis to the left of W ; T is to the right of W .

e) Using your answers to the earlier parts of this problem, provethat a Giffen good must be inferior.

4. (STEP I: F; STEP II: no switch; STEP III: R; STEP IV: no switch)You consume two goods, X and Y . Suppose that from Monday to Tuesday,your income falls. From Tuesday to Wednesday, the price of X falls. You areexactly as happy on Wednesday as on Monday.a) Draw your budget lines for all three days. Label the three days’ optimum

points M for Monday, T for Tuesday, and W for Wednesday.b) In terms of the points M , T and W , what would it mean for X to be a

normal (as opposed to inferior) good? What would it mean for Y to be anormal good?

c) Y is called a Figgen good if it is true that “when the price of X goes down,the quantity demanded of Y goes up”. In terms of points M , T and W ,

4–13

what would it mean for Y to be a Figgen good? (Be careful to keep yourX’s and Y ’s straight!)

d) True or False: Every Figgen good is a normal good. Give a completejustification for your answer.

4–14

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 4

1.a) Fewer.b) No.

2. The full picture is:

M

T

MONDAYWEDNESDAYTUESDAYWINE

ROSES

with the Wednesday optimum somewhere on the darkened part of the Wednes-day budget line.

a) In going from the Monday optimum M to the Tuesday optimum T, consumptionof wine must go down.

b) No, because the Monday optimum M is outside the Tuesday budget line.c) Wednesday.d) Yes. You certainly buy less on Wednesday. If you bought more wine on Wednesday,

the Wednesday optimum would have ‘to be to the right of (and consequently below)the Monday optimum M; this would require the two indifference curves to cross.

e) No. The change from Tuesday to Wednesday is a pure income effect. Thus itsdirection depends on whether wine is a normal or an inferior good.

3. The picture is:

MT

W

WINE

ROSES

M must be to the right of W because it is at a steeper point on the sameindifference curve. It is given that W is to the right of T. Therefore M is to theright of T, which makes wine a normal good. So true.

4. The picture is:

4–15

A

C

OTHER GOODS

B

EGGS

Eggs are inferior because B is to the right of C. Eggs are not Giffen becauseB is to the left of A.

5. X is normal in C, D, and E. X is Giffen in B. Y is inferior in C and D. Y is Giffenin C.

6.a) The picture shows your old and new budget lines.

A B

C

X

Y

OLDNEW

COMPENSATED

b)) The substitution effect is the move from A to C and the income effect is the movefrom C to B.

c) The substitution effect is a rightward move from A to C; C is at a flatter place onthe same indifference curve.

d) If X is normal, the income effect is a rightward move from C to B.e) If X is inferior, the income effect is a leftward move from C to B.f) False; the opposite is true. If X is normal, then B is left of C is left of A, so B is

left of A, so consumption must rise. If X is inferior, B could be either left or rightof A, so consumption could rise or fall.

7. The picture is:

4–16

W

Wine

Roses

MT

M is to the left of T when wine is Giffen; T is to the left of W always; M is tothe left of W when wine is inferior.

Part f) is true: If wine is Giffen then M is left of T, and T is always left of W,so if wine is Giffen then M is left of W, which is to say that if wine is Giffen thenwine is inferior.

8.a) The picture is:

W

X

Y

M

T

b) X is inferior if and only if W is left of T.c) Yes, it is true; W is at a flatter point on the same indifference curve.d) It means that M is right of T.e) True. If X is inferior, then W is left of T (by part b) and right of M (by part c) so

M is right of T, which makes X a Figgen good (by part d).f) True. If X is Giffen, it is inferior, so part e) applies.

9. The picture is:

MT

W

EGGS

WINE

4–17

True. T is necessarily to the left of W. So if W is left of M, then T is left ofM and eggs cannot be a Giffen good.

10. The picture shows that X is Giffen, so it must also be inferior. The points ($3,4)and ($6,5) are on the demand curve for X.

11. The substitution effect leads to more Y. The income effect leads to less Y. Theincome effect is small, so you probably consume more Y.

12.

pp

pp

pp

A

C

B

B is directly below A (given) andC is left of A (geometry). ThusC is left of B so shoes aredefinitely inferior for Tara. Sofalse.

SHOES

AOG

13.

pppp

pp

A

C

B

SOCKS

SHOES

B is directly to the left of A(given) and C is above A(geometry). Thus C isabove A, so socks must benormal. So true.

14.

pp

pp

pp

GREEN EGGS

HAM

A

C

B

Original optimum is at A; newoptimum is at B. Substitutioneffect is from A to C ; incomeeffect is from C to B. Thegraph reflects the inferiority ofham by the fact that B is aboveC . Also, C is above A bygeometry. It follows that B isabove A, so the statement inpart b) is True.

15.

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pp

pp

pp

KIDNEYS

LIVER

A

C

B

a) C is above A by geometry; B isbelow A (given). Therefore B isbelow C , so liver must be a normalgood for Leopold.b) Because liver is normal, it cannotbe Giffen.

16.

M

SODAS

A

EGGS

(DRAWING IS NOT TO SCALE!)

In April, Frieda chooses point A. In May, she chooses pointM.The indifference curve tangent at A must pass to the left ofM;otherwise the curves tangent at A and M would cross. ThereforeM is on a higher indifference curve, and the answer to part a)is that Frieda is happier in May.

For part B, there are two ways to get the answer:

Method I: Draw the budget line shown, parallel to the Mayline but tangent to the April curve. Note that X is right ofA by geometry and A is right ofM (given) so X is right ofM, making eggs inferior.

Method II (not shown): Draw a budget line tangent to thehigher indifference curve but parallel to the (steeper)April budget line. The tangency Y will lie to the left of M,which is left of A. Y left of A makes eggs inferior.

The underlying intuition: Eggs got cheaper, so the substitutioneffect says "buy more eggs". ButFrieda buys fewer eggs, whichcan only be due to the income effect. She's effectively richer,and the income effect is saying "fewer eggs". Thus eggsmust be inferior.

X

17.a) True. When his income goes up, Herman must by more Munster cheese, becausethere’s nothing else to buy.

b) True. When the price of Munster cheese goes up, Herman is surely forced to buyless of it. There’s nothing else to cut back on.

18.a) It is a hyperbola.b) It is a vertical line.c) −1

19. In these circumstances, you consume either no X or only X. When you consumeno X, a change in the price of X has no effect on your well–being, so no compensationis called for. When you consume only X, a change in the price makes you betteroff if it allows you to consume any more X at all, and worse off it it allows you toconsume less X. Thus your income must be compensated by just enough to keepyour consumption of X constant. For example, if the price of X were to double,your income would also be doubled in the imaginary experiment described in thetextbook. It follows that your compensated demand curve looks like this:

4–19

Q

P

20. True. The compensated demand curve eliminates the income effect. For a normalgood, this means that a price increase yields a smaller quantity reduction along thecompensated demand curve than along the uncompensated demand curve. For aninferior good, the reverse is true.

21. True, since the uncompensated demand curve differs from the compensated de-mand curve only by the incorporation of the income effect, and the income effectfrom a change in the price of bubblegum is likely to be a small one. (Even if theprice of bubblegum were to multiply tenfold, it is unlikely that your lifestyle wouldchange appreciably.) On the other hand, housing consumes a large part of mostpeople’s budgets, so that even a modest rise in the cost of housing could have asubstantial income effect.

22. Your income elasticity of demand is 1. Your (uncompensated) price elasticity ofdemand is −1.

23. It means that when your income goes up, your consumption of the luxury goodincreases by a greater proportion than your income does. If your income increasesby 1%, your consumption of luxury goods increases by more than 1%. But youcannot increase your consumption of all goods by more than 1% without violatingthe budget constraint. Therefore not all goods can be luxuries.

In fact, this can be made more precise. When your income increases by 1%,your expenditures on goods must increase by exactly 1% “on average.” Thus theaverage income elasticity of demand for all goods must be 1. In the averagingprocess, goods must be weighted according to the share of your income that isspent on them. Suppose that you consume only X and Y. Write kX and kY for thefraction of your income that you spend on X and the fraction that you spend onY. Write ηX and ηY for your income elasticities of demand for X and Y. Then wemust have

kX · ηX + kY · ηY = 1.

If you want to prove this formula, start with the expressions

kX =PX ·X

I

kY =PY · Y

IPX ·∆X + PY ·∆Y = ∆I.

(First explain what each of these expressions means and why it is true.) Theninsert the expressions for kX , kY , ηX and ηY into the formula and use algebra tosimplify.

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24. The demand for gasoline from Gus’s, because it has more substitutes (such asgasoline from the competing gas station across the street).

25. Revenue rose 123% even though quantity fell by 17%, so the price must have risenby 140%. Price elasticity is therefore (−17)/140 = −.12.

26.

pp

pp

A

B

SPEED

SAFETY

pp

C

Without a seat belt, the driver is at Aand with a seat belt the driver is at B.Assuming speed and safety are normal,B is above and to the right of C . Bygeometry,C is above and to the left of A.Thus B must be above A (peoplecertainly drive faster). But B could beeither left or right of A (either more orfewer lives might be saved). So true.

27.

pp

pp

A

B

LEISURE HOURS

pp

C

INCOME

24

48

72The substitution effect (A to C ) is leftward.The income effect (C to B) is rightward ifleisure is a normal good; leftward if leisure isan inferior good.

If leisure is inferior, then B issurely left of A. That is, a higherwage leads to less leisure, hencemore labor. So in this case thelabor supply curve certainly slopesupward.

If leisure is normal, B could beleft or right of A, so the laborsupply curve could slope eitherdirection. So part e) is True.

The person whose income is derived entirely from wages feels a large incomeeffect from a wage change. In that case (assuming leisure normal) B is far to theright of C , hence likely to be far to the right of A, so labor hours respond stronglyto a wage change; that person's labor supply curve is relatively flat.

28.a) $2250. $0.b) $0.c) The budget line is the flatter line in this picture:

SPENDING TODAY

SPENDING NEXT YEAR

1800

2250

2500

1667

d) Finding $400 shifts the budget line out parallel to itself till it passes through($2200,$0) and ($0,$2350). Being informed of a $500 raise next year does thesame thing. A rise in the interest rate to 50% shifts the budget line to the steeperline in the above picture.

4–21

e) Both would lead to the same budget line, hence the same optimum point, hencethe same amount of spending both today and tomorrow.

f) The tangency is at ($1000,$1000).g) As already noted, the budget line shifts as in the above picture. You decrease

current spending, increase future spending, and are happier.h) The substitution effect is leftward and upward along the illustrated indifference

curve. You cannot determine the direction of the income effect.

Answers to Numerical Exercises

N1.a) The equation of the indifference curve can be written y = c/x for some constantc. Differentiating gives the slope as −c/x2 = −y/x.

b) The equation of the budget line is x + y = 40. The equality between the slope ofthe indifference curve and the slope of the budget line can be written −y/x = −1.Combining these equations gives x = y = 20. Thus the answer is 20.

c) Now the equations are 4x + y = 40 and −y/x = −4. This gives x = 5 and y = 20.Thus the answer is 5.

d) Your demand curve goes through (P = 1, Q = 20) and (P = 4, Q = 5).e) The original indifference curve passes through (20, 20), so its equation must be

xy = 400. The slope of the compensated budget line is −4; at a tangency betweenthis line and the indifference curve we must have −y/x = −4. Solving theseequations together gives x = 10 and y = 40. So the answer is 10.

f) Your consumption falls by 15, from 20 to 5. Of this, the fall from 20 to 10 (10units) is due to the substitution effect and the fall from 10 to 5 (5 units) is due tothe income effect.

N2.a) b∆I.

b) η =I ·∆X

X ·∆I=

I · b∆I

X ·∆I=

bI

X.

c) η = 1− a/X.d) η → 1e) 1

N3.a) 1− c/X = η.b) If X = 0, η = −∞, and if P = 0, η = 0.

N4. −1.

4–22

Chapter Five:

The Behavior of Firms

General Discussion

In teaching the theory of the firm, it is common to begin with production,derive the various cost curves, and then derive the firm’s supply behavior. Whilethis order is the “logical” one, it presents significant pedagogical difficulties. Themost serious is that, for the duration of several lectures, students are utterly baffledas to what all of the production machinery is for .

The present chapter seeks to address this difficulty, by showing students “upfront” how the firm’s supply behavior is determined by its marginal cost curve. Thishas the added advantage of reinforcing one of the important lessons of consumertheory—the principle of equimarginality— and showing students that the sameprinciple underlies the behavior of both consumers and firms. Once students haveseen the importance of the marginal cost curve, they tend to be far more tolerantof the time taken in later chapters to determine how it arises.

Because the goal is a quick appreciation of the fact that optimization is thesame thing as equating costs and benefits at the margin, almost no time at allis devoted to discussing why marginal cost should be upward sloping. A singleexample—that of a farm on which some acres are more fertile than others—is morethan enough to satisfy students at this stage. Talk of diminishing marginal returnswill come soon enough in Chapter 6.

Section 6.1 derives an upward sloping (or U-shaped) marginal cost curve fromthe assumption of diminishing marginal returns. Thus Chapter 5 plus Section 6.1constitutes a complete treatment of the firm’s supply behavior in the short run.Some instructors will want to cover part or all of Chapter 6 before returning toChapter 5, and the structure of the book makes this easy to do. Indeed, onceChapter 6 has been covered, the main ideas of Chapter 5 should take less than alecture.

Although logical purists will want to cover production before mentioning costs,and although, as I have said, the book can easily accomodate this viewpoint, I wouldlike to make one more argument against extreme logical purity. The argument isthat the usual order of things is really no more “logical” than the order in thetextbook. If we were true logical purists, we would never mention supply until aftera full treatment of the firm, we would never mention demand until after consumertheory, and we would never use mathematics without first insisting on a completelogical foundation for the real number system. The latter would disqualify manyoutstanding economists from ever publishing anything.

In practice, we never insist on truly logical orders of presentation in any ma-terial. Nobody seriously suggests that school children should understand Cauchyconvergence before learning to perform decimal arithmetic, although it is certainlya logical prerequisite. It seems to me to be less extreme, but no more defensible,to insist that students learn details of production without the motivation of firstseeing cost curves in use.

If you agree, cover chapter 5 before chapter 6. If you disagree, go to chapter6 directly. Let a thousand flowers bloom.

5–1

Additional Problems

1. Which of the following circumstances might affect the prices charged by ayoung doctor just out of medical school and why?a) The high cost of tongue depressors.b) The high cost of X-ray machines (assume that every doctor must have

one X-ray machine in his office).c) The high cost of a medical education.d) The fact that this particular young doctor is heavily in debt due to student

loans.e) The doctor’s discovery that his loan payments will be higher than he had

expected.f) The fact that only a limited number of people are permitted to become

doctors.g) An epidemic.h) The fact that this doctor has recently been sued for malpractice. Fortu-

nately for him, the public is unaware of the lawsuit, but unfortunately forhim, his insurance company is well aware of it and has raised his rates.

i) It becomes generally known that this doctor’s insurance company hasraised his rates.

j) Malpractice insurance rates for all doctors go up.k) The doctor in the office next door suffers fatal consequences when he

attemts to remove his own appendix.l) The doctor decides to join a very expensive country club.

2. Suppose that you own a river that many people would like to cross by car.You have recently purchased several ferry boats and have been charging peopleto take their cars across. It has recently occurred to you that if you built atoll bridge instead, the crossing time would be shorter, and therefore peoplewould be willing to pay more per crossing than they are on the ferry boats.Unfortunately, if you build the bridge you will just have to scrap the boats,because nobody else has any use for them. When you are deciding whether tobuild the bridge, which of the following numbers are relevant:a) the cost of building the bridge,b) the amount of revenue you could earn from a bridge,c) the cost of the ferry boats,d) the amount of revenue you earn from the ferry boats?

3. There is only one doctor in the town of Erewhon. Every time he treats a pa-tient, he must use a pair of disposable rubber gloves. He also finds it necessaryto keep an X-ray machine in his office, which he rents for $500 oer year. Thetown council has decided to help the doctor meet expenses, and is undecidedbetween two plans. Under Plan A, the council will provide the doctor withunlimited free rubber gloves for use in his practice; under Plan B, the councilwill provide him with an X-ray machine. Which plan will benefit the doctor’spatients more and why?

5–2

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 5

1. If the benefits are still $1.5 billion and the cost of continuing is $1.2 billion withcertainty then the project should be completed.

2. Vandalism at ABC is a fixed cost and does not affect prices. Pilferage at XYZ isa marginal cost. So true.

3. The president’s salary is a fixed cost and has no effect on prices. The workers’wages are variable costs and therefore cause the price to rise.

4. Plan A affects variable cost and hence price; Plan B affects a fixed cost and hencedoes not affect price. The patients benefit from Plan A but not Plan B.

5. The retraining course is a fixed cost, so it will not affect the price of eye exams.But if some dentists are driven out of dentistry (or out of Smallville) by this newexpense, then the price of a dental exam can rise.

6. False. The opposite is true. One department store does not change its prices inresponse to a rise in fixed costs. But if there are initially many stores and someare driven from the industry, then prices will rise.

7. False. Sunk costs are sunk.8.a) This increases the marginal cost of producing hamburgers and so can affect Waldo’s

behavior, including his prices.b) This is equivalent to a). A tax of 50 cents per hamburger is, from Waldo’s point

of view, no different than an increase in the price of meat. Therefore the price ofa hamburger can be affected.

c) This is a fixed cost, and therefore has no effect on Waldo’s behavior unless it driveshim out of business.

d) This appears at first to be equivalent to c), but it is not. The difference is that in c),only Waldo pays the fine, whereas here every restaurant in town pays it. If some ofthose other restaurants leave the marketplace, the demand for Waldo’s hamburgerswill rise, leading to a change in his marginal revenue curve and a change in his price.

e) This cost is completely sunk and has no effect on behavior. Note that this sunkcost is not equivalent to the fixed cost in part c). The fixed cost in c) does notbecome sunk until Waldo decides to keep the restaurant open another year. Thusit can affect his decision about whether to remain in business, but not the price ofhamburgers if he remains. The cost here is sunk from the beginning, and so hasno effect on anything. In other words, in part c) Waldo might go out of business,but in part e) he will not.

f) This causes a change in demand, consequently a change in marginal revenue, con-sequently a change in quantity, and consequently a change in price.

A few general comments about this problem are in order. One is that studentssometimes think that Waldo gets to decide which costs to count as fixed and whichto count as marginal, as though this were a matter of accounting procedures. Buta cost either is fixed or it isn’t, regardless of how Waldo keeps his books.

Another comment: Students sometimes say in response to part c) or part e)that although marginal cost is unchanged, meaning that price will not change,Waldo can attempt to compensate for his loss in some other way, by using cheapermeat or hiring fewer waitresses. These students have missed the point entirely. If

5–3

Waldo is a profit maximizer, he is already using the profit–maximizing quantity ofmeat and hiring the profit–maximizing number of waitresses. Any change in thisstrategy will make Waldo worse off, not better.

Finally, students sometimes attempt to answer this question by using the sup-ply and demand apparatus that we learned in Chapter 1. This is illegitimate forthe following reason: In Chapter 1, we made some reasonable guesses about whensupply curves will shift. For example, we said that an increase in the price offertilizer causes a leftward shift in the supply curve for wheat. Now, however, weare embarking on a more careful and rigorous examination of firm behavior, whichwill lead in forthcoming chapters to a more careful and rigorous examination ofthe sources of supply curves. Thus we no longer want to make guesses aboutchanges in supply behavior; we want to deduce changes in supply behavior fromfirst principles.

The ultimate reward (which comes in Chapter 7) is this: we will use the ideas ofthis chapter to figure out how and when supply curves shift. Then we will combinethese ideas with the ideas of Chapter 4, which tell us how and when demand curvesshift, and with the ideas of Chapter 1, which tell us how shifts in supply and shiftsin demand affect prices and quantities. This will enable us to make predictionsabout prices and quantities without resorting to any guesswork.

9. (a), (b) and (d) are relevant; (c) is a sunk cost.10.a) False. The salary increase does not affect the marginal cost of providing seats at

the ballpark, nor does it affect marginal revenue (since it does not affect demand).Hence no effect on price.

Sometimes students attempt to argue that there is an effect on the marginalcost of hiring ballplayers. But the team is not selling ballplayers; it is selling seatsat the ballpark. Only the marginal cost of providing those seats is relevant.

For example, it is probable that the number of janitors hired to clean up afterthe game goes up with the number of seats that are filled. Thus an increase injanitors’ salaries, unlike an increase in players’ salaries, could cause an increase inticket prices.

Of course, it remains the case that whenever a player gets a heavily publicizedsalary increase, sportswriters report that the fans will pay through higher ticketprices. This is why some people are sportswriters and other, different, people areeconomists.

b) Now the demand for tickets is changed, leading to a change in marginal revenueand possibly a change in price. The change in price is due entirely to the change indemand, and is unaffected by the amount that the Cubs pay to acquire the player.If, contrary the Cubs’ hopes, the player has no effect on the demand for tickets,there will be no change in ticket prices.

11. We have the following chart:

Quantity Total Revenue Marginal Revenue Total Cost Marginal Cost1 $20 $20 $2 $22 $36 $16 $6 $43 $48 $12 $11 $54 $56 $8 $18 $75 $60 $4 $26 $8

If the firm must produce a whole number of items, it produces 4 and sells themat a price of $14. If it can produce fractional numbers, it presumably produces somequantity between 4 and 5 and sells them at a price between $12 and $14.

5–4

12.a) Quantity 2 at a price of $18.b) Quantity 1 at a price of $20.c) Quantity 2 at a price of $18.d) It produces nothing.

13. If the area consists entirely of stores, then Wilma is correct. Rents are fixed coststhat do not affect prices. The reason that rents are high is that stores are willingto pay a lot for this location, where prices are high. But if many of the buildings inthe area are used for office space, or anything other than stores, then Fred mightbe right. The high rents (caused perhaps by a high demand for office space inthis location) have driven some stores out of the area, raising the demand for theproducts of those that remain, and consequently increasing prices.

Answers to Numerical Exercises

N1. x2 − (x− 1)2 = 2 · x− 1 dollars per liter.N2. (y/100)2.N3. (y/100)2−((y−1)/100)2 = y/5000−1/10000 dollars per centiliter = y/50−1/100

dollars per liter. If the number of liters is x = y/100, then we can write this as2 · x− 1/100 dollars per liter.

N4. This is correct within a penny.N5. Let z be the number of milliliters, so that x = z/1000. Total cost is (z/1000)2.

Marginal cost is (z/1000)2 − ((z − 1)/1000)2 = z/500000 − 1/1000000 dollars permilliliter = z/500− 1/10000 dollars per liter = 2 · x − 1/10000 dollars per liter.We now see that when we estimate marginal cost by $2 · x, we are off by no morethan one one– hundredth of a cent. If you measure in even smaller units, you willfind that the error in the approximation can be made arbitrarily small. Thus whenthere is no limit to the divisibility of the orange juice, we can say that the marginalcost is exactly $2 · x per liter.

5–5

Chapter Six:

Production and CostsGeneral Discussion

The chapter introduction uses simple and concrete examples to explain thedistinction between short-run and long-run decision-making, and then explainsthat we will study the short run and the long run as separate topics.

Section 6.1 develops the complete short-run theory without reference to thelong run. Section 6.2 develops the complete long-run theory without reference tothe short-run. Section 6.3 ties the two theories together.

This organization offers the instructor a lot of options. Some will want tocover only 6.1, moving on directly from there to Chapter 7 (Competition). Thishas the advantage of deferring the more difficult material in 6.2 and 6.3 until afterstudents have developed a little more sophistication. Others will want to cover6.1 and 6.2, giving full accounts of short-run and long-run considerations, whiledeferring or skipping over the subtle relationships of 6.3. Those who prefer thetraditional full-blown approach will want to use the entire chapter.

A more radical option is to cover 6.1 but skip 6.2 and 6.3 completely. Althoughthis omits a lot of important material, I believe that it is a reasonable approach forclasses that do not consist primarily of economics majors. If a student does not goon in economics, I would far prefer that he come away with a good feeling for theworkings of competitive markets, the functioning of the price system, and the roleof property rights—the material of Chapters 7 through 14— than that he be ableto derive a long run marginal cost curve directly from a production function.

6–1

Additional Problems

1. True or False: An upward shift in the variable cost curve is always accompa-nied by an upward shift in the marginal cost curve.

2. Bob Thomason produces theorems using hours of labor and Big Machines. Inthe short run, his labor is a variable factor but the number of Big Machinesis fixed. When he works for L hours using M Big Machines, Bob can produceL · M theorems. There are only 3 Big Machines in the world, and they canonly be rented in whole number quantities (you can not employ 1/2 of a BigMachine). Bob’s time is worth $1 per hour, and it costs $1 per hour to rent aBig Machine.a) Draw Bob’s short run total cost curve on the assumption that he em-

ploys 1 Big Machine. Do the same on the assumption that he employs2 Big Machines. Do the same on the assumption that he employs 3 BigMachines.

b) Draw Bob’s long run total cost curve.c) Repeat parts a) and b) with “total cost” replaced by “average cost.”d) Repeat parts a) and b) with “total cost” replaced by “marginal cost.”

3. True or False: When a firm’s short run and long run total costs are equal, thefirm is on its expansion path.

4. True or False: A firm operating at the minimum point of its long run averagecost curve must also be operating at the minimum point of its short run averagecost curve.

5. True or False: In the long run, the firm always chooses the least expensiveproduction process. Thus long run average cost is never greater than shortrun average cost.

6. True or False: In the long run, the firm always chooses the least expensiveproduction process. Thus long run marginal cost is never greater than shortrun marginal cost.

(Warning: The above is a quite difficult problem for students. Don’t assign itunless you are prepared to spend a lot of time going over it. The following is evenmore difficult:)

7. Suppose that a firm is operating at a point on its expansion path, producingthe quantity Q. Show that the short-run and long-run marginal cost curvescross at quantity Q.

8. Suppose that a firm experiences constant returns to scale at all levels of output.True or False: Whenever the firm increases its use of inputs, its output ex-pands proportionately. Thus this firm never experiences diminishing marginalreturns to labor.

9. True or False: If a firm only uses one input, then diminishing marginal returnsand decreasing returns to scale will both set in at the same point.

6–2

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 6

1. The following pictures are all “per hour”:

LABOR (WORKERS)

OUTPUT(ENVELOPES)

LABOR (WORKERS)

w

$ $/ENVELOPE

ENVELOPESENVELOPES

TP

AP=MP

TC

50

$.10 MC=AC=AVC

10

500

50

$5

2. The following pictures show the new curves in boldface, with the original curvesreproduced for comparison:

LABOR (WORKERS)

OUTPUT(ENVELOPES)

LABOR (WORKERS)

w

$ $/ENVELOPE

ENVELOPESENVELOPES

TP

AP=MP

TC

50

$.10

MC=AVC

10

500

50

$5

$10

$.05

$12.50

100

1000

AC

3. Let Q be the quantity of envelopes. If Q > 200 then it pays to rent the machinewhereas if Q < 200 it pays not to rent the machine. The long-run total and averagecost curves take the following form:

6–3

$

$/ENVELOPE

ENVELOPES

TC

$.10

$.05

200ENVELOPES

200

AC

4. Quantity VC TC AC AVC

1 $12 $42 $42/unit $12/unit2 $20 $50 $25 $103 $26 $56 $18.67 $8.674 $30 $60 $15 $7.505 $36 $66 $13.20 $7.206 $46 $76 $12.67 $7.677 $60 $90 $12.86 $8.578 $80 $110 $13.67 $10

5. Average cost will rise; average variable cost and marginal cost will remain unaf-fected.

6. True.7. False. The two prescriptions are equivalent. Either amounts to staying on the

expansion path.8. In this case the firm could reduce expenditures on L and increase expenditures

on K and stay on the same isocost curve. In the process it could attain higherand higher isoquants until it reached the point where MRTSLK = PL/PK . Theobvious reason for doing this is that a higher level of output (and presumablyprofits) could be attained for constant expenditures on inputs.

9. True. The firm will stay on the 3-unit isoquant, but move to a point where theslope reflects the new relative prices of the two inputs.

10.a) If the firm cuts back to 2 units of labor, it must increase capital by 2 units (toa total of 3 units) to maintain its output level of 193. Thus MRTSLK = 2.MPL = 215− 193 = 22 and MPK = 237− 193 = 44.

b) SRTC = 2× 4 + 4× 10 = 48. In the long run, the firm employs 3 units of capitaland 3 of labor so LRTC = 3× 4 + 3× 10 = 42.

c) LRTC = 55, since the firm employs 1 unit of capital and 7 of labor.d) Decreasing returns to scale because 2 units of capital and 4 of labor would produce

less than twice as much. Therefore the LRAC curve must be increasing.

6–4

11. The pictures are:

Secretaries

Typewriters

2 4 6

3

6

9

} Isoquants

TP

MPL

TC

VC

LRTC

SECRETARIES

MANUSCRIPTS

5

5

MANUSCRIPTS PER SECRETARY

SECRETARIES5

1

5 MANUSCRIPTS

30

50

$

MANUSCRIPTS5

50

$

$ per manuscript $ per manuscript

MANUSCRIPTS MANUSCRIPTS

MC=AVC

AC

5

6

10 LRAC=LRMC

6–5

12. The isoquants and isocosts are as follows:

WORKERS

BUCKETS

1 2

1

2

The expansion path passes through the following points:

Workers Buckets1 11 22 32 43 53 6

The product and cost curves are as follows:

Workers TP VC TC MPL(Buckets of Water) ($) ($) (Buckets of Water

per Worker)1 2 2 7 22 4 2 7 23 5 4 9 14 5 4 9 05 5 6 11 0

Buckets of Water AC MC LRTC LRAC LRMC($/bucket) ($/bucket) ($) ($/bucket) ($/bucket)

1 7 1 3 3 32 3.50 0 4 2 13 3 1 7 2.33 34 2.25 0 8 2 15 2.20 1 11 2.25 3

Answers to Numerical Exercises

N1.a) They are hyperbolas with equations KL = 1, KL = 4, KL = 9, KL = 16.b) To compute MRTSLK , suppose that the number of units of labor is reduced by

1, to 4. How much capital must the firm employ to produce 10 units of output?The answer is 25, which is an increase of 5 units. Thus the MRTSLK is 5 units ofcapital per worker.

The MPL is given by√

20 · 5−√

20 · 4 ≈ 1.06.

6–6

The MPK is given by√

20 · 5−√

19 · 5 ≈ .25.c) Yes.d) To produce 10 units of output, the firm must employ 5 units of labor, for a total

cost of $20 + $5 = $25.e) The condition MPK = MPL can be written as

√K · L−

√(K − 1) · L =

√K · L−

√K · (L− 1)

which implies that K = L. Thus the firm must choose K and L so that K = Land

√K · L = 10. This forces K = 10, L = 10. The long run total cost is $10 +

$10 = $20.f) Constant.

6–7

Chapter Seven:Competition

General Discussion and Teaching Suggestions

1) I believe that the best test of understanding this material is the ability towork problems in comparative statics. (For example: When the price of steel goesdown, what happens to the price and quantity of Ford automobiles, in the shortrun and in the long run?) I believe that one of the primary goals of a chapter oncompetition should be to develop that ability. Therefore I have included severalworked examples in the chapter, a wealth of problems at the end (see especiallyproblems 1, 10, 11 and 12), and a special section summarizing the basic principlesthat the student must master (Section 7.7).

2) For many students, it can be helpful to present a taxonomy of costs, clas-sifying them according to the time periods over which they are fixed or variable,and according to whether they are felt by one firm or the entire industry. All ofthis is implicit in the text, of course, but it can be useful to place an explicit charton the blackboard, something like this:

A. Industry-Wide B. Firm-Specific

1. Sunk

2. Avoidable only by exit

3. Fixed in short run

Variable in long run

4. Variable

One can then fill in the boxes with examples, such as: In Box 1A a one-time-only surprise tax on firms in the industry; in Box 1B a one-time-only fine to be paidby the firm; in Box 2A an annual license fee; in Box 2B a yearly fine for a safetyviolation that the firm cannot correct; in Box 3A a rise in the price of capital;in Box 3B a rise in the cost of some firm-specific capital (e.g. the constructionof a highway near land used by the firm, increasing the cost of land, which issubstitutable with another factor in the long run); in Box 4A a rise in labor costs;in Box 4B a firm-specific fine per unit sold (e.g. a bar generates much noise andthe owners agree to reimburse the neighbors with a fee of 5 cents per drink sold).

Then one can work through the short-run and long-run consequences of achange in each kind of cost. Some cases are disposed of quickly; for example thosein row 1 have no effect whatsoever and those in rows 2 and 3 have no short-runeffects.

In addition to the effects of changes in the various kinds of costs, studentsmust also learn the effects of demand shifts. If they really know all of this, thenthey really understand the theory of competition.

7–1

3) It is traditional in this subject to assert that all costs are variable in thelong run. It seems to me that there are some important exceptions (e.g. an annuallicense fee that does not vary with the size of the firm), and the text allows for thispossibility.

4) Students who understand this chapter should be able to work the numericalexercises at the end. I tell my students that if they cannot perform these exercises,then they have missed a fundamental point.

7–2

Additional Problems

1. If North Liberty, Iowa were to impose an excise tax on all corn grown in NorthLiberty, the consumers of corn would actually pay part of the tax.

2. True or False: In a competitive industry, some firms might be more efficientthan others on average, but all firms are equally efficient at the margin.

3. True or False: In the short run, competitive firms choose output levels tominimize their short-run average costs.

4. True or False: In the short run, a firm will shut down if its total revenue failsto exceed its fixed costs.

5. True or False: A firm that shuts down must be earning negative profits, buta firm that earns negative profits might not shut down.

6. The Z.Z. Top Company earbed zero profit in 2004 and, thanks to an increasein demand, a positive profit in 2005. True or False: The average cost ofproducing a Z.Z. Top was lower in 2005 than in 2004.

7. True or False: If the demand for beer increases, then beer makers will not onyearn higher total profits in the short run, they will also earn higher averageprofits per can.

8. True or False: If a firm’s long run average and marginal cost curves are identi-cal to its short run average and marginal cost curves, then the firm’s shutdownprice is always below its break even price.

9. True or False: In the long run, a rise in the wage rates of industrial workerswill cause the price of haircuts to rise.

10. True or False: In a competitive constant-cost industry, an excise tax is partlypassed on to consumers in the short run but completely passed on to consumersin the long run.

11. Suppose a series of bombings destroys several of the video stores in your neigh-borhood.a) What happens to the price and quantity of videos sold at one of the

remaining stores in the short run?b) What happens in the long run?

