analyzing economic problems - cairo...

During the technology bubble of the late 1990s, new start-ups and established companies invested

billions of dollars to exploit new opportunities created by the Internet. Some high-profile start-ups,

such as Amazon.com, have survived but have yet to make a profit. A very few, the most noteworthy

example being eBay, have survived and become quite profitable. Big bets on the Internet economy

devastated some traditional companies, such as Corning in the optical fiber manufacturing industry,

while others such as Walgreen’s have smoothly and profitably incorporated new technologies into

their existing business models.

Amid the euphoria of the bubble years, many gurus preached that the rules of economics

had changed and that the New Economy, built around the Internet, was destined to be fundamen-

tally different from the Old Economy. The demise of scores of Internet start-ups that failed to

generate sufficient demand, or were unable to control costs, or withered in the face of new com-

petitors, is compelling testimony that this prediction was untrue. The fundamental principles of

microeconomics—the main subject of this book—have not materially changed, and they are just as

relevant for a New Economy built around the Internet, broadband, and wi-fi as they were for the

Old Economy that predated these technological developments.

Is the New Economy Really New?

1.1W H Y S T U D Y M I C R O E C O N O M I C S ?

1.2T H R E E K E Y A N A LY T I C A L T O O L S APPLICATION 1.1 Generating Electricity: 8760

Decisions per Year

1A N A LY Z I N G E C O N O M I CP R O B L E M S

C H A P T E R

1.3P O S I T I V E A N D N O R M AT I V EA N A LY S I S

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To develop this point further, let’s take a closer look at a number of firms that made significant

investments to exploit opportunities created by the Internet:

• The Internet auction company eBay does what traditional markets have done for centuries. It

brings together sellers of goods with buyers of goods. eBay facilitates the trading of goods ranging

from Beanie Babies and baseball cards to motorcycles and high-performance automobiles. Seeking

ways to make its markets work more smoothly, eBay has invested in mechanisms that facilitate ex-

change in traditional markets, including customer reviews, fraud protection, and mediation services.

• The Internet bookseller Amazon.com faces many of the same problems as traditional business

firms. It must figure out how to set prices for the books it sells, especially in light of pressure from

competitors such as Barnes & Noble, Columbia House, and Wal-Mart. And it must figure out the

appropriate mix of resources to employ, just as traditional business firms must do. Among other

things, it must decide how many workers to hire to maintain its Web site and how much warehouse

space to lease to store the books it ships to consumers. Amazon.com hopes to make a profit in the

next couple of years.

• Corning Inc. is perhaps best known as the producer of Pyrex glass cookware, but in the late 1990s it

sold its glass cookware business, along with a number of other profitable business units, to focus on

achieving dominant market share in the fiber-optic cable manufacturing market. With telecommuni-

cations companies such as Level 3, Global Crossing, and Worldcom launching ambitious plans to

build nationwide fiber-optic networks to capitalize on anticipated growth in Internet traffic, Corn-

ing’s big bet seemed eminently sensible in the late 1990s. And for a time, the market rewarded Corn-

ing’s ambitions: as late as September 2000, Corning’s stock price was $113 a share (by contrast, in

summer 2003, it was less than $10 a share). Unfortunately, Corning became a high-profile victim of

the crash of the telecom sector. Spurred by forecasts

that Internet traffic would double every three months,

numerous companies entered the telecommunications

business with plans to build vast fiber-optic networks.

But those forecasts proved to be grossly exaggerated,

and the long-haul telecommunications market experi-

enced a meltdown that saw 60 carriers file for bank-

ruptcy between 2000 and 2002. For its part, Corning’s

optical fiber business experienced a decline in revenue

of over 40 percent between 2000 and 2001, leading

one Merrill Lynch analyst to liken Corning’s situation to

a “nuclear winter” (the barren landscape and devastat-

ing loss of life following a nuclear war).

Microeconomic themes are prominent parts of

the stories we have just described. The success of eBay

illustrates just how important markets and prices are.

eBay makes money because, in effect, it creates

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markets and allows prices to “clear” these markets. The ongoing challenges facing Amazon.com

illustrate the importance of understanding the constraints that business firms face. Amazon makes

decisions on the organization of its operations and on prices, recognizing that it does not fully con-

trol its own destiny. Its executives would undoubtedly love to be able to double sales every month

(as Amazon did in 1997 and 1998), while maintaining a big margin between its prices and costs. But

wishing these things were so does not make them so. Amazon is constrained by market demand, by

the actions of competitors, and by the limitations imposed by what is feasible technologically. The

collapse of the long-haul telecom market that has made life so difficult for Corning illustrates the

power of market forces in keeping companies from capturing profits. The competitive dynamic that

played out in the market for long-haul telecommunications has occurred in many other markets

throughout history and around the world: when profit opportunities are freely available to all firms,

the profits often do not last or may never be realized in the first place! This is one of the most

important lessons of microeconomics.

Microeconomics can help you understand the world around you. Nearly all microeconomic

studies, whether about competition on the Internet, the purchasing behavior of individual house-

holds, or the study of social phenomena such as crime and marriage (yes, economists have studied

these), rely on three powerful analytical tools—constrained optimization, equilibrium analysis, and

comparative statics analysis.

C H A P T E R P R E V I E W In this chapter, you will

• Learn the distinction between microeconomics and macroeconomics.

• See why economics can be considered the science of constrained choice, dealing with the

allocation of scarce resources.

• Learn the distinction between endogenous and exogenous variables.

• Be introduced to the study of constrained optimization and learn about marginal reasoning.

• Be introduced to equilibrium analysis.

• Learn how comparative statics can be applied both to constrained optimization and to

equilibrium analysis.

• Learn the distinction between positive analysis and normative analysis.

1 . 1 W H Y S T U D Y M I C R O E C O N O M I C S ? 3

1.1W H Y S T U D YM I C R O E C O -N O M I C S ?

Economics is the science that deals with the allocation of limited resources to satisfyunlimited human wants. Think of human wants as being all the goods and services thatindividuals desire, including food, clothing, shelter, and anything else that enhances thequality of life. Since we can always think of ways to improve our well-being with moreor better goods and services, our wants are unlimited. However, to produce goods andservices, we need resources, including labor, managerial talent, capital, and raw mate-rials. Resources are said to be scarce because their supply is limited. The scarcity ofresources means that we are constrained in the choices we can make about the goodsand services we produce, and thus also about which human wants we will ultimatelysatisfy. That is why economics is often described as the science of constrained choice.

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Broadly speaking, economics is composed of two branches, microeconomics andmacroeconomics. The prefix micro is derived from the Greek word mikros, whichmeans “small.” Microeconomics therefore studies the economic behavior of individualeconomic decision makers, such as a consumer, a worker, a firm, or a manager. It alsoanalyzes the behavior of individual households, industries, markets, labor unions, ortrade associations. By contrast, the prefix macro comes from the Greek word makros,which means “large.” Macroeconomics thus analyzes how an entire national economyperforms. A course in macroeconomics would examine aggregate levels of income andemployment, the levels of interest rates and prices, the rate of inflation, and the natureof business cycles in a national economy.

