NameVersion A

Economics 100B

Practice Final Examination

March 28, 2003

Be sure to mark your form number on your scantron. Students who fail to do so will be slatheredwith non-nonsequitors and roasted in platitudes, by the university Vice President for Public Rela-tions and Damage Control. O�enders will also lose 10 points from their exam scores.

True False Questions: Answer A for True, B for false. Each correct answer is worth 2 points. Eachwrong answer is worth zero. Answers left blank are worth 1 point.

1. If the supply is perfectly elastic, then an upward shift of the demand curve will lead to ahigher price and quantity in equilibrium.

2. If the production function is f(x; y) = minf2x+ y; x+ 2yg; then there are constant returns toscale.

3. A �xed factor is a factor of production that is used in �xed proportion to the level of output.

4. The marginal product of a factor is equal to the derivative of the production function withrespect to the amount of this factor, holding the amounts of other factor inputs constant.

5. It is possible to have decreasing marginal products for all inputs, and yet have increasingreturns to scale.

6. If there are increasing returns to scale, then average costs are a decreasing function of output.

7. If the average cost curve is U shaped, then the marginal cost curve must cross the averagecost curve at the bottom of the U .

8. Price equals marginal cost is a suÆcient condition for pro�t maximization.

9. If there are constant returns to scale in a competitive industry, then the long run industrysupply curve for that industry is horizontal.

Economics 100B 2

10. A discriminating monopolist is able to charge di�erent prices in two di�erent markets. Ifwhen the same price is charged in both markets, the quantity demanded in market 1 isalways greater than the quantity demanded in market 2, then in order to maximize pro�ts,the monopolist should charge a higher price in market 1 than in market 2.

11. A price discriminating monopolist charges p1 in market 1 and p2 in market 2. If p1 > p2; itmust be that the absolute value of the price elasticity in market 1 at price p1 is smaller thanthe absolute value of the price elasticity in market 2 at price p2.

12. The area under the marginal cost curve measures total variable costs.

13. Third degree price discrimination occurs when a monopolist sells output to di�erent peopleat di�erent prices, but every unit that an individual buys costs the same amount.

14. In the Cournot model, each �rm chooses its actions on the assumption that its rivals willreact by changing their quantities in such a way as to maximize their own pro�ts.

15. If a pure public good is provided by voluntary contributions, economic theory predicts thatin general too little will be supplied.

Multiple Choice Questions: Each correct answer is worth 5 points. Each blank answer is worth 1point. Each wrong answer is worth 0 points.

16. The 100 envy-ridden cottagers who live in a circle around Lake Invidious all have the sameutility function, U(c; l; r) = c� l2� r2; where c is a cottager's own consumption and l and r arethe consumptions of the cottager's right and left side neighbors respectively. Each cottageris endowed with one unit of consumption and can costlessly destroy any of this endowment.What would be the socially optimal uniform consumption level for all villagers? If all villagerswere consuming this uniformly optimal amount, would any individual want to consume moreif he could do so without a�ecting consumption by others?

(a) 1=2; yes

(b) 1=2; no

(c) 1=4; yes

(d) 3=4; no

(e) 1, yes

Practice Final Examination 3

17. Kitty Littar, and Scoop Doggie Doo are noncooperating duopolists who produce questionablemusic concerts. The market inverse demand function for these concerts is given by p(Y ) =100 � 2Y; where Y is the total number of concerts produced. Kitty's cost of producing YKconcerts is cK(YK) = 20yK and Scoop's cost of producing yS concerts is cS(yS) = y2S. At theCournot-Nash equilibrium, how many concerts will Kitty produce?

(a) 8

(b) 10

(c) 14

(d) 16

(e) 24

18. Ferdinand Peach, president of Faul Way Motors and Robert Putz, CEO of Pryceler Corp.,are colluding duopolists in the market for fresh lemons. The demand curve for fresh lemonsis given by x = a� p where x is the total quantity of fresh lemons sold and p is the price perlemon. If Putz and Peach have identical marginal costs of $c per lemon and if they decideto share the market equally, what will be the total quantity and price in the fresh lemonmarket?

(a) x = (a� c)=2 and p = (a+ c)=2.