12. Every doctor in Coconino County uses disposable tongue depressors to examinepatients, and also must keep exactly one X-ray machine in his office. Thetongue depressors cost 10 cents each and the X-ray machine rents for $100 ayear. The county is considering a plan to provide each doctor with unlimitedfree tongue depressors. An alternative plan is to provide each doctor with afree X-ray machine.a) If medicine is a competitive industry in Coconino County, compare and

contrast the short-run effects of the two plans, both for the town as awhole and at each individual doctor’s office.

b) If medicine is a constant-cost competitive industry in Coconino County,compare and contrast the long run effects of the two plans, both for thetown as a whole and at each individual doctor’s office.

c) If medicine is an increasing-cost competitive industry in Coconino County,compare and contrast the long run effects of the two plans, both for thetown as a whole and at each individual doctor’s office.

7–3

13. The Wall Street Journal reports that a number of Atlantic City casinos mightshut down because of enormous outstanding debts. Comment.

14. True or False: If all people are equally efficient dishwashers, then a tax ondishwashing will be paid entirely by demanders.

15. True or False: A firm that wants to maximize its short-run profits whouldoperate at the minimum point of its short-run average cost curve.

16. In the city of Rochester, taxi drivers form a competitive constant cost industry.Each cab driver always rents exactly one cab and also pays for gas.a) Suppose the city decides to pay half of all the drivers’ gas expenses. Copy

the following chart into your blue book and fill in each box with “goesup”, “goes down”, “unchanged”, or “uncertain”:

Short Run Long RunPrice

Industry-Wide QuantityQuantity per Firm

Profit per FirmNumber of Firms

b) Repeat part a), assuming that the city decides to pay for half of all thedrivers’ cab rental expenses instead of their gas expenses.

17. The table below shows the market demand curve for widgets and the marginalcost curve of a typical firm. Each firm has fixed costs of $60.

Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity$10 97520 95030 90040 80050 600

Quantity Marginal Cost1 $102 203 304 405 50

Answer the following questions and be sure to show enough work so Ican see how you got your answers.a) What is the break-even price in this industry?b) In long run equilibrium, how many firms are in the industry?c) When the industry is in long run equilibrium, what point corresponds to

a price of $20 on the short run industry supply curve?

18. Many supermarkets charge cereal manufacturers for the right to display theirproducts prominently. True or False: If this practice were banned, cerealmanufacturers would be better off in the long run.

19. Suppose there is an increase in the cost of fire insurance for department stores.a) In the short run, and assuming competition, could this affect prices of

goods sold at department stores? Why or why not?b) In the long run, and assuming competition, could this affect prices of

goods sold at department stores? Why or why not?c) Would your answers change if instead of competition there were only one

department store in town?

20. By law, each private school in Rochester must have a standard-sized gym-nasium that costs $1,000,000 to construct. The Rochester City Council has

7–4

decided to offer aid to the local private schools and is undecided about how todo it. One possibility is to subsidize teachers’ salaries; the other is to provideeach school with the required gym.a) If there is only one private school in town, which plan is more beneficial

to the families who send their children there?b) If private schools constitute a competitive industry, then how does subsi-

dizing teachers’ salaries affect the price and quantity of schooling in theshort run, both for an individual school and for the market as a whole?

c) If private schools constitute a competitive industry, then how does pro-viding free gymnasia affect the price and quantity of schooling in the longrun, both for an individual school and for the market as a whole?

21. In the city of Rochester, taxi drivers form a competitive constant cost industry.Each cab driver always rents exactly one cab and also pays for gas.a) Suppose the city decides to pay half of all the drivers’ cab rental expenses.

What happens to the number of rides offered by each individual driver inthe short run?

b) Suppose the city decides to pay half of all the drivers’ cab rental expenses.What happens to the number of rides offered by each individual driver inthe long run?

c) Suppose the city decides to pay half of all the drivers’ gas expenses. Whathappens to the number of rides offered by each individual driver in theshort run?

22. Suppose there is a fall in the demand for shoes. In the long run, what happensto the price of shoes, the quantity produced by the entire industry, and thequantity produced by an individual shoemaker? Does your answer depend onwhether the industry is constant-cost, increasing-cost or decreasing-cost? Ifso, how?

23. If the market for pizza is competitive, then a rise in the price of cheese andtomatos could either increase or decrease the quantity of pizzas sold at a givenpizza parlor.

24. If the restaurant industry is competitive and the wholesale price of food falls,then we can be sure that in the long run existing restaurants will serve morefood than before.

25. Suppose that a decision is made to provide a government subsidy of $1000per year to every restaurant in the town of Llareggub, regardless of how manymeals that restaurant serves. In the long run, what happens to the number ofmeals per year served at any of the restaurants currently in business? Carefullyexplain your answer.

26. True or False: When a firm is able to earn positive profits, its average cost ofproduction is lower than when it earns zero profits.

27. True or False: A competitive firm earns positive profits when it faces increas-ing returns to scale and negative profits when it faces decreasing returns toscale.

28. True or False: If a firm earns negative profits in the short run, it will leavethe industry in the long run.

29. Suppose automobiles are produced competitively. In each of the followingcircumstances, determine the short-run effect on price and quantity of cars,both for the auto industry as a whole and at the Ford Motor Company:

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a) The price of steel goes down.b) A new government policy goes into effect whereby every producer of au-

tomobiles is given a gift of $100,000 per year.c) An excellent new mass transportation system is developed.

30. Sweaters provided by a competitive constant cost industry. Determine howeach of the following circumstances would affect the price of sweaters and thequantity of sweaters sold by the Better Sweater Company.a) The government announces that it will pay $500 per year to any firm

engaged in making sweaters. Answer both in the short run and in thelong run.

b) The government announces that it will pay $5 per sweater to any companyengaged in making sweaters. Answer in both the short run and the longrun, and be as precise as possible about the size of the price change.

31. Repeat the preceding problem, determining long run instead of short run ef-fects. Do any of your answers depend on whether the industry is constant costor increasing cost?

32. Suppose there is a fall in the price of factory space. How does this affect theprice and quantity of baskets produced at the WorldWideWicker Company?a) Answer in the short run.b) Answer in the long run, assuming a constant-cost industry.

33. Suppose there is a new excise tax of $5 per haircut, and assume that barbershops form a competitive constant-cost industry. What happens to the priceand quantity of haircuts at Beyond Salon?a) Answer in the short run. When you shift supply curves, use your knowl-

edge of how far they must shift to get an unambiguous answer to whetherquantity at Beyond Salon goes up, goes down, or remains the same.

b) Answer in the long run. When you shift supply curves, use your knowledgeof how far they must shift to determine whether quantity at Beyond Salongoes up, goes down, or remains the same.

c) In the long run, what happens to industry-wide quantity? What happensto the number of firms in the industry? Support your answer, making useof your answer to part (b).

34. Widgets are supplied by a constant-cost industry. One day the governmentorders 50 gadget-makers to instantly start making widgets instead of gad-gets. (This all takes place in a country where the government can do suchthings.) These 50 new widget-makers have exactly the same costs as the ex-isting widget-makers.a) In the short run, what happens to the price of widgets, the industry-wide

quantity, and the quantity produced at Herman’s widget farm?b) What happens in the long run?

35. Suppose that wheat is purchased only by poor people. Their demand for wheatis given by the following schedule:

Price Quantity$1 per bushel 10 bushels

2 83 74 5

Now suppose that in the spirit of Christmas, a coalition of rich people decide

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to buy wheat and resell it to poor people for half of whatever the rich people haveto pay.

a) List some points on the new demand curve for wheat.b) Suppose that the rich announce their plan just before Christmas, and

suppose that in the short run, the supply of wheat is fixed at 7 bushels.(That is, the supply curve for wheat is vertical at 7.) How much do poorpeople benefit from the generosity of the rich?

c) Suppose instead that the rich announce their plan a year in advance, andsuppose that wheat is supplied by a competitive constant-cost industry.Is this better or worse for poor people than if the rich had made a last-minute announcement as in part a)?

36. Suppose corn is produced only in Iowa and consumed only in California. Sup-pose there is a general rise in the incomes of Californians. True or False: Inorder to predict the long-run effect on the price of apples, it is necessary toknow whether apples are a normal or an inferior good for Californians. Whatadditional assumptions might your answer depend on?

37. Apple pies are provided by a competitive constant cost industry. Granny’sApple Pie Shop is one of the firms in this industry. In each of the followingcircumstances, determine which is greater: the number of pies per day thatGranny sells in the short run or the number of pies per day that Granny sellsin the long run. (Assume that Granny remains in the industry in the longrun.)a) A new law requires all apple pie shops to purchase an annual license.b) The price of apples increases.c) The demand for apple pies increases.

38. Gregor’s Glassware is a firm in a competitive constant-cost industry. Supposethat an earthquake shuts down half of Gregor’s competitors. What happensto the price and quantity sold of Gregor’s merchandise, both in the short runand in the long run? Justify your answers.

39. A new government regulation requires each bicycle manufacturer to purchasean air purification system to reduce hazardous fumes in the workplace. Whathappens to the price of bicycles in the long run?a) Answer assuming that bicycles are produced by a competitive industry.b) Answer assuming that bicycles are produced by a single monopolist.

Justify your answers.

40. Suppose that bicycles are produced by a competitive constant-cost industry.Suppose that bicycling declines in popularity as more people take up in-lineskating.a) What happens to the profits of bicycle manufacturers in the short run?b) What happens to the number of bicycles produced per firm in the short

run?c) What happens to the profits of bicycle manufacturers in the long run?d) What happens to the number of bicycles produced per firm in the long

run?Justify all of your answers.

41. Suppose that ginseng tea is provided by a competitive constant-cost industryand that a new highly publicized study shows that drinking tea increaseslife expectancy. What happens to the amount of tea produced by a singlemanufacturer?

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a) Answer in the short run.b) Answer in the long run.

42. Suppose that the gizmo industry is in long-run equilibrium when the govern-ment suddenly orders a whole lot of new firms to enter the industry. They areforced to enter even if profits are driven below zero.a) What happens in the short-run after the new firms enter? What hap-

pens to price, industry-wide quantity, and quantity supplied by individualfirms?

b) What happens in the long run? (You may assume a constant-cost industryif that helps you.)

43. Determine whether each of the following statements is true or false and givereasons for your answers.a) True or False: In a competitive constant cost industry, an excise tax

causes price to rise in the short run, and to rise even farther in the longrun.

b) True or False: In a competitive constant cost industry, a fall in demandcauses each firm to supply less in the short run, and even less in the longrun.

44. Determine whether each of the following statements is true or false and givereasons for your answers.a) If fixed costs rise in a competitive constant cost industry, the number of

firms does not change in the short run but falls in the long run.b) If demand increases in a competitive constant cost industry, the output

of a single firm increases in the short run but returns to its original levelin the long run.

45. In each of the following situations, determine the effect on the price and quan-tity of drinks served at the Airliner Tavern. Answer first in the short run, thenin the long run assuming that taverns form a constant cost indusry, then in thelong run assuming that taverns form an increasing cost industry, then in thelong run assuming that taverns form a decreasing cost industry. (Obviouslythis problem can be shortened by, for example, omitting the case of decreasingcosts.)a) The wholesale price of liquor goes up.b) The owners recalculate and discover that last month’s redecoration actu-

ally cost 15% more than they’d thought.c) A disgruntled customer threatens to sue after being mistakenly served lye

instead of rye. In exchange for a large payoff, the customer offers not onlyto withhold suit, but also to keep his mouth (or what is left of it) shutabout the incident.

d) The same incident occurs as in part c), but the newspapers have alreadyfound out about it.

e) The yearly price of liquor licenses goes up.f) The city council passes a one-time emergency tax measure, requiring every

local tavern owner to immediately contribute $30 to the town treasury.g) The owners of a neighboring establishment complain about the noise from

the Airliner, and they win a court order requiring the Airliner to com-pensate them. The court rules that the Airliner must pay the neighbors5 cents for each drink it serves.

h) A general breakdown in family life leads to a lot more people going outto taverns.

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i) A wealthy couple decide they really want to build a house precisely onthe site now occupied by the Airliner.

j) There is a general rise in the price of land.

46. In each of the following situations, determine the effect on the price and quan-tity of car washes sold at Al’s Car Wash. Answer first in the short run, thenin the long run assuming that car washes form a constant cost indusry, then inthe long run assuming that car washes form an increasing cost industry, thenin the long run assuming that car washes form a decreasing cost industry.(Obviously this problem can be shortened by, for example, omitting the caseof decreasing costs.)a) The cost of mechanical car wash equipment goes up.b) The motel next door to Al’s wants to expand and offers to buy him out.c) One of Al’s major pieces of equipment breaks down and needs to be re-

paired.d) There is an epidemic of equipment failures at car washes all over town.e) The mayor declares a one-time only Car Wash Appreciation Day, on which

every car wash owner in the city is given $1000 out of city funds.f) The mayor declares that Car Wash Appreciation Day will become an

annual event.g) An influential member of the city council invents an automatic car-polishing

machine. When the council member discovers that no car wash wants tobuy the machine, legislation is pushed through requiring every car wash toown one. (The council member’s supply curve for car-polishing equipmentis upward sloping.)

h) There is a general rise in wage rates.i) A story on 60 Minutes reveals that Al subscribes to the deconstructionist

school of literary criticism. Workers throughout the city are so revoltedthat they will not work for Al unless he pays them 50 cents an hour morethan they can earn at any other car wash.

j) A large office building is constructed, making it impossible to see Al’s CarWash from the road.

k) The city begins using salt to clear ice off the roads in winter. (Salt causescars to rust unless it is washed off frequently.)

47. In each of the following situations, determine the effect on the price and quan-tity of goose liver sold at Bambi’s House of Goose Liver. Answer first in theshort run, then in the long run assuming that goose liver restaurants form aconstant cost indusry, then in the long run assuming that goose liver restau-rants form an increasing cost industry, then in the long run assuming thatgoose liver restaurants form a decreasing cost industry. (Obviously this prob-lem can be shortened by, for example, omitting the case of decreasing costs.)a) Due to ahealth scare, the city requires all goose liver purveyors to discard

their inventory and replace it with fresh goose liver.b) An incompetent but enthusiastic health inspector takes office, and is ex-

pected to periodically order all goose liver purveyors to discard their in-ventory at random times.

c) Bambi’s vindictive ex-husband is appointed health inspectorand is ex-pected to find Bambi $5,000 per year for spurious health violations.

d) Bambi’s vindictive ex-husband is appointed health inspector and is ex-pected to fine Bambi one-tenth of her revenueseach year for spurioushealth violations.

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e) A careless employee leaves the freezer door open and all of Bambi’s gooseliver needs to be replaced.

f) A medical journal reports that goose liver can cause cancer.g) A medical journal reports that goose liver can prevent cancer.h) Bambi’s freezer needs to be replaced.i) Bambi has a fight with the owner of Tiny’s Discount Goose Liver Em-

porium, which supplies all of the goose liver restaurants in town. Conse-quently, she must now import all of her goose liver from the next county,and must pay additional shipping fees.

j) Bambi and Tiny make up, and as a sign of friendship, Tiny agrees tosupply Bambi with goose liver at half price from now on.

k) Bamgi and Tiny make up, and as a sign of friendship Tiny gives her 100free pounds of goose liver (but continues to charge the usual price whenBambi orders more).

l) A new law requires all restaurant owners who serve goose liver to pass acourse on “The Role of Goose Liver in a Secular Society”. Th local collegecharges $500 tuition for the course.

m) There is a fall in the wage rate for restaurant dishwashing services.n) A new landfill comes to occupy the property next to Bambi’s. The odor

from the landfill is offensive to customers.o) A new movie theater opens next door to Bambi’s, and is the only movie

theater in town that allows movie-goers to bring in their own goose liverinstead of buying it at the concession stand.

48. Widgets are supplied by a constant-cost competitive industry. Each individualfirm faces a fixed cost of $6 and marginal costs given by the following table:

Quantity Marginal Cost1 $12 23 34 4

Quantity Marginal Cost5 56 67 78 8

Industry-wide demand is given by the following table:Price Quantity$1 12002 10003 9004 800

Prie Quantity5 7006 5007 3008 200

a) What is the break-even price in this industry? (Hint: For each possibleprice, figure out what quantity each firm will provide and what its profitwill be. Don’t forget the $6 fixed cost.)

b) In long run equilibrium, how many firms are there in this industry?

49. Moose-nose pies are produced by a competitive constant-cost industry. Theindustry is in long-run equilibrium and there are exactly 100 firms. The follow-ing chart shows the industry-wide demand curve and the marginal cost curveof a typical firm:

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Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity$5 25010 20015 15020 10025 50

Quantity Marginal Cost1 $52 103 154 205 25

What are the firm’s fixed costs?

50. Widgets are produced by a competitive constant cost industry where each firmhas fixed costs of $10. The following chart shows the industrywide demandcurve and the marginal cost curve of a typical firm.

Industrywide Demand Firm’s Marginal Cost CurvePrice Quantity$10 3000$20 2500$30 2000$40 1500$50 1000$60 500

Quantity Marginal Cost1 $102 $203 $304 $405 $506 $60

In long run equilibrium, how many firms are in the industry?

51. The following tables show the market demand curve for widgets and themarginal cost curve at a typical firm. The industry is constant-cost and eachfirm has fixed costs of $60. Answer the questions below.

Firm’s Marginal Cost Curve Industry-Wide DemandQuantity MC

1 $40 per widget2 603 804 1005 1206 140

Price Quantity$40 per widget 100060 95080 900100 850120 750140 600

a) What is the break-even price in this industry?b) In long-run equilibrium, how many firms are in this industry?

52. Mood rings are provided by a competitive constant-cost industry currentlyconsisting of 100 identical firms. The following graphs show an individualfirm’s Total Cost for producing various quantities of output, and the marketdemand curve:

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Firm’s Total Cost Industry DemandQuantity Total Cost

$0 3001 4002 4503 5104 5905 7006 8407 10208 1250

Price Quantity$360 400290 500230 600180 700140 800110 90080 1000

a) What is the current price of a mood ring?b) In the long run, how many firms will enter or exit this industry? (Don’t

worry if your answer is not a while number.)

53. The following chart shows the industry-wide demand for widgets and themarginal cost curve of a typical firm. The industry is constant-cost and isin long run equilibrium. The price of a widget is $7.

Industrywide Demand Firm’s Marginal Cost CurvePrice Quantity$10 500$9 1000$8 1500$7 2000$6 2500$5 3000

Quantity Marginal Cost1 $12 $23 $34 $55 $76 $9

a) On the industry’s short-run supply curve, what quanitity is associatedwith a price of $9?

b) What are the firm’s fixed costs? (Your answer should be a number ofdollars.)

54. Moose-nose pies are produced by a competitive constant-cost industry. Theindustry is in long-run equilibrium and Moose-Nose pies sell for $25 each. Thefollowing chart shows the industry-wide demand curve and the marginal costcurve of a typical firm:

Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity$5 10010 12515 15020 25025 300

Quantity Marginal Cost1 $52 103 154 205 25

a) How much are the fixed costs at each firm? (Your answer should be anumber.)

b) Answer in the short run: If a fall in demand causes the equilibrium priceof moose-nose pies to fall to $15, what is the new (industry-wide) equilib-rium quantity of moose-nose pies? By how much does the industry-widequantity fall in the short run? (Your answer should be a number.)

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55. Widgets are produced by a constant cost industry, where fixed costs are $12per firm per year. The industry is in long-run equilibrium. The followingcharts show the industry-wide demand curve and the marginal cost curve ata typical firm:

Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity

($/Widget) (Widgets/Year)$2 12004 8006 6008 50010 40012 300

Quantity Marginal Cost(Widgets/Year) ($/Widget)

1 $22 43 64 85 106 12

a) In long run equilibrium, how many widgets does the industry produceeach year?

b) Suppose the government wants the industry to produce 800 widgets peryear in the long run and plans to accomplish this by giving every widgetfirm an annual cash gift. How big should the gift be? (Your answer shouldbe a number of dollars per firm.)

c) Supose the government wants the industry to produce 800 widgets peryear in the long run and plans to accomplish this by giving every widgetfirm a subsidy for each widget they produce. How big should the subsidybe? (Your answer should be a number of dollars per widget.)

d) Between the annual cash gift and the subsidy per widget, which plan ismore expensive for the taxpayers?

56. Widgets are provided by a competitive constant-cost industry where each firmhas fixed costs of $30. The following charts show the industry-wide demandcurve and the marginal cost curve of a typical firm.

Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity$5 150010 120015 90020 60025 30030 20035 14040 50

Quantity Marginal Cost1 $52 103 154 205 256 307 358 40

a) What is the price of a widget?b) How many firms are in the industry?

For the remaining four parts of this problem, suppose the government imposesan excise tax of $15 per widget.

c) In the short run, what is the new price of widgets?d) In the short run, how many firms leave the industry?e) In the long run, what is the new price of widgets?f) In the long run, how many firms leave the industry?

57. Widgets are provided by a constant cost industry, where fixed costs are $3 perfirm per year. The industry is in long-run equilibrium. The following charts

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show the industry-wide demand curve and the marginal cost curve at a typicalfirm:

Industry-Wide Demand Firm’s Marginal Cost CurvePrice Quantity

($/Widget) (Widgets/Year)$2 12005 8009 60014 50020 40027 300

Quantity Marginal Cost(Widgets/Year) ($/Widget)

1 $22 53 94 145 206 27

Suppose the government wants the industry to produce 1200 widgets per yearin the short run, and plans to accomplish this by offering firms a subsidy foreach widget they produce. How big should the subsidy be? (Your answershould be a number of dollars per widget .)

58. Dogfood is provided by a competitive constant-cost industry in which eachfirm has the following marginal cost curve:

Quantity Marginal Cost(# of Cans per Year) (Price per Can)

1 52 103 154 205 256 307 35

The industry is in long run equilibrium and dogfood sells for $10 per can. Nowa new law requires each dogfood firm to buy a license for $25 a year. In thelong run, what is the new price of dogfood?

59. Widgets are provided by a constant-cost industry. The following charts showthe foreign demand for American widgets and the marginal cost curve of atypical American widget firm.

Foreign Demand Firm’s Marginal Cost CurvePrice Quantity$3 1505 1407 1209 10011 9013 8015 7017 60

Quantity Marginal Cost1 $32 53 74 95 116 137 158 17

Initially, American firms are not allowed to sell to foreigners. In the U.S. ,widgets sell for $7 apiece.a) What is the fixed cost of running a widget firm?

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Now the government decides to issue 10 export licenses; a firm with an exportlicense can sell as many widgets to foreigners as it wants to. The exportlicenses are sold at auction to the highest bidders.b) What is the price of an American widget sold on the foreign market?c) What is the price of an export license?d) After the export licenses are issued, what is the new price of an American

widget sold in America? Be sure to justify your answer.

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 7

4.a) This is a change in a fixed cost; nothing happens.b) This is a fall in marginal cost. Gus’s MC curve falls; that is, his supply curve shifts

rihtward. The industry supply curve also shifts rightward, leading to a lower pricefor cab rides and hence a lower (flat) demand curve for Gus’s services. Price isdown; quantity can go either way.

c) Demand for cab rides falls, so price falls. (Flat) demand for Gus’s cab rides fallsaccordingly, and therefore quantity falls.

d) Normally, we expect that the demand for Gus’s cab rides is flat at the going marketprice for cab rides. This expectation is justified by the assumption that Gus’s cabrides are no different than anyone else’s. But in this problem, we depart from thatassumption. The demand for cab rides generally is unchanged; likewise for supply;thus the industry price of cab rides is unchanged. But the demand for Gus’s cabrides falls, hence the price and quantity of Gus’s cab rides falls.

e) Sunk cost; no effect.f) This increases the opportunity cost of driving a cab. To completely solve the prob-

lem, you’ve got to decide whether it’s an increase in fixed costs or in marginal costs.The answer depends on what you assume about Gus’s alternative opportunities.

Suppose first that Gus must choose between driving a cab and working in afactory; he can’t do both. In that case, the wages of factory workers are a fixedcost of driving a cab; you give up the same factory job whether you collect one farea day or ten fares a day. A change in fixed cost has no effect on price or quantity.

But suppose alternatively that Gus can moonlight, working in the factory forpart of the day and driving the cab for the other part of the day. Then eachadditional cab fare requires him to lose more time in the factory, making factorywages a variable cost. In this case, the analysis is exactly as in Exhibit 7.9.

g) Ordinarily, we expect exit to be impossible in the short run, but in this example,firms are forced to exit immediately. Therefore the industry supply curve shiftsleft, price rises, the (flat) demand curve for Gus’s cab rides rises accordingly, andhis quantity rises also.

h) Industry supply shifts leftward (because all the other firms’ supply curves shiftleftward); price up; Gus’s quantity up.

i) Change in fixed costs does not affect anything.j) Two ways to do this:

Method I: Treat city-owned cabs as a separate good from private cabs. Thecity-owned cabs reduce demand for private cabs, so price falls, Gus’s (flat) demandcurve falls, and his quantity falls.

Method II: Treat city-owned cabs and private cabs as identical goods. Supplyof cab rides increases, so price falls, Gus’s (flat) demand curve falls, and his quantityfalls.

k) Industry supply shifts rightward (because all other firm’s supply curves shift right-ward); price down; Gus’s quantity down.

l) Gus’s MC curve shifts up (that is, his supply curve shifts left). Very few firms areaffected, so industry supply hardly moves; we can assume (to a good approxima-tion) that it doesn’t move at all. Therefore price unchanged and Gus’s quantity

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down.m) Sunk cost; no effect.

2. False; a competitive firm does not need to lower its price to “steal customers”.3. False; the profit on the last item produced is zero, but that doesn’t make the firm’s

total profit equal to zero.4. False; in Exhibit 7.6, if the price is above P0 but below the minimum of the average

cost curve, the firm earns negative profit but continues to produce in the short run.5. False. Although typesetting is not a part of the short run marginal cost of

producing books (so that a change in the cost of typesetting would have no effecton the price of books in the short run), firms do take account of typesetting costsin deciding whether to enter. Thus the cost of typesetting does enter into thedetermination of the industry’s long run supply curve.

6. People with no special skills must be indifferent between engraving gold jewelryand the next best opportunity.

Therefore the opportunity to keep the gold dust must be exactly offset bylower wages in this industry.

7. False. More homeless people will move to New York, increasing crowding atshelters, making it more difficult to get handouts, and so forth, until New York isagain no more attractive than the next best alternative.

8. True in the long run because the supply of dishwashing services will be flat.9.a) At a price of $6, the quantity of car washes demanded is 200 (2 car washes per

consumer times 100 consumers) and the quantity supplied is also 200 (4 per suppliertimes 50 suppliers). Therefore $6 is an equilibrium price.

b) Car washes must break even selling at $6. Variable costs are $(3+4+5+6) = $18and revenue is $6× 4 = $24, so fixed costs must be $(24− 16) = $8.

10.a) Break-even price falls so industry supply moves vertically downward. Price falls,

flat demand curve for Gus’s services falls, Gus’s quantity falls.b) Variable cost falls, so Gus’s MC curve falls. Break-even price falls so industry sup-

ply moves vertically downward. Price down, flat demand curve for Gus’s servicesdown. Price falls by less than the change in MC; Gus’s supply curve falls verticallyby the full change in MC, so Gus supplies more rides.

c) Industry-wide demand falls; no change in price; no change in quantity. (Somefirms, possibly including Gus’s, will exit.)

d) To keep customers, Gus must lower his price. But he was earning zero profit tobegin with, so he won’t be willing to do this. Therefore Gus exits.

e) Sunk cost; no effect.f) As in the answer to problem 4, this can be interpreted either as an increase in fixed

costs or an increase in variable costs. Under the first interpretation, see Exhibit7.14; under the second, see Exhibit 7.15.

g) No change in the cost of operating a cab service, so no change in anything. (In theshort run, the remaining firms earn positive profits; these profits draw entry tillthe original equilibrium is restored.)

h) Break-even price rises by $1 so price of cab rides rises by $1 and Gus supplies morerides.

i Break-even price up; price up; Gus supplies more rides.j Can be analyzed just as in 10c).k Break-even price falls so price of cab rides falls; Gus, who was earning zero profit

to beging with, exits.

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l Gus’s marginal cost curve rises; his profits become negative and he exits.m Gus exits the industry rather than make this payment.

11.a) Break-even prices fall so industry supply moves vertically down (i.e. leftward).

Price falls, flat demand curve for Gus’s services falls, Gus’s quantity falls.b) Variable cost falls, so Gus’s MC curve falls. Break-even prices fall so industry

supply moves vertically downward (i.e. leftward). Price down, flat demand curvefor Gus’s services down. Price falls by more than the drop in MC; Gus’s supplycurve falls vertically by exactly the drop in MC; therefore Gus supplies fewer rides.

c) Industry-wide demand falls; price rises; quantity up.d) To keep customers, Gus must lower his price. He might either do this or leave the

industry. If he lowers his price, he provides fewer rides.e) Sunk cost; no effect.f) As in the answer to problem 4, this can be interpreted either as an increase in fixed

costs or an increase in variable costs. Under either interpretation, industry supplymoves vertically upward and price rises, so flat demand curve for Gus’s servicesrises. On first interpretation he moves along his supply curve and supplies morerides; on second interpretation his supply curve moves also.

g) No change in the cost of operating a cab service, so no change in anything.h) Break-even price rises so price of cab rides rises and Gus supplies more rides.i Industry supply moves vertically up; price up; Gus supplies more rides.j Can be analyzed just as in 11c).k Industry supply moves vertically down so price of cab rides falls; Gus, either sup-

plies fewer rides or exits.l Gus’s marginal cost curve rises; he either supplies fewer rides or exits.

m Gus either makes the payment, which becomes a sunk cost and has no furthereffect, or leaves the industry.

12.a) Break-even prices falls so industry supply falls. Price falls, flat demand curve for

Gus’s services falls, Gus’s quantity falls.b) Variable cost falls, so Gus’s MC curve falls. Break-even price falls so industry

supply falls. Price down, flat demand curve for Gus’s services down. A goodanswer: Demand for Gus’s services is down, his supply curve has shifted rightward,so quantity could move either way. A more in-depth answer: Assume the cost of gasper cab ride has fallen by, say, 50 cents. Then the break-even price has also fallenby 50 cents. Demand and supply fall by exactly the same distance, so quantity isunchanged.

c) Industry-wide demand falls; price falls; quantity down. (Some firms, possibly in-cluding Gus’s, will exit.)

d) To keep customers, Gus must lower his price. He might either do this or leave theindustry. If he lowers his price, he provides fewer rides.

e) Sunk cost; no effect.f) As in the answer to problem 4, this can be interpreted either as an increase in fixed

costs or an increase in variable costs. Under the first interpretation, see Exhibit7.19a; under the second, see Exhibit 7.19b.

g) No change in the cost of operating a cab service, so no change in anything.h) Break-even price rises so price of cab rides rises and Gus supplies more rides.i Industry supply moves vertically up; price up; Gus supplies more rides.j Can be analyzed just as in 12c).

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k Industry supply moves vertically down so price of cab rides falls; Gus, either sup-plies fewer rides or exits.

l Gus’s marginal cost curve rises; he either supplies fewer rides or exits.m Gus either makes the payment, which becomes a sunk cost and has no further

effect, or leaves the industry.13.

a) Price does not change in the long run.b) More in the long run, because we are moving along a flat supply curve.c) Quantity does not change in the long run.d) Profits do not change in the long run.

14.a) Price does not change in the long run.b) More in the long run, because we are moving along a flat supply curve.c) Quantity does not change in the long run.d) Profits do not change in the long run.

15.a) Price does not change in the short run.b) Quantity does not change in the short run.c) Quantity does not change in the short run.d) Profits do not change in the long run.

16.a) In the short run, the gift has no effect. So all that matters is the excise tax. Thisis an increase in a variable cost, so the picture is exactly as in Exhibit 7-9.

b) The firm faces the same (flat) demand curve as before, but its supply curve is shiftedleft. Therefore each firm provides fewer shoes. Because the price is unchanged,demanders purchase the same number of shoes as before. Therefore the number offirms must increase.

17.a) Industry supply curves shifts rightward 800. Equilibrium quantity shifts rightward

by less than 800; that is, more patients are served, but the increase is less than800.

b) In the long run, price must return to original level so quantity returns to originallevel. Thus private clinics serve exactly 800 fewer patients.

18.a) Exactly 50 cents because flat supply curve drops 50 cents.b) Less than 50 cents because upward sloping supply curve drops 50 cents.

19. False. They seek to maximize profit, period. In long run equilibrium, assuming aconstant cost industry, average cost is minimized, but this is not the goal of anyfirm.

20. In Upper Slobbovia, the entire tax is passed on; in Middle Slobbovia, a portionof the tax is passed on; in Lower Slobbovia, none of the tax is passed on.

21. True. The long run supply curve shifts vertically upward by the amount of thetax. The new equilibrium point is to the left of the old one, and consequentlyhigher than the old price plus the tax.

22. False. The first year’s entry causes the short run supply curve to shift rightward.Therefore the price will be below its original level.

Answers to Numerical Exercises

7–20

N1.a) Each firm produces 5 widgets, earning revenue of $50, with total cost $36. Profitis $14, which is positive, so the industry is not in long run equilibrium.

b) Positive profit draws entry till te price falls to $6, where each firm produces 3widgets and profit is zero.

N2. The price is $15. At this price, each firm produces 3 widgets and earns zero profit.Consumers demand 450 widgets so there are 150 firms in the industry. At a priceof $10, each of 150 firms would produce 2 widgets, so the quantity on the short runsupply curve is 300.

