demand and elasticity - cairo university...

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Demand and ElasticityA high cross elasticity of demand [between two goods indicates that they] compete in the same market. [This can

prevent a supplier of one of the products] from possessing monopoly power over price.

U . S . S U P R E M E CO U RT, D U P O N T C E L LO P H A N E D EC I S I O N , 1 9 5 6

6

C O N T E N T S

n this chapter, we continue our study of demand and demand curves, whichwe began in the previous chapter. Here we explain the way economists mea-

sure how much quantity demanded responds to price changes, and what such respon-siveness implies about the revenue that producers will receive if they change prices.In particular, we introduce and explain an important concept called elasticity thateconomists use to examine the relationship between quantity demanded and price.

ISSUE: Will Taxing Cigarettes MakeTeenagers Stop Smoking?

ELASTICITY: THE MEASURE OFRESPONSIVENESS

Price Elasticity of Demand and the Shapes ofDemand Curves

PRICE ELASTICITY OF DEMAND: ITS EFFECTON TOTAL REVENUE AND TOTALEXPENDITURE

ISSUE REVISITED: Will a Cigarette Tax Decrease Teenage SmokingSignificantly?

WHAT DETERMINES DEMAND ELASTICITY?

ELASTICITY AS A GENERAL CONCEPTIncome ElasticityPrice Elasticity of SupplyCross Elasticity of DemandCHANGES IN DEMAND: MOVEMENTS

ALONG THE DEMAND CURVE VERSUSSHIFTS IN THE DEMAND CURVE

Demand Shifters

THE TIME PERIOD OF THE DEMAND CURVEAND ECONOMIC DECISION MAKING

REAL-WORLD APPLICATION: POLAROIDVERSUS KODAK

In ConclusionAPPENDIX: HOW CAN WE FIND A

LEGITIMATE DEMAND CURVE FROM THESTATISTICS?

An Illustration: Did the Advertising ProgramWork?

How Can We Find a Legitimate Demand Curvefrom the Statistics?

I

Governments, business firms, supermarkets, consumers, and law courts need a way tomeasure how responsive demand is to price changes—for example, will a 10 percentcut in the price of commodity X increase quantity of X demanded a little or a lot?Economists measure the responsiveness of quantity demanded to price changes via aconcept called elasticity. Marketers sometimes use estimates of elasticity to decide howto price their products or whether to add new product models. A relatively flat de-mand curve like Figure 1(a) indicates that consumers respond sharply to a change in

104 Chapter 6 DEMAND AND ELASTICITY

Public health experts believe thatincreased taxes on cigarettes can

be a major weapon in the battle to cutteenage smoking. Imagine yourself on apanel of consultants helping a congressionalcommittee draft new legislation to deal withthis issue. As the youngest member of thegroup, you are asked for your opinion abouthow effective a big tax increase on cigaretteswould be in persuading young people tostop smoking. How would you respond?What sorts of statistical data, if any, wouldyou use to help find your answer? And howmight you go about analyzing the relevantnumbers?

This chapter will help you answer suchquestions. As often happens in economics, we will see that careful investigationbrings some surprises. This is true in the case of taxes to discourage teenage smok-ing. A tax on cigarettes may actually benefit teenagers’—and other citizens’—health.And it will, of course, benefit government finances by bringing in more tax money.Nothing surprising so far. Instead, the surprise is this: The more effective the tax isin curbing teenage smoking, the less beneficial it will be to the government’s fi-nances, and vice versa; the more the tax benefits the government, the less it will con-tribute to health. The concept of elasticity of demand will make this point clearer.

ISSUE: Will Taxing Cigarettes Make Teenagers Stop Smoking?

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ELASTICITY: THE MEASURE OF RESPONSIVENESS

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price—the quantity they demand falls by 2.5 units (from 4 units to 1.5 units) whenprice rises $10. That is, they demand or buy much less of the product when price riseseven a little bit. Such a “touchy” curve is called elastic or highly elastic. A relativelysteep demand curve like Figure 1(b), which indicates that consumers respond hardlyat all to a price change, is called inelastic. In this graph, a $10 price rise cuts quantitydemanded by only 1 unit.