(b) x = 2(a� c)=3 and p = (a+ 2c)=3

(c) x = a� c and p = c

(d) x = (a+ c)=2 and p = (a� c)=2

(e) x = a� 2c and p = 2c

19. Federico Fino runs the Local Arthouse Theater which shows strange foreign movies and sellsstale popcorn. Since Federico �shes the popcorn out of the dumpsters at the Major MultiplexCinema across town, his marginal cost for popcorn is $0 per bag. Nobody in town is willingto pay more than $3 to see one of these movies, but at $3 per movie, he can sell enough ticketsto �ll his theater. Each moviegoer's demand curve for popcorn is given by x = 4�p where x isthe number of bags purchased and p is the price. To maximize pro�ts per customer, Federicoshould:

(a) Charge $11 for the movie and 0 for the popcorn.

(b) Charge $3 for the movie and 0 for the popcorn.

(c) Charge $3 for the movie and $2 per bag for the popcorn.

(d) Charge $5 for the movie and $2 for the popcorn.

(e) Charge $5 for the movie and 0 for the popcorn.

Economics 100B 4

20. Al Fresco is the monopolist pasta supplier in Negaunee, Michigan, and his cost curve formaking pasta is given by c(y) = y2. The demand curve for pasta in Negaunee is given byy = a� bp. In order to maximize pro�ts, Al should set:

(a) y = a=(2 + 2b) and p = (a+ 2ab)=b(2 + 2b).

(b) y = a=(2b� 1) and p = 2a=(2b� 1).

(c) p = a=(2b+ b) and y = a� (ab=(2b+ 2)).

(d) p = a=(2 + b) and y = a� (ab=(2 + b)).

(e) y = (a=2)� b and p = (a=2b) + 1.

21. A competitive �rm uses two variable inputs and has a production f(x1; x2) = (x1 + 3x2)1=2;

where x1 and x2 denote quantities of inputs 1 and 2. The price of output is 6, the price ofinput 1 is 1 and the price of input 2 is 4. What are the �rm's pro�t-maximizing quantitiesof input 1, input 2, and output?

(a) x1 = 36; x2 = 0; output is 6.

(b) x1 = 0; x2 = 27; output is 9.

(c) x1 = 9; x2 = 0; output is 3.

(d) x1 = 18; x2 = 6; output is 6.

(e) x1 = 36=25; x2 = 36=25; output is 12=5.

22. A competitive �rm has the production function y = x1=3. The cost of each unit of the inputx is w and the price of a unit of output is p. The �rm has a �xed cost of FC. The conditionaldemand function for the input x is given by:

(a) x = (p=3)3=2.

(b) C = wx + FC.

(c) x = y1=3.

(d) x = y3.

(e) y = wx=p.

23. The demand for Professor Bongmore's new book is given by the function Q = 5; 000� 100p.If the cost of having the book typeset is 7,000, if the marginal cost of printing an extra copyis 4, and if he has no other costs, then he would maximize his pro�ts by:

(a) having it typeset and selling 2,300 copies.

(b) having it typeset and selling 2,500 copies.

(c) not having it typeset and not selling any copies.

(d) having it typeset and selling 4,600 copies.

(e) having it typeset and selling 1,150 copies.

Practice Final Examination 5

24. Suppose that Dent Carr's long run total cost of repairing s cars per week is c(s) = 4s2 + 64.If the price he receives for repairing a car is 48, then in the long run, how many cars will he�x per week if he maximizes pro�ts?

(a) 6.

(b) 0.

(c) 12.

(d) 9.

(e) 18.

25. George runs a cookie factory. His cookies are made with sugar, peanut oil, and soybean oil.The number of boxes of cookies that he produces is f(su; po; so) = minfsu; po+ 2sog where suis the number of bags of sugar, po the number of canisters of peanut oil, and so the number ofcanisters of soybean oil that he uses. The price of a bag of sugar is 9. The price of a canisterof peanut oil is 6. The price of a canister of soybean oil is 13. If George makes 254 boxes ofcookies in the cheapest way possible, how many canisters of soybean oil will he use?

(a) 127

(b) 0

(c) 84.67

(d) 169.33

(e) 42.33

26. When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product offertilizer is 1 � (N=200) bushels of corn. If the price of corn is $3 per bushel and the priceof fertilizer is $0.90 per pound, then how many pounds of fertilizer per acre should FarmerHoglund use in order to maximize his pro�ts?

(a) 140

(b) 280

(c) 74

(d) 288

(e) 200

27. Suppose that the production function is f(x1; x2) = (xa1+ xa

2)b; where a and b are positive

constants. For what values of a and b is there diminishing technical rate of substitution?

(a) for any value of a if b < 1.