Constrained choice is important in both macroeconomics and microeconomics.For example, in macroeconomics we would see that a society with full employmentcould produce more goods for national defense, but it would then have to producefewer civilian goods. It might use more of its depletable natural resources, such as nat-ural gas, coal, and oil, to manufacture goods today, in which case it would conserve lessof these resources for the future. In a microeconomic setting, a consumer might decideto allocate more time to work, but would then have less time available for leisure activ-ities. The consumer could spend more income on consumption today, but would thensave less for tomorrow. A manager might decide to spend more of a firm’s resources onadvertising, but this might leave less available for research and development.

Every society has its own way of deciding how to allocate its scarce resources.Some resort to a highly centralized organization. For example, during the Cold War,governmental bureaucracies heavily controlled the allocation of resources in theeconomies of Eastern Europe and the Soviet Union. Other countries, such as those inNorth America or Western Europe, have historically relied on a mostly decentralizedmarket system to allocate resources. Regardless of its market system, every societymust answer these questions:

• What goods and services will be produced, and in what quantities?

• Who will produce the goods and services, and how?

• Who will receive the goods and services?

Microeconomic analysis attempts to answer these questions by studying thebehavior of individual economic units. By answering questions about how consumersand producers behave, microeconomics helps us understand the pieces that collectivelymake up a model of an entire economy. Microeconomic analysis also provides the foun-dation for examining the role of the government in the economy and the effects of gov-ernment actions. Microeconomic tools are commonly used to address some of the mostimportant issues in contemporary society. These include (but are not limited to) pollu-tion, rent controls, minimum wage laws, import tariffs and quotas, taxes and subsidies,food stamps, government housing and educational assistance programs, governmenthealth care programs, workplace safety, and the regulation of private firms.

4 C H A P T E R 1 A N A LY Z I N G E C O N O M I C P R O B L E M S

1.2T H R E E K E YA N A LY T I C A LT O O L S

To study real phenomena in a world that is exceedingly complex, economists con-struct and analyze economic models, or formal descriptions, of the problems they areaddressing. An economic model is like a roadmap. A roadmap takes a complex physi-cal reality (terrain, roads, houses, stores, parking lots, alleyways, and other features)and strips it down to bare essentials: major streets and highways. The roadmap is anabstract model that serves a particular purpose—it shows us where we are and how we

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can get where we want to go. To provide a clear representation of reality, it “ignores”or “abstracts from” much of the rich detail (the location of beautiful elm trees orstately homes, for example) that makes an individual town unique and charming.

Economic models operate in much the same way. For example, to understand howa drought in Colombia might affect the price of coffee in the United States, an econ-omist might employ a model that ignores much of the rich detail of the industry,including some aspects of its history or the personalities of the people who work in thefields. These details might make an interesting article in Business Week, but they do nothelp us understand the fundamental forces that determine the price of coffee.

Any model, whether it is used to study chemistry, physics, or economics, mustspecify what variables will be taken as given in the analysis and what variables are tobe determined by the model. This brings us to the important distinction betweenexogenous and endogenous variables. An exogenous variable is one whose value is takenas given in a model. In other words the value of an exogenous variable is determinedby some process outside the model being examined. An endogenous variable is avariable whose value is determined within the model being studied.

To understand the distinction, suppose you want to build a model to predict howfar a ball will fall after it is released from the top of a tall building. You might assumethat certain variables, such as the force of gravity and the density of the air throughwhich the ball must pass, are taken as given (exogenous) in your analysis. Given theexogenous variables, your model will describe the relationship between the distancethe ball will drop and the time elapsed after it is released. The distance and timepredicted by your model are endogenous variables.

Nearly all microeconomic models rely on just three key analytical tools. Webelieve this makes microeconomics unique as a field of study. No matter what thespecific issue is—coffee prices in the United States, or decision making by firms onthe Internet—microeconomics uses the same three analytical tools:

• Constrained optimization

• Equilibrium analysis

• Comparative statics

Throughout this book, we will apply these tools to microeconomic problems.This section introduces these three tools and provides examples of how they can beemployed. Do not expect to master these tools just by reading this chapter. Rather, youshould learn to recognize them when we apply them in later chapters.

C O N S T R A I N E D O P T I M I Z AT I O NAs we noted earlier, economics is the science of constrained choice. The tool ofconstrained optimization is used when a decision maker seeks to make the best(optimal) choice, taking into account any possible limitations or restrictions on thechoices. We can therefore think about constrained optimization problems as havingtwo parts, an objective function and a set of constraints. An objective function is therelationship that the decision maker seeks to “optimize,” that is, either maximize orminimize. For example, a consumer may want to purchase goods to maximize hersatisfaction. In this case, the objective function would be the relationship thatdescribes how satisfied she will be when she purchases any particular set of goods.Similarly, a producer may want to plan production activities to minimize the costs ofmanufacturing its product. Here the objective function would show how the total costsof production depend on the various production plans available to the firm.

1 . 2 T H R E E K E Y A N A LY T I C A L T O O L S 5

exogenous variable Avariable whose value is takenas given in the analysis ofan economic system.

endogenous variable Avariable whose value is deter-mined within the economicsystem being studied.

constrained optimizationAn analytical tool for makingthe best (optimal) choice,taking into account anypossible limitations orrestrictions on the choice.

objective function Therelationship that a decisionmaker seeks to maximize orminimize.

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Decision makers must also recognize that there are often restrictions on thechoices they may actually select. These restrictions reflect the fact that resources arescarce, or that for some other reason only certain choices can be made. The constraintsin a constrained optimization problem represent restrictions or limits that are imposedon the decision maker.

Examples of Constrained OptimizationTo make sure that the difference between an objective function and a constraint isclear, let’s consider two examples. See if you can identify the objective function and theconstraint in each example. (Do not attempt to solve the problems. We will presenttechniques for solving them in later chapters. At this stage the important point issimply to understand examples of constrained optimization problems.)

L E A R N I N G - B Y - D O I N G E X E R C I S E 1.1Constrained Optimization: The Farmer’s Fence

Suppose a farmer plans to build a rectangular fence as a pen for his sheep. Hehas F feet of fence and cannot afford to purchase more. However, he canchoose the dimensions of the pen, which will have a length of L feet and a

width of W feet. He wants to choose the dimensions L and W that will maximize the areaof the pen. He must also make sure that the total amount of fencing he uses (the perimeterof the pen) does not exceed F feet.

Problem

(a) What is the objective function for this problem?

(b) What is the constraint?

(c) Which of the variables in this model (L, W, and F ) are exogenous? Which are endoge-nous? Explain.