N3.a) $20 (the price at which profit is zero)b) 150 (the quantity demanded divided by the quantity supplied per firm)c) Prior to the tax, the short-run supply curve contains points ($5, 150), ($10,300),($15,450),

etc. With the tax, the short-run supply curve shifts vertically upward $15 and nowcontains points ($20,150),($25,300), etc. The point ($25,300) is on both the supplyand demand curves, so it is the new equilibrium. The price is $25.

d) No firms leave in the short run.e) In the long run, price must rise by the full amount of the tax, from $20 to $35.f) Each firm provides 4 widgets. 140 widgets are demanded. Therefore the number

of firms must fall from 150 to 140/4=35. So 115 firms leave the industry.N4.a) At a price of $20, total cost and total revenue each equal $80. So $20 is the

break-even price, and this is the price of a widget.b) Each firm produces 4 widgets; 600 are sold, so the number of firms is 600/4=150.c) Each firm’s supply curve shifts a distance $15, so the new supply curve is given by

Price Quantity$20 125 230 335 440 5

With 150 firms, this gives an industry-wide supply curve of

Price Quantity$20 125 30030 45035 60040 750

$25 is now the price at which quantity supplied equals quantity demanded, sothis is the new price of widgets.

d) Nobody leaves the industry in the short run.e) The (flat) long-run supply curve shifts upward $15, so the new price is $35.f) Firms get to keep $20 per widget, so they supply 4 widgets each; 140 must be

supplied altogether, so there are now 140/4=35 firms. Thus 115 leave the industry.N5.a) The break-even price is $7; at this price each firms’ total revenue and total costs

are both equal to $28.b) Each firm produces 4 widgets.c) The industry-wide quantity is 24, so there must be 6 firms.d) The industry-wide supply curve is

7–21

Price Quantity$2 64 125 187 2411 3013 36

This crosses industry-wide demand at a price of $13, so that is the new equi-librium price. At that price, each firm produces 6 widgets.

d) In the long run, the price must return to the break-even level of $7. At that price,consumers demand 60 widgets, and each firm produces 4, so there must be 15 firms.

N6. The equilibrium price is $5. At that price, there are 80 firms in the industry, eachwith fixed costs of $10 and total costs of $25. Also, each firm has a total revenueof $25, so profits are zero.

N7.a) Profit maximization requires P = MC. Zero profits requires P = AC. ThusMC(Q) = AC(Q), where Q is the number of kites each firm produces. From theexpressions given in the problem we get

2Q = Q +100Q

,

so that Q = 10 and consequently P = 20. That is, each firm produces 10 kites andearns zero profit when P = 20. Consequently the long run industry supply curveis flat at P = 20.

b) Since P = 20, we can solve for the equilibrium value of Q and get Q = 7000. Theindustry produces 7000 kites, of which 10 are produced at any given firm. It followsthat there are 700 firms in the industry.

c) In the short run, supply is fixed at Q = 7000. Solving for the equilibrium price, weget P = 40. Each kite maker supplies 10 kites at an average cost of 20 and sellsthem at a price of 40, for a profit of 20 per kite or 200 per firm.

d) The new long-run equilibrium Q is 8000, so there must be 800 firms, of which 100are new. All firms earn zero profit.

N8.a) Fire extinguishers are a fixed cost, so MC does not change. The cost of a fireextinguisher is equal to the number of fire extinguishers, which equals the numberof firms, so each firm’s TC is up by F , and consequently AC is up by F/Q.

b) Solving for MC = AC, we get Q =√

100 + F , P = 2√

100 + F .c) Since P = 2

√100 + F , we get F = P 2/4 − 100. Each of the F firms produces

Q =√

100 + F = P/2 kites, so the industry supply is

Q =(

P 2

4− 100

)· P

2=

P 3

8− 50 · P.

d) Using the above expression for industry supply and solving for the equilibriumgives P = 40, Q = 6000. Each firm produces 20 kites, so there are 300 firms in all.They earn zero profit.

7–22

Chapter Eight:

Welfare Economics and the Gains from TradeTeaching Suggestions

1) Exhibit 8–13 shows “Another Way to Do It,” where “It” is the act ofcalculating consumers’ surplus in the face of a market distortion. Students who arehaving trouble with the first way to do it should not allow themselves to becomedistracted by this, and need reassurance that it is far more important to learn oneway completely than to learn two ways partially.

Those students who are on top of things will find this exhibit useful, becausesome problems to be encountered in future chapters are easier this way. (No prob-lems here in Chapter 8 have that characteristic.) There is of course an analogous“other way to do it” for producers’ surplus, and it is equally useful. Students canbe assigned to work it out, or it can easily be presented in lecture.

2) In order to impress students with the power of the welfare theorem, it canbe useful to present some simple situations in which the theorem does not hold.An obvious candidate is the prisoner’s dilemma, which appears in Chapter 11 butcan be covered now. Quicker and easier examples arise from failures of collectiveaction: Everybody on the street would be happier if everybody on the street spentan afternoon picking up trash, but it is not to any individual’s advantage to goout and pick up trash. (This is, of course, a prisoner’s dilemma, but in much lessformal guise.) These make good intuitive sense to students. You can challenge theclass to come up with other interesting examples.

By pointing out that the welfare theorem fails in these cases—the equilibriumoutcomes are not Pareto- optimal—you can drive home both the meaning of thetheorem and the fact that its success in competitive markets is non- trivial.

3) In explaining the difference between the Pareto criterion and the efficiencycriterion, it can be helpful to start with a simple one-good example. One way todo this is to start right off by working end-of-chapter problem 4 at the blackboard,or by assigning it early on for students to think about.

4) Students sometimes arrive with remarkable misconceptions about the Invis-ible Hand. One of the most pervasive is to equate it with “survival of the fittest”in some version of social Darwinism. They (incorrectly) believe that markets areefficient precisely because inefficient producers can not survive, in perfect analogywith biological evolution.

Tell them that the truth is more subtle. The Invisible Hand Theorem relies(among other things) on the equalization of marginal cost across firms (as in thediscussion back in Chapter 7), which in turn depends on the existence of competi-tive prices, i.e. going market rates of exchange that no individual can affect. Thereis no biological analogue to the competitive price system. Some analogue of naturalselection might very well be important in explaining some economic phenomena,but the Invisible Hand is quite a different thing.

5) If you want to discuss normative criteria, I think it can be instructive topush them to extremes. Ask your students whether the Rawlsian veil of ignorance(discussed in the appendix to the chapter) throws light on animal rights issues.E.g., if you are behind the veil and don’t yet know whether you’ll be born a personor a cow, do you want people to be permitted to eat cows? This question in itselfseems less interesting to me than the meta-question: Do we learn anything fromthinking about questions like this in this way? I don’t know the answer to the

8–1

meta-question. But I do think we learn something from thinking about the meta-question.

6) The appendix to the chapter exposits some philosophical points that usuallyget briefer treatment in textbooks at this level. I think that the appendix is writtenat a level where students can easily read it on their own.

8–2

Additional Problems

1. If the price of haircuts rises from $10 to $11, consumers’ surplus will fall by10%.

2. If Jack Daniels whiskey sells for $10 a bottle and if 1,000 bottles were sold lastyear, then the total value of those bottles to consumers was $10,000.

3. Suppose that people buy diamond jewelry only because they welcome theopportunity to display their wealth. What would be the welfare effects oftaxing diamond jewelry?

4. Michael Kinsley, writing in the New Republic of january 22, 1989, says “Whenan Impressionist painting thought to be worth $15 million is suddently worth$30 million, the world is not $15 million richer. However, the owner’s claim onthe world’s existing wealth has doubled.” Is he right? (Extra credit: Look upthe article in question. In what sentence does the first economic error occur?)

5. True or False: A firm that is required by law to cut its production in half willlose half its producers’ surplus.

6. Brownies sell for $2.50 apiece, and you are only permitted to buy them inwhole number quantities. You buy one per day. Now sellers begin offeringhalf-brownies at $1.25 per day. What can you say about the number you willbuy?

7. If consumers buy 1000 heads of lettuce per week, and if the price of lettucefalls by 10 cents per head, then the consumers’ surplus will increase by $100.

8. Suppose that an effective price ceiling is imposed on bread at the wholesalelevel.a) In the wholesale market, where your grocer is the consumer, what happens

to the actual price that he pays for bread?b) In the retail market, in which your grocer is the producer, what happens

to the supply curve for bread? Why?c) True or False: A price ceiling on bread at the wholesale level will cause

the retail price of bread to rise.

9. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the governmentimposes an export tax of $1 per bushel on all domestically grown wheat thatis shipped abroad.a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

10. Suppose the U.S. supply and demand curves for wheat cross at a price of $5 perbushel, but American producers can sell as much wheat as they want to on theworld market at a price of $8 per bushel. Now suppose the government imposesa tax of $1 per bushel on all wheat grown in the United States, regardless ofwhether it is sold domestically or abroad.a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to the

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tax?

11. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the governmentimposes a sales tax of $1 per bushel on all wheat sold by American producersto American consumers. Suppose also that American consumers are free tobuy wheat on the world market at the going $8 price if they want to.a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

12. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the governmentimposes a sales tax of $1 per bushel on all wheat sold by American producersto American consumers. Suppose also that American consumers are forbiddento buy wheat from foreigners, so all wheat sold in America must be producedin America.a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

c) Given the existence of the tax, what is the deadweight loss due to theprohibition on foreign wheat?

13. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the governmentoffers American farmers a subsidy of $1 for every bushel of wheat that theyship abroad. (Wheat sold in the U.S. earns no subsidy.)a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

14. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the governmentoffers American farmers a subsidy of $1 for every bushel of wheat they grow,regardless of where that wheat is sold.a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

15. Suppose the U.S. supply and demand curves for wheat cross at a price of $5per bushel, but American producers can sell as much wheat as they want toon the world market at a price of $8 per bushel. Now suppose the government

8–4

offers American farmers a subsidy of $1 for every bushel they sell in the U.S.(There is no subsidy for wheat that is shipped abroad.)a) What price must Americans pay for wheat before the tax is imposed?

What price must Americans pay for wheat after the tax is imposed?b) Before and after the tax is imposed, calculate the gains and losses to all

relevant groups of Americans. What is the deadweight loss due to thetax?

16. The U.S. supply and demand curves for cars cross at $15,000; coincidentally,$15,000 is also the price at which (identical) cars can be purchased from abroad(in any quantity). One day the government sets a new price ceiling of $10,000per car. To prevent long lines from forming, the government agrees to sell carsfor $10,000 apiece to any American buyer who can’t find an American car tobuy. The government gets these cars by buying them from abroad. Illustratethe gains and losses to all relevant groups of Americans and illustrate thedeadweight loss.

17. Suppose Americans can buy any number of birdcages on the world market at aprice P0. American manufacturers have an upward-sloping supply curve thatintersects the American demand curve at a price above P0.a) At what price must American birdcages sell? Illustrate the gains to Amer-

icans from the existence of the world market.b) Suppose the government imposes a quota, by which only Q0 birdcages

per year can be imported from abroad, where Q0 is less than the numbercurrently being imported. Show that there is exactly one price consistentwith Americans being willing to import exactly Q0 birdcagees per year,and explain why the price will rise to that level.

c) Who wins and who loses as a result of the quota? Use a graph to illustratethe deadweight loss.

d) is the quota better or worse for Americans than a tariff that reduces thequantity of imported birdcages to Q0?

18. The following graph shows the American supply and demand curves for wid-gets.

100 200 300 400 QUANTITY

10

20

30$

PRICE S

D

Answer the following questions:

8–5

a) Suppose that foreign widget suppliers will provide any quantity of widgetsat $10 apiece. How many widgets are imported?

b) Suppose that foreign widget suppliers will provide any quantity of widgetsat $10 apiece, and that the government wants to limit the number ofimported widgets to 100. What size tariff can they impose to accomplishthis goal?

c) Suppose there are no foreign suppliers. Suppose also that the governmentdistributes 100 ration tickets, and only the holders of ration tickets arepermitted to buy widgets, so that only 100 widgets can be sold in total.Ration tickets can be freely bought and sold. What is the price of a rationticket?

19. The American demand and supply curves for cars cross at a price of $15,000.However, foreign suppliers will provide any number of (identical) cars for$10,000 apiece.Suppose the government simultaneously:a) bans the importation of foreign carsb) forbids American sellers to raise their prices above $10,000 andc) allows the President’s brother to buy all the cars that are produced in

America and resell them to consumers at whatever price the consumersare willing to pay.

Show the gains and losses to all relevant groups of Americans (including thePresident’s brother) and illustrate the deadweight loss.

20. Ordinarily, Americans import 7,000 cars a year from Japan. This year, to limitimports, the government has printed up 2,000 import licenses and distributedthem at random. Only the holder of an import license can buy a Japanese car.An import license can only be used once, but before it is used, it can be freelybought and sold. Use a graph to illustrate the price of an import license.

21. Suppose that any number of American typewriters can be sold abroad at theprice P0, which is higher than the price at which the supply curve of Americanproducers crosses the demand curve of American consumers.a) What price will American consumers have to pay for American typewrit-

ers? Why? Show on a graph the number of typewriters that Americanswill buy. Show the number that American producers will sell. Show thenumber exported. Show the consumers’ and producers’ surplus gained byAmericans.

b) Let Q0 be the number of typewriters that would be sold in the UnitedStates if there were no foreign market. Suppose that legislation is en-acted requiring American producers to sell at least Q0 typewriters inAmerica before selling any abroad. At what price would these typewrit-ers sell? What quantity would producers now wish to export? Show theconsumers’ surplus, the producers’ surplus from domestic sales, and theproducers’ surplus from foreign sales.

c) Who gains and who loses from this legislation? What, if anything, is thedeadweight loss?

22. The American supply and demand curves for bananas cross at a price of $5.Coincidentally $5 is also the world market price at which foreigners will sellany quantity Americans want to buy.A new law sets a price ceiling of $2 for bananas in America and requiresAmerican sellers to sell only to Americans. To eliminate waiting lines thegovernment agrees to provide bananas (at $2 apiece) to any American who

8–6

can’t find a willing seller. The government buys its bananas on the worldmarket.Illustrate the gains and losses to all relevant groups of Americans and illustratethe deadweight loss.

23. Suppose that Americans can buy as much Columbian coffee as they want to at$10 per pound, but are prevented by law from selling any coffee to Colombians.However, American producers’ supply curve for coffee intersect the Americandemand curve for coffee at a price of $5 per pound.a) How much coffee will be imported from Colombia? Why? (Assume that

coffee grown in the U.S. is identical to coffee grown in Colombia.)b) The U.S. government announces that it will supply coffee to any Amer-

ican citizen who wants it at a price of $3 per pound. It will get thiscoffee by buying from Colombia. Show on a graph the new price of coffeein America, the quantity sold by American producers, and the quantitybought by American consumers.

c) Show the gains and losses to all relevant parties from the program de-scribed in part b). What is the deadweight loss?

24. Suppose that the equilibrium price of peanut butter is $5 per pound. TheU.S. government has agreed to sell peanut butter for $2 per pound, and toprovide whatever quantity consumers want to purchase at that price. Toacquire this quantity of peanut butter, the government is prepared to paywhatever price is necessary to get suppliers to provide it. All of the revenuethat the government collects by selling peanut butter will be used to makewelfare payments.a) Use a graph to illustrate the effects of this program on four groups of

citizens: the consumers of peanut butter, the producers of peanut butter,the recipients of welfare, and the taxpayers.

b) Use your graph to illustrate the deadweight loss that this program creates.

25. Suppose that it is now between harvests, so that the number of oranges is infixed supply. The demand curves for oranges are the same in Toronto andMontreal, but there are many more oranges in Toronto than in Montreal.a) On one graph, show the demand and supply curves for oranges in both

cities. Show the market price of oranges in each city.b) Show the consumers’ and producers’ surpluses in each city.c) Now suppose that oranges can be costlessly transported. In light of the

price difference between oranges in the two cities, what do you expectsuppliers to do? How does this affect the supply curves in each city?When does the process stop?

d) Do parts a) and b) over again, after the process described in part c) takesplace.

e) Are consumers made unambiguously better off by the transportation oforanges? Are producers? Is society?

26. In equilibrium, oranges sell for $5 apiece. According to the efficiency criterion,which is better: A sales tax that causes the price of oranges to fall to $4 apiece,or a price ceiling (that is, a legal maximum price) of $4 per orange? Why?

27. Suppose:• The American supply and demand curves for coffee cross at $5 a pound.• Foreigners are willing to sell coffee to Americans in any quantity for $9 a

pound, but they are unwilling to buy coffee from Americans at any price.

8–7

• The U.S. government sets a price ceiling of $3 a pound for coffee andagrees to provide as much coffee as necessary to prevent waiting lines fromforming. The government gets its coffee by buying it from foreigners.

• The revenue the government collects from selling coffee is all given awayto the president’s brother.

Use a graph to illustrate the effects of the government’s policy, showing thegains and losses to all relevant groups of Americans. Use your graph to illus-trate the deadweight loss.

28. The American demand and supply curves for oranges cross at a price of $8.All Americans are free to buy or sell on oranges on the world market at aprice of $5 each. One day, the U.S. government announces that it is willing topay $6 apiece for American oranges and to buy as many oranges as Americanswant to sell at that price. The government then takes those oranges and resellsthem on the world market for $5 each. Use a graph to show how this planaffects all relevant groups of Americans, and to illutrate the deadweight loss.

29. Widgets are produced by a competitive constant-cost industry. In long-runequilibrium, widgets sell for $3 apiece.Suppose now that the government requires each widget manufacturer to payan annual license fee of $100, whereupon the long-run equilibrium price ofwidgets rises to $5 apiece.a) Approximately how many widgets does each firm produce?b) Draw a diagram showing the industry-wide demand for widgets and the

new short-run supply of widgets. On this diagram, identify an area equalto the sum of all license fees paid by all the firms. (Hint: Paying thelicense fee and selling at $5 must be exactly as attractive as not payingthe license fee and selling at $3.)

c) Use your diagram to illustrate the deadweight loss from the license fee inthe long run. (Hint: Remember that in the long run, producers earn zeroprofit with or without the license fee, so your calculation can ignore theproducers.)

30. Broomsticks are manufactured by two firms which constitute a competitive in-dustry. Neither firm has any fixed costs. There are two consumers, W.W.Westand W.W.East. The following charts show the marginal cost of producing var-ious quantities of broomsticks at each firm, and the marginal value of variousquantities to each customer:

Marginal CostQuantity Firm A Firm B

1 $2 $42 3 53 4 64 5 7

Marginal ValueQuantity W.W.West W.W.East

1 $10 $92 8 83 6 74 4 6

a) What quantity of broomsticks are sold and at what price? How many arebuilt by Firm A and how many by Firm B? How many are bought byW.W.West and how many are bought by W.W.East?

b) How much producers’ surplus is gained in this market? How much con-sumers’ surplus? How much social gain? Your answers to all three ques-tions should be numbers.

8–8

31. “If it weren’t for secretaries, business would collapse. Therefore, secretariesshould be paid as much as corporate executives.” Comment.

32. “In an efficiently run society, people who work equally hard would receiveequal wages.” Comment.

33. A doctor wrote a letter to the Des Moines Register where he said, “Why shouldI get $50 for a procedure in Iowa and a physician in New York get twice asmuch? That does not seem equitable.” Comment.

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THIS PAGE SHOULD BE LEFT BLANK

8–10

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 8

1.

12 24 36

A

B

C

Because you choose to buy the second dozen, we knowthat E+ F+G is at least $12. It follows that P > $1.

Because you choose not to buy the third dozen, we knowthat H+I is less than $12. It follows that P'' < $1.

Therefore $1 is somewhere between P'' and P, so thenumber of brownies you would buy at $1 is somewherebetween 12 and 36.

P

D

EP'

F

G

H

I

P''

Quantity (brownies)

Price per brownie

D

2.

1000

C

P

P minus $.10

Quantity

Price

D

D

False. Consumer surplus increases by C+D.ButC=$100, so consumer surplus increases bymore than $100.

3.a) From buying the widgets.b) A gadget.c) The shaded rectangle is subtracted from consumer surplus:

A

B

Price

Quantity

D

10

30 31

4. a-d are all preferred to e according to the efficiency criterion and c is preferred toe according to the Pareto criterion.

5. False; you can never prove anything is bad (according to the efficiency criterion or

8–11

any other sane criterion) by listing its costs. You must also consider the benefits(in this case the benefit to the consumers) and weigh the costs against the benefits.

6. True, if the amount of land is really fixed. Since the amount of land can’t change,there is no possibility of deadweight loss. The figure below illustrates this.

AB

Price

Quantity

D

C

D'

D

E

Without Tax With TaxConsumers’ Surplus A+B A+BProducers’ Surplus C+D+E E

Tax Revenue - C+DSocial Gain A+B+C+D+E A+B+C+D+E

It should be noted, however, that this picture is unlikely to correspond to anyimportant market in the real world. Generally, one is not interested in land per se,but rather in goods like “land suitable for farming” or “land suitable for ranching.”These goods are not in fixed supply. “Land suitable for farming” can be producedvia such activities as the removal of boulders, irrigation and so forth. The supplycurve for such land is therefore upward sloping, and a sales tax on such land doescreate deadweight loss.

7. One possibility: Take from taxpayers the amount C + D + F + G + (23)E. Give

to consumers F + G + (13)E and give to producers C + D + (

13)E.

8. False. The line lengths adjust until the value of the waiting time is the same inboth countries.

9. In Middle Slobbovia, the value of wasted time will be less than in either Upper orLower Slobbovia, as those with relatively low time values can be hired to do someof the waiting.

10a. True:

AB

Price

Quantity

D

C

D E

SS'

F

G H

I J K

No excise tax Excise TaxCS A+B+ C APS I+ J+K+L LTaxRevenue I+ J

DeadweightLoss C +K

The excise tax causes even fewer potatosto be supplied, hence creates a deadweightloss.

L

$2

10b. False:

8–12

Price

Quantity

D

S

No sales tax Sales TaxCS A+B A+BPS H HTaxRevenue C +D

"DeadweightGain" C +D$2

D'

A B

C D EF G

H

The point is simply that the sales tax makes people less willing to wait in linefor the item and so saves society the cost of some line-standing. Instead of payingfor the item with valuable time that is recovered by nobody, the consumers paywith cash that goes to the tax recipients.

In fact, a sufficiently large sales tax can eliminate all line standing (thoughthere is still a deadweight loss associated with the tax). Can you draw the corre-sponding picture?

11. The Senator is proposing a price control. In terms of Exhibit 8-14 in the textbook,his plan will increase the deadweight loss from C + E to B + C + D + E.

12. True. The “price to demanders” in the wholesale market for wheat—that is, theprice that bakers pay for wheat, inclusive of the value of their time—would rise.This price is part of the marginal cost of producing bread, so marginal costs risein the bread market; hence prices rise as well.

13.Price

Quantity

D

SA

B

C

D

P

P

0

1

A pound ofpotatos sells for P0 (at anyhigher price, sellers would not be able tosell their desired quantities, and pricewould drop). Price to consumers must beP1 (at any lower price, buyers would notbe able to buy their desired quantities andprice would rise). Therefore price of rationticket must be P1-P0. CS is A, PS is C ,value of ration tickets is price of ration tickettimes quantity of ration tickets, or B. Thusdeadweight loss is D.

25

8–13

14.

A

Quantity

Price

D

SS'

B CD E F

GH

Initially the government collectsD+E+F+G+H in license fees.

After the excise tax is imposed, thegovernnment collects G+H inlicense fees plus A+B+D+E inexcise tax.

Total revenue could either rise orfall, depending on whether F isless or more than A+B.

15.

A

Quantity

Price

D

S

B C

D

1000 2000

E

Before the program, CS=A+B+C and PS=D+E.

With the program, the price ofpotatos rises to P.Consumer surplus falls to A. Sellers are willing topay B+D for permits, and all of this goes to thegovernment. Therefore total surplus is A+B+D.The deadweight loss is C+E.

P

16.

A

Quantity

Price

D

S

BC D

EP

F G H

S is the supply curve for commercial toymanufacturers.

Santa causes the price of commercial toysto drop to P. Commercial toy makers produceQ toys and consumers end up with Q+1,000,000.

Producer surplus falls from B+E to E.

To compute consumer surplus: The value ofall the toys is A+B+ C+D+E+F+G+H. Consumerspay P*Q=E+F. So consumer surplus rises fromA to A+B+C+D+G+H.

Social gain rises from A+B+E toA+B+C+D+E+G+H. The "deadweight gain" istherefore C+D+G+H.

Q Q+1,000,000

8–14

17.Price

Quantity

D

SA

B CD

E

FG

H

No price floor Price floor

CS A+B+ C APS E+G B+ C +D+E+GCost to taxpayers C +D+E+G+H

SG A+B+ C +E+G A+B-H

DWL C +E+G+H{Q . purchased by govt.18.

Price

Quantity

D

S

AB

C D E F5

6

Consumers are always free to buy orangesat $5, so their consumer surplus(A+B+C +D+E+F) cannot be affected.

Producers now get $6 instead of $5 fororanges, so PS rises from G to C+G.

Govt buys quantity Q and takes a loss of$1 per orange, so loss is C+D.

DWL is D.

G

Q

19. The triangle on the left reflects the fact that people purchase foreign cars thatcould have been produced more cheaply at home. The triangle on the right reflectsthe fact that people now buy fewer cars. Can you explain why?

20.Price

Quantity

D

S

A

BC D E F G10000

No tax Tax

U.S. buyers pay 10000 12000U.S. sellers get 10000 10000

CS A+B+ C +D+E+F+G A+BPS I ITax Revenue C +D+E+FDW Loss G

HI

12000

8–15

21.Price

Quantity

D

S

A

BC D E F G

10000

No tax Tax

U.S. buyers pay 10000 10000U.S. sellers get 10000 8000

CS A+B A+BPS C+D+I ITax Revenue C

DW Loss D8000

HI

22. Americans can get cars for $8000, so they won’t pay more than $8000 for anAmerican car. Therefore American producers sell exclusively abroad where theycan get $10,000. The graph is as follows:

Price

Quantity

D

S

A

BC D E F G 8000

No subsidy Subsidy

U.S. buyers pay 10000 8000U.S. sellers get 10000 10000

CS A+B A+B+ C +D+E+F+GPS C+D+I C +D+ ICost to taxpayers C +D+E+ F+G+HDW Loss H

HI

10000

If American producers can’t sell abroad, they’ll have to accept $8000 per carand the graph becomes:

Price

Quantity

D

S

A

BC D E F G 8000

No subsidy Subsidy

U.S. buyers pay 10000 8000U.S. sellers get 10000 8000

CS A+B A+B+ C +D+E+F+GPS C+D+I ICost to taxpayers D+ E+ F+G+HDW Loss D+H

HI

10000

8–16

23.Price

Quantity

D

S

A

BC D E F G10000

No subsidy Subsidy

U.S. buyers pay 10000 10000U.S. sellers get 10000 12000

CS A thru G A thru GPS I C+D+ICost to taxpayers C +D+EDW Loss E

HI

12000

24.Price

Quantity

D

S

A

BC D E F G 8000

No subsidy Subsidy

U.S. buyers pay 10000 8000U.S. sellers get 10000 10000

CS A+B A+B+ C +D+E+F+GPS C+D+I C+D+ICost to taxpayers C +D+E+F+G+HDW Loss H

HI

10000

25.

A

Quantity

Price

D

S

B CD

1000 2000

E

F GH

I

NO SUBSIDY SUBSIDY

CS A+B+ C APS F+G+H+I B+ C+D+F+G+H+ITaxpayers - -(C+D+E)

DWLoss C+E

b) One example of a plan everyone would prefer:Take B+C/2 from consumers, take C/2+D+E/2 fromtaxpayers, and give B+ C+D+E/2 to producers.

There are many other correct answers to b).

26. In order for demanders to want exactly 500 foreign widgets, the price to demandersof a foreign widget must be $6. Of this, $2 goes to the foreign widget maker so $4must be the price of the ration ticket.

8–17

27.Price

Quantity

D

SP0

Qd Qs

A

B CD

EF

Farmers must cut back productionfrom Qs to Qd. This requires apayment of C +D+F. So consumerslose B+ C , farmers gain B+ C+D,taxpayers lose C +D+F, anddeadweight loss is C +F.

28.Price

Quantity

D

S

A

B C D

E

F15

25

Before the law, Americans earn $15 perhour. CS (earned by firms) is A+B+ C +Dand PS (earned by American workers)is F.

After the law, firms hire Q0 Americansat $25 per hour and Q1-Q0 foreignersat $15 per hour. CS is A+D and PS isB+F. Deadweight loss is C .

Q0 Q1

29.Price

Quantity

D

MC

A B

PS must fall by the amount of the per-firmsubsidy in order to maintain the zero-profitcondition.

If price falls by $1 (in diagram) then PSfalls by A+B, so A+B=$8000.

New quantity is Q so A= Q x $1 = $ Q .

Since A<A+B, we have Q<8000.

Thus the govt pays more than $1 per widgetproduced.

{$1

Q

With an excise subsidy of $1 per widget, price would fall by the same amount, so consumersare indifferent between the two subsidies. Firms earn zero profit no matter what, so they arealso indifferent. Govt pays $1 per widget under the excise subsidy, but more than $1 perwidget under the per-firm subsidy. Thus the excise subsidy is more efficient.

30. True. The MC curve in Exhibit 8.18 becomes flat, so area B disappears and thesocial cost (A) is equal to the loss to the victim.

8–18

31.

POPEYE

WIMPY

0

0

Blackened dot shows endowment point.Shaded area is region of mutualadvantage.Darkened lines show contract curve.The only competitive equilibrium isat the bottom right corner of the box.

32. He will produce either all nuts or all berries depending on the relative price.33. His own demand curve is not important for determining supply side decisions in a

world with free trade and many differing producers. He simply takes market pricesas given and chooses to produce where his production possibility frontier has slopeequal to the relative prices in the economy. This allows him to obtain the budgetline which is the farthest from the origin and thus the highest indifference curve.

Chapter Nine:Knowledge and Information

Teaching Suggestions

1) In the study guide that accompanies this textbook, there is reprintedHayek’s article on the use of knowledge in society. I always assign this articleas required reading. It is one of very few pieces of economic writing that genuinelymeets two criteria: it is completely accessible to students, and it is profound. Infact, the accessibility tends to mask the profundity: Students have the idea thatnothing so easy to read could possibly be important. I assign it after I have coveredthe material of Section 9.1, so that students know what themes to watch for.

2) In the text, there are many examples of ways in which prices enable themarket to make use of specialized information, even though that information isunavailable to any central planner: the fact that linseed oil is used to make the inkfor books, that there are two ways to get chickens to lay more eggs, and so forth. Itis worth emphasizing to students that when Hayek talks about the knowledge of theparticular circumstances of time and place, he is referring also to information thatis even more specialized. He is referring to the knowledge that one of the typists isbored this afternoon and would not mind being asked to help with some filing, orthat if you stack things just right you can squeeze one additional odd-shaped parcelinto the delivery van. The importance of such knowledge for economic planning,and the mechanism by which it is used under a price system, is Hayek’s greatinsight and the theme of this chapter.

3) I do not ordinarily cover the material of 9.2 and 9.3 in class. It is fun and

8–1

interesting, but there is usually just no time. Occasionally I have had a little extratime at the end of the semester and used it to come back to this.

4) The material on efficient markets presents a paradox which an occasionalbright student might notice. If the price of an asset contains all of the informa-tion relevant to that asset’s future performance, then nobody has any incentive toexpend resources investigating more fundamental variables. But if nobody inves-tigates such variables, how can the information they contain become incorporatedin the price of the asset? On the one occasion when a student asked me this,I commended him heartily for his insight, told him that many economists hadbeen troubled by the same thing, made some noises about models with informedand non-informed agents, and referred him to the famous paper by Grossman andStiglitz. I don’t know whether he looked it up.

5) As to the example on signaling in the animal kingdom, things are actuallyworse than described in the textbook. The text says that male birds signal theirreproductive fitness to females by devoting resources to the production of extrav-agant tails. These resources are wasted from a social point of view, in that anagreement among all males to grow tails only half their present length would be aPareto-improvement. But no such agreement is enforceable.

That much is in the text. Here is what’s left out: Male birds with long tails aremore likely than average to have had fathers with long tails. This is so because ofthe laws of heredity. It follows that male birds with long tails are more likely thanaverage to have had mothers who are particularly attracted to long tails; after all,their mothers did choose to mate with their fathers. Thus long- tailed males arelikely to have received genes from their mothers that, if present in a female, causeattraction to long tails. When a long-tailed male mates, it is often to a female withan attraction to long tails. Thus any female offspring are likely to receive genesfrom both sides that incline her to choose long-tailed males.

At the same time, a female with an attraction to long tails is likely to havehad a mother with the same attraction, hence a father with a long tail, hence tobe carrying genes that cause long tails in males. When she mates it is likely tobe with a long-tailed male, so that the male offspring can receive genes from bothsides that produce long tails.

The upshot is that the traits of long tails in males and an attraction for longtails in females reinforce each other in a particularly strong way, and there can beexplosive growth in tail length in a very short time. This is a famous example in bi-ology, due to R.A. Fisher, whose book on natural selection I recommend. A popularaccount is in Richard Dawkins’s The Blind Watchmaker, which I also recommend,subject to the caveat that the reader ignore the remarks about economists that aremade in that book. Dawkins’s The Selfish Gene is a delightful book which looksat biology the way an economist would look at it.

6) For insightful commentary on executive compensation in general and theJensen/ Murphy results cited in the textbook in particular, see K. McLaughlin,“Individual Compensation and Firm Performance: The Economics of Total OutputContracts,” preprint (1990).

8–2

Additional Problems

1. Citizens are chosen randomly to serve on juries, and are required to serve ifchosen. True or False: Since the selection of jury members is random, nobodycan alter his behavior to avoid it. Thus there is no social loss associated withthe jury system.

2. Parking space is in short supply at MacAdam University. At a cost of $10,000,the University has just constructed a new parking lot containing 100 parkingspaces. True or False: In order to insure that the spaces are allocated effi-ciently, the University should sell them at a price of $100 apiece.

3. True or False: The calculation of deadweight loss due to a price control isoverly optimistic since it fails to take account of the costs of misallocation ala Hayek.

Remark: If you assign problem 3, you should probably allow some time for classdiscussion, since the answer is subtle. If people are able to compete for the good byhiring line-standers, purchasing advertisements, etcetera, then there is a deadweightloss as in chapter 8, but no misallocation since goods still go to the highest bidders.Thus the answer is false. If there are no markets for such activities, so that peoplehave to wait in line themselves, then if people all have the same value of time, theanswer is still false, for the same reason. If goods are allocated via waiting lines,and there is no market for waiting services, and people have very different valuesof time, then goods could end up being allocated to people who value them littlebut value their time even less. This is a misallocation, though it seems debatablewhether we should attribute it to the price control or to the lack of a line-standingmarket.

Finally, if people are somehow effectively prohibited from any form of competitionother than price— and it is worth emphasizing to students that this is more unlikelythan it might first sound—so that the goods are allocated essentially randomly tothose consumers who happen to be right in the vicinity when the goods appear onthe shelves—there is certainly a loss due to misallocation, but on the other hand,the losses due to line-standing disappear.