(b) for any values of a and b if ab < 1.

(c) for any values of a and b if a > b.

(d) for any value of b if a < 1.

(e) None of the above.

Economics 100B 6

28. A �rm has the production function, f(x; y) = 10x3=5y2=5. The slope of the �rm's isoquant atthe point (x; y) = (50; 10) is: (Pick the closest one.)

(a) �5.

(b) �1:50.

(c) �0:67.

(d) �0:30.

(e) �2:50.

29. Jan's utility function is C �H2; where C is consumption and H is hours worked per day. Shecan work in the city for 8 hours per day, earning $100 a day. Alternatively, she can rent asmall farm from the landlord, Mr. Porksni�er. If she rents the farm, she can work as manyhours a day as she wishes. If she works H hours per day, she can sell her crops for a total of$20H per day, but she must pay Mr. Porksni�er an annual rent of $R. Mr. Porksni�er wantsto charge the highest rent $R that he can and still be able to get Jan to work for him. Whatis the highest rent he can charge? A penny less than:

(a) $100 per day.

(b) $64 per day.

(c) $60 per day.

(d) $50 per day.

(e) $36 per day.

30. The 130 campers at Bear Creek Campground love their own camp�res, but hate the smokefrom their neighbors' camp�res. Each camper's utility function is U = 26f � f2 � s where fis the number of hours her own camp�re burns per day and where s is the amount of smokein the air. It happens that s is 10 times the average amount of hours that campers use their�res. The campground authority could make all campers better o� by limiting the numberof hours of camp�re per day for everyone. How many hours of camp�res per day should theauthority allow each camper in order to make the typical camper as well o� as possible?

(a) 8

(b) 13

(c) 6

(d) 9

(e) Campers will be best o� if they are free to choose their own amounts of camp�re.

Practice Final Examination 7

31. Two stores are located side by side. They attract customers to each other and to themselvesby advertising. The pro�t functions of the two stores are (75 + x2)x1 � 2x2

1for store 1, and

(120 + x1)x2 � 2x22for store 2, where x1 and x2 are total advertising expenditures by stores 1

and 2 respectively. If each store sets its advertising expenditures independently (as in Nashequilibrium), how much would store 1 spend on advertising?

(a) 28

(b) 30

(c) 25

(d) 33

(e) None of the above.

32. The marginal cost curve of a �rm is MC = 12y. Total variable costs to produce 8 units ofoutput are:

(a) 192.

(b) 384.

(c) 64.

(d) 256.

(e) 28.

33. A competitive �rm has the short run cost function c(y) = 3y3 � 24y2 +96y+10. The �rm willproduce a positive amount in the short run if and only if the price is greater than:

(a) 24.

(b) 96.

(c) 48.

(d) 51.

(e) 47.

34. A �rm has the short run total cost function c(y) = 4y2 + 36. At what quantity of output isshort run average total cost minimized?

(a) 3

(b) 2

(c) 9

(d) 0.67

(e) None of the above.

Economics 100B 8

35. In the absence of government interference, there is a constant marginal cost of $5 per ouncefor growing marijuana and delivering it to buyers. If the probability that any shipment ofmarijuana is seized is 0.10 and if a shipment is seized, the shipper is �ned $45 per ounce andthe shipment is con�scated, then the equilibrium price of marijuana per ounce is:

(a) 10.56.

(b) 9.50.

(c) 50.

(d) 4.50.

(e) 5.50.

36. Touchie McFeelie's production function for comic books is :1J1=2L3=4; where J is the numberof jokes and L is the number of hours of cartoonists labor that he uses. If Touchie can varyboth jokes and cartoonists' labor and if old jokes cost $ 1 each and cartoonists' labor costs$6 per hour, then the cheapest way to produce comics books requires using jokes and laborin the ratio J=L =

(a) 6.

(b) 8.

(c) 2.

(d) 2=3.

(e) 4.

37. A computer software �rm has developed a new and better spreadsheet program. The programis protected by copyrights, so the �rm can act as a monopolist for this product. The demandfunction for the spreadsheet is q = 50; 000� 100p. Any single consumer will want only onecopy. The marginal cost of producing and distributing another copy and its documentationis just $10 per copy. If the company sells this software at the pro�t maximizing monopolyprice, the number of consumers who would not buy the software at the monopoly price butwould be willing to pay at least the marginal cost is:

(a) 50,000.

(b) 12,250.

(c) 14,500.

(d) 24,500.

(e) None of the above.