Solution

(a) The objective function is the relationship that the farmer is trying to maximize—in thiscase, the area LW. In other words, the farmer will choose L and W to maximize the objec-tive function LW.

(b) The constraint will describe the restriction imposed on the farmer. We are told that thefarmer has only F feet of fence available for the rectangular pen. The constraint willdescribe the restriction that the perimeter of the pen 2L + 2W must not exceed the amountof fence available, F. Therefore, the constraint can be written as 2L + 2W ≤ F .

(c) The farmer is given only F feet of fence to work with. Thus, the perimeter F is anexogenous variable, since it is taken as given in the analysis. The endogenous variables areL and W, since their values can be chosen by the farmer (determined within the model).

By convention, economists usually state a constrained optimization problem likethe one facing the farmer in the following way:

max(L,W )

LW

subject to: 2L + 2W ≤ F

E

S

D


constraints The restric-tions or limits imposedon a decision maker in aconstrained optimizationproblem.

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The first line identifies the objective function, the area LW, and tells whether it isto be maximized or minimized. (If the objective function were to be minimized, “max”would be “min.’’) Underneath the “max” is a list of the endogenous variables that thedecision maker (the farmer) controls; in this example, “(L, W ) ” indicates that thefarmer can choose the length and the width of the pen.

The second line represents the constraint on the perimeter. It tells us that thefarmer can choose L and W as long as (“subject to” the constraint that) the perimeterdoes not exceed F. Taken together, the two lines of the problem tell us that the farmerwill choose L and W to maximize the area, but those choices are subject to the con-straint on the amount of fence available.

We now illustrate the concept of constrained optimization with a famous problemin microeconomics, consumer choice. (Consumer choice will be analyzed in depth inChapters 3, 4, and 5.)

L E A R N I N G - B Y - D O I N G E X E R C I S E 1.2Constrained Optimization: Consumer Choice

Suppose a consumer purchases only two types of goods, food and clothing.The consumer has to decide how many units of each good to purchase eachmonth. Let F be the number of units of food that she purchases each month,

and C the number of units of clothing. She wants to maximize her satisfaction with the twogoods. Suppose the consumer’s level of satisfaction when she purchases F units of food andC units of clothing is measured by the product FC, but she can purchase only limitedamounts of goods per month because she must live within her budget. Goods cost moneyand the consumer has a limited income. To keep the example simple, suppose the consumerhas a fixed monthly income I, and she must not spend more than I during the month. Eachunit of food costs PF and each unit of clothing costs PC .

Problem

(a) What is the objective function for this problem?

(b) What is the constraint?

(c) Which variables (PF , F, PC , C, and I) are exogenous? Which are endogenous? Explain.

(d) Write a statement of the constrained optimization problem.

Solution

(a) The objective function is the relationship that the consumer seeks to maximize. In thisexample she will choose the amount of food and clothing to maximize her satisfaction,measured by FC. Thus, the objective function is FC.

(b) The constraint represents the amounts of food and clothing that she may choose whileliving within her income. If she buys F units of food at a price of PF per unit, her totalexpenditure on food will be (PF )(F ). If she buys C units of clothing at a price of PC per unit,her total expenditure on clothing will be (PC )(C ). Therefore, her total expenditure will be( PF )(F ) + ( PC )(C) . Since her total expenditure must not exceed her total income I, theconstraint is ( PF )(F ) + ( PC )(C) ≤ I .

(c) The exogenous variables are the ones the consumer takes as given when she makes herpurchasing decisions. Since her monthly income is fixed, I is exogenous. The prices offood PF and clothing PC are also exogenous, since she cannot control these prices. The

E

S

D


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consumer’s only choices are the amounts of food and clothing to buy; hence, F and C arethe endogenous variables.

(d) The statement of the constrained optimization problem is

max(F,C)

FC

subject to: ( PF )(F ) + ( PC )(C) ≤ I

The first line shows that the consumer wants to maximize FC, and that she can choose Fand C. The second line describes the constraint: Total expenditure cannot exceed totalincome.

Similar Problem: 1.3


function must take these cost differences intoaccount.

• If the company expects the demand for electricityto be low for a long period of time, it may want toshut down production at some of its plants. Butthere are substantial costs to starting up and shut-ting down plants. Thus, if the company expects thedemand for electricity to be low for only a shorttime (e.g., a few hours), it might not want to shutdown a plant that will be needed again when thedemand goes up.

• The company must also take into account thecosts of transmitting power from the generatorsto its customers.

• There is a spot market for electricity during eachhour of the day. A company may buy or sell powerfrom other electric power companies. If the com-pany can purchase electricity at a low enoughprice, it may be able to lower the costs of serviceby buying some electricity from other producers,instead of generating all of the required electricityitself. If it can sell electricity at a high enoughprice, the company may find it profitable to gener-ate more electricity than its customers need. It canthen sell the extra electricity to other powercompanies.

Electric power companies typically make productiondecisions on an hourly basis—that’s 8760 (365 daystimes 24 hours per day) production decisions a year!1

Examples of constrained optimization are all around us.Electric power companies typically own and operateplants that produce electricity. A company must decidehow much electricity to produce at each plant to meetthe needs of its customers.

The constrained optimization problem for a powercompany can be complex:

• The company needs to generate enough power toensure that its customers receive service duringeach hour of the day.

• To make good production decisions, the companymust forecast the demand for electricity. Thedemand for electricity varies from one hour toanother during the day, as well as across seasonsof the year. For example, in the summer the highestdemand may occur in the afternoon when cus-tomers use air conditioners to cool offices andhomes. The demand for power may declineconsiderably in the evening as the temperature falls.

• Some of the company’s plants are relatively expen-sive to operate. For example, it is more expensiveto produce electricity by burning oil than by burn-ing natural gas. Plants using nuclear fuel are evenless costly to run. If the company wants to producepower at the lowest possible cost, its objective

A P P L I C A T I O N 1.1

Generating Electricity: 8760 Decisionsper Year

1For a good discussion of the structure of electricity markets, see P. Joskow and R. Schmalensee, Marketsfor Power: An Analysis of Electric Utility Deregulation (Cambridge, Mass: MIT Press, 1983).

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Marginal Reasoning and Constrained OptimizationConstrained optimization analysis can reveal that the “obvious’’ answers to economicquestions may not always be correct. We will illustrate this point by showing howconstrained optimization problems can be solved using marginal reasoning.

Imagine that you are the product manager for a small beer company that producesa high-quality microbrewed ale. You have a $1 million media advertising budget forthe next year, and you have to allocate it between local television and radio spots.Although radio spots are cheaper, television spots reach a far wider audience. Televi-sion spots are also more persuasive and thus on average stimulate more new sales.