4. Suppose that land can be neither created nor destroyed, so that the supplycurve for land is perfectly vertical.a) Suppose that a law is passed which sets a maximum allowable price for

land, and that this price is below equilibrium. Show the deadweight loss.b) Suppose instead that a law is passed under which a national lottery will

be held and the winners will be given free land, which they can not sell.Exactly enough winners are chosen to distribute all of the land in thecountry. Is there a deadweight loss associated with this plan? Explain.

c) Give an example of a real social cost of the plan described in part b) thatis not reflected in your measure of deadweight loss. How could the planbe modified to eliminate this cost?

5. Suppose that the supply curve for land is perfectly vertical, and that the priceof land is legislated to be at some level below equilibrium.a) Show the deadweight loss.b) Suppose that people could somehow be prevented from engaging n costly

activities in their attempts to acquire scarce land. Show that the dead-weight loss is now zero.

8–3

c) True or False: In the case of part (b), there is no social loss due to theprice control.

6. Suppose that in equilibrium Americans consume 1000 fruitcakes per year. Thegovernment is considering two plans to increase fruitcake consumption. UnderPlan A, fruitcake buyers receive a subsidy that causes consumption to rise to3000 fruitcakes per year. Under Plan B, the government gives away enoughfruitcakes to raise consumption to 3000 per year. True or False: Since in eachcase the number of fruitcakes is identical, it follows that the two plans areequally socially desirable.

7. No fruitcakes are produced in the United States. Americans can buy any num-ber of fruitcakes from abroad at a price of $10 each. At this price, Americansbuy 1000 fruitcakes per year.The U.S. government has decided to make fruitcakes available to Americancitizens at a price of $3 each. The government will provide as many fruitcakesas people want to buy at this price, and will get them by purchasing themfrom foreigners.a) Show the gains and losses to all relevant groups of Americans as a result

of this program. Compute the deadweight loss.b) Suppose that the government modifies the program. It will continue to

sell fruitcakes at $3, but it will provide only 1000 per year, choosingrandomly those citizens who will be permitted to buy them. Computethe deadweight loss now.

c) In part b), can you think of any real social costs of the program that arenot taken into account by your analysis?

8 Suppose the equilibrium price of potatos is $4 a pound. To gain the supportof potato farmers, the government agrees to buy potatos at $7 a pound, andto buy as many potatos as farmers want to sell. Then the government resellsthe potatos to demanders, at whatever price demanders are willing to pay forthat quantity.a) Use a graph to illustrate how this program affects potato farmers, potato

consumers, the taxpayers, and the recipients of the government’s revenuefrom potato sales. Illustrate the deadweight loss from this program.

b) Suppose that instead of reselling the potatos, the government gives themaway for free to the same people who would otherwise have bought them.How does this affect your calculations in part a)? How does it affect thedeadweight loss?

c) If you heard that the government was buying potatos and giving themaway, would you consider your deadweight loss calculation an adequatemeasure of this program’s social cost? If so, why? If not, give an explicitexample of something your calculation leaves out.

8–4

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 9

1. False, or at least not necessarily true. Although the elves want to be as helpful aspossible, they have no way of knowing where their services are most valuable. Asa result, they might end up spending a lot of time repairing old black and whitetelevision sets when they could be repairing the space shuttle. If humans are ableto bid against each other for the elves’ services, the elves will be able to concentratetheir efforts where they do the most good. This makes humans better off; on theother hand, the actual payments to the elves make them worse off. The net effecton humans could go either way.

2. None of the council members has the expertise to determine the extent of the riskfrom the chemical plant and none has the expertise (or information) to determinethe extent of the benefits. It is reasonable to expect that the company ownersand their insurers (who are experts in assessing risks) have access to more suchinformation than the council has. Under the councilman’s proposal, they have theincentive to make use of such information. If the chemical company agrees to bearall of the costs of reimbursement, we may infer that it expects to earn enough fromthe plant to more than cover these costs. Similarly, if the insurance company iswilling to bear the risk in exchange for a price that the chemical company is willingto pay, we may infer that it expects the amount of damage to the townspeople tobe less than the gains to the chemical company.

The councilman’s suggestion creates an incentive for those with easiest accessto the relevant information to analyze that information and act on it in a sociallydesirable way.

3. (a) If price gouging were prohibited, less ice would have been transported to theaffected area. (b) But even if the effect in (a) could have been prevented, therewould have been no incentive to allocate that ice to those who needed it the most.Social welfare would have been reduced. (c) The pure altruist might know thatice is worth $50 a pound to some people and not want it to fall into the hands ofthose who value it at only $10 a pound. If he’s not sure who’s who, the only wayto find out is to set a high price. Later, he can donate the $50 to general floodrelief efforts.

4. False; there are many things that divisional managers know that central manage-ment does not and indeed can not know. These include general facts: John andHarry don’t get along, so putting them next to each other on the assembly linetends to slow things down; when you let Judy go five minutes over on her coffeebreak, she becomes much more productive for the rest of the afternoon; Fred thejanitor is better at computer repairs than the computer repairman that the com-pany sends out. But even more importantly, the divisional managers are aware ofvery specific facts—knowledge of the particular circumstances of time and place—that can not possibly be communicated to central management in any systematicway: Judy is feeling bored this afternoon and would enjoy tackling a tough assign-ment; computer #7 is making strange noises, so perhaps we should be sure we havebackups of all its data; Mary’s desktop is clear right now, so its a good place to setdown some files while we sort through them.

Can you imagine central management making decisions about where to set

8–5

the files down? Central managers don’t know about Mary’s clear desktop, theydon’t know how bulky the files are; they don’t know how long you’ll need to lookat them, and they don’t know when Mary needs her desk back. John and Harry’slong-standing feud could perhaps in principle be explained to the management—but how is management to know that George and Helen just had a quarrel fiveminutes ago and shouldn’t be assigned to work together today?

Countless decisions are made every day that require specific knowledge avail-able only to one or a few people. There is an advantage to having decisions madeby those with access to this knowledge.

5.a) Under competition, price equals marginal cost equals $6 per sword. At this price,Aramis buys 2, Porthos buys 1, and Athos buys 2, for a total of 5 swords.

b) In part a) the social gain is the total value of the swords ($10 + $8 + $7 + $9 +$6 = $40) minus the total cost of producing them (5 × $6 = $30), or $10. Nowthe total value of the swords is reduced to $7 + $5 + $4 + $3 + $9 = $28, and thesocial gain is reduced to $(-2). The planner’s decision leads to a social loss of $12.

6. Plans (c) and (d) are equivalent. Under Plan (c) a young person is told, “Youmust pay $100 in tax. You may also join the army if you wish, in which case youwill receive a wage of $100.” Under Plan (4), the same young person is told, “Youmust enter the army, unless you hire someone else to take your place at a wageof $100.” (The market- clearing wage must be the same in each case, because thearmy is of the same size in each case.) Whichever way you word it, the youngperson’s choices come down to: sacrifice $100 or join the army.

Under Plan (a), the army consists of exactly the same young people as underPlans (c) and (d): those with the lowest opportunity costs. Thus from a welfarepoint of view, plans (a), (c) and (d) are equally desirable. Of course young peopleprefer plan (a), under which the cost of the army is shared by all, and other citizensprefer plans (c) and (d), under which young people bear the entire cost.

Plan (b) appears at first to be equivalent to plans (c) and (d), but it differsin one crucial respect: Under Plan (b), some young people with high opportunitycosts will be drafted instead of others with lower opportunity costs. This can notbe avoided unless the officers of the Selective Service system know every detail ofevery young person’s talents, ambitions, plans, and circumstances. Thus Plan (b)is inferior to the other plans on welfare grounds, despite the fact that a graphicalanalysis as in Chapter Eight would reveal no deadweight loss. The additional socialcosts are borne entirely by young people; young people as a group are worse offunder Plan (b) than any of the others, whereas for other citizens Plan (b) is neitherbetter nor worse than Plans (c) and (d).

Incidentally, the equivalence of Plans (c) and (d) is a new way to see that avolunteer army is no more expensive than a draft in any meaningful sense. Soldiersare paid a market- clearing wage in (c) and no wage at all in (d), but each individualcitizen is equally well off under either plan.

One further remark: If the young people who are chosen to be taxed in Plan(c) are exactly the same as the young people who are drafted in Plan (d), thenthe plans really are equivalent from each individual person’s point of view. If onlysome young people are drafted in Plan (d), but all young people share the taxburden in Plan (c), then Plan (c) allows a more equal division of the burden, butthe cost to young people as a group remains the same.

7.a) In the simple case where there is a homogeneous product called land, the Fabiansare correct. The idea is that even if the tax is 99 percent, owners will look for thehighest possible bidder in the marketplace in order to maximize their rents (this

8–6

of course presumes there are no costs to searching for such bidders). This ensuresthat the land will be distributed efficiently and there will be no social loss. Thekey idea here is that the quantity of land supplied will not be reduced in responseto the distortionary taxation; thus there is no deadweight loss. Nevertheless, whenland is differentiated by quality (i.e., well maintained vs. mismanaged land) theFabians argument breaks down. In this case, the tax causes a reduction in thequality of land and thus a reduction in social welfare through a deadweight loss.

b) If it were costly to locate high bidders, then a 99% tax could discourage such effortsand cause land to be misallocated.

8.

D

S$5

Q

PIn the best case scenario, the shadedarea is the deadweight loss. This areabreaks up into rectangles, with eachrectangle representing the marginalcost of providing a haircut minus themarginal value of that haircut.

But this assumes that haircuts are givento the consumers who value them most.If instead some of the haircuts go toconsumers who value them less, thesocial loss will be greater.

9.

DQuantity

Price S

P'

P{T

A

B

C

a) Suppose that parking spots are sold at the artificially low price P . The “full” pricemust rise to P ′ in order to equilibrate supply and demand. Thus the price of aticket must be T . Consumers’ surplus is A, producers’ surplus is C, and the totalvalue of the tickets is T times the number of tickets, which is B. Comparing withthe situation before the lottery we have

Without Lottery With LotteryConsumers’ Surplus A AProducers’ Surplus B+C C

Value of Tickets - BSocial Gain A+B+C A+B+C

Thus parkers are neither better nor worse off when the plan is instituted. Thearea B is transferred from the University to the winners of the lottery tickets.

Warning: Do not become confused by the fact that some ticket winners arealso parkers. Such people gain part of area A in their capacity as parkers and partof area B in their capacity as ticket winners.

8–7

b) The effects are identical, since in either case all that happens is that some wealthis transferred from the University to randomly chosen students.

The plan in part a) was actually proposed recently by a faculty member atthe University of Rochester. He circulated petitions in its favor, which were signedby a large number of faculty, students, and staff. A rival petition, favoring themore straightforward approach of randomizing tuition (and, for faculty and staff,randomizing salaries) gathered considerably less support, for reasons that are notentirely clear.

c) Now some of the tickets will end up in the hands of students who value them lessthan others do, creating social waste. The most extreme cases are those where aticket ends up in the hands of a student who has no use for it whatsoever, becausehe has no car. But there are losses in other cases as well. If lottery winner Maxinewins a ticket that she values at $5, and lottery loser Saul would be willing to pay$15 for that ticket, then preventing the transaction creates a social loss of $10.

10.

DQuantity

Price

A

B C

S

In the graph, consumers gain area B + C, while producers lose the same area.(This does not, however, account for the value of the producers’ good feelingsdue to their burst of generosity.) This calculation presumes that all pizza willbe delivered to consumers who like pizza. If instead large amounts of pizza aredelivered to consumers who don’t like pizza then the net result could be to makeconsumers either better or worse off.

11.

DQuantity

Price S

A

B C

S'

DE

FG

Santa causes the supply curve for toysto shift rightward by 1,000,000.Consumers end up with Q2 toys, ofwhich Q1 come from commercialmanufacturers and the remaining1,000,000 come from Santa.

Santa causes CS to rise from A toA+B+C +F+G and PS to fall from B+Dto D. Net social gain from Santa Clausis C +F+G.

This presumes the toys go to the childrenwho value them most. Otherwise, thetrue social value is less.

Q1 Q2

8–8

12.

DQuantity

Price

A

B C

D

1000

$10

$3

a) Consumers gain B+ C . Taxpayers loseB+C +D. Deadweight loss is D.

b) True. Area D consists of rectangles,each equal to the $10 cost of a pound ofcoffee minus the value of that coffee to aconsumer.

c) Consumers gain B. Taxpayers lose B.Deadweight loss is zero.

d) Coffee might not go to those who valueit the most.

13.

DQuantity

Price

A

B C D

$40

500 600

F

G

E

H IP

a) New price is P.

b) Consumers gain B+C +D. Producers loseB+C +D+E+F+G+H+I. Recipients of freewidgets gain G+H+I. Deadweight loss is E+F.

c) Govt. does not know which firms canproduce widgets most cheaply, but the computationassumes that widgets are produced by the lowcost producers.

14. In situation (a) college is not worth the cost and in situation (c) it fails to signalintelligence. But in situation (b) bright students can use college as a valuablesignal.

15. Suppose that all applicants with incomes over $70,000 have revealed their incomes.Then if your income is $70,000, you can only gain by revealing it. The same is trueat every income level. Thus all incomes are voluntarily revealed.

16.a) If the company had to charge the same rate, then only high risk persons wouldbe insured in equilibrium. This occurs because the rate charged by the insurancecompany would have to be prohibitively high for low risk individuals if the insurancecompany desires non-negative profits. If the rate were set lower, the insurancecompany would go out of business as all the high risk individuals would purchasetoo much insurance.

b) In this case the company could charge different rates to individuals who are indifferent risk categories. Thus the adverse selection problem would seem to bemitigated. But there is a hitch. Since there are people who would purchase in-surance with the prior knowledge that they have AIDS, the insurance companiesare forced to price at a higher rate. One possible outcome: This rate drives outall the individuals who do not have AIDS and thus the only people who purchaseinsurance are those who have already contracted the disease.

17. It would promote social welfare in the sense that the law defines low qualityversus high quality automobiles. Thus, a new market in which high quality usedcars are traded has been opened due to the law. Prior to the law such a market didnot exist because of the adverse selection problem. With the new market opened,

8–9

buyers and sellers of high quality used cars can trade and thus welfare is increased.18. In a large enough group the insurance company has a good idea of the number of

risky versus non-risky individuals (i.e., it could extrapolate from the entire popu-lation). Thus, the company can charge an intermediate price for a fixed quantityof coverage to both low risk and high risk individuals. The high risk individualswill be subsidized by the low risk individuals but since the low risk individuals aretypically given the insurance as a “fringe” benefit, they are essentially forced tosubsidize these people. This works to combat the adverse selection problem andcould be socially preferable in the presence of incomplete information.

19. The warranty implies the sellers are responsible for the quality of the automobile.This yields the desirable result that high quality automobiles will be sold with amore comprehensive warranty and thus are distinguishable from low quality cars.The ability to distinguish cars ends the adverse selection problem and increasessocial welfare. On the other hand, buyers would have less incentive to care fortheir cars (since they could always invoke the warranty if something went wrong),which is a moral hazard problem.

20. False. Although the percentage increase in existing claims would be minimal, thevolume of future claims would increase due to moral hazard. Moral hazard ariseshere because persons care less about the well-being of their automobile when theyare not responsible for any of the damages. The lack of caring causes an increase inauto thefts and accidents which yields a higher number of claims to the insurancecompany. Thus rates must increase.

8–10

Chapter Ten:Monopoly

General Discussion and Teaching Suggestions

1) Beyond what is covered in the text, there are many interesting topics inmonopoly pricing that you can mention in class, use in constructing exam problems,or assign students to write short papers on. One is the all-or- nothing offer: If allconsumers are identical, the monopolist computes the quantity that each consumerwould buy at the competitive price, packages the good in boxes containing thisquantity, and charges an amount equal to the full consumers’ surplus. (Since themonopolist collects the entire consumers’ and producers’ surpluses, he wants tomaximize the sum of the two, hence the choice of the competitive quantity.) Withall consumers truly identical, this is equivalent to a two-part tariff. With someheterogeneity among consumers it is not. You can ask students to think about thecircumstances under which the monopolist might want to use all-or-nothing offersin preference to two-part tariffs or the ordinary forms of price discrimination. Ofcourse, this will very quickly bring you into sophisticated research areas, wherestudents can not be expected to have much insight. But some students are intriguedby hearing about the problems.

2) With regard to all-or-nothing offers, I report for the record that a studentin a Principles(!) course recently approached me after class on the very day whenI first defined consumers’ surplus, and suggested that if the producer packaged hisgoods in quantities equal to what the consumer was going to buy anyway, he couldcharge the full consumers’ surplus. Teaching has its rewards.

3) Another interesting monopoly pricing topic is the block booking of movies,wherein studios require theaters to purchase a package of movies as opposed tobeing able to pick and choose among them. (Diamonds at wholesale are sold ina similar way.) The layman’s (and apparently the Supreme Court’s) explanation,which makes no sense (see below), is that the studio, having monopoly control ofa popular film, uses it to force theaters to book its less popular films as well. Adebunking of this, and an alternative explanation, are to be found in Stigler’s “ANote on Block Booking” from The Supreme Court Review (1963) and reprintedin Stigler’s book The Organization of Industry . Students readily understand andenjoy this.

I quote from Stigler:

Consider the following simple example: . . . Gone With the Wind isworth $10,000 to the buyer, while . . . Getting Gertie’s Garter is worthlessto him. The seller could sell the one for $10,000, and throw away thesecond, for no matter what its cost, bygones are forever bygones. Insteadthe seller compels the buyer to take both. But surely he can obtain nomore than $10,000, since by hypothesis this is the value of both films tothe buyer. Why not, in short, use his monopoly power directly on thedesirable film? It seems no more sensible, on this logic, to block book thetwo films than it would be to compel the exhibitor to buy Gone With theWind and seven Ouija boards, again for $10,000.

The explanation of the practice must lie elsewhere. The simplestplausible explanation is that some buyers would prize one film much morerelative to the other. Consider the two buyers:

A would pay $8,000 for film X and $2,500 for film Y.

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B would pay $7,000 for film X and $3,000 for film Y.

If the seller were to price the two films separately, he would receive:1. $5,000 for the sale of Y, at $2,500 per buyer. A higher price would

exclude A and reduce receipts.2. $14,000 for the sale of X, at $7,000 per buyer on the same logic.The total received is $19,000. But with block booking, a single price

of $10,000 can be set for the pair of films, and $20,000 will be received.

10–2

Additional Problems

1. True or False: Any producer, if he were in business at all, would choose tooperate at a point where marginal cost equals marginal revenue. This is soregardless of whether the industry is competitive or monopolized.

2. True or False: The only way a monopolist can charge a higher than competi-tive price is by selling a lower than competitive quantity.

3. Suppose that a monopolist with a fixed marginal cost curve increases his out-put due to a shift in demand. True or False: We may be sure that the priceof output will increase as well.

4. Suppose that a monopolist with a fixed marginal cost curve increases his pricedue to a shift in demand. True or False: We may be sure that the quantityof his output will increase as well.

5. Suppose that the demand for widgets undergoes a parallel shift upward. Inwhich case does the price of widgets adjust further: When the widget industryis competitive or when it is monopolized? (This question is rather difficult formany students.)

6. What’s wrong with this picture?

D

Quantity

Price

MC

MR6 8

7

10

7. There is only one doctor in the town of Llareggub. He pays $.50 apiece fordisposable syringes and $100 per year to rent an X-ray machine. To show itsappreciation for the doctor, the town council plans either to begin paying allof his syringe bills or all of his X-ray machine rental bills. Which plan willbenefit the doctor’s patients more and why?

8. Broomsticks are manufactured by two firms which constitute a competitive in-dustry. Neither firm has any fixed costs. There are two consumers, W.W.Westand W.W.East. The following charts show the marginal cost of producing var-ious quantities of broomsticks at each firm, and the marginal value of variousquantities to each customer:

Total CostQuantity Firm A Firm B

1 $2 $102 3 193 4 264 5 32

Total ValueW.W.West W.W.East

$10 $377 56 42 1

a) What quantity of broomsticks are sold and at what price? How many are

10–3

built by Firm A and how many by Firm B? How many are bought byW.W.West and how many are bought by W.W.East?

b) How much producers’ surplus is gained in this market? How much con-sumers’ surplus? How much social gain? Your answers to all three ques-tions should be numbers.

c) Suppose now that Firms A and B band together and form a single (non-competitive) firm, and that this merger has no effect on the industry-widemarginal cost curve. Now how many broomsticks are sold and at whatprice?

d) What is the size of the deadweight loss due to the formation of themonopoly? Your answer to this question should be a number .

9. True or False: If the customers of a monopolist could get together and bribehim to act like a competitor, then they could make both themselves and himbetter off.

10. Elmer is a monopolist in the carrot industry. His customers have formed anorganization that proposes to rent the carrot patch from Elmer and operate itfor the mutual good of the customers. Use a graph to illustrate the market forcarrots. On your graph, show the lowest rental fee that Elmer will accept andthe highest rental fee customers are willing to pay. Does the deal get struck?

11. Widgets are produced by a competitive industry and sold for $5 apiece. Eachwidget firm must have a license. The government sets the highest license feethat widget firms are willing to pay.If the widget industry were monopolized, widgets would sell for $8 apiece.The government is considering imposing an excise tax that would cause theprice of widgets to rise to $8.Use a graph to illustrate the following:a) The size of the excise tax (i.e. the tax per widget).b) The government revenue from the excise tax.c) The amount by which license fees will have to change if the tax is imposed.d) The net gain to the government from imposing the excise tax (accounting

for both the excise tax revenue and the license fees).Now nswer the following:

e) Does the excise tax lead to a net gin or a net loss in government revenue?f) Suppose that in addition to licensing sellers, the government also licenses

buyers: Only licensed widget buyers can buy widgets, and the governmentcharges the highest annual license fee buyers will pay. (You can assumebuyers are all identical.) Under this new assumption, does the excise taxincrease or decrease government revenue?

12. True or False: A monopolist with a U-shaped marginal cost curve mightchoose to operate on the downward sloping portion of that curve.

13. The domestic hatpin industry is monopolized. The diagram below showsthe U.S. demand curve for hatpins and the monopolist’s marginal cost curve.There is also a world market for hatpins, where the going price is $9.

10–4

A BC D E

F G H IJ K L M N O

P QR S

T

2

4

12

9

MC

D

MR

PRICE

QUANTITY

a) Suppose all Americans are free to buy and sell hatpins in the foreignmarket. What is the deadweight loss from the existence of the domesticmonopoly?

b) Suppose it is illegal for Americans to buy or sell hatpins in the foreignmarket. What is the deadweight loss from the existence of the domesticmonopoly?

c) Suppose it is illegal for Americans to sellhatpins to foreigners, but legalfor Americans to buy hatpins from foreigners. What is the deadweightloss due to the domestic monopoly?

d) Suppose it is illegal for Americans to buyhatpins from foreigners, but legalfor Americans to sell hatpins to foreigners. What is the deadweight lossdue to the domestic monopoly?

e) Suppose the demand, marginal revenue and marginal cost curves are asin the picture above, but the world price is $1 instead of $9. Redraw thepicture accordingly and answer questions a) through d) again.

f) Suppose the demand, marginal revenue and marginal cost curves are asin the picture above, but the world price is $3 instead of $9. Redraw thepicture accordingly and answer questions a) through d) again.

g) Suppose the demand, marginal revenue and marginal cost curves are asin the picture above, but the world price is $12 instead of $9. Redraw thepicture accordingly and answer questions a) through d) again.

14. In the town of Nwot there are many dentists but just one eye doctor. Aresenior citizens more likely to be offered discount prices for dental exams or foreye exams? Justify your answer.

15. True or False: A monopolist is best off operating on the inelastic portionof the demand curve, where he can charge high prices without losing manycustomers.

16. Comment on the following reasoning: “The oil companies collude with eachother to charge a monopoly price for gasoline. They are able to do this becausegasoline is a virtual necessity for which demand is highly inelastic.”*

17. True or False: Because a monopolist is able to charge a higher price thancompetitors could, his marginal revenue is higher than what a competitor’swould be.

18. True or False: The calculation of deadweight loss due to monopoly may be

* The delightful observation that economic theory reveals a contradiction between thetwo halves of this common argument is made in Browning and Browning’s textbook.

10–5

overly optimistic, because it does not account for costs of misallocation a laHayek.

19. True or False: The calculation of deadweight loss due to monopoly may beoverly optimistic, because it does not account for resources spent in attemptsto maintain the monopolist’s market position.

20. True or False: Devices like “50 cents off” coupons are used only under com-petition, since a monopolist can always require his customers to pay full price.

21. Copy centers usually give substantial discounts to customers with large orders.Do you think they are price discriminating? Why or why not?

22. True or False: If General Motors could require all GM car owners to buy allof their replacement parts directly from GM, it would charge monopoly pricesfor those replacement parts.

23. Consider a monopolist who produces his product in two different plants, eachwith its own marginal cost curve. Describe how he determines the quantity toproduce at each plant and the price to charge for it.

24. Under what circumstances might the monopoly owner of a camera store wantto offer discounts to his own employees?

25. (Note to instructor: This is a good problem to assign immediately after studentshave worked problem 23 in the textbook.) Snidely Whiplash owns all the housesin the Yukon Territory, where he charges the highest rent the citizens (who areall identical) are willing to pay. Snidely has just bought all the grocery stores intown, and is considerint selling groceries at a price below the competitive priceso that he can charge even more for housing (because low grocery prices willmake the Yukon Territory an even more attractive place to live). Is Snidely’splan a good one?

26. The Little Red Violin School offers music lessons to children. Each studentmust buy a violin from the school and then pay for lessons. Many of thechildren continue their lessons for years; many others drop out after a fewweeks. Should the Little Red Violin School charge a high or a low price forthe violins? Should it charge a high or a low price for lessons? Why?

27. There are three stores at Eastview Mall. Each store has some monopoly power.Eastview charges customers an admission fee to the mall, and charges rent tothe stores. All customers are identical.a) Illustrate how Eastview determines the admission fee to the mall.b) Suppose Eastview requires all stores in the mall to set competitive prices.

How will this affect the admission fee to the mall? How will it affect therent the stores are willing to pay?

c) If Eastview wants to maximize profits, is it a good idea to require storesto set competitive prices?

28. Suppose the University of Rochester has 1000 identical students. One day, theUniversity suddenly makes two simultaneous announcements:a) We’re raising prices in the dining halls by enough to increase the dining

halls’ profits by $100,000 (that is, $100 per student) per year.b) We’re cutting tuition by $100 per student per year.

Should students applaud or oppose this pair of policies?

29. A monopoly movie theater has two customers—Gene, who never buys popcornbut is willing to pay $(A+B+C+E+F+G) to see the movie, and Roger, who is

10–6

willing to pay nothing at all to see the movie but just comes to buy popcorn.The accompanying graph shows Roger’s demand curve for popcorn and themarginal cost of providing that popcorn.

Quantity

Price

D

MC

A

B CD

EF G H

50

60

40

Suppose you’re deciding whether to charge 40 cents a bag or 50 cents a bagfor the popcorn (you’ve already ruled out all other options). Which four areason the graph would you want to measure in order to make this decision? (Youcan assume that you always want to keep both customers.)

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THIS PAGE SHOULD BE LEFT BLANK

10–8

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 10

1.a) Fixed cost, no change.b) MC falls, price falls.c) Demand falls, MR falls, price falls.d) Demand falls, MR falls, price falls.e) Sunk cost, no effect.f) This is a rise in fixed costs if Gus has to choose between working at the factory

and driving a cab; in this case he’ll either quit to work at the factory or nothingwill change. It’s a rise in variable costs if Gus can moonlight; in this case, MC up,price up.

g) Not relevant.h) Not relevant.i) Not relevant.j) Demand falls, MR falls, price falls.k) Not relevant.l) Rise in MC, price rises (or Gus quits).m) Either a rise in fixed costs (no effect) or Gus quits rather than pay.

2. False, because of the phrase “unlike competitors”. Anybody can charge any pricehe wants to for anything. However, there is only one profit-maximizing price tocharge, and it is foolish to deviate from this price, whether you are a monopolist,a competitor, or anything in between.

3.

DQuantity

Price

MR

MC

MC'

$10

$9

PS rises by the area marked

minus the area marked

4. It drops vertically a distance $1.5. Refer to Exhbit 10-2 in the text. Customers will offer up to C + D + E and the

monopolist will accept anything over C + D−H. Since C + D + E > C + D−H,a deal will be struck. Thus true.

6. From problem 4, we know that a $1 sale tax causes the MR curve to drop $1.We also know that an excise tax causes the MC curve to rise $1. Therefore thetwo taxes yield the same quantities, the same price to demanders (read off the olddemand curve) and the same price to the monopolist.

7. False; it is more detrimental, since the monopolist produces less to begin with, sothat the gap between marginal cost and marginal value of the last unit producedis greater for a monopolist than for a competitor.

10–9

8. True, or at least often true. Suppose that the amount of land in existence isQ0. The marginal cost curve lies along the horizontal axis between 0 and Q0 andbecomes vertical at Q0. In the left-hand panel below, a monopolist supplies thefull quantity Q0 to the marketplace. However, in the right-hand panel, he suppliesthe smaller quantity Q1, causing deadweight loss.

D

MR

Q0 Q

P

D

MR

Q0 Q

P

Q1

9.

D

Quantity

Price

MR

MCA B

C D EF G H

I

{T No excise tax Excise tax of $ T

PS F+G+H+I ITax Revenue C +D+F+G

An excise tax of $T improves thewelfare of Americans:

(We know from the text thatC +D+F+G+I, which is the PS thatwould be earned by a monopolist,is greater than F+G+H+I.)

10.Keeping in mind that the demand curve is the marginal value curve, we can

compute the entries in the following table (“Price” means the price correspondingto the given quantity on the demand curve.)

Quantity Price TR MR TC MC

1 $10 $10 $10 $22 $9 $18 $8 $4 $23 $7 $21 $3 $5 $34 $6 $24 $3 $11 $45 $5 $25 $1 $15 $46 $4 $24 $(-1) $19 $47 $2 $14 $(-10) $24 $58 $1 $8 $(-6) $29 $5

A competitive industry produces at the intersection of the supply (marginalcost) and demand curves, at a quantity of 6 and a price of $4. A monopolistproduces only as long as marginal revenue exceeds marginal cost, which is to saythat he produces 3 items and sells them at $7. The deadweight loss under monopolyarises from the monopolist’s failure to produce items 4, 5 and 6 on which the excessof marginal value over marginal cost is $2, $1 and $0 respectively, so the deadweight

10–10

loss comes to $2 + $1 + $0 = $3.(Alternative calculation: Under competition, social gain is TV − TC = $41−

$19 = $22, wherease under monopoly, social gain is TV − TC = $26 − $7 = $19;the $3 difference is the deadweight loss.)

11. You need to know which is bigger: A + B + C + D + F + G + I + J (the gainunder monopoly) or A+B +C +D+E +F +G+H (the gain under competition).Equivalently, you need to know which is bigger: I +J or E +H. So measure areasI, J , E and H.

12. True. No price control can make a natural monopolist behave like a competitor.In the diagram below, any price ceiling below P will drive the monopolist out ofbusiness altogether, since at any lower price he is unable to cover the average costof production. When the price is P, the monopolist produces quantity Q, whichis more than the ordinary monopoly quantity but still less than the competitivequantity. Only through a subsidy can the monopolist be induced to produce morethan Q.

P

Q

D

MR

MC AC

Quantity

Price

13. False; the exact opposite is true. The two panels of Exhibit 10–5 in the textbookshow quantities produced under zero-profit regulation (QZ) as compared with theoptimal quantities QC . In Panel B, the natural monopolist produces less thanis optimal, while in Panel A, the non- natural monopolist produces more than isoptimal. There is no other way to draw the pictures, given that MC crosses ACat AC’s minimum and that AC is downward sloping when it crosses demand for anatural monopolist; upward sloping otherwise.

14. True, if regulation takes the form of a restriction on profit, or on the excess ofprice over average cost. Since discrimination is costly (by definition, it requires notalways hiring the best person for the job), an unregulated profit-maximizing firmhas an incentive to avoid it. However, a firm which is able, but not permitted, toearn high profits can choose to discriminate without losing anything.

15. Total sweaters = 7; total men’s sweaters = 4; price of men’s sweater = $7; totalwomen’s sweaters = 3; price of women’s sweater = $12.

16. False; under heavy competition there is no price discrimination.17. To observe that this is price discrimination is a good partial answer. A complete

answer requires explaining why families with children have a higher elasticity ofdemand for hotel rooms than other travelers. One answer might be that familieswith children are far less likely to be on business trips than other travelers, andhence more apt to change their travel plans if they find the hotels are too expensive.Another is that families traveling with children tend to have more expenses (becausethey have children) and/or to be less well off (because they can’t afford to leave

10–11

the children home with a nurse), and are consequently more sensitive to price thanother travelers.

18. This appears to be price discrimination in favor of U.S. tourists. To supportthis view, one would need to explain why U.S. tourists have a higher elasticity ofdemand for meals at certain restaurants than the natives do. But it seems thatthis is the exact opposite of the truth: tourists, if they are to eat at all, must eatin restaurants, whereas natives have the option of eating at home. Also, nativesare more likely than tourists to know of other, more out-of-the-way restaurants.

Perhaps, then, we should look for an explanation that does not involve pricediscrimination. This means looking for ways in which meals served to Americansare not the same goods (from the restaurants’ viewpoint) as meals served to Cana-dians. One possibility (and this is just a guess) is that Americans are better tippers,so that they actually pay more (inclusive of tip) for their meals than Canadiansdo. Of course, this keeps the staff happy and enables the management to paylower wages. Thus, it is effectively less expensive to serve Americans than it isCanadians.

We repeat that this explanation is a guess. If you have a better one, pleasesend it to the author in care of Thomson Publishing.

19. To support a diagnosis of price discrimination, we must ask why riders withtraveling companions have a more elastic demand for cab rides than riders who arealone. Walter Oi suggests that it is because three riders who know each other candecide to rent a car and split the cost three ways, whereas riders who are alonemust pay the entire cost of a rental car. In the same spirit, it seems reasonable thatpeople traveling in groups of three are more willing to get on buses and subways,which take longer than cabs, since they have friends to pass the time with and canprotect each other from getting lost.

20.a) The $5 fee is offered to those customers who are not as excited about visiting thereand don’t value the experience highly. Those people who are especially interestedare those who want to take pictures to enjoy in the future, so they are probablywilling to pay more to enter the community. This pricing schedule is to lure theelastic demanders (non camera users) into the market.

b) It may be more costly to admit camera users as the “photographers” may imposeon the inhabitants of the community by being distractive and noisy. The extra fivedollars compensates the Indians for the added irritation. Or perhaps people withcameras create competition for postcards manufactured by the Indians themselves.

c) This is left for the reader to decide. Some additional information may includediscussions with the inhabitants to whether the cameras disturb their lifestyle.