Practice Final Examination 9

38. A price-discriminating monopolist sells in two separate markets such that goods sold in onemarket are never resold in the other. It charges p1 = 3 in one market and p2 = 7 in the othermarket. At these prices, the price elasticity in the �rst market is �2:50 and the price elasticityin the second market is �0:80. Which of the following actions is sure to raise the monopolistspro�ts?

(a) Lower p2.

(b) Raise p2.

(c) Raise p1 and lower p2.

(d) Raise both p1 and p2.

(e) Raise p2 and lower p1.

39. A monopolist has a constant marginal cost of $2 per unit and no �xed costs. He faces sepa-rate markets in the U.S. and England. He can set one price p1 for the American market andanother price p2 for the English market. If demand in the U.S. is given by Q1 = 8; 400�700p1;and demand in England is given by Q2 = 5; 000� 500p2; then the price in America will:

(a) be larger than the price in England by 1.

(b) be smaller than the price in England by 1.

(c) equal the price in England.

(d) be larger than the price in England by 3.

(e) be smaller than the price in England by 3.

40. Ann and Bruce each own a pizza store in Frostbite Falls, MN. Demand for pizza is givenby Q = 200 � 40P . Each has the cost function C = 60 + 3Q. If Ann and Bruce behave asduopolists each earns a pro�t of

(a) $0.

(b) $� 42:22.

(c) $35.56.

(d) $97.78.

(e) $40.

Economics 100B 10

41. Suppose that the market demand curve for bean sprouts is given by P = 3; 580� 5Q; whereP is the price and Q is total industry output. Suppose that the industry has two �rms, aStackleberg leader and a follower. Each �rm has a constant marginal cost of $80 per unit ofoutput. In equilibrium, total output by the two �rms will be:

(a) 350.

(b) 175.

(c) 525.

(d) 700.

(e) 87.50.

42. The demand for y is given by y = 256=p2. Only two �rms produce y. They have identicalcosts c(y) = y2. If they agree to collude and maximize their joint pro�ts, how much outputwill each �rm produce?

(a) 2

(b) 5

(c) 10

(d) 12

(e) 16

43. Suppose that in a Hawk-Dove game similar to the one discussed in your workbook, the pay-o� to each player is �4 if both play hawk. If both play dove, the payo� to each player is1 and if one plays hawk and the other plays dove, the one that plays hawk gets a payo�of 4 and the one that plays dove gets 0. In equilibrium, we would expect hawks and dovesto do equally well. This happens when the fraction of the total population that plays hawk is:

(a) 0.43.

(b) 0.21.

(c) 0.11.

(d) 0.71.

(e) 1.

Practice Final Examination 11

44. A small co�ee company roasts co�ee beans in its shop. The unroasted beans cost the com-pany 200 cents per pound. The MARGINAL cost of roasting co�ee beans is 150� 10q + q2

cents per pound when q pounds are roasted. The smell of roasting beans imposes costs onthe company's neighbors. The TOTAL amount that neighbors would be willing to pay tohave the shop stop roasting altogether is 5q2; where q is the number of pounds being roasted.The company sells its output in a competitive market at 450 cents per pound. What is thesocially eÆcient amount of co�ee for the company to roast?

(a) 10 lbs.

(b) 15 lbs.

(c) the square root of 10 lbs.

(d) 45 lbs.

(e) None of the above.

45. The Sons of Knute had a hunting lodge up on Loon Lake which burned down last winter.They plan to rebuild it this summer and are trying to decide how large the new lodge shouldbe. The organization has 50 members. The marginal rate of substitution of each of thembetween square feet of hunting lodge and money for other goods is 1:2� :0004y where y is thesize of the hunting lodge in square feet. If the new hunting lodge will cost $20 per squarefoot to rebuild, what is the eÆcient size for the new hunting lodge?

(a) 1,000 square feet

(b) 1,200 square feet

(c) 2,000 square feet

(d) 2,400 square feet

(e) None of the above.

ANSWER KEY

Version A

Economics 100B

Practice Final Examination

May 26, 1999

Exam

Question

Number Answer

1 F2 T3 F4 T5 T6 T7 T8 F9 T10 F11 T12 T13 T14 F15 T16 C17 C18 A19 A20 A21 C22 D23 A24 A25 B26 A27 D28 D29 B30 A31 A32 B33 C34 A35 A36 E37 D38 B39 A40 B41 C42 A43 A

Economics 100B 2

44 A45 C