To understand the impact of a given amount of money spent on radio and TVadvertisements, you have studied the market. Your research findings, presented inTable 1.1, estimate the new sales of your beer when a given amount of money is spenton TV advertising and on radio advertising. For example, if you spent $1 million onTV advertising, you would generate 25,000 barrels of new beer sales per year. By con-trast, if you spent $1 million on radio advertising, you would generate 5,000 barrels ofnew sales per year. Of course, you could also split your advertising budget between thetwo media, and Table 1.1 tells you the impact of that decision, too. For example, if youspent $400,000 on TV and $600,000 on radio, you would generate 16,000 barrels ofnew sales from the TV ads and 4,200 barrels in new sales from the radio ads, for a totalof 16,000 + 4,200 � 20,200 barrels of beer overall.

In light of the information in Table 1.1, how would you allocate your advertisingbudget if your objective is to maximize the new sales of beer?

This is a constrained optimization problem. You want to allocate spending onTV and radio in a way that maximizes an objective (new sales of beer) subject to theconstraint that the total amount spent on TV and radio must not exceed your $1 mil-lion advertising budget. Using notation similar to that introduced in the previoussection, if B(T, R) represents the amount of new beer sales when you spend T dol-lars on television advertising and R dollars on radio advertising, your constrained


TABLE 1.1 New Beer Sales Resulting from Amounts Spent on TV and Radio Advertising

New Beer Sales Generated (in barrels per year)

Total Spent TV Radio

$ 0 0 0$ 100,000 4,750 950$ 200,000 9,000 1,800$ 300,000 12,750 2,550$ 400,000 16,000 3,200$ 500,000 18,750 3,750$ 600,000 21,000 4,200$ 700,000 22,750 4,550$ 800,000 24,000 4,800$ 900,000 24,750 4,950$1,000,000 25,000 5,000

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optimization problem is

max(T, R)

B(T, R)

subject to: T + R = 1,000,000

A quick reading of Table 1.1 might suggest an “obvious” answer to this problem:Allocate your entire $1 million budget to TV spots and spend nothing on radio. Afterall, as Table 1.1 suggests, a given amount of money spent on TV always generatesmore new sales than the same amount of money spent on radio advertising. (In fact, agiven amount of TV advertising is five times as productive in generating new sales asis the same amount of radio advertising.) However, this answer is incorrect. And thereason that it is incorrect illustrates the power and importance of constrained opti-mization analysis in economics.

Suppose you contemplate spending your entire budget on TV ads. Under thatplan, you would expect to get 25,000 barrels of new sales. But consider, now, whatwould happen if you spent only $900,000 on TV ads and $100,000 on radio ads. FromTable 1.1, we see that your TV ads would then generate 24,750 barrels of new beersales, and your radio ads would generate 950 barrels of new beer sales. Thus, underthis plan your $1 million budget generates new beer sales equal to 25,700 barrels. Thisis 700 barrels higher than before. In fact, you can do even better. By spending$800,000 on TV and $200,000 on radio, you can generate 25,800 barrels of new beersales. Even though Table 1.1 seems to imply that radio ads are far less powerful thanTV ads, it makes sense in light of your objective to split your budget between radioand TV advertising.

This example highlights a theme that comes up repeatedly in microeconomics:The solution to any constrained optimization problem depends on the marginalimpact of the decision variables on the value of the objective function. The marginalimpact of money spent on TV advertising is how much new beer sales go up for everyadditional dollar spent on TV advertising. The marginal impact of money spent onradio advertising is the rate at which new beer sales go up for every additional dollarspent on radio advertising. You want to allocate some money to radio advertisingbecause once you have allocated $800,000 of the $1,000,000 budget to TV, themarginal impact of an additional $100,000 spent on TV advertising is less than themarginal impact of an additional $100,000 spent on radio advertising. Why? Becausethe rate at which new beer sales increase when we allocate that next $100,000 to TVadvertising is (24,750 − 24,000)/100,000, or 0.0075 barrels per additional dollar spenton TV advertising. But the rate at which new beer sales increase when we allocate thenext $100,000 to radio advertising is (24,000 + 950 − 24,000)/100,000 or 0.0095 bar-rels per additional dollar spent on radio advertising. Thus, the marginal impact ofradio advertising exceeds the marginal impact of TV advertising. In light of that, wenow want to allocate this additional $100,000 of our advertising budget to radio,rather than TV. (In fact, as we already saw, you would want to go even further andallocate the last $200,000 in your budget to radio spots.)

In our advertising story, marginal reasoning leads to a not-so-obvious conclusionthat might make you uncomfortable, or perhaps even skeptical. That’s fine—that’s howstudents often react when they first encounter marginal reasoning in microeconomicsclasses. But whether you realize it or not, we all use marginal reasoning in our dailylives. For example, even though pizza may be your favorite food and you may prefer to


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eat it rather than vegetables like carrots and broccoli, you probably don’t spend all ofyour weekly food budget on pizza. Why not? The reason must be that at some point(perhaps after having eaten pizza for dinner Monday through Saturday nights), theadditional pleasure or satisfaction that you get from spending another $10 of your foodbudget on a pizza is less than what you would get from spending that $10 of yourbudget on something else. Although you may not realize it, this is marginal reasoningin a constrained optimization problem.

The term marginal in microeconomics tells us how a dependent variable changes asa result of adding one unit of an independent variable. The terms independent variableand dependent variable may be new to you. To understand them, think of a relationshipbetween two variables, such as between production volume (what economists calloutput) and the total cost of manufacturing a product. We would expect that as a firmproduces more, its total cost goes up. In this example, we would classify total cost asthe dependent variable because its value depends on the volume of production, whichwe refer to as the independent variable.

Marginal cost measures the incremental impact of the last unit of the independentvariable (output) on the dependent variable (total cost). For example, if it costs an extra$5 to increase production by one unit, the marginal cost will be $5. Equivalently, mar-ginal cost can be thought of as a rate of change of the dependent variable (again, totalcost) as the independent variable (output) changes. If the marginal cost is $5, total costis rising at a rate of $5 when a new unit of output is produced.

We will use marginal measures throughout this book. For example, we will use itin Chapters 4 and 5 to find the solution to the consumer choice problem described inLearning-By-Doing Exercise 1.2.

E Q U I L I B R I U M A N A LY S I SA second important tool in microeconomics is the analysis of equilibrium, a conceptfound in many branches of science. An equilibrium in a system is a state or conditionthat will continue indefinitely as long as exogenous factors remain unchanged—that is,as long as no outside factor upsets the equilibrium. To illustrate an equilibrium, imag-ine a physical system consisting of a ball in a cup, as is depicted in Figure 1.1. Here theforce of gravity pulls the ball downward toward the bottom of the cup. A ball initiallyheld at point A will not remain at point A when the ball is released. Rather, it will rockback and forth until it settles at point B. Thus, the system is not in equilibriumwhen the ball is released at A because the ball will not remain there. It would be in


equilibrium A state orcondition that will continueindefinitely as long as factorsexogenous to the systemremain unchanged.