21. This seems to be an example of a two part tariff. The marginal cost of providinga subscriber with an additional cable channel is zero. Thus subscribers are chargedzero per channel, but also pay an entry fee. If all subscribers are identical, theentry fee is equal to the total value of all the channels.

Typically, “premium” channels such as HBO and Cinemax are priced sepa-rately. Why do you suppose this is?

22. The market for groceries can be represented by Exhibit 10-11 in the text. When heraises the price of groceries, Snidely will have to cut the rent on houses by C+D+E.Because his consumer surplus at the grocery store rises by only C + D−H, this isnot a good idea for Snidely.

10–12

23.

DQuantity

Price

MR

MCA B

C D E

FG H

a) F+G+Hb)C +D+F+Gc) tuition receipts fall by C +D+Ed) going with the monopolist means collecting an additional C +D-H in rent but losing C +D+E in tuition. The loss exceeds the gain so going with the monopolist is a bad idea.

24.a) Without an admission charge, the bookstore sets a monopoly price and earnsC + D + F + G. If it can charge admission, the bookstore sets a competitive priceand earns a total surplus (on book sales plus admission charges) of A + B + C +D + E + F + G + H. Therefore the bookstore will pay up to A + B + E + H forthe right to charge admission.

b) Students will lose their entire surplus of A + B, so tuition must be cut by thisamount.

c) The university is surely willing to sacrifice A + B in tuition in order to receive apayment of A + B + E + H, so yes, the bookstore will get permission.

25. False; in terms of Exhibit 10-11, Fredonians lose C + D + E in consumer surplusand get back only C + D −H in payments from the electric company.

26. True that consumers would be better off (the admission fee allows Wegman’s tocapture all their surplus, so they’re surely better off without it); false that socialgain would increase (Wegman’s would now charge a monopoly price, causing adeadweight loss).

27.

Quantity(Dept store merchandise)

Price

D

MR

MC

A B

C D E

F

G H

a) Department store merchandise is priced competitivelyat P. The monopoly parking lot owner charges the maximumconsumers will pay for a space, which is A+B+ C+D+E.

b) The monopoly department store charges P'. Thecompetitive parking lots charge marginal cost, which iszero.

c) Consumers are better off with a monopoly store andcompetitive parking lots, which leaves them a surplus ofA+B (as opposed to zero in the opposite situation). Storeowners getC+D+F+G, for a social gain of A+B+ C+D+F+G. In the opposite situation, store owners get F+G+H and the parking monopolist gets A+B+ C+D+E for a higher social gain.

P

P'

28. Part a) is true, part b) is false. If Hughes attempts to prevent competitors fromresharpening, it is presumably charging over $100 per resharpening and so musthave a diverse base of customers.

29. Strategy 1: Charge 50 cents a bag for popcorn and charge A + B + C to enterthe theater. Thelma won’t come, and you’ll earn A + B + C from Louise.

Strategy 2: Charge 50 cents a bag for popcorn and charge A to enter thetheater. They both come and you earn 2A.

Strategy 3: Charge 40 cents a bag for popcorn and charge A + B + C to enter

10–13

the theater. They both come, but you lose B + C + D at the popcorn stand, soyour total gain is 2(A + B + C)− (B + C + D) = 2A + B + C −D.

Strategy 3 is best if and only if 2A+B+C−D > A+B+C and 2A+B+C−D >2A; that is A > D and B+C > D. So you need to measure areas A, D, and B+C.

30. Strategy 1: Charge $60. Maximal admission fee is $300 (otherwise Eve balks).You earn $400 profit selling 40 widgets to Adam, $300 profit selling 30 widgets toEve, and $600 in admission fees. Total gain: $1300.

Strategy 2: Charge $50. Admission fee is $675. Profit from selling widgets iszero. Total gain: $1350.

Strategy 3: Charge $40. Admission fee is $1200. Loss from selling 60 widgetsto Adam and 60 to Eve is $1200. Total gain: $1200.

Conclusion: Charge $50.31.a) If you want both Gene and Roger to see the movie, you must charge $4 for

admission; in that case you can charge 60 cents for popcorn and earn $2 in producersurplus from Roger at the popcorn stand. Your total is $4 + $4 + $2 = $10. But abetter solution is to charge 50 cents for popcorn and $18 for admission. Then onlyRoger will attend, but you earn $18.

b) If you are willing to drive Gene away, you can charge Roger $18 for admission andsell popcorn for 50 cents. Your gain is $18. But a better solution is to charge $9for admission and 60 cents for popcorn. Then you earn $2 producers’ surplus atthe popcorn stand for a total of $9 + $9 + $2 = $20.

c) If you are willing to drive Roger away, you can charge Gene $25. But a bettersolution is to charge $23 admission and sell popcorn for 40 cents. You lose $6 atthe popcorn stand, so your total gain is $23 + $23− $6 = $40.

Answers to Numerical Exercises

N1. For the quantity Q, the demand price is given by P = (a − Q)/b. Thus totalrevenue is given by Q · P = (aQ−Q2)/b. Now marginal revenue is

aQ−Q2

b− a(Q− 1)− (Q− 1)2

b=

a− 2Q + 1b

≈ a− 2Q

b

when 1 unit is small.N2.a) From the answer to N1, we see that marginal revenue in markets A and B is given

by

MRA =100− 2QA

10= 10− QA

5

MRB =8− 2QB

2= 4−QB .

For any given positive Q, we have

10− Q

5> 4−Q

so thatMRA(Q) > MRB(Q),

which implies that elasticity is greater in market A than in market B.b) The monopolist sets MRA(QA) = MRB(QB) = 0. In view of the formulas for

marginal revenue in N2a), this gives QA = 50, QB = 4. Getting price from thedemand curves, we find that PA = 5, PB = 2.

10–14

c) We must solve the equations

10− QA

5=

QA + QB

21= 4−QB .

The solution is QA = 40, QB = 2. The prices are given by PA = 6, PB = 3.d) While it is true that for any given quantity, demand is more elastic in market A,

it is also true that demand in market A at the quantity 40 is less elastic than thedemand in market B at the quantity 2 . Thus in part c), the higher price is foundin market A.

The explanation of part b) is more subtle. Here the elasticity in each marketis equal to 1 at the quantity being sold. Since the elasticities in both marketsare equal, you might expect the prices in both markets to be equal. Indeed, thisexpectation is correct for any elasticity other than 1. However, for elasticity 1, theargument on pages 351–352 of the text breaks down (can you see why?) and leavesus with the possibility of different prices in the two markets.

e) If we equate the marginal cost of QA + QB with the marginal revenues of QA inmarket A and QB in market B, using the formulas for marginal revenue from parta), we write

10− QA

5=

QA + QB

3= 4−QB

which gives QA = 20, QB = −2! Obviously, this makes no sense, so let us reconsiderthe situation. The picture is as shown below (this is the analogue of Exhibit 10–10):

4

MR

MRAMRB

MC

75/4 50 54Q

P

25/4

10

4

(The scales on the axes has been distorted so that everything fits.) Now wesee the problem: At the price where MC crosses MR, there is no correspondingquantity on the MRB curve. The monopolist produces 75/4 units and sells themall in market A at a price of 65/8.

N3.a) If either were less than 1, the monopolist could simultaneously increase revenueand decrease cost by decreasing his quantity.

b) Since

30(

1− 1|ηA|

)= 10

(1− 1

|ηC |

),

we have |ηA| =3|ηC |

2|ηC |+ 1.

c)32.

10–15

Chapter Eleven:

Market Power, Collusion and OligopolyTeaching Suggestions

1) It is worth pointing out that concentration is not the same as oligopoly, andthe relationship between them is at least controversial.

2) One way in which a firm can attempt to develop a degree of market power isthrough a reputation for the quality of its products and services. There are severalpoints in this chapter where it is natural to introduce this topic. The discussion ofthe repeated prisoner’s dilemma suggests that firms would never gain from costlyattempts to maintain such a reputation.

Suppose that I operate a firm for my entire lifetime, which is three years. Inany given year I can produce either a low-quality product, or, at greater expenseto myself, a high-quality product. Consumers do not discover the quality of theproduct until after they have owned it for a year. Then it seems plausible thatI would produce high-quality products in year 1 in order to develop a reputationthat increases the demand for my products in year 2. But this is not the case. Inyear 3, I have no incentive to produce high-quality products (since it is my lastyear in business). Because everyone knows this, nothing I do in year 2 can helpmy reputation. Thus I have no incentive to produce high- quality products in year2. Because everybody knows this, nothing I do in year 1 can help my reputation.Thus I might as well produce low quality products in year 1.

On the other hand, firms clearly do produce products that are of higher qualitythan consumers are able to verify at the time of purchase. You might point thisout to your students and ask in what important way the real world fails to fit theassumptions of our model. (Two candidates for the culprit: uncertain lifetimes andcontinuous time.) Perhaps firms need infinite lifetimes to avoid the paradox, whichexplains why stores like Sears are set up to outlive their founders.

The topic arises again in the discussion of monopolistic competition. Thetext contains a few inadequate words about the welfare consequences of imperfectcompetition and mentions the social loss arising from advertising that just movescustomers from one firm to another. Counterbalancing this is the possibility thatadvertising, and the use of brand names, is a device for disseminating informationabout reputation, and thus provides firms with an incentive to produce high-qualityitems.

3) The chapter offers some examples of creative responses to regulation, andthe ensuing unexpected consequences. I have been told of a wonderful example,whose historical accuracy I have not been able to verify. In renaissance Europe,regulations forbade unlicensed actors to speak on stage. The result was the adventof modern pantomime.

4) Examples of unexpected consequences tend to make students perk up. Someother striking ones: Certain pesticides are banned because of potential health haz-ards. This raises the cost of growing fruits and vegetables, increases their price,and lowers the quantity demanded. The fall in fruit and vegetable consumption canbe more damaging to health than the pesticides were. (This example is suggestedby the biologist Bruce Ames.)

5) Another unexpected consequence: Airlines must now require infants to havetheir own seats, since this is safer than allowing them to sit on parent’s laps. Butit also greatly increases the cost of air travel for families (who must pay for the

11–1

additional seats), and consequently many travel by car instead of by air. Since cartravel is much more hazardous than air travel, the safety regulations lead to anincrease in infant deaths. (See the January/February 1991 issue of The Margin fordata supporting this scenario.)

6) If you want to stir things up, you can suggest another possible unexpectedconsequence, though this one is entirely speculative (i.e., aside from anecdotes,I know of no evidence on the magnitude of this effect). Legislation that forbidsdiscrimination in hiring increases the cost of hiring even for non-discriminators,since they may be forced to defend against a lawsuit without merit. One result isthat employers choose to hire fewer people, the equilibrium wage falls, and eventhe groups that are discriminated against can be made worse off.

11–2

Additional Problems

1. The following passage by Professor William Shepherd of the University ofMichigan appeared in the Antitrust Bulletin in the Spring of 1986. Analyze itcritically, with particular attention to the appropriateness of the analogy fromsports.

The need is to provide a reasonable degree of competitive parity,so that effective competition can occur among comparable rivals. Theimbalance between dominant and small firms usually applies only “soft”or ineffective competition to the dominant firm, while putting the smallfirms under severe pressure or threats. This problem can be seen clearlywith an analogy from sports.

Consider football “competition” between a large university and asmall college. The university could finance a 100- player squad, withplatoons and specialists at all positions, while the small college mightmanage to assemble just 30 players, most of whom would have to playboth offense and defense. Such a gross imbalance would prevent the gamefrom involving any meaningful competition. The university team wouldhave an easy time, while the small college team would merely be punished.

Severe mismatches like this are usually carefully prevented, by sepa-rating athletes and teams by their sizes, ages, sex, professional–amateurstatus, and so forth. Heavyweight boxers are not permitted to fight fly-weights, etc. Even within equalized subgroups, a variety of rules andlimits must usually be applied, in order to protect competitive parity.Indeed, in all competition (sporting and other), the need to equalize theweapons and chances is regarded as crucial.

2. Suppose that the industry supply curve for gizmos is a straight line throughthe origin, and that the demand curve is a straight line whose slope has thesame absolute value as the supply curve. If all of the gizmo manufacturerscould merge into a single firm, they could produce at zero marginal cost. Bythe efficiency criterion, should they be allowed to merge?

3. The firms that produce personal computers have never banded together toform a cartel. True or False: We may infer that at least one firm would failto benefit from the existence of such a cartel.

4. At a recent party where there were several simultaneous conversations, every-body ended up shouting to be heard over everybody else. But they could allhave been heard better (and saved wear and tear on their vocal cords) if theyhad all spoken more quietly. True or False: Therefore, all of the shouting wasirrational.

(The above makes a good problem for Chapter 12, where students are thinkingabout ill-defined property rights, or for the present chapter, where students arethinking about the unenforceability of cartels.)

5. Suppose that in a certain industry there are exactly two identical firms, withlinear upward sloping marginal cost curves. If these firms act as Cournotoligopolists, will industry output be more or less than 2/3 of the output undercompetition? How do you know?

*6. Consider an industry in which there are exactly two firms with identical flatmarginal cost curves. Price and output in the industry are determined asfollows: first firm 1 announces how much it will produce; then firm 2 decides

11–3

how much to produce; then production takes place and all output is sold at aprice read off the demand curve.a) Will the industry output be greater or less than it would be under Cournot

behavior?b) Which firm is better off: firm 1 or firm 2?

7. True or False: In the long run, a monopolistic competitor will operate at thelowest possible average cost.

8. Many bars have afternoon “Happy Hours” where drinks are sold at a reducedprice. True or False: Because bar owners voluntarily engage in this prac-tice, we may infer that a law banning Happy Hours would make bar ownersunhappy.

11–4

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 11

1. Yes. The merger will not change the price or quantity of output and thus will notchange consumer surplus, but it will lower costs so producer surplus will be higher.

2. Conceivably a vertical merger could be used to prevent resales. Suppose that amonopoly steel manufacturer wants to sell cheaply to auto makers and expensivelyto construction firms. The steel firm worries that auto makers can buy cheaplyand resell to construction firms. But if the steel firm acquires an auto maker as asubsidiary, it can sell cheaply to the auto maker while ordering it not to engage inresales.

3. This appears to form of resale price maintenance but there is no apparent mo-tivation as retail stores don’t usually compete in the candy market by providingexpertise on the product. Therefore, we don’t know the answer!

4. It would increase. It would decrease.5. Salesmen provide services to their customers in the form of education about the

product, assistance when something goes wrong, and so forth. Customers valuethese services and are willing to pay for them, but will of course prefer to getthem for free. With more than one salesman in the territory, customers can getservices from one salesman and patronize another. This removes the incentive forany salesman to offer services, which significantly lowers the value of the product.Thus salesman are granted exclusive territories, so that those customers they makehappy are certain to buy from them.

This theory predicts that exclusive territories will be found in markets forproducts where salesmen offer a significant amount of service before the product ispurchased.

****3. False. The opposite is true. The value of dealer services must exceed the cost of

producing them at the margin or the wholesaler would lower the maintained price.If the marginal value of dealer services falls off rapidly, Exhibit 11–4 would bereplaced by the following exhibit, in which the gain from retail price maintenance(B′−C) is greater than in 11–4. (Here the marginal value of dealer services at thequantity provided is P1 − P2.)

11–5

6.

Q

A

B

D

C

1 QPMQuantity

Price MC2MC1

D2

D1

Since only a few customers value the additional services, the demand curvemay not shift a constant distance right at every price, but may twist somewhatas in the above graph. In this case, social welfare can decrease. Before the pricemaintenance at PM , consumer plus producer surplus is A+B +C. After imposingPM , the marginal cost curve shifts to MC2 and demand moves to D2 (with theaddition of extra services). Now QPM is produced, and consumer plus producersurplus is A + B + D, perhaps less than before.

7a.

A

B C

Quantity

Price

D

P

Pc

M

Consumers’ surplus = A;Producers’ surplus = B;deadweight loss=C.

7b. The marginal cost curve will rise to PM as firms incur cost to produce moreextras. If anything less is produced in the way of extras, then the airline couldcompete and attract additional customers. The airlines will compete all economicprofits away.

11–6

7c.

A

B C

Quantity

Price

D

P

Pc

M

D'

X

Demand shifts upward as the services have extra value to customers. Newconsumers’ surplus = A + X; new producers’ surplus=0.

7d. Services whose marginal value exceeds their marginal cost would have been offeredunder competition. Therefore X < B and the regulation reduces net social gain.

8. False. The opposite is true. The value of dealer services must exceed the cost ofproducing them at the margin or the wholesaler would lower the maintained price.If the marginal value of dealer services falls off rapidly, Exhibit 11–4 would bereplaced by the following exhibit, in which the gain from retail price maintenance(B′−C) is greater than in 11–4. (Here the marginal value of dealer services at thequantity provided is P1 − P2.)

A

C

Quantity

Price

D

P

PD'

B'

1

0

MC'

MCP2

9. One frequently cited alternative theory is that the manufacturer is acting as anenforcer for a cartel among the dealers. Under what circumstances do you findthis theory either more or less plausible than the theory that is elaborated in thetextbook?

10. One possibility: When a new product is introduced, the manufacturer might wantto keep sales volume up even at the expense of profits, in order to gain visibilityfor the product. Retailers won’t share this incentive, since the profits they sacrificenow are compensated for by future sales that go mostly not to themselves but toother retailers.

11. False. Even if all firms would benefit, a cartel is unlikely to be enforceable.12. False, because of the Prisoner’s Dilemma. Each worker can rationally calculate

that his own voluntary contribution is unlikely to be critical in determining thesuccess of the union, and therefore chooses not to join. It is important to noticethat workers will elect not to join regardless of whether or not they believe that

11–7

others are joining. It is possible that all workers could benefit from an outsideenforcer who requires them to unionize.

13. False. Under perfect competition every firm charges the same price.14. Though the new firm faces a reduced marginal cost curve, it won’t exercise any

monopoly power because new firms could enter and charge the lower competitiveprice and attract all of the customers. Therefore, price will equal marginal costand no firms will enter. The threat of new firms entering is enough to force themerged firm to price competitively, where the new marginal cost curve intersectsthe demand curve.

15. The industry output is equal to N/(N + 1) times the output of a competitiveindustry. When N is large, the Cournot industry’s output and the competitiveindustry’s output are approximately equal.

16. Refer to Exhibit 11–9 in the text. Suppose that firm A believes that the other N−1firms together produce quantity QB . Then firm A’s marginal revenue curve is MRA

and it produces the monopoly quantity QA = (1/2) · (QC − QB). Since all firmsare identical, each produces the same quantity; thus we have QB = (N − 1) ·QA.Combining the two equations gives

QA =1

N + 1·QC

so that industry-wide output is

n ·QA =N

N + 1·QC .

As the number of firms gets large, this quickly approaches the competitive quantityQC .

17. There is no equilibrium with three vendors. The leftmost vendor will alwayswant to move right until he shares his spot with another vendor. Likewise for therightmost vendor. Thus in equilibrium, all three vendors would have to occupythe same location, and each would get 1/3 of the market. But by moving slightlyaway from that location, either vendor could secure more than 1/3 of the marketfor himself (because the distance from that location to one of the two endpointsmust exceed 1/3). Therefore there’s no equilibrium.

18. With four vendors, there’s an equilibrium in which two vendors occupy the location1/4 of the way from the left endpoint and the other two occupy the location 1/4of the way from the right endpoint. Everyone gets 1/4 of the market, and nobodycan do better by moving.

With five vendors, there is an equilibrium with two at the 1/6 mark, one inthe middle, and two at the 5/6 mark.

19.a) Any location at all is an equilibrium. Regardless of how the vendors are located,anyone who moves will lose as many customers on one side as he gains on the other.

b) They can’t be all on one semicircle. If, for example, B were located between A andC within a semicircle semicircle as shown, then B could do better by leaping toany point on the opposite semicircle. However, as long as they are not on the samesemicircle, any distribution is an equilibrium. (Try proving this! All you need toshow is that if B moves to any other point on the chord AC, he fails to improve hissituation, and if he moves to any point on the other side of the chord AC, he alsofails to improve his situation. Thus B has no incentive to move, and by the sameargument neither does A or C.)

11–8

Answers to Numerical Exercises

N1.a) 50− Psteel/2.b) Qsteel = 50− Psteel/2.c) Quantity of steel = 25 tons. Price of steel = $50 per ton. Quantity of cars = 25.

Price of cars = $75 per car.d) Quantity of cars = 50. Price of cars = $50 per car.

N2.a) A browser and an operating system sell for $33.33 each; the price of the packageis $66.66.

b) An operating system sells for $50 and a browser sells for $25; the price of thepackate is $75.

c) The price of the package is $50.N3.a) Dr. Miles sells 50 bottles of medicine at $25 per bottle. Consumers’ surplus is

$625. Producer’s surplus is $1250.b) To get the optimal quantity, maximize benefits minus costs. That is, maximize

5 ·C −C2 −C, to get C = 2. The optimal amount of service costs retailers $2 perbottle to provide, and is worth $(5 · 2− 22) = $6 per bottle to consumers.

c) If C is less than P1 − P0, retailers make a positive profit on each bottle, so it isworth increasing C to lure competitors’ customers away. Thus C rises to P1 − P0.The socially optimal value for C, by part b), is $2 per bottle.

d) At a wholesale price of P0 dollars per bottle, the retail price will be P0 + C dollarsper bottle. However, consumers, who receive $V worth of services, feel as thoughthey are paying P0 +C−V = P0− 4 ·C +C2 dollars per bottle. At this price theypurchase Q = 100− 2 · (P0 − 4 · C + C2) bottles. Thus demand is given by

Q = 100 + 8 · C − 2 · C2 − 2 · P0.

In order to maximize Q for any given P0, Dr. Miles sets C = $2 per bottle. Thatis, he requires retailers to sell for $2 per bottle over wholesale.

e) The demand curve facing Dr. Miles is now Q = 108 − 2 · P0. To maximize profit,Dr. Miles sells 54 bottles to retailers at a wholesale price of $27 per bottle. These54 bottles sell on the retail market at $29 apiece. The retail demand curve isQ = 112 − 2 · P1. The area under this demand curve, down to a price of $29 andout to a quantity of 54 is the new consumers’ surplus. That is, consumers’ surplusis $729. Producer’s surplus is $1458.

Notice that there is a net gain in social surplus of $312. (That is, ($729-$625)+($1458-$1250).) Where does this come from? First, on each of the 54bottles sold there are dealer services with a value of $6 per bottle. These servicesare produced at a cost of $2 per bottle, for a net social gain of $4 per bottle, or$216 altogether. Second, the number of bottles sold has increased from 50 to 54,and the total value of those bottles to consumers is $96. Since they are producedat zero marginal cost, this $96 is pure social gain. These two gains add up to givethe increase in social surplus: $216 + $96 = $312.

N4.a) Profit = P (100− P ) is maximized at P = 50, so this is what he charges.b) The two monopolists charge price P1 and P2. The cost to consumers of crossing

the bridge is P = P1 + P2. So Q = 100 − P = 100 − P1 − P2 travelers cross thebridge. The first monopolist earns

P1Q = P1(100− P1 − P2)

Maximizing with respect to P1 (and treating P2 as a constant, we find that themaximum occurs at

P1 =100− P2

2

11–9

and similarly

P2 =100− P1

2Solving the last two equations simultaneously gives

P1 = P2 = $33.33

c) Consumers are better off with one monopolist charging $50 than with two monop-olists charging a total of $66.67. An analogous argument shows that consumerswill pay less for their operating systems plus software if the operating system andthe software are provided by a single monopolist.

11–10

Chapter Twelve:

Game Theory

12–1

THIS PAGE SHOULD BE LEFT BLANK

12–2

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 12

1. I. (Right, Down). II. (Right, Up), (Left, Down), and (Right, Down). III. (Right,Up). IV. (Right, Down). V. None. VI. (Left, Up) and (Right, Down). VII. (Left,Up) and (Right, Down). VIII. (Left, Up).

2. I. (Right, Up), (Left, Down), and (Right, Down). II. (Right, Up), (Left, Down),and (Right, Down). III. (Right, Up). IV. (Right, Up), (Left, Down), and (Right,Down). V. (Left, Down) and (Right, Down). VI. (Right, Down). VII. (Left, Up)and (Right, Down). VIII. (Left, Down) and (Right, Down).

3. I. Yes. Yes. II. No. No. III. Yes. No. IV. Yes. Yes. V. No. No. VI. No. No.VII. No. No. VIII. Yes. No.

4. I. (Right, Down). II. (Left, Down). III. (Right, Up). IV. (Right, Down). V.(Right, Down). VI. (Right, Down). VII. (Right, Down). VIII. (Right, Down).

5. I. (Right, Down). II. (Right, Up). III. (Right, Up). IV. (Right, Down). V. (Left,Down). VI. (Right, Down). VII. (Left, Up). VIII. (Left, Up).

7.

161621

141421

55

2010

1020

912

129

1515

8. a) V. b) VIII, or the prisoner’s dilemma. d) II or VII. e) VI.9. No.

10. In 12.1, if the strong pig goes first we get (Left, Down); if the weak pig goesfirst we still get (Left, Down). In 12.2, we get (Left, Up) no matter who goes first.In 12.3, if Fred goes first we get (Left, Up) but if Ethel goes first we get (Right,Down). In 12.4, if Dot goes first, we get either (Left, Up) or (Right, Down), but ifDitto goes first, we get either (Right, Up) or (Left, Down).

11. True.12. False.

12–3

Chapter Thirteen:

External Costs and BenefitsGeneral Discussion

1) Coase’s seminal article is easy to find on the Web. In the absence of guid-ance, students find it difficult, partly because several different ideas are developedsimultaneously and it is sometimes hard to tell what the examples are supposedto illustrate. But with a bit of preliminary background—consisting, say, of class-room coverage of this chapter—the article is quite accessible. The examples areentertaining, and students like the fact that they are derived from real litigation.

2) In formulating the Coase Theorem, the text emphasizes the (short-run)equivalence of property rights and liability rules. It will come as a surprise tomany professors of economics that liability rules are not equivalent to propertyrights in the long run. After considerable confusion in the literature, this issue wascompletely clarified by H. E. Frech in the paper cited in the text. In the presenceof potential entry, a liability rule (say, all polluting steel factories must reimburseneighboring laundromats for damage done to their business; or, alternatively, laun-dromats must bear the full cost of pollution from steel factories) does not convey awell-defined property right, because the right to use the contested resource changeshands at the time of entry or exit. Thus a liability rule favoring laundromats isnot the same thing as awarding laundromat owners property rights to the air, bothbecause the laundromat owner who closes his business must sacrifice his controlover the use of the air, and because anyone who opens a laundromat can use theair for free.

Another way to say this is that a change in property rights is a lump sumtransfer, whereas a change in liability rules taxes one activity and subsidizes an-other. Thus property rights have no allocational consequences in either the shortrun or the long run, but in the long run liability rules matter.

For a starker example, consider the liability rule at a crosswalk. For simplicity,suppose that either 1) drivers are liable for all injuries to pedestrians or 2) pedes-trians are liable for all injuries to themselves. Many—I dare say most—economistswould be comfortable saying that in case 1), the pedestrians have been awardedproperty rights to the intersection, while in case 2) drivers have been awarded thosesame property rights. From this they conclude that if there were no transactionscosts between drivers and pedestrians, the rule of liability would not matter. Bothbeliefs are wrong.

It is not correct that liability rule 1) is equivalent to awarding property rights topedestrians. One reason is that while, in principle, a pedestrian in the intersectioncan charge drivers for the right to enter, he can not under this liability rule chargeanother pedestrian for the right to enter. Another reason is that his rights disappearonce he steps up onto the opposite sidewalk. Moreover the rule of liability matters:under rule 1), there will be more pedestrians in the intersection; under rule 2) therewill be more drivers. Neither outcome is efficient.

It is possible to argue that in a world with literally zero transactions costs,where every potential pedestrian could be a party to a single negotiation, the ruleof liability would not matter. But there is this crucial distinction: when there isa well-defined property right, the optimal allocation of resources can be achievedin a negotiation involving only a finite number of participants. If somebody ownsthe intersection, only he and the users who value it most must be parties to the

13–1

negotiation; all others are then excluded from the intersection by fiat. But underthe pro- pedestrian liability rule, every potential pedestrian—in principle an infinitenumber of parties—must be included in the negotiation. Anyone who is excludedcan costlessly enter the intersection and muck up the agreement.

I would like to propose what seems to me to be a useful terminology forall this (although, because it is non- standard, this terminology is not used inthe textbook). Let us define a property right to be any right of control over aresource that meets this condition: when there are no transactions costs amongfinite collections of agents, the transfer of the property right from one firm toanother has no effect on the allocation of resources. (The restriction to firms is toavoid getting tangled up in income effects.) Then part of Coase’s theorem becomes:In the short run, liability rules are property rights.

All of this comes down to a subtle collection of issues perhaps best not airedin the classroom, unless you plan to devote a lot of time to law and economics.But for those students who want to think more deeply about such things, there isfurther discussion in the text, plus as much of the above as you care to share withthem.

3) There are two additional important qualifications of the Coase Theoremthat seem to be missing from Coase’s paper. One is the need to take accountof income effects. This seems to be widely understood among economists, and Ibelieve that the discussion of free agency in the text will make it widely understoodamong students. The second is a less widely known observation, clearly expositedin a paper of Ralph Turvey (who references Buchanan and Stubblebine): As anexample in the text shows, a Pigou tax in the partial absence of transactions costscan be worse than no tax at all, and also worse than the same Pigou tax in thepresence of full transactions costs that preclude all negotiations.

4) The text surveys a variety of sources of transactions costs. Many of thesecome down, in one way or another, to the fact that some contracts are unenforceable(for example, when one party’s behavior can not be observed). That is, they comedown to principal–agent problems. An interesting feature of such problems, whichis not emphasized in the book, but which your students might want to hear about, isthat agents can be made better off if they are able to constrain their own behavior.

For example: A one-time borrower would like to default on his debt when itcomes due. Because lenders know this, they will not lend to him. If the borrowercan somehow pre-commit himself to paying, he can secure a loan. Thus, eventhough he prefers default once the loan is obtained, he is better off in a world with-out that option than in a world with it. This is an example of time-inconsistency ,which occurs when an agent can make himself better off by guaranteeing at timeA that he will not do the thing that he most wants to do at the later time B.

Time-inconsistency comes up in an important way in macroeconomics.Governments benefit from unexpected inflation, and lose when inflation is

less than expected. (See Section 9.3 in the textbook for one reason why.) Thusthey would like to engage in continual unexpected inflation, which is unfortunatelynot possible (just as the borrower can not secure loans that he has no incentiveto repay). If the government could credibly promise not to inflate, inflationaryexpectations would vanish, yielding an outcome that is preferable to the one wheregovernment is unconstrained. (See various papers of Robert Barro and DavidGordon for more on this.)

5) For another example: consider a firm owned and operated by several part-ners, each of whom has an incentive to shirk. Shirkers can not be detected. Thus

13–2

in order to prevent shirking, the partners agree that when output falls, indicatingthe presence of a shirker, everyone will be punished so severely that all shirking isdeterred. If implemented, such an agreement improves everyone’s welfare. Unfortu-nately, each potential shirker knows that the agreement will never be implemented:When the time comes to mete out the punishment, there will be a unanimous voteto change the rules.

Thus all partners are better off if they can bind themselves to really carry outthe punishment. (This harks back to the “Chinese bargemen” example of ChapterEleven.) Perhaps one way in which they do this is by giving ownership of thefirm to some outside party with the power to fire them all. The partners becomemanagers, and the outside party is called a stockholder. Maybe this is an importantreason for the separation of ownership from control.

The preceding paragraph suggests that the separation of ownership from con-trol evolves as a solution to a principal– agent problem. It is also, however, thesource of a new principal–agent problem. Will a salaried manager work as hard asone whose income is directly tied to the performance of the company? Yes, if theowners can completely monitor his performance, but no otherwise. Thus managers,and in particular corporate officers, are often encouraged or required to hold largeamounts of corporate stock, to give them an appropriate interest in the company’sperformance.

Separating management from ownership solves one principal– agent problemonly to create a new one. Large equity positions for corporate officers solve the newproblem, but create yet another one: Since the outside owners of the corporationhold diversified portfolios, they want the corporation to maximize expected returnswithout regard to risk; but at the same time, the officers, much of whose wealthis tied up in a single company, will want that company to behave in a way thatis risk-averse. Again, if owners can completely monitor officers’ behavior, there isno problem, but in the absence of perfect monitoring a problem arises. Ken Juddonce suggested to me that this makes it desirable for corporate officers to have agreat deal of personal wealth, since there is reason to believe that behavior becomesmore nearly risk-neutral as wealth increases. This theory is developed in Chapter18 of this textbook.

6) For yet another example: Publishers bring out new editions of textbooksevery three years, partly to combat the used market. In the absence of this motive,they might bring out new editions only every five years. When a student buys anew book in the first year of an edition, he pays the present value of its use tohimself plus what he will receive at resale; that is, he pays the present value ofits use to him and to the two students who will use it after him. If new editionswere spaced every five years, resale prices would be higher, students would bewilling to pay more for new books and the publisher would save on productioncosts. (Ultimately, this leads to entry and a fall in the cost of textbooks.) Thus apublisher who promised credibly to space new editions farther apart could benefitboth himself and his customers. Unfortunately, no such promise is enforceable. Thepublisher always wants to bring out a “surprise” new edition, rendering obsoletebooks that have been sold under false pretenses.

In summary, publishers and students can both gain from a bargain in whichstudents pay more for the books and publishers agree not to bring out new editions.But because publishers have every incentive to renege on their promises, the dealcan not be struck to begin with. If publishers could find a way to constrain theirown future freedom, they would want to do so.

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7) At the risk of belaboring this point, I would like to present one additionalset of time-inconsistency examples, taken from the paper of Lott and Roberts thatis cited in the text. Suppose that under a regime of rent control, a landlord and aprospective tenant want to contract for a rental fee in excess of the legal maximum.At the legal maximum, the landlord would not be willing to rent to this tenant; thusboth gain if the deal is struck. The law discourages this in a clever way: it specifiesthat the tenant can report the agreement after he has lived in the apartment, andcan sue to retrieve his “overpayments.” The law also makes it impossible for thetenant to waive this right. The landlord, knowing this, and knowing that the tenanthas no incentive to forego such behavior, will not rent to him. If the tenant couldsomehow constrain his own future behavior, he would be better off.

Another example is that of a firm and a prospective employee who want tocontract for a salary that is below the legal minimum wage. Here again, if theemployee can sue for back wages ex post, then there can be no employment. Buthere Lott and Roberts suggest a solution. Suppose that the potential employee hascommitted some crime that would surely come to light in the process of collectingback wages; suppose in particular that the employee is an illegal alien. This guar-antees that he will not exercise his “rights” in this matter and makes it possiblefor him to be hired. It follows that a general amnesty for illegal aliens would makemany illegal aliens worse off!

8) There is much more to be said on the subject of law and economics, andmuch of it can be found in the references in the text. One particularly interestingexample, due to Posner, concerns the award of punitive damages. By and large,punitive damages are not permitted in negligence cases. Posner argues that thisis consistent with the hypothesis that the common law fosters efficiency, since it isappropriate for tortfeasors to pay for the social costs of their actions and not more.He also makes a related point which is particularly appropriate here:

Punishment for negligence would close an important safety valve inthe negligence system. A standard of care is necessarily a crude approx-imation to optimality. Allowing enterprises a choice whether to complyor pay the social costs of violation may permit a closer approximation.Suppose there is a rule that a dam owner is responsible for flood dam-age unless his dam is at least 16 feet high. Presumably the rule reflectsa judgment that the cost of raising the dam is less than the cost of thefloods that a lower dam would fail to contain. One owner thinks the ruleis incorrect. He estimates that the only flood likely to occur is one thatwould swamp a 16-foot dam and therefore that he can save money byviolating the rule. Courts are not infallible and we give maximum play toindividual judgment if we let the dam owner act on his estimate. If he iswrong he will have to pay a judgment, but if he is correct an unnecessaryexpenditure on dam building will have been saved.*

Pedagogically, this is a nice topic to cover because it ties in the present materialwith the material on knowledge in society from Chapter Nine. Those who own damsare likely to have better information about local conditions than those who makelaws, and we want this information taken into account when dams are or are notbuilt. Punitive damages constitute an artificial incentive to ignore such informationand are therefore contraindicated.

* Posner, A Theory of Negligence.

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9) If you cover the material on the Good Samaritan Rule, you might wantto mention the “last clear chance doctrine.” In the Ploof case, the court heldthat the owner of a dock can not deny its use to a ship in trouble if the ship hasno alternative means to rescue itself. By denying the use of the dock, its ownerbecomes liable for damage to the ship. The logic here seems contrary to that ofthe Good Samaritan Rule, and bolsters the claim that the Good Samaritan Ruleis an isolated aberration in its apparent tolerance of inefficiency.

10) If you have the luxury of being able to spend a significant amount of timeon law and economics, there are a host of issues you can raise regarding both themeaning and the desirability of an efficiency standard. Steven Margolis in theJournal of Legal Studies (approximately 1985) poses the following conundrum: Aand B live on adjoining properties. B wants to build a wall along the property line,and values such a wall at $50 more than the cost of building it. A is a studentwho knows that he will have a high future income, but can not borrow against thisbecause of imperfect capital markets. If A could borrow against his future income,he would be willing to pay $100 to prevent the wall from going up, but givenhis current budget constraint he is only willing to pay $10. Under an efficiencystandard, should B be allowed to build the wall?

One common formulation of the efficiency standard is that courts should seekto achieve that allocation of resources that would come about in a world with notransactions costs. According to this formulation, the wall should be prohibited,since in a world without transactions costs, capital markets would be perfect and Awould bribe B not to build the wall. But, as Margolis points out, this is probablynot the outcome that is intended by those who formulate the standard in this way.The fact of the matter is that capital markets are imperfect and it is not withinthe court’s power to change that fact. Taking this as given, the efficient outcomeis for B to build the wall.

There is room for much argument on either side of this issue. I imagine thatwith the right class—one where the students are bright, interested in the law, andintellectually curious—you could generate a quite lively discussion on this topic.I have done so successfully with graduate students, but have never tried it withundergraduates.

11) Continuing to explore the efficiency standard, there is another conundrumthat seems to come up repeatedly in these discussions. I am not sure of its source(though I believe that it is referenced in Landes and Posner’s book on tort law,which I do not have in front of me as I write this). Consider a man who would liketo have sexual intercourse with a particular woman and would be willing to pay$100,000 to do so; she would be willing to pay $50,000 to prevent him. Should hethen be allowed to commit rape? This is too easy: there is no need to allow coercionhere because the efficient outcome will be reached through voluntary transactions.But now what if coercion is essential to the man’s enjoyment? The act is worthlessto him unless he knows that the woman is not being compensated. Here theefficiency standard seems to mandate sanctioning the rape, which is a conclusionthat most people find distasteful. I believe that Posner has tried to dispense withthis one by claiming that for $100,000 the man should certainly be able to find awoman who will put on a convincing show of being forced, but this really evadesthe question. We can hypothesize that the man requires actual coercion for hispleasure and that nothing else will do.

Is there a way out of this? I don’t know. I have never tried raising this issueor anything like it in class, and I would not do so unless I had budgeted several

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weeks for law and economics. This rules out bringing it up in any standard microcourse, but for more specialized courses I think it is an appropriate example.

12) Steve Cheung’s article on tenant farming in the Journal of Political Econ-omy is another good source of examples for the material in this chapter.

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Additional Problems

1. Explain the reason for the following phenomenon: At parties in which severalconversations are simultaneously in progress, it is common for everybody tobe shouting to be heard over everybody else, whereas they would all be heardbetter (and save wear and tear on their vocal chords) if they all spoke in normaltones of voice.

2. True or False: A profit-maximizing monopolist whose firm was a source ofnegative externalities might produce exactly the socially optimal level of out-put.

3. Consider a competitive industry in which there is an upward-sloping long runindustry supply curve due to a factor price effect. Explain why the privatemarginal cost curve of the firms in the industry lies above the social marginalcost curve. Which of these marginal cost curves coincides with the long runindustry supply curve?

The next twelve problems (#4 through #15) have multiple parts that can beassigned independently of each other. Thus each of these problems is really threeor four different problems. Problems 4a, 4b, and 4c are essentially identical toproblems 1, 2 and 3 in the textbook; Problem 7a is essentially identical to problem4 in the textbook.

4. Suppose Japanese cars and American cars are identical from their owners’point of view, but Japanese cars cause harmful pollution while American carsdo not. Each American owner of a Japanese car imposes $1,000 worth ofpollution costs on his neighbors. Suppose the U.S. supply and demand curvescross at a price of $10,000, but Americans can buy as many cars as they wantto from Japan at $7,000 apiece.a) Suppose the U.S. government imposes a tariff of $1,000 apiece on all

Japanese cars sold in the United States. Illustrate the gains and lossesto all relevant groups of Americans. Does the tariff increase or decreasesocial welfare? By how much?

b) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in theUnited States, both foreign and domestic. Illustrate the gains and lossesto all relevant groups of Americans. Does the tax increase or decreasesocial welfare? By how much?

c) Suppose the U.S. government offers a subsidy of $1,000 per car to allAmerican car makers. Illustrate the gains and losses to all relevant groupsof Americans. Does the subsidy increase or decrease social welfare? Byhow much?

5. Suppose Japanese cars and American cars are identical in every way. Theproduction of American cars creates pollution costs of $1,000 per car. Thereare no pollution costs associated with driving cars or with the manufacture ofJapanese cars. The U.S. supply and demand curves cross at a price of $10,000,but Americans can buy as many cars as they want to from Japan at $7,000each.a) Suppose the U.S. government imposes an excise tax of $1,000 on every

car manufactured in the United States. Illustrate the gains and losses toall relevant groups of Americans. Does the excise tax increase or decreasesocial welfare? By how much?

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b) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in theUnited States, both foreign and domestic. Illustrate the gains and lossesto all relevant groups of Americans. Does the tax increase or decreasesocial welfare? By how much?

c) Suppose the U.S. government offers American car buyers a subsidy of$1,000 for each imported car they buy. (There is no subsidy for domesticcars.) Suppose also that American car manufacturers are forbidden to sellcars to foreigners. Illustrate the gains and losses to all relevant groups ofAmericans. Does the subsidy increase or decrease social welfare? By howmuch?

6. Suppose Japanese cars and American cars are identical in every way. EachAmerican who owns a car (regardless of whether that car is Japanese or Amer-ican) imposes $1,000 worth of pollution costs on his neighbors. Suppose theU.S. supply and demand curves cross at a price of $10,000, but Americans canbuy as many cars as they want to from Japan at $7,000 apiece.a) Suppose the U.S. government imposes a tariff of $1,000 apiece on all

Japanese cars sold in the United States. Illustrate the gains and lossesto all relevant groups of Americans. Does the tariff increase or decreasesocial welfare? By how much?

b) Suppose the U.S. government imposes an excise tax of $1,000 on everycar manufactured in the United States. Illustrate the gains and losses toall relevant groups of Americans. Does the excise tax increase or decreasesocial welfare? By how much?

c) Suppose the U.S. government imposes a tax of $1,000 on all cars sold in theUnited States, both foreign and domestic. Illustrate the gains and lossesto all relevant groups of Americans. Does the tax increase or decreasesocial welfare? By how much?

7. There are two mange cures on the market: Mange-Away, which is made inthe United States and sold by producers who have an upward-sloping supplycurve, and Look-Ma-No-Mange, which is made in Mexico and available in anyquantity at $5 a dose. The supply curve for American Mange-Away crossesthe (U.S.) demand curve for mange cures at a price of $8 per dose.To the individual mange sufferer, Mange-Away and Look-Ma-No-Mange areinterchangeable products. But although American Mange-Away cures the dis-ease, it also leaves the patient contagious to others. Mexican Look-Ma-No-Mange both cures the disease and renders the patient noncontagious; thus,every user of Look-Ma-No-Mange confers $1 worth of external benefits on hisneighbors.a) Suppose the U.S. government imposes an excise tax of $1 on every dose

of Mange-Away produced in the United States. Illustrate the gains andlosses to all relevant groups of Americans. Does the excise tax increase ordecrease social welfare? By how much?

b) Suppose the U.S. government offers American mange sufferers a subsidyof $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There isno subsidy for American Mange-Away.) Suppose also that the makers ofMange-Away are free to sell their products to foreigners at the going worldprice. Illustrate the gains and losses to all relevant groups of Americans.Does the subsidy increase or decrease social welfare? By how much?

c) Suppose the U.S. government offers American mange sufferers a subsidyof $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There is

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no subsidy for American mange-away.) Suppose also that the makers ofMange-Away are forbidden to sell their product to foreigners. Illustratethe gains and losses to all relevant groups of Americans. Does the subsidyincrease or decrease social welfare? By how much?

d) Suppose the U.S. government offers American mange sufferers a subsidyof $1,000 for every dose of mange cure they buy. Illustrate the gains andlosses to all relevant groups of Americans. Does the subsidy increase ordecrease social welfare? By how much?

8. There are two mange cures available: Mange-Away, which is made in theUnited States and sold by producers who have an upward-sloping supply curve,and Look-Ma-No-Mange, which is made in Mexico and available in any quan-tity at $5 a dose. The supply curve for American Mange-Away crosses the(U.S.) demand curve for mange cures at a price of $8 per dose.To the individual mange sufferer, Mange-Away and Look-Ma-No-Mange are in-terchangeable products. But although Mexican Look-Ma-No-Mange cures thedisease, it also leaves the patient contagious to others. American Mange-Awayboth cures the disease and renders the patient noncontagious; thus, every userof Mange-Away confers $1 worth of external benefits on his neighbors.a) Suppose the U.S. government imposes a tariff of $1 per dose on all Mexican

Look-Ma-No-Mange in the United States. Illustrate the gains and lossesto all relevant groups of Americans. Does the tariff increase or decreasesocial welfare? By how much?

b) Suppose the U.S. government offers a subsidy of $1 per dose to the Amer-ican manufacturers of Mange-Away. Illustrate the gains and losses to allrelevant groups of Americans. Does the subsidy increase or decrease socialwelfare? By how much?

c) Suppose the U.S. government offers American mange sufferers a subsidyof $1,000 for every dose of mange cure they buy. Illustrate the gains andlosses to all relevant groups of Americans. Does the subsidy increase ordecrease social welfare? By how much?

9. Two mange cures are available: Mange-Away, which is made in the UnitedStates and sold by producers who have an upward-sloping supply curve, andLook-Ma-No-Mange, which is made in Mexico and available in any quantityat $5 a dose. The supply curve for American Mange-Away crosses the (U.S.)demand curve for mange cures at a price of $8 per dose. Mange-Away andLook-Ma-No-Mange are interchangeable products in every way.Both products not only the cure the disease; they also render the patient non-contagious. Thus any user of either mange cure confers $1 worth of externalbenefits on his neighbors.a) Suppose the U.S. government offers American mange sufferers a subsidy

of $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There isno subsidy for American Mange-Away.) Suppose also that the makers ofMange-Away are free to sell their products to foreigners at the going worldprice. Illustrate the gains and losses to all relevant groups of Americans.Does the subsidy increase or decrease social welfare? By how much?

b) Suppose the U.S. government offers American mange sufferers a subsidyof $1 for each dose of Mexican Look-Ma-No-Mange they buy. (There isno subsidy for American mange-away.) Suppose also that the makers ofMange-Away are forbidden to sell their product to foreigners. Illustratethe gains and losses to all relevant groups of Americans. Does the subsidy

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increase or decrease social welfare? By how much?c) Suppose the U.S. government offers a subsidy of $1 per dose to the Amer-

ican manufacturers of Mange-Away. Illustrate the gains and losses to allrelevant groups of Americans. Does the subsidy increase or decrease socialwelfare? By how much?

d) Suppose the U.S. government offers American mange sufferers a subsidyof $1,000 for every dose of mange cure they buy. Illustrate the gains andlosses to all relevant groups of Americans. Does the subsidy increase ordecrease social welfare? By how much?

10. Suppose the price at which American car makers’ supply curve crosses theAmerican demand curve is $10,000 per car. However, manufacturers can sellas many cars as they want to in the world market at a price of $15,000 percar. Every time a car is produced in the United States, the factory creates$2,000 worth of pollution.a) Suppose the U.S. government imposes an export tax of $2,000 on all cars

that are shipped abroad. Illustrate the gains and losses to all relevantgroups of Americans. Does the tariff increase or decrease social welfare?By how much?

b) Suppose the U.S. government imposes an excise tax of $2,000 on every carmanufactured in the United States, regardless of where that car is sold.Suppose also that U.S. citizens are free to buy cars on the world marketif they want to. Illustrate the gains and losses to all relevant groups ofAmericans. Does the excise tax increase or decrease social welfare? Byhow much?

c) Suppose the U.S. government imposes an excise tax of $2,000 on every carmanufactured in the United States, regardless of where that car is sold.Suppose also that U.S. citizens are prohibited from buying foreign cars.Illustrate the gains and losses to all relevant groups of Americans. Doesthe excise tax increase or decrease social welfare? By how much?

d) Suppose the U.S. government imposes a sales tax of $2,000 on all cars soldin the United States. Illustrate the gains and losses to all relevant groupsof Americans. Does the tax increase or decrease social welfare? By howmuch?

11. Suppose the price at which American car makers’ supply curve crosses theAmerican demand curve is $10,000 per car. However, manufacturers can sellas many cars as they want to in the world market at a price of $15,000 percar. Every American who drives a car imposes $2,000 worth of pollution costson his neighbors.a) Suppose the U.S. government imposes an excise tax of $2,000 on every car

manufactured in the United States, regardless of where that car is sold.Suppose also that U.S. citizens are prohibited from buying foreign cars.Illustrate the gains and losses to all relevant groups of Americans. Doesthe excise tax increase or decrease social welfare? By how much?

b) Suppose the U.S. government imposes a sales tax of $2,000 on all cars soldin the United States. Illustrate the gains and losses to all relevant groupsof Americans. Does the tax increase or decrease social welfare? By howmuch?

c) Suppose the U.S. government offers American car makers a subsidy of$2,000 for each car they export. (There is no subsidy for cars sold in theU.S.) Illustrate the gains and losses to all relevant groups of Americans.

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Does the subsidy increase or decrease social welfare? By how much?

12. Suppose the price at which American car makers’ supply curve crosses theAmerican demand curve is $10,000 per car. However, manufacturers can sellas many cars as they want to in the world market at a price of $15,000 percar. There are no external costs associated with either car production ordriving. However, whenever cars are exported they are sent via ships thatpollute United States coastal waters, causing pollution damage that amountsto $2,000 per exported car.a) Suppose the U.S. government imposes an export tax of $2,000 on all cars

that are shipped abroad. Illustrate the gains and losses to all relevantgroups of Americans. Does the tariff increase or decrease social welfare?By how much?

b) Suppose the U.S. government imposes an excise tax of $1 on every doseof Mange-Away produced in the United States. Illustrate the gains andlosses to all relevant groups of Americans. Does the excise tax increase ordecrease social welfare? By how much?

c) Suppose the U.S. government offers American car buyers a subsidy of$2,000 for every car they buy. Illustrate the gains and losses to all relevantgroups of Americans. Does the subsidy increase or decrease social welfare?By how much?

13. Suppose that cookies are produced in the United States and sold both do-mestically and abroad. American consumers will buy only American cookies.Cookie production creates pleasant aromas, so that every time a box of cookiesis produced in the U.S., those who live near the factores enjoy $2 worth of ben-efit. The benefit is the same regardless of whether the cookies are ultimatelysold in the U.S. or abroad.The price at which the cookie manufacturers’ supply curve crosses Americans’demand curve is $5 per box. Manufacturers can sell as many cookies as theywant to in the world market at a price of $10 per box.a) Suppose the U.S. government offers American cookie makers a subsidy

of $2 for each box of cookies they export. (There is no subsidy for carssold in the U.S.) Illustrate the gains and losses to all relevant groups ofAmericans. Does the subsidy increase or decrease social welfare? By howmuch?

b) Suppose the U.S. government offers American cookie makers makers asubsidy of $2 for each box of cookies they produce. Illustrate the gainsand losses to all relevant groups of Americans. Does the subsidy increaseor decrease social welfare? By how much?

c) Suppose the U.S. government offers American cookie buyers a subsidy of$2 for every box of cookies they buy. Illustrate the gains and losses toall relevant groups of Americans. Does the subsidy increase or decreasesocial welfare? By how much?

14. Suppose each can of deodorant that is consumed in the U.S. creates $3 worthof positive externalites to Americans. Deodorant used abroad does not conferpositive externalities on Americans.The price at which the American deodorant supply curve crosses Americans’demand curve is $5 per can. Manufacturers can sell as much deodorant asthey want to in the world market at a price of $10 per can.a) Suppose the U.S. government imposes an export tax of $3 on every can of

deodorant shipped abroad. Illustrate the gains and losses to all relevant

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groups of Americans. Does the tariff increase or decrease social welfare?By how much?

b) Suppose the U.S. government offers American deodorant manufacturers asubsidy of $3 for every can of deodorant they produce, regardless of wherethat can is sold. Illustrate the gains and losses to all relevant groups ofAmericans. Does the subsidy increase or decrease social welfare? By howmuch?

c) Suppose the U.S. government offers American consumers a subsidy of $3for every can of deodorant they buy. Illustrate the gains and losses toall relevant groups of Americans. Does the subsidy increase or decreasesocial welfare? By how much?

15. The price at which Americans’ demand curve for blue jeans crosses the man-ufacturers’ supply curve is $10. Manufacturers can sell as many blue jeans asthey want to in the world market at a price of $15.There are no externalities involved in the production or wearing of blue jeans,but there is an externality when American blue jeans are are shipped abroad:Blue jeans create good will toward Americans and allow us to reduce ourdefense expenditures. Each pair of American blue jeans sold abroad reducesthe U.S. defense budget by $2.a) Suppose the U.S. government offers American clothing manufacturers a

subsidy of of $2 for each pair of blue jeans they produce. Illustrate thegains and losses to all relevant groups of Americans. Does the subsidyincrease or decrease social welfare? By how much?

b) Suppose the U.S. government offers American clothing manufacturers asubsidy of of $2 for each pair of blue jeans they export. Illustrate thegains and losses to all relevant groups of Americans. Does the subsidyincrease or decrease social welfare? By how much?

c) Suppose the U.S. government imposes a sales tax of $2 a pair on all bluejeans sold in the United States. Illustrate the gains and losses to allrelevant groups of Americans. Does the tax increase or decrease socialwelfare? By how much?

d) Suppose the U.S. government passes a law requiring all American con-sumers to buy their blue jeans from abroad. Illustrate the gains andlosses to all relevant groups of Americans. Does the law increase or de-crease social welfare? By how much?

16. Snidely Whiplash owns a competitive factory that produces widgets for saleon the world market. He also owns several houses near the factory, which herents to identical tenants. The factory pollutes the air. The following diagramshows the world price of widgets and the social and private marginal costcurves at Snidely’s factory.

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A

B

C

D

MCMC PSP

QQ Q0 1

world priceof widgets

a) Is it more profitable for Snidely to produce Q0 widgets or Q1 widgets?(Be sure to account both for the producer surplus at the widget factoryand the amount he’ll be able to charge for housing.)

b) How and why might your answer change if the residents are not all iden-tical?

17. The widget industry is competitive. Widget factories pollute the neighbor-hoods where they are located. The attached diagram shows the demand,private and social marginal cost curves for the industry. The cost of movingthe neighbors elsewhere is B + C + (1/2)D.

A

BC

D

MC MCPS

Q

P

D

Q Q0 1a) Suppose widget firms face no penalty for polluting. How many widgets

are produced? Do the neighbors move away? Why or why not? What isthe social gain?

b) Suppose widget firms are subject to a Pigou tax. How many widgets areproduced? Do the neighbors move away? Why or why not? What is thesocial gain?

c) According to the efficiency criterion, is the Pigou tax a good policy?

18. Whenever you purchase a stereo, you bid the price of stereos up, which hasnegative consequences for all other purchasers of stereos. Does it follow thatthe social cost of purchasing a stereo is greater than your private cost? Is thisan argument for taxing the purchase of stereos?

19. “According to the Coase Theorem, freed slaves will continue to do the samework that they did under slavery.”a) Explain the argument underlying this assertion.b) What important factors does the argument overlook?

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c) In what general circumstances would you expect the quoted statement tobe true? To be false?

20. A set of railroad tracks runs through the town of Nwot, and long freight trainsoften block the flow of traffic. The town government has gone to court torequest the right to regulate the passage of the trains. Under various assump-tions, discuss the senses in which the judge’s decision matters and the sensesin which it might not. What factors should the judge take into account inrendering his decision?

21. Courts have recently been called upon to decide whether surrogate motherhoodcontracts should be enforced. Under these contracts, a couple hires anotherwoman to bear a child which the couple adopts as soon as it is born. Oftenthe contract contains a clause forbidding the biological mother to have anycontact with the child once it is adopted. Sometimes the biological motherchanges her mind after the child is born and attempts to acquire the right tovisit the child, or even raise it as her own.The court must decide whether surrogate motherhood contracts should beenforceable as written, or whether the biological mother should have the rightto change her mind. What effect does the court’s decision have on the numberof surrogate motherhood contracts that get written? What effect does it haveon the number of surrogate mothers who eventually get to visit or raise theirbiological children? Who benefits from a decision in favor of enforcing thecontracts and who benefits from the opposite decision? If you were the judge,what would you decide and why?

22. Bakers produce cookies at a private marginal cost of 5, but a social marginalcost of only 3, since each cookie being baked creates 2 worth of pleasant aromasfor bypassers to enjoy. Assuming a competitive market for cookies, use a graphto show all of the social gains from the existence of the cookie industry. Nowsuppose that bakers are offered a subsidy of 2 pr cookie baked and recomputethe social gains. Is the subsidy a social improvement?

23. Discuss the pros and cons of the following statement: “Entry to decreasingcost industries should be subsidized by the government”.

24. The following graph depicts the demand for widgets and the social and privatemarginal costs of producing widgets. The externalities are in the form ofpollution which is breathed by people who live near widget factories.

A

BC

D

Quantity

Price

Demand

MCMC

privatesocial

Suppose the government imposes a rule that says widget firms must pay a penaltyequal to the pollution costs that are imposed on the neighbors (firms that haveno neighbors pay no penalties). The penalties are used to make welfare payments

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to people who do not live near widget firms. Assume also that all neighbors areidentical. Then fill in the blanks in the following sentences:

a) The neighbors will choose to move if the cost of moving is less than.

b) According to the efficiency criterion, the neighbors should move if the costof moving is less than .

c) According to the efficiency criterion, it would be better to have no penaltyat all for polluting if the cost of moving is between and

.

25. A competitive firm pollutes the air. Consider three possible legal rules:

A. The firm can pollute as much as it wants to with no penalty.B. The firm must pay a fine equal to the amount of damage it causes; this

fine is paid to the mayor’s brother.C. The firm must compensate the neighbors for all the damage it causes.

Suppose it is extremely expensive for the neighbors to move away or to protectthemselves from the pollution in any way. Then which of the three legal rulesabove leads to an efficient outcome? Answer in each of the following fourscenarios, and justify your answers:a) Very high transactions costs all around.b) Zero transactions costs between the firm and the neighbors; very high

transactions costs between the firm and the mayor’s brother.c) Very high transactions costs between the firm and the mayor’s brother;

zero transactions costs between the firm and the neighbors.d) Zero transactions costs all around.e) Repeat parts a) through d) on the assumption that it is almost (but not

quite) costless for the neighbors to move away.

26. A competitive firm creates negative externalities by polluting the air. Trans-actions costs are high, so there is no possibility of negotiation between the firmand the affected neighbors.

B

C

D

Quantity

Price

Demand

MCMC

privatesocial

Three policies are being considered:A. The firm is given the legal right to pollute all its wants to, with no penalty.B. The firm is subject to a Pigou tax (i.e. an excise tax equal to the exter-

nality); the proceeds from the Pigou tax are used to provide benefits topeople 3,000 miles away.

C. The immediate neighbors are entitled to compensation from the firm forall damage caused by pollution.

In each of the following circumstances, determine which of the three policies leadto efficient outcomes and which lead to inefficient outcomes.

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a) The neighbors’ cost of moving is less than Cb) The neighbors’ cost of moving is between C and C + D.c) The neighbors’ cost of moving is between C + D and B + C + D.d) The neighbors’ cost of moving is greater than B + C + D.

(Hint: In each case figure out what the efficient outcome is- –should the neigh-bors move or shouldn’t they?—and then figure out which of the policies will yieldthat outcome and which won’t.)

27. A competitive firm pollutes the air. The following graph shows the demandfor the firm’s product and the private and social marginal cost curves. Thenumbers in the graph indicate areas.

a) Suppose:• there is no legal penalty for polluting• there are no transactions costs, and• it is impossible for the neighbors to move.

What quantity does the firm produce? Give a concrete description of a dealthat might be struck between the firm and the neighbors (including the exactamount of money that changes hands). What is the social gain (your answerto this should be a number).

b) Suppose:• the firm is required to reimburse the neighbors for pollution damage• there are no transactions costs, and• it is impossible for the neighbors to move.

What quantity does the firm produce and why?

c) Suppose:• the firm is required to pay a Pigou tax for pollution damage• there are no transactions costs between the firm and the neighbors who

breathe the pollution; however, it is impossible for the firm or the neigh-bors to negotiate with the recipients of the tax revenue.

• it is impossible for the neighbors to move.What can you say about the quantity produced by the firm? What can yousay about the social gain in this situation compared to part a)?

d) Suppose:• transactions costs are so high that negotiation is impossible• it would cost the neighbors $6 to move.• there is no legal penalty for pollution.

Do the neighbors move? Why or why not? What is the social gain?

e) Suppose:

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• transactions costs are so high negotiation is impossible• it would cost the neighbors $6 to move• the firm is legally required to reimburse the neighbors for all pollution

damage.Do the neighbors move? Why or why not? What is the social gain?

28. Baseball games attract more fans when there is suspense regarding the out-come. They also attract more fans when the team has been winning. Thus ateam’s revenues depend in complicated ways on the qualities of other teamsin the league: If the other teams are either much better or much worse thanthe home team, there is no suspense, and if they are all just a bit better, thehome team loses more often than it wins. Thus whenever a team improvesits performance, the revenues of all other teams are affected in complicatedways. Assume that teams can improve their quality through costly invest-ments. What determines a teams’ optimal investment in quality from thepoint of view of the league as a whole? How does this optimal investmentdiffer from the investment that teams would choose if they maximized onlytheir own revenues? Suppose that it is costly for teams to negotiate amongthemselves whenever one team wants to take action to improve itself, butthat it is costless for teams to lay down some general ground rules. Whatsorts of ground rules might you expect to observe? Sometimes two teams canboth improve themselves through a mutually beneficial trade. What sorts ofrestrictions on trading might you expect to observe?

This is intended as a “thought problem,” and I do not have any specific answersin mind. I suspect that the problem is very difficult.

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 13

1.

$5 A

B

C

D

MCMCprivate

social

Q Qe o

a) He produces Qe. His PS is A; thegain to the orchard owners is B.

b) A subsidy leading him to produceQo would increase social gain by C .PS is A+B+C , gain to orchard ownersis B+ C +D, cost to taxpayers is B+ C+D.

c) In the sense that Qo will be thequantity produced with or without thesubsidy, because the orchard ownerswill pay the beekeeper to raise morebees if necessary..Quantity

Price

2. It is impossible to tell. If the neighbors remain in the area and do nothing to protectthemselves from the noise, then the social cost of the expansion is $350 ($50 to thetaxpayers and $10 × 30 = $300 to the neighbors), while the social benefit is only$300. That’s a reduction in social welfare. But perhaps the neighbors will eithersoundproof their houses or move to a different area at a cost substantially less than$10 per neighbor. In that case, the expansion could improve social welfare.

3. True, since students would have a reduced incentive to take precautions likesticking to well-lighted paths, staying alert to their surroundings, and learningself-defense techniques. If there were no transactions costs between the universityand the students, the answer would be false, since the university would offer topay students enough to induce them to take exactly the same amount of care thatstudents take when the university is not liable. However, the key transactionscost here is the unobservability of the students’ behavior. Unless the universityconstantly monitors the students, they will agree to the deal, accept the money,and still behave recklessly. This transactions cost prevents the deal from beingstruck in the first place.

4. False. Married couples split the housework in the way that minimizes joint costsand then subsidize each other through side payments. There might be an exceptionfor couples who are already married when the law comes into effect, because thosehusbands experience a negative income effect and so might end up choosing lessleisure and more housework. But for couples who are not yet married and stillnegotiating the terms of their relationship, there should be no effect.

5. One could as easily assert that Farmer Smith should bear the costs of the damage,since it is caused by the lettuce. Removing the lettuce would solve the problem aswell as removing the rabbits would.

6. True, in the sense that every monopolist would produce the competitive quantity.This is the quantity that maximizes social surplus, so there is always a deal thatcan be struck between the monopolist and his customers whereby both benefit fromthis behavior.

7. Assume first that there are no transactions costs between the beekeeper and thecar dealer. In that case, your decision does not matter in the sense that it has no

13–19

effect on the number of bees that are kept, the procedures used to contain the bees,the number of cars sold, the investment in tents by the car dealer, whether the cardealer will move away, and so forth. It matters in the sense that the beekeeperprefers one decision and the car dealer another.

Alternatively, if there are transactions costs, then all of the things that wereleft unaffected in the preceding paragraph can indeed be affected. A ruling for thecar dealer could induce the beekeeper to rein in his bees (say with better netting)or to scale back his operation, while a ruling for the beekeeper could induce thecar dealer to erect a tent or to move.

Since there are only two parties and they are in close proximity, the assumptionof no transactions costs seems the more reasonable.

If a large collection of motorists is involved, the transactions costs can becomeconsiderable. It is difficult for the motorists to collectively negotiate with thebeekeeper, particularly if different motorists are affected on different days. Manymotorists might not even recognize the source of the problem.

In this case, some factors relevant to the decision are: How much would it costthe beekeeper to prevent his bees from flying over the roadway, either by containingthem or moving elsewhere? What alternatives are available to motorists? Can theyeasily take a different route or would it be very costly to do so? How much damageto the bees actually do to the cars, and how much does it cost motorists to copewith this damage, either by having it repaired or by deciding to tolerate it?

8. False. Monopolies underproduce; firms that create externalities overproduce. Itmakes no sense to complain that a firm is simultaneously producing too little andtoo much. In fact, these problems tend to cancel each other.

9.a) If there are low costs of transacting, the rules don’t affect whether your roommatedecides to play his stereo. They do affect who might have to bribe whom.

b) In this case it would most likely be difficult to make arrangements (or contracts)with a large number of people in your dormitory. Thus, transactions would at leastas high as in part a. and the rules are more likely to effect the outcome.

c) Some considerations are: Would it be easy for you to study elsewhere, or to wearearplugs? Could your roommate find some other location or activity that he wouldenjoy almost as much? And how much does it really matter whether you passeconomics?

10.a) Only (iii) and (iv) are affected.b) It would be a mistake to rule against the laundromat if the steel factory could easily

install filters in its smokestacks to prevent soot from falling on the laundromat. Itwould be a mistake to rule for the laundromat if the laundromat could easily erectan awning to protect against soot.

11.a) If there are no transactions costs between the employees and the firm, then thecourt’s ruling has no effect on the number of children the employees will have, theextent of the safety equipment installed by the company, or the ultimate numberof birth defects. The assumption of no transactions costs contains the assumptionthat the workers are as aware of the problem as the company is, and that allcontracts between the workers and the company are enforceable.

b) Yes, because this introduces a large transactions cost. As long as the workersare not entitled to compensation from the company, there is no problem, becauseworkers can “bribe” the company to install safety equipment and can verify thatthe equipment has been installed. However, if the company is liable for birthdefects, it might want to “bribe” employees to forego having children in the future.Since such a contract is unenforceable, the optimal balance of safety equipment

13–20

and foregone reproduction might not be achieved.c) This remedies the potential problem in part b), since it once again makes the

relevant contracts enforceable. This puts us back into the situation of part (a).Without transactions costs, the contracts will only be signed if the cost to employeesof signing them is less than the cost to the firm of preventing the radiation exposure.The fact that the contracts are possible insures that the court’s decision will notmatter.

d) Now we are once again in the realm of transactions costs. In this case, there is acase to be made for absolving the company of liability. If the company is not liablefor birth defects, it still has every incentive to install safety equipment, since theworkers can still pay bribes. However, if the company were fully liable, workerswould have no incentive to practice restraint in reproduction, and the number ofbirth defects could be more than is optimal.