Force of gravity

A

B

FIGURE 1.1 Equilibrium with a Ball and CupThis physical system is in equilibrium when theball is resting at point B at the bottom of the cup.The ball could remain there indefinitely. Thesystem will not be in equilibrium when the ball isat point A because the force of gravity would pullthe ball toward B.

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equilibrium if the ball were released at B. The system will remain in equilibrium whenthe ball is at B until some exogenous factor changes; for example, if someone were totip the cup, the ball would move from B to another point.

You may have encountered the notion of an equilibrium in competitive marketsearlier in an introductory course in economics. In Chapter 2 we will provide a moredetailed treatment of markets, supply, and demand. But for now let’s briefly review howthe analysis of supply and demand can illustrate the concept of equilibrium in a market.

Consider the worldwide market for coffee beans. Suppose the demand and supplycurves for coffee beans are as depicted in Figure 1.2. The demand curve tells us whatquantity of coffee beans (Q) would be purchased in that market at any given price.Think of a demand curve as representing the answer to a set of “what if” questions. Forexample, what quantity of coffee beans would be demanded if the price were $2.50 perpound? The demand curve in Figure 1.2 tells us that Q2 pounds would be purchasedif the price of coffee beans were $2.50 per pound. The demand curve also shows usthat Q4 pounds would be purchased if the price were $1.50 per pound. The negativeor downward slope of the demand curve shows that higher prices tend to reduce theconsumption of coffee.

The supply curve shows what quantity of coffee beans would be offered for sale inthe market at any given price. You can also view a supply curve as representing theanswer to a set of “what if ” questions. For example, what quantity of coffee beanswould be offered for sale if the price were $1.50 per pound? The supply curve inFigure 1.2 shows us that Q1 pounds would be offered for sale at that price. The supplycurve also indicates that if the price were $2.50 per pound, Q5 pounds would beoffered for sale. The positive (or upward) slope of the supply curve suggests thathigher prices tend to stimulate production.

How is the concept of equilibrium related to this discussion of supply anddemand? In a competitive market, equilibrium is achieved at a price at which themarket clears—that is, at a price at which the quantity offered for sale just equals thequantity demanded by consumers. The coffee bean market depicted in Figure 1.2 willclear when the price is $2.00 per pound. At that price the producers will want to offer


Quantity (pounds)

Demand (D)

Supply (S )Excesssupply

Excessdemand

Pric

e pe

r po

und

(dol

lars

)

Q4

Q5Q3Q2

1.50

2.50

2.00

Q1

FIGURE 1.2 Equilibrium in the Market for Coffee BeansThe equilibrium price of coffee beans is $2.00 per pound. Atthat price the market clears (the quantity supplied and thequantity demanded are equal at Q3 pounds). The marketwould not be in equilibrium at a price above $2.00 becausethere would be excess supply. The market would also not bein equilibrium at a price below $2.00, since there would beexcess demand.

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Q3 pounds for sale, and consumers will want to buy just that amount. (In graphicalterms, as illustrated by Figure 1.2, equilibrium occurs at the point where the demandcurve and the supply curve intersect.) All consumers who are willing to pay $2.00 perpound are able to buy it, and all producers willing to sell at that price can find buyers.The price of $2.00, therefore, could stay the same indefinitely because there is noupward or downward pressure on price. There is, in other words, an equilibrium.

To understand why one state of a system is in equilibrium, it helps to see whyother states are not in equilibrium. If the ball in Figure 1.1, were released at someposition other than at the bottom of the cup, gravity would move it to the bottom.What happens in the competitive market at non-equilibrium prices? For example, whywould the coffee market not be in equilibrium if the price of coffee were $2.50 perpound? At that price, only Q2 pounds would be demanded, but Q5 pounds would beoffered for sale. Thus, there would be an excess supply of coffee in the market. Somesellers would not find buyers for their coffee beans. To find buyers, these disappointedproducers would be willing to sell for less than $2.50. The market price would need tofall to $2.00 to eliminate the excess supply.

Similarly, one might ask why a price below $2.00 is not an equilibrium price.Consider a price of $1.50. At this price the quantity demanded would be Q4 pounds,but only Q1 pounds would be offered for sale. There would then be excess demand inthe market. Some buyers would be unable to obtain coffee beans. These disappointedbuyers will be willing to pay more than $1.50 per pound. The market price would needto rise to $2.00 to eliminate the excess demand and the upward pressure that it gener-ates on the market price.

C O M PA R AT I V E S TAT I C SOur third key analytical tool, comparative statics analysis, is used to examine howa change in an exogenous variable will affect the level of an endogenous variable inan economic model. (See the discussion of exogenous and endogenous variables onpage 5.) Comparative statics analysis can be applied to constrained optimization prob-lems or to equilibrium analyses. Comparative statics allows us to do a “before-and-after” analysis by comparing two snapshots of an economic model. The first snapshottells us the levels of the endogenous variables given a set of initial values of exogenousvariables. The second snapshot tells us how an endogenous variable we care about haschanged in response to an exogenous shock—that is, a change in the level of someexogenous variable.

Let’s consider an example of how comparative statics might be applied to a modelof equilibrium. In the spring of 1997, heavy rains soaked Central America, strikesdisrupted Colombia, and frosts hit Brazil. All of these exogenous shocks affected theworld market for coffee beans, causing coffee prices on the Coffee, Sugar & CocoaExchange in New York to soar to a 20-year high. The price of coffee beans rose fromabout $1 per pound at the beginning of the year to more than $3 per pound in May.

We can use comparative statics to illustrate what happened in the market forcoffee beans. The heavy rains, strikes, and frost all led to a decrease (a leftward shift)in the world’s supply curve for coffee beans. Before these events the supply curve wasS1 and the demand curve was D1, as shown in Figure 1.3. The first snapshot of themarket shows an equilibrium price for coffee beans (an endogenous variable) of $1 perpound, and an equilibrium quantity (also an endogenous variable) of Q1. The exoge-nous shocks moved the supply curve to the left, to S2. However, because consumerdemand for coffee is largely unaffected by heavy rains, strikes, and frost, it is quite


comparative staticsAnalysis used to examinehow a change in some exoge-nous variable will affect thelevel of some endogenousvariable in an economicsystem.

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reasonable to assume that the location of the demand curve did not change. Thesecond snapshot of the market indicates an equilibrium price of coffee beans of about$3 per pound, with an equilibrium quantity of Q2. The comparative statics analysisshows that the exogenous shocks led to an increase in price from $1 per pound to $3per pound and a decrease in quantity from Q1 to Q2.

Almost every day you can find examples of comparative statics in The Wall StreetJournal or in the business section of your local newspaper. Typical items deal withexogenous events that influence the prices of agricultural commodities (such as corn,soybeans, wheat, coffee, and cotton), livestock, and metals (such as copper, gold, andsilver). It is not unusual to see headlines such as “Coffee Prices Jump on News ofColombian Labor Strike,” “Corn Prices Surge as Export Demand Increases,” “SoybeanPrices Leap on Dry Weather Worries,” and “Silver Prices Soar on Signs of TightSupplies.” When you see headlines such as these, think about them in terms of compar-ative statics.

The following two exercises illustrate how comparative statics analysis might beused with a model of market equilibrium and a model of constrained optimization.

L E A R N I N G - B Y - D O I N G E X E R C I S E 1.3Comparative Statics with Market Equilibrium in the U.S. Market for Corn

Suppose that in the United States the quantity of corn demanded Qd dependson two things: the price of corn P and the level of income in the

nation I. Assume that the demand curve for corn is downward sloping, so that more cornwill be demanded when the price of corn is lower. Assume also that the demand curve shiftsto the right if income rises (i.e., higher income increases the demand for corn). Thedependence of the quantity of corn demanded on the price of corn and income is repre-sented by the demand function Qd(P,I ).

Suppose the quantity of corn offered for sale, Qs, also depends on two things: the priceof corn, P, and the amount of rain that falls during the growing season, r. The supply curve

E

S

D


Quantity (pounds)

Pric

e pe

r po

und

Q2

S2 S1

D1

$1.00

$3.00

Q1

FIGURE 1.3 ComparativeStatics in the Market forCoffee BeansThe heavy rains in Central Amer-ica, the strikes in Colombia, andthe frost in Brazil caused a left-ward shift in the world’s coffeebean supply curve from S1 to S2

(the supply fell). The equilibriumprice of coffee beans rose from $1to $3 per pound. The equilibriumquantity of coffee beans pro-duced and sold decreased fromQ1 to Q2 pounds.

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is upward sloping, so that as the price of corn rises, more corn will be offered for sale.Assume that the supply curve shifts to the right (more corn is produced) if there is morerain. The relationship showing the quantity of corn supplied at any price and amount ofrainfall is the supply function Qs(P,r).

In equilibrium the price of corn will adjust so that the market will clear (Qd = Qs ).Let’s call the equilibrium quantity exchanged Q∗ and the equilibrium price P∗. We canassume that the market for corn is only a small part of the U.S. economy, so that nationalincome is not noticeably affected by events in the market for corn.

Problem

(a) Suppose that income rises from I1 to I2. On a clearly labeled graph, illustrate how thechange in this exogenous variable affects each of the endogenous variables.

(b) Suppose that income remains at I1 but that the amount of rainfall increases from r1 tor2. On a second clearly labeled graph, illustrate how the change in this exogenous variableaffects each of the endogenous variables.

Solution

(a) As shown in Figure 1.4, the change in income shifts the demand curve to the right(increases demand), from D1 to D2. The location of the supply curve, S1, is unaffectedbecause Qs does not depend on I. The equilibrium price therefore rises from P∗

1 to P∗2 . So

the change in income leads to a change in equilibrium price.The equilibrium quantity also rises, from Q∗

1 to Q∗2. So the change in income also leads

to a change in quantity.

(b) As shown in Figure 1.5, the increase in rainfall shifts the supply curve to the right(increases supply), from S1 to S2. The location of the demand curve, D1, is unaffected


Quantity of corn

Pric

e of

cor

n

Q1* Q2

*

D2: demand for cornwhen income is I2

D1: demand for cornwhen income is I1

P2*

P1*

S1: supply of corn

D1 D2

S1

FIGURE 1.4 Comparative Statics: Increase in IncomeWhen income rises from I1 to I2, the demand curve shifts from D1 to D2 (demand increases). Theequilibrium market price will rise from P 1* to P 2*. The equilibrium market quantity will rise fromQ1* to Q2*.

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because Qd does not depend on r. The equilibrium price therefore falls from P∗1 to P∗

2 . Sothe change in rainfall leads to a change in equilibrium price.

The equilibrium quantity rises, from Q∗1 to Q∗

2. So the change in rainfall also leads toa change in quantity.

Similar Problems: 1.2, 1.4, 1.5, and 1.6

L E A R N I N G - B Y - D O I N G E X E R C I S E 1.4Comparative Statics with Constrained Optimization

In the farmer’s fencing problem (Learning-By-Doing Exercise 1.1), the exo-genous variable is the perimeter of the fence F, and the endogenous variablesare the length L and width W of the pen. You may have solved a problem like

this one before: The area is maximized when the farmer builds a square pen. (You do notneed to know how to arrive at that conclusion in this exercise. Just trust that it is correct.)

Problem If the farmer is given an extra length of fence �F (where �, the Greek letterdelta, means “the change in”), how will the dimensions of the pen change? In other words,how will a change in the exogenous variable �F be reflected by changes in the endogenousvariables �L and �W ?

Solution Since the optimal configuration of the pen is a square, we know that the lengthand width of the pen will each be one-fourth of the perimeter, so L = F/4 and W = F/4.Therefore, �L = �F/4 and �W = �F/4. This comparative statics result tells us, for

E

S

D


Quantity of corn

Pric

e of

cor

n

D1, Demand for corn

S2

S1

S1: supply of corn whenrainfall is r1

S2: supply of corn whenrainfall is r2

Q1* Q2

*

P2*

P1*

FIGURE 1.5 Comparative Statics: Increase in RainfallWhen rainfall increases from r1 to r2, the supply curve shifts from S1 to S2 (supply increases). Theequilibrium market price will fall from P 1* to P 2*. The equilibrium market quantity will rise from Q1*to Q2*.

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M icroeconomic analysis can be used to study both positive and normative questions.Positive analysis attempts to explain how an economic system works or to predicthow it will change over time. Positive analysis asks explanatory questions such as “Whathas happened?” or “What is happening?” It may also ask a predictive question: “Whatwill happen if some exogenous variable changes?” In contrast, normative analysisasks prescriptive questions, such as “What should be done?” Normative studies typi-cally focus on issues of social welfare, examining what will enhance or detract from thecommon good. In so doing, they often involve value judgments. For example, policymakers may want to consider whether we should raise the minimum wage to benefitthe least skilled and least experienced workers.

We have seen illustrations of positive questions throughout this chapter. In thefarmer’s fencing problem (Learning-By-Doing Exercise 1.1), one positive question is,“What dimensions of the sheep’s pen will the farmer choose to maximize the area ofthe pen?” Another is, “How will the area of the pen change if the farmer is given onemore foot of fence?” In the consumer choice problem (Learning-By-Doing Exer-cise 1.2), positive analysis will tell us how the consumer’s purchases of each good willdepend on the prices of all goods and on the level of her income. Positive analysis willhelp the manager of the electricity generator (Application 1.1) to produce any givenlevel of service with the lowest possible cost. Finally, positive analysis enables us tounderstand why a particular price of a commodity such as coffee beans is in equilib-rium and why other prices are not. It also explains why heavy rains, strikes, and frostresult in higher commodity prices.