In short, a reasonable expectation is that there will be an optimal number ofbirth defects unless both the firm is liable for damage and the sterilization require-ment is disallowed. If the law adopts both these positions, then the number ofbirth defects could go up.

12.

A BC D

Quantity

Price

E F G H$8000$7000

No Tariff TariffCS A+B+C+D+E+F+G A+BPS I C+D+IExternality D+E+F+G+H FTariff Revenue — F

A+B+C+I-H A+B+C+D+I

The tariff creates a net gain of D + H.13. Refer to the graph for problem 3. With the tax, CS = A + B, PS = I, the

externality is D + E + F , and the tax revenue is C + D + E + F , for a total ofA+B+C +I. The tax creates a net social gain of H, and so is better that nothing,but not as good as the tariff of problem 3.

14. Refer to the graph for problem 3. With the subsidy, Americans will still pay$7,000 for cars, but American carmakers will charge a price of $8,000. Thus CS =A + B + C + D + E + F + G, PS = C + D + I, the externality is F + G + H, andthe cost of the subsidy is C +D +E, for a total of A+B +C +D +−I−H, whichamounts to a net social gain of D.

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15.

A BC D

Quantity

Price

E F G H$5$4

S

D

No Sales Tax Sales TaxCS A+B A+BPS C+D+I IExternality F D+E+FTax Revenue — C

A+B+C+D+F+IA+B+C+D+E+F+I

The sales tax creates a net gain of E.16. Under monopoly, social gain is A+B +C +D+F +G. Under competition, social

gain is A + B + C + D + E + F + G + H −M . So the breakup adds E + H −Mto social gain; in order to determine whether this increment is positive, it sufficesto know the values of E, H and M .

17.a) The firm produces quantity 70. The neighbors could pay the firm anywhere be-tween $5 and $12 to decrease its output from 80 to 70. Social gain is $8.

b) If the neighbors stay, they are subjected to $24 in pollution costs; therefore theywill leave. Social gain is $25 in PS minus $6 in moving costs, i.e. $19.

c) Now there is no incentive to move. Social gain is reduced to $8.18.a) Drivers gain A+B +C and pedestrians lose B +C +D so the social gain is A−D.

b) Drivers gain A and pedestrians neither gain nor lose so the social gain is now A;that is, social gain increases by D.

c) Because now pedestrians will have no incentive to avoid accidents.d) Without air bags, drivers medical costs are G+H +L+M +Q+R. With air bags,

their medical costs are Q + R + S + T . So you’d want to compare G + H + L + Mwith S + T .

e) Without air bags, the social gain (computed in part a)) is A−D. With air bags,the social gain is A + B + C + G + H + I − P . So air bags improve social gain ifand only if B + C + D + G + H + I > P .

f) Drivers would be willing to pay G + H + I + L + M + N + O for airbags.g) Drivers will now be willing to pay G+H + I +L+M +N +O−X, where X is the

amount of the tax. Thus they will buy airbags if and only if G+H+I+L+M+N+O−X > Y where Y is the cost of an airbag. On the other hand, the social benefitsof air bags exceed their costs if and only if B+C+D+G+H+I−P > Y . To makesure that drivers buy air bags if and only if their social benefits exceed their costs,we want G+H +I +L+M +N +O−X = B+C +D+G+H +I−P ; equivalentlyX = L+M +N +O−B−C−D +P . This can be simplified further if you noticethat L = B and M = C+D; thus the optimal tax is X = N +O+P . A more directroute to the same conclusion is this: Airbags increase the externality from reckless

13–22

driving by N+O+P (from B+C+D to L+M+N+O+P = B+C+D+N+O+P );to get drivers to internalize that additional externality, we have to charge them anequivalent amount.

19. True. Suppose that driving carefully to the drug store creates an expected accidentloss of $10 to someone else (because even careful drivers sometimes have accidents)but the value to you of the trip is only $5. The trip is inefficient. But if youare a careful driver, the negligence standard protects you from liability, so you goanyway.

20. The advantage is that everyone in the vicinity of the accident has a full incentiveto take any cost-justified measure that would avert the collision. The disadvantageis that people will stay away from areas where accidents are common, which maybe inefficient.

21.a) A. C −B + A.b) C −D.c) A < C −D. C −B + A < C −D.d) Social gain from completion < social gain from breach, or D −B + A < 0.e) Expectation damages, since the inequality in part d) is equivalent to the second

inequality in part c)22. It does not follow that expectation damages are the appropriate standard. Al-

though expectation damages lead to efficient breaches of contract, they might notlead to an efficient number of contracts being signed in the first place. A full anal-ysis of the problem must account for the fact that the number of contracts signedwill vary depending on the legal standard that is in force. Such a full analysisis provided by David Friedman in “An Economic Analysis of Alternative DamageRules for Breach of Contract,” Journal of Law and Economics 23 (1989). Fried-man establishes that either expectation or reliance damages could be more efficient,depending on circumstances.

13–23

Chapter Fourteen:

Common Property and Public GoodsGeneral Discussion

1) Ken McLaughlin has given me the solution to the check-splitting problem inthis chapter. (The problem concerns a group of ten diners who are not able to getseparate checks for their meals. Thus the private cost of ordering a $10 dessert isonly $1, and the number of desserts ordered is greater than optimal.) The solution:Each diner pays the entire check!

Now a diner will order a $10 dessert if and only if it is worth at least $10 tohim. Why should diners agree to such a scheme? Since every dish that gets boughtis paid for 10 times, the restaurant will be willing to pay the diners a large lumpsum in exchange for their eating there.

A similar principle applies in labor economics. Since no employee of GeneralMotors can be monitored perfectly, he will sometimes work less hard than is optimalfrom the firm’s point of view. A profit-sharing plan is a very poor solution: if thefirm has 10,000 employees then a given worker will put forth $1 worth of extra effortonly if it increases profits by $10,000. The solution: Each employee should receivein salary an amount equal to the corporation’s entire profits. Now the opportunityto increase profits by anything more than $1 will elicit that $1 worth of extraeffort. Where does all the money come from to pay these enormous salaries? Eachemployee pays a large lump sum to General Motors in order to “purchase” his job.

Unfortunately these schemes only work if all diners (or all workers) are iden-tical, so that the same lump sum payment is appropriate for each.

2) As I typed the preceding few paragraphs, I became concerned about whetherthe check-splitting solution is stable. Once the diners have come to the restaurant,a diner can say to the manager: “I value that $10 dessert at $3. If you give itto me for $2, you will collect $20 and make a clear $10 profit. Otherwise I won’tbuy it.” If the diner is credible, the manager will agree, and the outcome is stillinefficient. Of course, foreseeing such bargaining, the restaurant is unwilling to paylarge lump sums to attract diners. It seems that we need some mechanism to rulesuch bargains out. Likewise at GM, management could bribe individual workersto do a bad job!

3) A potential solution to the public goods problem is for one agent to privatizethe public good by acquiring all of the assets whose values are affected by it. Forexample, suppose that a streetlamp will raise the value of each of the 20 houseson the street by $10 apiece. The streetlamp costs $100 to build. For the usualreasons, no individual finds it in his interest to contribute. In this case there is aprofit opportunity: one entrepreneur buys all of the houses on the street, buildsthe streetlamp, and resells the houses for a total of $200 more than he paid forthem. The market provides the public good in the optimal quantity with no needfor collective action.

Likewise, when a group of retail stores are located near each other, securityand clean-up for the surrounding area are public goods. In principle, the publicgood problem can be solved by a single entrepreneur buying all of the property,providing the desired services, and leasing the property back to the original tenants(at a rental rate that reflects the value of the services being provided). You canpoint out to your students that shopping malls are a striking example of preciselythis principle in action.

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4) For an interesting historical account of some partial private solutions to thepublic goods problem, put your students onto Coase’s paper on “The Lighthousein Economics.” It is reprinted in his book “The Firm, the Market and the Law.”

5) The public goods discussion focuses, as is traditional, on non-rivalrous andnon-excludable consumption goods. For an interesting continuation of this line ofthought, you can tell your students about Paul Romer’s discussion of non- rival-rous and non-excludable production goods, in the May 1990 American EconomicReview .

14–2

Additional Problems

1. The residents of Alphaville and Betaville are identical in their tastes and op-portunities, except that those in Alphaville hate crowds quite intensely whilethose in Betaville consider crowding to be only a mild annoyance. Each townhas a free aquarium. True or False: Crowding at the Betaville aquarium hasa lower social cost than crowding at the Alphaville aquarium.

2. At the Marketplace Mall water fountain, there is always a line to get a drink.a) What determines the length of the line? If all mallgoers have an equal

demand for water, what is the social value of the water fountain?b) The mall management has decided to try an experiment: From now on,

the newest arrival at the water fountain will be allowed to go directly tothe front of the line instead of the back. Is this a social improvement?

3. Suppose you have invented a delicious new soup, but you are worried that if youtry to market it, Campbell’s, Lipton and the other major soup manufacturerswill copy your idea. What can you do to protect yourself?

(The problem above is based on an idea of Jack Hirshleifer. The solution isto buy stock in Campbell’s and Lipton and then give them your soup idea forfree. I include this here because it illustrates the same general principle thatis involved when a private entrepreneur purchases a collection of neighboringproperties, provides a public good, and then resells the properties at their new,higher value. The public good here is the soup recipe, and the neighboringproperties are the soup company stocks.)

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 14

1.a) 8. 56. 0.b) 4 or 5. 40c) 8 or 10 fish per day.

2.a) With free entry, 2 miners work in Mine A and 5 in Mine B. (Miners must allocatethemselves so that they are indifferent between the two mines.) The social optimumconsists of 3 miners in Mine A and 4 in Mine B, for a total output of 132 nuggetsper day. An entry fee of 5 nuggets per day in Mine B achieves this optimum;alternatively, so does an entry fee of 1 nugget per day in Mine A and 6 in Mine B,or 2 in Mine A and 7 in Mine B, etc. The wicked queen charges 16 nuggets perday to enter Mine A and 21 to enter Mine B, thereby achieving the social optimum(and grabbing all the surplus for herself).

3.a) If the narrow road is more pleasant than the wide road, drivers on the wide roadwill switch to the narrow road, making the narrow road less pleasant; this continuesuntil the two roads are equally desirable. If the narrow road is less pleasant thanthe wide road, drivers on the narrow road will switch to the wide road, makingthe narrow road more pleasant; again this continues until both roads are equallypleasant to drive on.

b) When one driver is added to the narrow road, the private marginal benefit (tothe new driver) is the same as when one driver is added to the wide road. This isbecause we already know that both roads are equally pleasant to drive on. However,the marginal social benefit from adding a driver to the narrow road is equal to hismarginal private benefit minus the costs he imposes on all other drivers by makingthe road less pleasant. Thus the marginal social benefit from a driver on the narrowroad is less than from a driver on the wide road.

c) A planner could move one car from the narrow road to the wide road. Since themarginal social benefit is greater on the wide road than on the narrow one, totalsocial benefit must increase. Another way to see this is that the driver who ismoved was already indifferent about which road to be on, so he neither gains norloses, but all of the other drivers on the narrow road gain from his departure.

d) The planner continues until the marginal social benefit from adding a driver is thesame on both roads.

If drivers entering the narrow road had to pay an entry fee equal to theexternality that they impose on other drivers, they would completely internal-ize the externality. Drivers would voluntarily stop entering the narrow road assoon as the marginal social benefit from adding a driver is the same on bothroads.

If the narrow road were owned, the owner would set exactly the optimal entryfee. This is so for the same reason that the giant who owns the forest sets theoptimal entry fee. Make sure that you can reproduce the argument in the contextof the present question.

14–5

4.a)Apples perdwarf

Dwarfs

A

B

Cost of entry{F

Q Q1 0

The line A denotes apples picked per dwarf and the line B denotes the marginalcontribution to the apple harvest. The reason the latter lies below the former isbecause of the crowding effect. This effect causes the marginal contribution ofeach new dwarf to be smaller then the actual size of his harvest because he has anegative effect on the dwarfs who are currently picking apples.

b) Prior to the giant, Q0 enter. The giant sets a fee of F so that Q1 enter.c)

Apples perdwarf

Dwarfs

A

B

{TQ Q1 0

C D EF

opportunitycost

The area C + D + E + F is the producer surplus and the number of dwarfswhich enter without any fee is Q0.

d) In the graph for part (c), Q1 is the optimal number of dwarfs and T is the optimalfee.

e) Not unless the revenues from the giant are redistributed in some way back to thedwarfs. Otherwise their producers’ surplus falls to F . With the giant’s welfaretaken into consideration the society is made better off. (It is also possible that thegiant would voluntarily undertake improvements to the forest that could increaseboth his own welfare and the dwarfs’; this would be reflected by an outward shiftof the A curve.)

f) Suppose that when X dwarfs enter the forest, they pick a total of A−BX applesand the marginal dwarf has an opportunity cost of CX (where A, B, and C arepositive constants). In the following diagram, the giant sets an entry fee of T tomaximize the area F + G = TX0, whereas under free entry the number of dwarfsentering is X1:

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Apples perdwarf

Dwarfs

A-BX

{TX X10

GF

CX

H

I

We can compute X0 = A2(B+C) and X1 = A

B+C . With a monopoly giant,

the giant gains area F + G = A2

4(B+C) and the dwarfs gain area I = A2C8(B+C)2 .

With free entry, the dwarfs gain area G + H + I = A2C2(B+C)2 . Thus the giant is

welfare-improving if and only if

A2

4(B + C)+

A2C

8(B + C)2>

A2C

2(B + C)2

or equivalently2B > C.

Since 2B is the absolute slope of the “marginal apple harvest” curve (notshown in the picture) and C is the absolute slope of the dwarfs’ marginal costcurve, the result is proved.

5. False. Any social gain must result from differences among fishermen. If they areidentical, then there is no social gain regardless of their ability.

6. True. If the total population is Q and everyone there visits the aquarium, thevalue of a visit still exceeds the cost of entry. The shaded area C + D + E isundissipated rent. Note however that if only Q′ visitors came to the aquarium, therents (A + B + C + D) would be greater.

$/visitor

Crowd sizeValue of a visit

Q ' Q

CA

E

Social Marginal Value

BD

7. True. Competition maximizes social gain, whereas a monopolist maximizes hisprivate gain. But with all consumers identical, all rents go to the owner. Thereforethe two conditions are equivalent.

8.a) For anyone with a T.V. this is non-excludable and non-rivalrous.b) Excludable and Non-rivalrous.

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c) Neither since it cannot be consumed by more than one person and it is costly toobtain.

d) Both non-excludable and non-rivalrous as long as the crowds are not excessive andthe park is free.

e) Non-excludable when there are no crowds and rivalrous since one person drinkingimplies another cannot.

9. Acting in your own self interest leads you to become a free rider. It is in yourbest interest to let others pay for the programming and then watch it for “free.”Actually giving money to the station implies some altruistic behavior.

10. False. The new subway makes the north side more attractive to many individualsand presumably the rents for apartments will be bid up.

11.a) If the price were larger everyone would move to Cleantown and if the price wereless everyone would move from Cleantown to Grimytown. The demand curve is asfollows:

Price perapartment

ApartmentsQ Q0 1

S

D

$200

where QT = QC + QG is the total number of apartments in Grimytown plus thosein Cleantown and the shaded area is the producer surplus. There is no consumersurplus because the demand curve is flat.

b) The shaded area is the increase in producer surplus as well as the increase in socialgain. There is still no consumer surplus. Only the apartment owners gain.

Price perapartment

ApartmentsQ Q0 1

S

D

$200D'

$300

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12.a)Price perapartment

ApartmentsQ QG T

S

D

$200CS

PS

The demand curve for Grimytown apartments is downward sloping since thosewho value the pollution at less than $100 are willing to pay more for the apartmentand thus gain consumer surplus. The area CS is consumer surplus and the area PSis producer surplus.

b)Price perapartment

Apartments

S

$200

E

A B

C D

The movement to the flatter demand curve is the result of the clean air stan-dards. Consumer surplus changes from A+C to A+B; this could be an increase ora decrease. Producer surplus increases from E to C +D +E. Social gain increasesby B + D. If we were to assume an upward sloping supply curve these results maybe altered although there would still be a social gain.

13. Yes. Every bidder submits a truthful bid. Suppose you are a bidder who valuesthe car at $100. You can reason thus: If the second highest bid is less than $100,then I want to win this auction, because I will get the car for less than $100. If thesecond highest bid is over $100, then I want to lose this auction, because then thecar would cost me more than $100. So: I want to win if the second highest bid isless than $100; I want to lose if the second highest bid is more than $100. How doI insure that I get what I want? Answer: Bid $100.”

Incidentally, this auction mechanism is essentially equivalent to the traditionalEnglish auction in which buyers call out successively higher bids until only oneremains. The final bidder will be the one who values the item most, and theamount he pays for it will be just a hair over the second highest bid.

14. The Bob/Carol/Dale example from the text works here too. Replace “streetlamp”with “pollution control” and use the same mechanism.

14–9

Answers to Numerical Exercises

N1.a) N · (300−N2)− TC where TC is the total cost of the bridge.b) 17. 187 (The social gain is non-zero only because it is not possible for a fractional

number of people to cross the bridge.)c) 10d) N = (300− T )

12 or the lowest integer closest to N .

e) T = 200 (this maximizes N · T where N is determined as in part d). The benefitof $2000 per day go to whoever collects the tolls.

N2. When the last dwarf enters the forest, he reduces the number of apples picked byeach other dwarf by some amount ∆A. Each of the Q dwarfs already in the forestexperiences this loss, so the full external cost of the dwarf’s entering is given byQ ·∆A. Since exactly one dwarf has entered, we can write ∆Q = 1, allowing us towrite the external cost as

Q ·∆A

∆Q.

But this last expression is the same as A/η.

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Chapter Fifteen:

The Demand for Factors of ProductionTeaching Suggestions

1) Students find this material considerably more difficult than anything thathas come before. It helps to stress that there are only a few major points: therelationship between demand and marginal product, the construction of the longrun demand curve, and the fact that the sum of factor payments precisely exhauststhe firm’s income. Unless your students are very strong, I would stay away fromsuch esoterica as regressive factors and the impossibility of Giffen factors (thoughthe latter is essentially proved in Exhibit 15–9 for those who want it).

2) In covering the topic of monopsony, the NCAA is a favorite example. Herewe have a cartel of buyers, paying monopsony wages for athletes. The monopsonywage, as illustrated in Exhibit 15–10, is lower than the competitive wage, andthere is no doubt that college athletes are paid less than they would be if collegeswere free to bid for their services. Just as the members of a sellers’ cartel have anincentive to cheat by offering lower prices, so the members of a buyers’ cartel havean incentive to cheat by offering higher wages. As with a buyer’s cartel, there needsto be a mechanism for punishing cheaters, and the vast majority of your studentswill be familiar with some of the mechanisms available to the NCAA.

3) In covering monopsony, you might want to mention the possibility of bilat-eral monopoly, where the rents available to a particular buyer–seller combinationare greater than to any other combination. Example: a specialized scientist whoseresearch meshes perfectly with the work in progress at one particular university, ora sports player whose particular skills are especially needed by a particular team.Here (despite the considerable amount of research effort that has gone into bar-gaining models in the past several years) all we can really say is that the wage willbe at some level that divides the excess rents between buyer and seller, and thatwe can’t predict exactly what the division will be.

4) If you want an example of a company town, the best one I know is Pullman,Illinois (now incorporated into Chicago), built and completely managed by thePullman railroad car company and populated by its employees.

5) For students who are using the calculus appendix, you have an opportunityto illustrate how economic theory can be used to reveal a truly remarkable andnon-intuitive fact about the behavior of firms. Let L(PL, PK) and K(PL, PK) bethe quantities of labor and capital that the firm employs when the wage rates oflabor and capital are PL and PK . Then

∂K

∂PL=

∂L

∂PK.

That is, the change in capital employment that results from a rise in the wagerate of labor is equal in magnitude to the change in labor employment that resultsfrom a rise in the rental rate on capital. It is by no means clear to the untrainedintuition that these quantities should have the same sign, let alone that they shouldbe equal .

Depending on whether you are using calculus in class, this is a fit topic eitherfor a lecture or for a challenging homework assignment. Either way, I would stressto students how remarkable it is that such a thing could fall out of our theory.

15–1

If you assign it for homework, you might or might not want to give the followingextremely helpful hint: first prove that ∂K/∂PL = ∂2π/∂PL∂PK , where π(PL, PK)is the profit earned by the firm.

15–2

Additional Problems

1. Suppose that in the short run skilled labor is a fixed factor and unskilled laboris a variable factor. A minimum wage law is passed which sets the minimumlegal wage at a level above what unskilled workers now earn but below whatskilled workers now earn. What is the effect on the wages of skilled workers?Does your answer depend on whether skilled and unskilled labor are substitutesor complements?

2. True or False: A rise in the wage need not lead to any reduction in employmentif producers are able to pass the increase on completely to their customers.

3. True or False: If firms earn zero profits, then the long run labor demand curveis always more elastic than the short run labor demand curve.Remark: This problem is hard and should not be assigned lightly. Studentswho have solved problems 11 and 2 in the textbook can combine their solutionsto obtain the (affirmative) solution to this one. But few students will be sosuccessful.

4. Suppose that capital and labor are substitutes. True or False: In the shortrun, a firm that has a lot of machinery will employ more workers than a firmthat has less machinery.

5. True or False: In a competitive industry with a factor price effect, the in-dustry’s upward-sloping long-run supply curve is also the social marginal costcurve. But if the firms in the industry are able to act as a monopsony in thelabor market (while remaining competitive in the output market) then theindustry supply curve lies above the social marginal cost curve.

6. Suppose that the government undertakes a successful campaign to deport allillegal aliens who are holding jobs in the U.S. Use a graph to show the gainsor losses to American workers, American owners of capital, and Americans asa whole.

7. Most of the people living on the north side of Boomtown are apartmentdwellers who commute into the center of town every day to go to work. Thecity is considering building a new subway line between the north side and thecenter of town. True or False: Since the landlords all live on the south side oftown, and the employers are all in the center of town, all of the benefits fromthe new subway will go to the working people on the north side of town.

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15–4

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 15

1. If the wages of apple pickers are measured in “apples per hour”, this is true.But if the wages of apple pickers are measured in “dollars per hour” where dollarsrepresent goods other than apples, then this is false. The rise in demand raises themarginal revenue product of labor as in Exhibit 15-3a.

2. True in the short run; false in the long run. Since the demand curve is vertical,the quantity produced won’t change. Thus in the short run, employment of laborwon’t change. In the long run, however, it is possible to produce the same quantityof output with a different combination of capital and labor, and the firm will doso. For example, if the demand curve is vertical at a quantity of 3, and if the wagerate increases from PL to P ′

L, then the firm moves from point A to point B in thefollowing diagram, reducing its employment of labor from LA to LB .

B

A

Slope = P' /P'L K

Slope = P /PL K

L LB A Labor

Capital

3. True. A fall in the wage rate from W to W ′ increases employment from L toL′ in the short run. Since capital and labor are complements in production, thisincrease makes capital more productive at the margin, so the demand for capitalshifts out from DK to D′

K in the second panel. This causes employment of capitalto rise from K to K ′, which increases the marginal productivity of labor, givingthe new short run labor demand curve D′

L in the first panel, and employment risesfurther to L′′. Since employment rises more in the long run than in the short run,the long run labor demand curve must be more elastic than the short run labordemand curve.

L L' L''

w

w'

$/unit

Labor

D'

DL

L

R

DD'

KK

Capital

$/unit

15–5

4.

w

w

Wagerate

Labor

MRP'L

R

MRPK Capital

Rental Rate

MRPL

L L L L3 2 1 0

0

1 LongRunLabor Demand 0

K K K0 1 2Initially, the wage rate of labor is W0 and the rental rate on capital is R0. The

firm hires L0 units of labor and K0 units of capital.Now the wage rate rises to W1. In the short run, the firm reduces its employ-

ment to L1. Assuming that capital and labor are substitutes in production, thiscauses the MRPK curve to rise to the level of the middle curve in Panel B. Thefirm increases its capital employment to K1.

The increased capital employment lowers the MRPL curve to the level of thedashed curve in Panel A, causing labor employment to fall to L2. This raisesthe MRPK curve still further, causing capital employment to rise to K2, and theprocess repeats. Eventually, the MRPL curve settles at the new level MRP ′

L. Herethe firm hires L3 units of labor. Thus the long run labor demand curve (through(W0, L0) and (W1, L3)) is more elastic than the short run demand curve MRPL.

5.a) The argument in Exhibit 14–9 shows that MRP ′L must lie to the left of MRPL.

(The higher wage rate reduces labor employment, which pushes MRPK leftward,which pushes MRPL leftward.) Thus when the wage rate goes up, the new long-run quantity of labor employed, being read off MRP ′

L, must be less than the oldquantity of labor employed. That is, long run labor demand slopes downward.

b) The argument in problem 3 shows that MRP ′L must lie to the left of MRPL.

(The higher wage rate reduces labor employment, which pushes MRPK rightward,which pushes MRPL leftward.) Thus when the wage rate goes up, the new long-run quantity of labor employed, being read off MRP ′

L, must be less than the oldquantity of labor employed. That is, long run labor demand slopes downward.

6. True. When the wage rate goes up, firms employ less labor than before. Sincelabor is a regressive factor, this shifts their marginal cost curves downward, leadingto a rightward shift in industry supply. This in turn leads to a fall in the price ofoutput, which is an additional reason for firms to reduce their quantities suppliedand consequently their employment of labor. For this reason, the industry supplycurve incorporates a greater scale effect than the sum of the individual firms’ supplycurves, and this makes it more elastic.

7. True. The reason why isocosts are straight lines is that their equations are givenby PK ·K + PL · L = C where PK , PL and C are constants. For a monopsonistin the labor market, PL is not constant: It varies with his employment of labor.Thus the isocosts are not straight lines.

15–6

8.

AB C

D EF

G H MRPL

S

MCL

Labor

Wage rate

L L cCompetitive Labor Market Monopsony

Consumer’s Surplus

(to firm) A+B+C A+B+D+EProducers’ Surplus

(to workers) D+E+F+G+H G+HSocial Gain A+B+C+D+E+F+G+H A+B+D+E+G+H

Deadweight Loss C+F

9. True. In the art for problem 8, suppose that a minimum wage is set at WC .Then MCL essentially becomes flat at WC , and the optimal amount for the firmto hire is LC . This is analogous to the fact that a price control on a good sold bya monopolist can increase his output.

10.a)

MRPL

Labor

Wage rate

L

A

B

The firm’s total revenue is A+B, of which B goes to labor. Thus (assumingfirms earn zero profits), A goes to capital. A is the revenue earned by capital,but if capital is supplied perfectly inelastically, then all of its revenue is producers’surplus. Thus the producers’ surplus earned by capital is area A.

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b)

MRPL

Labor

Wage rate

C

D EF

G

LL'

ss

ww'

The labor supply increases from LS to L′S . The wage rate falls from W to

W ′. American workers lose D, American owners of capital gain D+E, and SouthKorean workers gain G. (That is, the producers’ surplus ofAmerican workers fallsfrom D+F to F, the producers’ surplus of American owners of capital rises fromC to C+D+E—this uses the result of part a)—and, since the total surplus to allworkers is F+G with Americans getting F, South Koreans must get G instead ofnothing.)

c) Since workers lose only D while capital owners gain D+E, it unambiguously helps.11. True. As the graph shows, a rise in the wage from W to W ′ causes the revenue

earned by capital to fall from A to A+B.

MPL

Labor

MPL

w'w

A

B

12. True. Suppose that labor and capital were substitutes in production. Then anincrease in the wage rate would cause an increase in the marginal product of capitalfrom MPK to MP ′

K in the following graph. The revenue earned by capital wouldincrease from D to D+F+G. But we already saw in Problem 10 that the revenueearned by capital goes down, not up. Thus capital and labor cannot be substitutesin production.

15–8

MP'K

Capital

MPK

MPK

CE

D G

F

13. The minimum wage law will eliminate much unskilled labor from the market.Apparently the union believes that this will increase the demand for skilled labor;thus skilled and unskilled labor must be substitutes in production.

Temporarily divide inputs into “unskilled labor” and “all other inputs,” where“all other inputs” comprises both capital and unskilled labor. Arguing exactly as inproblem 11, we see that unskilled labor and all other inputs must be complements.That is, a fall in the employment of unskilled labor increases the demand for allother inputs on average. On the other hand, a fall in the employment of unskilledlabor increases the demand for skilled labor. Thus a fall in the employment ofunskilled labor must decrease the demand for capital. In other words, unskilledlabor and capital must be complements.

It follows that the owners of capital will oppose the minimum wage.14. The gains go to the factors that are in fixed supply. The one factor that is most

clearly in fixed supply is land in the no-tax zones. (Although even this is lessclear than it seems—if it is possible to build upward, then the amount of “land”available for use in the area can be increased without limit). Firms can come andgo, customers can come and go, producers of machinery and workers can come andgo, so in the long run they gain very little from the policy.

Answers to Numerical Exercises

N1.a) The slope of an isocost is −W/R. In long run equilibrium, the slope of the isocostis equal to the slope of the isoquant, so that

−W

R= −K

L.

Thus we can writeK =

W · LR

,

L =R ·KW

.

b)

L = Q ·√

R

W,

K = Q ·√

W

R.

c)W · L + R ·K = 2 ·Q ·

√W ·R.

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d) The long run marginal cost is flat at 2 ·√

W ·R.e) Price = marginal cost = 2 ·

√W ·R. It is possible to answer this question without

any information about demand only because the firm’s marginal cost curve is flat.f) Labor receives W · L = Q ·

√R ·W .

Capital receives R ·K = Q ·√

R ·W .The firm’s total revenue is 2 · Q ·

√R ·W , which exactly covers the cost of hiring

labor and capital.N2.a) Suppose that each firm produces q units of output using k units of capital and l

units of labor. As in N1b, we get l = q ·√

RW , k = q ·

√WR . Adding up over all

firms in the industry we get

L = Q ·√

R

W,

K = Q ·√

W

R.

b)

Q ·√

R

W= W,

Q ·√

W

R= 4 ·R.

Dividing one equation by the other and solving, we get

W

R= 2.

c) Since each firm must be on its own supply curve, N1e) tells us that

P = 2 ·√

W ·R.

Substituting the expressions for the factor supply curves, we get

P = 2 ·√

L ·K/4 =√

L ·K.

Combining the results of N2a) and N2b), we can replace L by Q ·√

1/2 and K byQ ·

√2 to get

P = Q.

The latter is the equation for the long run industry supply curve.d) Combining the demand curve with the supply curve just derived, and using the

other results that were obtained alont the way, we get

Q = 750P = 750

L = 750 ·√

1/2

K = 750 ·√

2

W = 750 ·√

1/2

R = 750 ·√

2/4.

15–10

e) Producers’ surplus in the output market is the triangle bounded by the price axis,the line P = 750, and the supply curve Q = P , or 281250. Producers’ surplus tolabor is bounded by the wage axis, the line W = 750 ·

√1/2 and the labor supply

curve L = W , or 140625. Producers’ surplus to capital is bounded by the rentalrate axis, the line R = 750 ·

√2/4, and the capital supply curve K = 4 · R, or

140625. All of the firms’ surplus is paid out to factors. Firms earn zero profit, aswe already knew from N1f).

15–11

Chapter Sixteen:

The Market for LaborGeneral Discussion

1) I had originally intended to include a section on unemployment, but becameconvinced that the topic was too complex—and perhaps also too “macro”—to bedealt with here. However, if you cover labor markets, the subject may come up inclass.

It is important to distinguish between voluntary unemployment (people choos-ing not to work because the going wage is insufficiently high to attract them) andinvoluntary unemployment (people who can not find a job at the going wage). Thedistinction is subtle, both empirically and theoretically.

Putting aside the difficult empirical questions, it is already hard just to pindown the definition of involuntary unemployment. Chuck Whiteman once told methat he was involuntarily unemployed as a quarterback for the Los Angeles Rams,in the sense that, given the going wage for that position, he preferred to supplymore hours than he was able to. Clearly we must control for abilities. It hasbeen suggested that you are involuntarily unemployed when you are identical toyour neighbor in every way, except that he’s working, you’re not working, and he’shappier than you are. This seems a reasonable start.

The next problem is to explain why there should ever be involuntary unemploy-ment, since our most basic models predict that competitive markets in general, andlabor markets in particular, should achieve a price at which the quantity suppliedand the quantity demanded are equal. Here we enter the realm of macroeconomics,and I think it is fair to tell students that they have now stepped beyond the boundsof the present course and will just have to wait a semester before they can find outwhat happens next. But there remain a few interesting tidbits we can throw out.

One is that we really don’t know how much unemployment is voluntary, andthat for all anybody really knows, it might all be voluntary. Half your students willhave “involuntarily unemployed” relatives to hold up as counterexamples. Withoutgetting into the unsavory details of their family lives, you can tell them that “all”does not mean literally every single case, but rather that models in which allunemployment is assumed to be voluntary fit the observed facts within reasonablestatistical limits. The model of unemployment in section 9.2 is an example (in factthe archetypal example) of an attempt at such a model.

An alternative you can mention is efficiency wage theory, which also appearsin Chapter 9: Employees can not be monitored at all times, and are sometimesable to shirk or to otherwise steal from their employers. In order to discouragesuch behavior, the employer must be able to threaten a substantial punishmentif the employee is caught. Since the harshest available punishment is to fire theemployee, the only way to have a reasonable deterrent is to make employees feelthat they have a lot to lose if they are fired. This requires paying them a wagehigher than the one that clears the market. Since the wage that gets paid is aboveequilibrium, there must be some workers who can not find work.

Another topic you can mention is the role of unemployment insurance andthe system of experience ratings. An employer’s experience rating determines thepercentage that he must contribute to the payment of his former employees’ un-employment compensation. It is usually an increasing function of the frequencywith which the employer has terminated workers in the past. The fact that theemployer does not pay the full compensation invites fraud: I, an employer, hire

16–1

you, my friend who really doesn’t want a job, fire you, and we split that portionof your unemployment check that comes from the government. The potential forsuch scheming has been put forth as an argument for 100% experience ratings.

If you find yourself discussing problems of measurement, students are amusedby the following observation: If you take a random sample of unemployed peopleand ask them how long they have been unemployed, the average response willusually be a gross overestimate of the average time that people spend unemployed.Reason: people who are unemployed for very short times are quite unlikely tohappen to be unemployed at the particular moment when you are taking yoursurvey. Thus they get undercounted.