As all of these examples suggest, applying microeconomic principles for predictivepurposes is important for consumers and for managers of enterprises. Positive analysisis also useful in the study of public policy. For example, policy makers might like tounderstand the effect of new taxes in a market, government subsidies to producers, ortariffs or quotas on imports. They may also want to know how producers and con-sumers are affected, as well as the size of the impact on the government budget.

Normative studies might examine how to achieve a goal that some people con-sider socially desirable. Suppose policy makers want to make housing more affordableto low-income families. They may ask whether it is “better” to accomplish this byissuing these families housing vouchers that they can use on the open housing marketor by implementing rent controls that prevent landlords from charging any rentermore than an amount controlled by law. Or, if government finds it desirable to reducepollution, should it introduce taxes on emissions or strictly limit the emissions fromfactories and automobiles?

These examples illustrate that it is important to do positive analysis beforenormative analysis. A policy maker may want to ask the normative question, “Should

1 . 3 P O S I T I V E A N D N O R M AT I V E A N A LY S I S 17

1.3P O S I T I V E A N DN O R M AT I V EA N A LY S I S

positive analysis Analysisthat attempts to explain howan economic system works orto predict how it will changeover time.

normative analysisAnalysis that typicallyfocuses on issues of socialwelfare, examining what willenhance or detract from thecommon good.

example, that if the farmer is given an extra four feet of fence, the length and the width ofthe pen will each be increased by one foot.

Similar Problems: 1.7, 1.8, and 1.11

Comparative statics is used to answer many questions that are central in microeco-nomics. Later we will use comparative statics to understand basic economic conceptssuch as demand curves and supply curves.

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CH A P T E R S U M M A R Y

• Economics is the study of the allocation of limitedresources to satisfy unlimited human wants. It is oftendescribed as the science of constrained choice.

• Microeconomics examines the economic behavior ofindividual economic decision units, such as a consumeror a firm, as well as groups of economic agents, such ashouseholds or industries.

• Economic studies are often conducted by construct-ing and analyzing models of a particular problem. Be-cause the real world is complex, an economic modelrepresents an abstraction from reality.

• In analyzing any model, one needs to understandwhat variables will be taken as given (exogenous vari-ables), as well as what variables will be determined withinthe model (endogenous variables).

• Three essential tools of microeconomic analysis are(1) constrained optimization, a tool that decision makersuse to maximize or minimize some objective functionsubject to a constraint (LBD Exercises 1.1 and 1.2);

(2) equilibrium analysis, used to describe a condition orstate that could continue indefinitely in a system, or atleast until there is a change in some exogenous variable;and (3) comparative statics, used to examine how a changein some exogenous variable will affect the level of someendogenous variable in an economic model, includingequilibrium (LBD Exercise 1.3) and constrained opti-mization (LBD Exercise 1.4).

• The term marginal in microeconomics measures theamount by which a dependent variable changes as theresult of adding one more unit of an independentvariable.

• Microeconomics provides tools we can use to exam-ine positive and normative issues. Positive analysisattempts to explain how an economic system works andto predict how the endogenous variables will change asexogenous variables change. Normative analysis consid-ers prescriptive questions such as “What should bedone?” Normative studies introduce value judgmentsinto the analysis.

RE V I E W Q U E S T I O N S

1. What is the difference between microeconomicsand macroeconomics?

2. Why is economics often described as the science ofconstrained choice?

3. How does the tool of constrained optimization helpdecision makers make choices? What roles do the objec-tive function and constraints play in a model of con-strained optimization?

4. Suppose the market for wheat is competitive, with anupward-sloping supply curve, a downward-sloping de-mand curve, and an equilibrium price of $4.00 per bushel.Why would a higher price (e.g., $5.00 per bushel) not be

an equilibrium price? Why would a lower price (e.g.,$2.50 per bushel) not be an equilibrium price?

5. What is the difference between an exogenous vari-able and an endogenous variable in an economic model?Would it ever be useful to construct a model that con-tained only exogenous variables (and no endogenousvariables)?

6. Why do economists do comparative statics analysis?What role do endogenous variables and exogenous vari-ables play in comparative statics analysis?

7. What is the difference between positive and nor-mative analysis? Which of the following questions

we implement a program of rent controls or a program of housing vouchers?” Tounderstand the options fully, the policy maker will first need to do positive analysis tounderstand what will happen if rent controls are imposed and to learn about theconsequences of housing vouchers. Positive analysis will tell us who is affected by eachpolicy, and how.

Microeconomics can help policy makers understand and compare the impacts ofalternative policies on consumers and producers. It can therefore help sharpen debatesand lead to enlightened public policy.

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1.1. Discuss the following statement: “Since supplyand demand curves are always shifting, markets neveractually reach an equilibrium. Therefore, the concept ofequilibrium is useless.”

1.2. In an article entitled, “Corn Prices Surge on Ex-port Demand, Crop Data,” The Wall Street Journal iden-tified several exogenous shocks that pushed U.S. cornprices sharply higher.2 Suppose the U.S. market for cornis competitive, with an upward-sloping supply curve anda downward-sloping demand curve. For each of the fol-lowing scenarios, illustrate graphically how the exoge-nous event described will contribute to a higher price ofcorn in the U.S. market.a) The U.S. Department of Agriculture announces thatexports of corn to Taiwan and Japan were “surprisinglybullish,” around 30 percent higher than had beenexpected.b) Some analysts project that the size of the U.S. corncrop will hit a six-year low because of dry weather.c) The strengthening of El Niño, the meteorologicaltrend that brings warmer weather to the western coastof South America, reduces corn production outside theUnited States, thereby increasing foreign countries’dependence on the U.S. corn crop.

1.3. A firm produces cellular telephone service usingequipment and labor. When it uses E machine-hours ofequipment and hires L person-hours of labor, it canprovide up to Q units of telephone service. The relation-ship between Q, E, and L is as follows: Q = √

EL. Thefirm must always pay PE for each machine-hour ofequipment it uses and PL for each person-hour of laborit hires. Suppose the production manager is told to pro-duce Q = 200 units of telephone service and that shewants to choose E and L to minimize costs while achiev-ing that production target.a) What is the objective function for this problem?b) What is the constraint?c) Which of the variables (Q, E, L, PE , and PL) areexogenous? Which are endogenous? Explain.

P R O B L E M S 19

PR O B L E M S

d) Write a statement of the constrained optimizationproblem.

1.4. The supply of aluminum in the United Statesdepends on the price of aluminum and the average price ofelectricity (a critical input in the production of aluminum).Assume that an increase in the price of electricity shiftsthe supply curve for aluminum to the left (i.e., a higheraverage price of electricity decreases the supply of alu-minum). The demand for aluminum in the United Statesdepends on the price of aluminum and on national income.Assume that an increase in national income shifts the de-mand curve for aluminum to the right (i.e., higher incomeincreases the demand for aluminum). In 2004, nationalincome in the U.S. increased, while the price of electricityfell, as compared to 2003. How would the equilibriumprice of aluminum in 2004 compare to the equilibriumprice in 2003? How would the equilibrium quantity in2004 compare to the equilibrium quantity in 2003?

1.5. Suppose the supply curve for wool is given byQs = P , where Qs is the quantity offered for sale whenthe price is P. Also suppose the demand curve for wool isgiven by Qd = 10 − P + I , where Qd is the quantity ofwool demanded when the price is P and the level ofincome is I. Assume I is an exogenous variable.a) Suppose the level of income is I = 20. Graph thesupply and demand relationships, and indicate the equi-librium levels of price and quantity on your graph.b) Explain why the market for wool would not be inequilibrium if the price of wool were 18.c) Explain why the market for wool would not be inequilibrium if the price of wool were 14.

1.6. Consider the market for wool described by thesupply and demand equations in Problem 1.5. Supposeincome rises from I1 = 20 to I2 = 24.a) Using comparative statics analysis, find the impact ofthe change in income on the equilibrium price of wool.b) Using comparative statics analysis, find the impact ofthe change in income on the equilibrium quantity ofwool.

1.7. You are the Video Acquisitions Officer for yourdormitory. The other officers of your dorm will tell you2See the article by Aaron Lucchetti, August 22, 1997, page C17.

would entail positive analysis, and which normativeanalysis?a) What effect will Internet auction companies have onthe profits of local automobile dealerships?

b) Should the government impose special taxes on salesof merchandise made over the Internet?

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how many videos they would like to rent during the year.Your job is to find the least expensive way of rentingthe required number of videos. After researching theoptions, you have found that there are three rental plansfrom which you can choose.

Plan A: Pay $3 per video, with no additional fees.

Plan B: Join the Frequent Viewer Club. Here you pay ayearly membership fee of $50, with an additional chargeof $2 for each video rented.

Plan C: Join the Very Frequent Viewer Club. In this clubyou pay a yearly membership fee of $150, with an addi-tional charge of $1 for each video rented.a) Which plan would you select if your instructions areto rent 75 movies a year at the lowest possible cost?b) Which plan would you select if your instructions areto rent 125 movies a year at the lowest possible cost?c) In this exercise, is the number of videos rentedendogenous or exogenous? Explain.d) Is the choice of plan (A, B, or C) endogenous orexogenous? Explain.e) Are total expenditures on videos endogenous orexogenous? Explain.

1.8. Reconsider the problem of the Video AcquisitionsOfficer in Problem 1.7. Suppose the officers of yourdorm give you a specified amount of money to spend,and want you to maximize the number of videos you canrent with that budget. You can choose from the samethree plans (A, B, and C) available in Problem 1.7.a) Which plan would you select if your instructionsare to rent the most movies possible while spending$125 per year?b) Which plan would you select if your instructionsare to rent the most movies possible while spending$300 per year?c) In this exercise, is the number of videos rentedendogenous or exogenous? Explain.d) Is the choice of plan (A, B, or C) endogenous orexogenous? Explain.e) Are total expenditures on videos endogenous orexogenous? Explain.

1.9. A major automobile manufacturer is consideringhow to allocate a $2 million advertising budget betweentwo types of television programs: NFL football gamesand PGA tour professional golf tournaments. The tablebelow shows the new sports utility vehicles (SUVs) thatare sold when a given amount of money is spent onadvertising during an NFL football game and a PGAtour golf event.


Total

New SUV Sales Generated (thousands of vehicles per year)

Spent (millions) NFL Football PGA Tour Golf

$0 0 0$0.5 10 4$1.0 15 6$1.5 19 8$2.0 20 9

The manufacturer’s goal is to allocate its $2 millionadvertising budget to maximize the number of SUVssold. Let F be the amount of money devoted to advertis-ing on NFL football games, G the amount of moneyspent on advertising on PGA tour golf events, andC(F,G) the number of new vehicles sold.a) What is the objective function for this problem?b) What is the constraint?c) Write a statement of the constrained optimizationproblem.d) In light of the information in the table, how shouldthe manufacturer allocate its advertising budget?

1.10. The demand curve for peaches is given by theequation Qd = 100 − 4P , where P is the price ofpeaches expressed in cents per pound and Qd is thequantity of peaches demanded (expressed in thousandsof bushels per year). The supply curve for peaches isgiven by Qs = RP , where R is the amount of rainfall(inches per month during the growing season) and Qs isthe quantity of peaches supplied (expressed in thousandsof bushels per year). Let P∗ denote the market equilib-rium price and Q∗ denote the market equilibrium quan-tity. Complete the following table showing how theequilibrium quantity and price vary with the amount ofrainfall. Verify that when R = 1, the equilibrium price is20 cents per pound and the equilibrium quantity is20 thousand bushels per year.

R 1 2 4 8 16

Q* 20

P* 20 16.67

1.11. Consider the comparative statics of the farmer’sfencing problem in Learning-By-Doing Exercise 1.4,where L is the length of the pen, W is the width, andA = LW is the area.a) Suppose the number of feet of fence given to thefarmer was initially F1 = 200. Complete the following

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table. Verify that the optimal design of the fence (the oneyielding the largest area with a perimeter of 200 feet)would be a square.

L 10 20 30 40 50 60 70 80 90

W 90 80

A 900

b) Now suppose the farmer is instead given 240 feet offence (F2 = 240). Complete the following table. By howmuch would the length L of the optimally designed penincrease?

L 20 30 40 50 60 70 80 90 100

W 100 90

A 2000

c) When the amount of fence is increased from 200to 240 (�F = 40), what is the change in the optimallength (�L)?

P R O B L E M S 21

d) When the amount of fence is increased from 200to 240 (�F = 40), what is the change in the optimalarea (�A)? Is the area A endogenous or exogenous inthis example? Explain.

1.12. Which of the following statements suggest apositive analysis and which a normative analysis?a) If the United States lifts the prohibition on importsof Cuban cigars, the price of cigars will fall.b) A freeze in Florida will lead to an increase in theprice of orange juice.c) To provide revenues for public schools, taxes onalcohol, tobacco, and gambling casinos should be raisedinstead of increasing income taxes.d) Telephone companies should be allowed to offercable TV service as well as telephone service.e) If telephone companies are allowed to offer cableTV service, the price of both types of service will fall.f ) Government subsidies to farmers are too high andshould be phased out over the next decade.g) If the tax on cigarettes is increased by 50 centsper pack, the equilibrium price of cigarettes will rise by30 cents per pack.

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analyzing economic problems - cairo...

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