Finally, to shake your students up a bit, point out to them that unemploymentis of course ceteris paribus a good thing. If we could all have our present incomeswithout working, we would be much happier. Bastiat exploits this in a number ofessays (all of which make delightful reading assignments): Robinson Crusoe works12 hours a day to make a fishing net, until one day some netting in perfect conditionwashes up on shore. Robinson is thrilled at first, but then realizes that if he usesthis netting he will be unemployed; therefore he throws it back. That sort of thing.

16–2

Additional Problems

1. Dick and Jane each recently received substantial inheritances when their auntpassed away. In response, Dick started working fewer hours but Jane startedworking more. Next week, Dick and Jane’s wage rate is going to fall.a) Can you say for sure what will happen to the number of hours Dick works?

Illustrate your answer with indifference curves.b) Can you say for sure what will happen to the number of hours Jane works?

Illustrate your answer with indifference curves.

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16–4

Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 16

1. True. This change corresponds to a parallel shift in the budget line that relatesconsumption to labor, and so there is only an income effect. Assuming that con-sumption and leisure are both normal goods, the individual will choose to havemore of each.

2. Jack’s budget line has a “kink” at eight hours, and we know that he choose pointA, on the steeper part of the budget line. Jill’s budget intersects the vertical axis atthe same place where Jack’s does (she has the same assets as Jack), has slope W ′′,and is tangent to the same indifference curve on which point A lies (she has thesame tastes as Jack and is equally happy). The only way to draw such a pictureis as shown below, with W ′′ larger than W but smaller than W ′, and with Jillchoosing point B, where she works fewer than 10 hours.

Labor

Consumption

8 10

A

B

slope w

slope w'slope w''

3. Before going to college, everyone has the budget line labeled N (for “non-graduate”) in the diagram below. They choose point A. Anyone who attendscollege gets a new budget line G (for “graduate”). The slope of G is determinedby the wage available to college graduates. The level of G is determined by therequirement that everyone be indifferent to attending or not attending college. Thereason for this is that if, for example, everyone preferred to attend college, peoplewould begin enrolling, bidding up the price of tuition until everyone was indifferentagain. Thus G must be tangent to the indifference curve containing A. The tuitioncost is the amount of consumption that one sacrifices in order to attend college,which is the distance T in the diagram. We can see from the diagram that collegegraduates, who choose point B must work more hours than non-graduates. Thusthe answer to part b) is false.

16–5

Labor

Consumption

A

B N

G

{T4. Dick’s non-labor income increased. Since we know he works more, he must view

leisure as an inferior good. Therefore, the wage rate increase leads to an incomeeffect of working more hours and the substitution effect of working more hours.Since these effects move in the same direction, Dick works more.

5. Unlike Dick in problem 4, Jane views both consumption and leisure as normalgoods. Therefore an increase in her wage has an ambiguous effect on hours worked.See Exhibit 15–5 for a graphical explanation. As the text mentions, if the wagewas very low to begin with, an increase in the wage leads to an increase in laborsupplied.

6.a) Just like Exhibit 16-5A in the text, except that point Q is to the right of Q′.b) No; Q is to the right of Q′ so it must be to the right of P . Therefore Horace’s labor

supply curve must slope up.7.a) In the diagram below, Hortense’s initial budget line is the line through O and P .

Her new budget line consists of the segment OP and the halfline beginning at Pand continuing through Q.

16–6

Labor(Hrs/Week)

Consumption

P

Q

35O

b) False. She now chooses point Q and works more hours.8.a) Car wash attendants must be indifferent between washing cars and the next best

occupation. Therefore the basic wage rate must drop. The new budget line is shal-lower than the old one out to 40 hours, then becomes steeper. The new optimumcould occur either to the right or left of the original, so the answer to part b) isfalse.

9. False; the opposite is true. When the wage increases, both men tend to workmore hours in response to the substitution effect. However, the man who earnsmost of his income in wages also feels an income effect, leading him to work fewerhours in opposition to the substitution effect. The man whose income is mostlyfrom other sources feels very little of this moderating income effect.

10. False. If workers come to enjoy their jobs, the supply curve of labor shifts out, thequantity supplied increases, and therefore the marginal product of labor decreases.So workers who enjoy their jobs more are less productive at the margin than thosewho enjoy them less.

11. The wage rate falls, less labor is supplied to the marketplace, and a given indi-vidual might supply either more or less labor than before.

12.a) The demand for labor will decrease since there aren’t many factories left who willemploy.

b) The workers’ non-labor income falls through low returns on their stock due todamage. Consequently, the workers will want to work more hours, implying anincrease in the supply of labor.

c) Assuming case (b) above holds, wage falls due to a demand decrease and supplyincrease. The amount of labor supplied to the marketplace in equilibrium can goeither direction; it depends on whether the demand curve or supply curve shiftedmore. Likewise the amount of labor supplied by any individual can go eitherdirection.

13. The wage rate rises, less labor is supplied to the marketplace, and a given (sur-viving) individual supplies more labor than before.

14. First, labor supply is reduced as only a half of the workers are available. However,there is also a less demand for the good as only half of the demanders are alive.Therefore, demand for labor also falls. The effect on the wage rate depends onthe magnitude of the demand and supply curve movements. The amount of laborsupplied to the marketplace falls. The change in labor supplied by any individualcould go either way as we do not know what happened to the wage rate. Forexample, a wage increase could imply more hours worked.

15. False; capital could either gain or lose. The fact that the level of output is

16–7

fixed means that for some reason society must operate on the single horizontal lineillustrated below. The rise in the marginal productivity of labor raises the totalproduct curve from TP to TP ′, and the value of capital changes from A to B. Inthe illustration, B is greater than A (so that capital benefits) but it is possible todraw the picture so that A is greater than B (make TP ′ much steeper), in whichcase capital would lose.

Labor

Output

TP

TP'

AB

16. This has no effect on the demand for labor, but increases the supply as in problem1. Thus the wage rate drops and the amount of labor employed increases.

17. The demand for labor falls equally in both cases. The supply of labor coulddecrease dramatically as a result of intertemporal substitution in case (a), while itcertainly increases as a result of the income effect in case (b). In case (a), outputand employment are down, while in (b) employment could be up (though outputis certainly down since choose less consumption when they are poorer.) The wagerate is down in (b) by more that in (a).

18. In either case the supply of labor shifts leftward due to the income tax. On theother hand, if we assume that people feel poorer when they are taxed (becausethey value whatever the government buys for them less than they value what theywould have bought for themselves), then there is an income effect that shifts thesupply of labor rightward, by a small amount in the case of a temporary tax andby a large amount in the case of a permanent one. In the temporary case, thereis also leftward pressure due to intertemporal substitution. We can conclude thatlabor supply shifts leftward quite far in response to a temporary tax, less far inresponse to a permanent tax. The temporary tax leads to a large rise in (pre-tax)wages and a large fall in employment and output. The permanent tax has smallereffects in the same directions.

19. True, because education is a form of investment in capital. Since the tax break ap-plies to other forms of investment but not to education, investors tend to substitutetowards those other forms of investment.

16–8

Chapter Seventeen:

Allocating Goods Over TimeGeneral Discussion

Sections 17.1 and 17.2 develop the student’s intuition for the meanings of in-terest rates and present values, separate from any discussion of how those variablesare determined in equilibrium. I think that these two sections will be popular withbusiness students. They can be used at almost any point in the course.

Section 17.3 turns to markets and equilibrium, developing the interest rateas the price of current consumption. Demand is derived from indifference curves,giving additional reinforcement to the basic ideas of consumer theory. In thissection, I take supply to be exogenous, making the model as simple as possible.The student is then invited to try a variety of exercises in comparative statics (a laExhibits 17-8 and 17-9), reinforcing yet another set of important skills. In section17.4, investment is introduced to the model, leading to a more sophisticated modelof the supply curve and another set of exercises in comparative statics.

I have chosen to cover the topic of government debt and its effect on marketinterest rates. Although government finance is widely perceived as a ”macro” topic,the basic issues are all really micro issues, and it is a subject that grabs studentattention.

The Ricardian Equivalence Theorem – that government debt, in certain cir-cumstances, has no real effects – is broken down into two separate propositions.The first is that if government debt does not affect interest rates, then governmentdebt is a matter of no consequence. This, I think, will be entirely non-controversialamong economists, although it surprises students, and the simplicity of the argu-ment pleases them. The second is that government debt does not in fact affectinterest rates; here there is of course much controversy and both sides of the argu-ment are presented. The pro-Ricardian case comes first because it is the simplest;then the other side receives its due.

The two Ricardian propositions are physically separated. The first spans pp.603–604 in Section 2, where it appears as a straightforward application of the con-cept of present value. (The relevant discussion really begins on p. 602, under theheading ”Should You Pay With Cash or Credit?”) The deeper and more contro-versial issues, which involve market equilibrium, are postponed to pp. 622–625.

17–1

Additional Problems

1. True or False: If you can afford to, it is a good idea to pay off your debts asquickly as possible, so that the interest charges don’t get too high.

2. Herman has an income of 2thisyearandwillhaveanincomeof3 next year. Atthe current interest rate he chooses neither to borrow nor to lend. True orFalse: If the interest rate goes up, Herman will become a lender and be betteroff.

3. Use an indifference curve diagram to show why an economics student whoexpects to get a good job when he graduates will spend more than a philoso-phy student who expects to be unemployed, even though both have the samecurrent income.

4. Herman has a choice between two jobs. One pays very little now, but promiseshigh raises in the future. The other has a higher starting salary, but lesspotential for future raises. True or False: Herman’s choice should depend onhis tastes. It’s all a matter of whether he’d rather consume a lot when he’syoung or a lot when he’s old.

5. In The New Republic (6/17/89) James K. Glassman explained that housinghas been a less good investment than stocks: ”If you bought a $200,000 housein Foggy Bottom in 1979, it would be worth $316,000 today. But if you bought$200,000 worth of stock in 1979, it would be worth $556,000 today – and you’dhave another $68,000 in dividend income.” In words that James K. Glassmanmight understand, explain what’s wrong with his calculation.

6. In The New Republic (6/17/89) James K. Glassman writes that ”stocks ap-preciate faster than real estate; they always have, and they always will. Thereason is that a share of stock is a piece of a company in which minds areproducing value. Real estate just sits there.” Comment.

Remark: The above problem has a rather nice twist, since the reason thatstocks appreciate faster than real estate is precisely that real estate does not ”justsit there” — it returns a stream of dividends in the form of housing services. (Thisis the missing term in the equation in the preceding problem also.)

7. To compute your income tax, you first add up your income from all sources.You then subtract deductions to get ”taxable income,” and your tax bill de-pends on your taxable income. One allowable deduction is mortgage interest:Every dollar that you pay in mortgage interest can be subtracted from yourtaxable income. True or False: Therefore, if you have a choice between payingcash for your house or taking out a mortgage, the tax law makes it a goodidea to take the mortgage.

8. True or False: When income tax rates fall, the value of the mortgage interestdeduction falls, making housing less desirable and reducing the market priceof housing.

9. The Wall Street Journal (9/19/91) printed a letter from Richard C. Leone,the chairman of the Port Authority of New York and New Jersey, opposing theprivatization of New York’s airports. He asserts that the airports are worthwell in excess of the Journal ’s $2.2 billion estimate, but that even at that pricea purchaser would find it impossible to earn back his investment.Comment, using words that Mr. Leone could understand.

17–2

10. The makers of the insecticide Roach-Prufe advertise that their product is soeffective it can only be bought by mail; grocery stores will not carry it for fearthat their customers will eliminate all of their roaches and never have to buyan insecticide again. Do you believe them? Why or why not?

11. Because of a reduction in world tensions, the U.S. will be able to reduce itsmilitary expenditures by $100,000,000 this year. Senator Smith says that weshould take this opportunity to cut taxes by $100,000,000. Senator Jones saysthat instead of cutting taxes, we should apply the $100,000,000 to reducingthe deficit. Use a simple model to compare and contrast the effects of theSmith and Jones plans. Your answer should include a careful discussion ofhow people’s current consumption decisions are affected by the two plans.

12. Upper and Lower Slobbovia are identical countries in which there is n suchthing as productive investment; all income is from endowment. The govern-ments of both countries have decided to impose an income tax and spendthe proceeds wastefully. The only difference is that in Upper Slobbovia, thetax-and-spend plan is in effect for this year only, whereas in Lower Slobboviathe plan is permanent and will be repeated every year. In both countries,this year’s taxes have been collected and wasted. Compare the two countries’interest rates, and compare their current consumption levels.

13. In 1981, the personal computer was introduced, creating a whole range of newopportunities for productive investment. Shortly thereafter, interest rates rosedramatically. Give a full explanation of how the new computers might havecontributed to the rise in interest rates. If you draw a graph and shift curves,be sure to explain why the curves shift as they do.

14. Suppose that the interest rate is 10%. The Government wants to build a postoffice at a cost of $100,000. It can pay for the post office either by a) a tax onjelly beans that raises $100,000 this year; b) borrowing the funds and imposinga tax on jelly beans that raises $110,000 next year; or (c) any combination ofa (a) and b) (such as rasing $50,000 in tax revenue this year and $55,000 nextyear). The government would like to minimize the present value of deadweightloss in the jelly bean industry. What policy should it follow?

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 17

1. False. This confuses a change in demand with a change in quantity demanded!!2. The interest rate and the price of bonds cannot move in the same direction. A

movement in the interest rate in one direction is always accompanied by a move-ment in the bond price in the opposite direction by definition.

3. False; it cost him three years worth of interest on the cost of the refrigerator.4. A perpetuity which pays $1 forever is worth $10 when the interest rate is 0.10.

An annuity for 17 years which pays a dollar each year is worth about $8.02. Thusthe statement is true.

5.a) You would have to value it at least at

$P

r(1 + r).

b) Doubling P doubles the cost of the punishment. Halving r more thandoubles the cost of the punishment. Halving r is the greater deterrent.

6. Rent costs $18,000/year, therefore with a market interest rate of 10 percent andconstant rent the cost of renting forever is $180,000. The discrepancy suggests thatthe market must be anticipating a rise in rents, so the statement is likely to be true.There is another possibility, however, and that is that the market anticipates a fallin the interest rate, which would raise the present value of a constant stream ofrents.

7. False. The California house sells for less than the New York house and returns thesame stream of dividends. Thus the rate of return is higher on the California house,and this compensates the owner for the risk. As long as the relative desirability ofthe two houses remains constant, the relative price of one in terms of the other cannot change.

8.a) $20 + $20/1.1 + $20/(1.1)2 = $54.71.b) $200.c) Never issue new editions. The present value of the publisher’s revenue is

equal to the present value of the stream of dividends that the book returns tostudents. New editions do not affect this stream, but they do raise costs.

d) If students expect a new edition every three years, the price of a bookfalls to $54.71 and publishers must issue new editions to capture the full stream ofdividends.

e) True. Book price would rise from $54.71 to $200, present value of revenueswould remain fixed, and costs would fall.

9. False. In present value terms the charges would be constant.10. What Mr. Will overlooks is that the ”average American” gets something in

return for those interest payments, namely the opportunity to defer taxes and earninterest.

11. Exactly what is wrong with it is the following: If the government buys me a suit ofclothes with borrowed money, then I avoid having to buy the clothes myself. That

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means that I have more money in the bank earning interest, and my grandchildrenhave a bigger inheritance.

Suppose that the government borrows $1 to buy me the clothes, that theinterest rate is 10%, and that I die after one year. My extra $1 in the bank willhave grown to $1.10. The debt that my grandchildren must be taxed to pay willalso have grown to $1.10. The larger inheritance exactly cancels out the debtburden.

12.a) Jeeter can spend $1000 today to buy a bond. He can put the bond in a

desk drawer and forget that he owns it. In 5 years, when the loan comes due, hecan hand the bond over to the bank. Since the bond grows in value at exactly thesame rate that Jeeter’s debt to the bank grows, the bond will exactly cover hisdebt. This strategy “feels” exactly like paying the loan off for $1000 today andbeing done with it.

b) Jeeter can spend $10,000 to buy Treasury Bills. The interest rate on thesebills is exactly equal to the rate at which the government debt is growing, sinceselling Treasury Bills is precisely the way in which the government borrows. When-ever the government gets around to taxing Jeeter, he can turn over his treasuryBills, which are guaranteed to be equal in value to his share of the national debt.This strategy “feels” to Jeeter exactly like paying off his share of the debt now andnever being charged any interest.

13. How about something like:DEAR ANN LANDERS: You really blew it in your reply to

Ladder Legs of Lina, Ohio. If Wanda Worker spends $100 a yearreplacing nylons, Wanda Worker would be willing to pay up to$100 for a single pair of nylons that last a year without runningor stretching. In fact, she’d be willing to pay considerably morethan $100, since she’d avoid all of that aggravation and timespent running to the drug store.

It shouldn’t have taken a call to a hosiery manufacturer toclue you in to the fact that they just don’t know how to makethese miracle nylons. What kind of a conspiracy of self- interestwould refuse to manufacture nylons that they could sell at $100a pair?

Three lashes with a wet noodle for this one, Ann.—Econ Whiz

14. False; they will have paid for medallions whose value is now zero. If the medal-lions were originally issued free of charge, then only the original medallion ownersreceived any benefit from them; whenever a medallion changed hands it sold forthe entire present value of the all of the monopoly profits that it was expected toconvey. If the abolition comes as a surprise, then anybody who ever purchased oneof these medallions will have paid more than it was worth.

15. False. The exact opposite is true. The monopolist wants his marginal revenue togrow at the rate of interest. (Be sure you see why this is so: How could he makehimself better off if marginal revenue were growing either more or less slowly?)Because the marginal revenue curve is steeper than the demand curve, a given risein marginal revenue corresponds to a smaller rise in price. Because price starts outhigher than marginal revenue and increases by less than does marginal revenue, thepercentage change in price must be less than the percentage change in marginalrevenue. Thus the monopolist controls availability so that price rises more slowly

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than the rate of interest.16. False because of the word ”always.” At higher interest rates the consumer may

become a net borrower and thus be made better off.17. True. Herman’s original budget line is tangent to an indifference curve at (2, 3).

His new budget line also passes through (2, 3). The geometry forces the new tan-gency to be northwest of the old one and on a higher indifference curve.

18. Both reduce the supply of current consumption. In case (a) demand falls a littleand in (b) it falls a lot. The interest rate is higher in case (a).

19. In case (a) the demand for current consumption falls a little and in (b) it fallsa lot. The effects on supply of current consumption are the same in both cases,unless labor supply decisions are important. They supply might fall much furtherin case (a) than in case (b), due to intertemporal substitution as studied in Chapter16.

20. False. The representative agent is poorer now, and has a lower demand curve forcurrent consumption. If his current consumption quantity is Q, then (Q − 1000)corresponds to 20% on the old demand curve. It must correspond to somethingless than 20% on the new demand curve.

21.

E

D

FutureConsumption

CurrentConsumption

A{$1.10

$1 {

Terry starts with an endowment of A, faces an interest rate of 10%, and there-fore has the pictured budget line with slope −1.10. If the government taxes him$1 and then provides him with $1 worth of current consumption, his endowmentpoint remains A (nothing has really changed). If the government borrows $1 toprovide Terry with $1 worth of current consumption, it then taxes him $1.10 in thefuture to repay the debt. Terry’s endowment point shifts to D (with $1 more inpresent consumption and $1.10 less in future consumption). Because Terry’s newendowment point is on his original budget line, his optimum consumption basketdoes not change. Each plan leads to the same demand for current consumptionand so to the same equilibrium interest rate.

22.The super-productive government taxes a dollar and gives back two dollars

worth of consumption moving the agent from point A to point B. Or the governmentborrows a dollar, turns it into two dollars worth of consumption and increases futuretaxes by $1.10. This is the movement from A to C. The new budget line still hasslope 1.1 and thus the interest rate remains unchanged.

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B

FutureConsumption

CurrentConsumption

A

$1 { {

C

$123.

False. The quantity of government spending matters (as well as how it isspent); it is the method of financing that does not matter.

24.Here are a few observations:First, Mr. Rohatyn asserts that borrowing will convert a 130billionlossintoa500

billion drain over 20 or 30 years. In other words, he treats a dollar paid 20years from now as equal in value to a dollar paid today. If he is really com-mitted to such reasoning, Mr. Rohatyn should be happy to offer you a loan of200billiontodayinexchangeforapaybackof300 billion in 20 years. Try writing tohim and see if he agrees.

Second, he asserts that one should not borrow to finance losses that havealready occurred, and elevates this dictum to ***”a basic economic principle.” Onthe contrary, people generally prefer to spread their consumption out evenly overtheir lifetimes rather than having some years of feast and some of famine. (This iswhy we tend to think of the Great Depression as a bad thing.) It follows that aone-shot unexpected large expense is precisely the sort of thing that ought to befinanced by borrowing. Your indifference curve analysis in part (b) should confirmthis assertion.

Third, he is wrong in thinking that a short-term tax surcharge would necessar-ily limit the costs of the bailout to the immediate future. Precisely because peoplelike to smooth out their consumption, they would borrow more (or, equivalently,save less) in the present to get through the temporary period of high taxes. Theresult would be the same as if the government had done the borrowing.

But not quite. For a variety of reasons, individuals must usually borrow athigher rates than the government does. Therefore, Mr. Rohatyn’s proposal comesdown to this: Let people attempt to borrow for themselves at high interest rates,rather than let the government borrow for them at lower rates.

Finally, some economists would argue that people are insufficiently sophisti-cated to borrow their way through the higher tax years (that is, some would arguethat people fail to move to the optimum point in the indifference curve diagram).If those economists are right, then Mr. Rohatyn is even farther off the mark, sincethese taxpayers in their naivete will fail to smooth out their consumption streamsunless the government leads the way by borrowing for them.

25.False. A rise in the interest rate raises the cost of investment and makes

investment less desirable. Of course the interest rate change itself must have acause and one possible cause is that investment has become more desirable for

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some other reason.26.

To the shoemaker, the hammer is capital. From the numbers given, we candeduce that the marginal product of capital is 15% per year. But the marginalproduct of capital must be equal to the market rate of interest. Thus the marketrate of interest is 15% per year. Since the house provides $10,000 worth of serviceper year forever, its value is the value of an annuity that pays $10,000 per yearforever; that is, $10, 000/.15 ≈ $66, 667.

27.The demand for current consumption increases because people are richer, and

the supply decreases because investment is more productive. For both reasons, theinterest rate rises.

28.People want to borrow therefore the interest rate increases.

29.People feel much poorer and may demand ***less current consumption than

before. Therefore the interest rate could fall. (On the other hand, the effectsdescribed in problem 28 still work in the direction of pushing the interest rateupward.)

30.The answer is contained in Exhibit 17-13b.

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Chapter Eighteen:

Risk and UncertaintyAdditional Problems

1. What are some of the consequences of prohibiting insurance companies fromcharging higher rates to people who are in high risk groups for AIDS? What aresome of the consequences of prohibiting insurance companies from requiringAIDS tests as a precondition for coverage?

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 17

1.It depends on the possible outcomes of the uncertainty, and it depends on the

odds. Had the doctor been given the opportunity to sacrifice a certain shilling inexchange for a mere 99% chance at a million pounds, he might have reconsideredhis position. Indeed, to forego suicide is to sacrifice the certainty of death for theuncertainties of life, buy most of us make this “unwise” choice.

2.False. Even if nothing is worth the certainty of death, it does not follow that

nothing is worth (say) a 50% chance of death.3.

False. A risk-averse person will always accept one side or the other of an unfairbet, provided he is permitted to wager a sufficiently small amount. The diagrambelow shows why. John starts at point A and is offered the unfair odds budgetline. If he is allowed to bet on state 1, and if he is allowed to bet an amount thatwill move him to a point- between A and B, then he will do so.

AB

State 1

State 2

Fair Odds

Unfair Odds

45 o

4.

Heads

45 oTails

Slope = -1

5.False. The risk-preferring person pictured below, given the opportunity to bet

on state 1 at the unfair odds that are indicated, would prefer not to bet. If theunfair odds were a bit less unfair, so that the line intersected the horizontal axis

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outside rather than inside the illustrated indifference curve, then he would chooseto bet.

State 1

State 2

Fair Odds

Unfair Odds

45 o

6.Suppose that the Cowboys are favored to beat the Rams. The “Rams” state

of the world occurs if the Rams beat the spread and the “Cowboys” state occursotherwise. This makes the fair odds budget line the line with slope -1 through thebettor’s endowment. The kinked boldfaced line is the budget line that the bettoris offered. He remains at his endowment, by refusing to bet.

Suppose, however, that this bettor has a different view of the odds than othersin the marketplace, and believes that the Rams are very unlikely to beat the spread.Then his indifference curve will be much steeper at the endowment point, since itmust be tangent to the bettor’s perception of what a fair odds line would be. In thiscase, the kinked budget line could cross the demand curve and the bettor wouldplace a bet on the Cowboys.

7. True. Refer to the following graph. If the sickly person with endowment E couldinsure at fair odds, he would select point A on the 45 degree-line, where he isindifferent between getting sick and staying well. If he can insure at odds thatare better than fair, as indicated by the budget line labeled “actual odds,” he willmove to point B. Note that the slope of the indifference curve at C must be thesame as the slope of the indifference curve at A (both slopes reflect fair odds) sothat B must lie to the right of C. Thus after insuring, this individual is better offif he gets sick than if he stays well.

A B

Get Sick

Stay Well

Fair Odds

Actual Odds

o

CE

45

8.False. Exhibit 18-10 demonstrates that the speculator is harmful to society

when he is wrong, and helpful when he is right.

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9.

Quantity(Tons)

Price

D

100 Quantity(Tons)

Price

D

100

a) The speculator stores wheat for delivery next year.b) He continues until this year's price is equal to his expectation ofnext year's price; this happens after he has stored ten tons of wheat.This year's supply is 90 tons. Next year's supply is 90 tons if heis right; 110 tons if he is wrong.c) Without speculator: social gain is A+B+ C With speculator: social gain is A+ C+D.Notice that D is bigger than B (same width, greater height), so thespeculator improves social welfare.d) Without speculator: social gain is A+B+ C +D+E With speculator: social gain is A+ C +D+E+FNotice that F is smaller than B (same width, less height), so thespeculator decreases social welfare.

90 90 110

A B C D E

80

F

10.False. Nobody would ever hold a portfolio that was below the efficient set,

but the individual stocks that make up the portfolio can lie below it. Consider,for example, Exhibit 18-12. An investor who wants to hold portfolio D must holdequal quantities of GSB and GSS. Even though GSB is below the efficient set –it has both greater variance and lower expected return than D has – it is still anessential component of the efficient portfolio D. (In the Exhibit, the efficient set isthe straight line connecting D with GSS. Can you see why?)

11.False; terrorists will take fewer hostages.

12.It is perfectly possible that alcohol mixes badly not with 18-year-olds as such,

but with drivers who have relatively little experience with alcohol. Raising thedrinking age will save 25 go 35 lives taken by 18-year-olds (taking the quotedstudies as reliable) but could very well increase the number of lives taken by 19-year-olds, who would now be in the same position that the 18-year-olds are in.The net number of lives saved could be well under 25. This fits right in withthe “Tweedledee/Tweedledum” and “Lumberjacks’ Income” examples in the text,where it is a mistake to assume blindly that a statistical relationship will continueto hold following a policy change.

13.a) C = A, D = B −Aπ, where π is the rate of inflation.b) As long as π doesn’t change, the expressions Ar + B and Ci + D are equal.c) Presumably, C is negative. Thus he will advise a reduction in the inflation

rate π.

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d) C stays the same. D changes to D′ = D−A(π′−π). Q remains unchanged.The change in government policy causes the coefficient D to change, rendering theold equation useless for making predictions. In this case the coefficient changes byjust enough so that the policy has no effect at all on car sales.

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Chapter Nineteen:

The Nature and Scope of Economic AnalysisGeneral Discussion and Random Thoughts

1) The text draws a number of analogies with physics. Here is another onethat I have used to good effect at appropriate times. Holding a pen, or better yetan apple, at arm’s length, one can ask the physical question: will this pen drop tothe floor within the next 30 seconds? No physicist can answer this question, buta physicist can give a fairly confident conditional answer: If you let go of the pen,and if you do not first put something between it and the floor that will catch it,and if nothing else intervenes, then the pen will drop to the floor. If you don’t letgo, then it won’t.

Similarly, the economist can not predict (say) the interest rate on treasurybills 6 months from now. But he can with some confidence make conditionalpredictions: if the harvest is as good as expected, and if the monetary authoritiesfollow such-and-such policies, and if nothing else intervenes, then the interest rateshould move in such-and- such a way. Predicting the weather, and to a largeextent predicting government policy, is no more the business of the economist thanpredicting whether you will drop the pen is the business of the physicist.

2) More on the role of assumptions: by all means let us make it clear to ourstudents that there is no such thing as a perfectly competitive firm, any morethan there is any such thing as a perfectly frictionless billiard table. Each is aparticularly useful fiction that captures certain important aspects of reality.

3) The textbook presents a naive version of the options pricing model and callsattention to its highly simplified nature (discrete time, only two possible future as-set values, and so forth). This simple model, however, leads to some remarkableconclusions with analogies that hold in the full- blown model: for example, theprobabilities that the stock price will go up or down are not needed to calculatethe option price. There is a general lesson here. A model is good when it suggestssurprising conclusions that are then found to hold in far more general circum-stances. This is a good example with which to illustrate the notion of robustness.

3) Regarding the rationality assumption, there is much more to say. I con-sidered including a section on alternatives, such as the “bounded rationality” and“satisficing” models, but became convinced that this was too far afield for an in-termediate course.

Nevertheless, I think it is an interesting topic for some informal class discus-sion. Before opening this Pandora’s box, however, I strongly recommend assigningthe reading on celebrity endorsements, where I have tried to make a strong casefor extreme caution in abandoning successful assumptions.

That said, there is no harm in some speculation about what might somedayreplace rationality. (Likewise, if I can be allowed one more analogy with physics,there is no harm in some speculation about what might someday replace quantumelectrodynamics; but there would be considerable harm in being too hasty to scrapthe only successful theory we have. Let us make sure that students understand thedistinction.)

To me, the most interesting inspiration for such speculation is the work ofTversky and Kahneman (see for example “Judgment under uncertainty: Heuristicsand biases” in Science 185 (1974), p.1123–1131, and reprinted in Diamond andRothschild’s Uncertainty in Economics. These two psychologists have made a fas-

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cinating attempt to categorize the systematic errors in judgment that people seemto make. These include insensitivity to priors, insensitivity to sample size, etc. Inone study they found that instructors systematically overestimate the effectivenessof punishments and underestimate the effectiveness of rewards. The reason is thatstudents who are punished for poor performance are more likely to improve justby virtue of the fact that their initial performance was poor; students who arerewarded for good perfomances are more likely to disimprove for the analogousreason. The interesting phenomenon is that highly experienced teachers systemat-ically fail to correct for this statistical phenomenon in their gut assessments of theefficacy of various teaching strategies.

Perhaps one day the discoveries of researchers like Tversky and Kahnemanwill be fully incorporated into a more general theory of rationality, which takesaccount of the costs of correcting certain systematic errors and hypothesizes thatpeople only behave “rationally” when the expected benefits outweigh the expectedcosts—that is, they behave rationally when it is rational to do so.

4) Another Tversky-Kahneman-like example is in Raiffa’s book Statistical De-cision Theory . Consider two urns, one containing 70 red balls and 30 white; onecontaining 30 white balls and 70 red. An urn is chosen at random, and 12 balls aredrawn with replacement. 8 are red and 4 are white. How likely is it that the selectedurn is the one with 70 red balls? Raiffa reports that his informal surveys indicatethat people grossly underestimate the probability. In particular, attorneys, whenasked whether the urn is “beyond a reasonable doubt” the predominantly red one,almost invariably reply in the negative. My own informal research bears this out.In fact, a quick calculation reveals that by any reasonable definition of a reasonabledoubt, the correct answer is yes. And yet, people whose profession it is to makesuch determinations are systematically wrong.

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Additional Problems

1. Suppose there are three goods in the world: X, Y and Z. An X can be tradedfor 3 Y’s, a Y can be traded for 2 Z’z, and an X can be traded for 5 Z’s. Whydo you not expect this situation to last?

2. In order to combat the used book market, the publisher of this textbookconsidered sewing a $100 bill into the binding of every 100th book. You wouldhave had to rip the book apart to see if you’d won. Would this have worked?(Take into account the circumstances under which it would even be desirablefor a publisher to combat the used book market. What effect would thisstrategy have on the price of used books? On the price of new books?

3. The Jolly Time Amusement Center offers its patrons the opportunity to playSkee-Ball and other games for 25 cents a play. Perfomance is rewarded withtickets, and large numbers of tickets can be exchanged for prizes, whose marketvalue is typically far less than the cost of playing long enough to win them.Sometimes customers sell tickets to each other for cash. Suppose that JollyTime could prevent these resales. Do you think it would want to?

In the remaining problems, attempt to explain the following phenomena by con-structing theories based on rational behavior. In each case, try to say somethingabout how you might test your theory.

4. People give each other gifts that they are not sure the recipient will like, whenthey could simply give cash instead. Recipients seem to prefer this. (Note:saying that gift-giving demonstrates that the giver cared enough to spend timeshopping is no answer. The giver could demonstrate the same amount of caringby increasing his cash gift sufficiently.)

5. Bank certificates of deposit are usually very ordinary looking pieces of paper,whereas shares of corporate stock are printed on very expensive paper withlots of artwork and calligraphy.

6. People like to all celebrate Christmas on the same day, but they also like toall celebrate their birthdays on different days.

7. A man paid $50 for a ticket to a Broadway show, indicating that he valuedthe ticket at least at $50. When he arrived at the theater, someone offeredhim $50 for his ticket, and he refused, indicating that he still felt the sameway. Then, when he looked in his pocket, he discovered that he had lost theticket and would have to pay $50 for a new one. This he refused to do, andwent home, indicating that he valued a ticket at less than $50.

8. Camera store owners often offer discounts on merchandise to their own em-ployees.

9. 60 years ago, the minimum allow bet at the racetrack was $2. Today the mini-mum allowable bet at the racetrack is $2. Yet everything else has skyrocketedin price.

10. In every culture, parents of daughters are more likely to divorce than parentsof sons.

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Price Theory and Applicationsby

Steven E. Landsburg

Solutions to Problem Set for Chapter 19Most of the problems in this chapter are intended to encourage speculation on

your part, and therefore the answers are not given here. In many cases, the authorof your textbook does not know the answers.

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