The precise measure used for this purpose is called the price elasticity ofdemand, or simply the elasticity of demand. We define elasticity of demand as theratio of the percentage change in quantity demanded to the associated percentagechange in price.

Demand is called elastic if, say, a 10 percent rise in price reduces quantity demandedby more than 10 percent. Demand is called inelastic if such a rise in price reduces quan-tity demanded by less than 10 percent.

Why do we need these definitions to analyze the responsiveness to price shown bya particular demand curve? At first, it may seem that the slope of the demand curveconveys the needed information: Curve DsDs is much steeper than curve DfDf in Fig-ure 1, so any given change in price appears to correspond to a much smaller changein quantity demanded in Figure 1(b) than in Figure 1(a). For this reason, it is tempt-ing to call demand in Panel (a) “more elastic.” But slope will not do the job, becausethe slope of any curve depends on the particular units of measurement, and econo-mists use no standardized units of measurement. For example, cloth output may bemeasured in yards or in meters, milk in quarts or liters, and coal in tons or hundred-weights. Figure 2(a) brings out this point explicitly. In this graph, we return to thepizza example from Chapter 5, measuring quantity demanded in terms of pizzas andprice in dollars per pizza. A fall in price from $15 to $11 per large pizza (points A andB) raises quantity demanded at Paul’s Pizza Parlor from 280 pizzas to 360 per week—that is, by 80 pizzas.

Now look at Figure 2(b), which provides exactly the same information, but mea-sures quantity demanded in slices of pizza rather than whole pizzas (with one pizzayielding eight slices). Here, the same price change as before increases quantity de-manded, from 8 3 280 5 2,240 slices to 8 3 360 5 2,880 slices—that is, by 640 slices,rather than by 80 pizzas.

Visually, the increase in quantity demanded looks eight times as great in Panel (b) asin Panel (a), but all that has changed is the unit of measurement. The 640-unit increase

ELASTICITY: THE MEASURE OF RESPONSIVENESS 105

The (price) elasticity of demand is the ratio of the percentage change in quantity demanded to the percentage change inprice that brings about the change in quantitydemanded.

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in Figure 2(b) represents the same increase in quantity demanded as the 80-unit in-crease in Figure 2(a). Just as you get different numbers for a given rise in temperature,depending on whether you measure it in Celsius or Fahrenheit, so the slopes of demandcurves differ, depending on whether you measure quantity in pizzas or in pizza slices.Clearly, then, slope does not really measure responsiveness of quantity demanded toprice, because the measure changes whenever the units of measurement change.

Economists created the elasticity concept precisely in response to this problem.Elasticity measures responsiveness on the basis of percentage changes in price andquantity rather than on absolute changes. The elasticity formula solves the units prob-lem because percentages are unaffected by units of measurement. If the governmentdefense budget doubles, it goes up by 100 percent, whether measured in millions orbillions of dollars. If demand for pizza trebles, it rises by 200 percent, whether wemeasure the quantity demanded in number of pies or slices. The elasticity formulagiven earlier therefore expresses both the change in quantity demanded and thechange in price as percentages.1

Furthermore, elasticity calculates the change in quantity demanded as a percentageof the average of the two quantities: the quantity demanded before the change in price hasoccurred (Q0) and the quantity demanded after the price change (Q1). In our example,the “before” pizza purchase is 280 (Q0), the quantity sold after the price fall is 360(Q1), and the average of these two numbers is 320. The increase in number of pizzasbought is 80 pizzas, which is 25 percent of the 320 average of the sales before and af-ter the price change. So 25 percent is the number we use as the purchase increasemeasure in our elasticity calculation. This procedure is a useful compromise betweenviewing the change in quantity demanded (80 pizzas) as a percentage of the initialquantity (280) or as a percentage of the final quantity (360).

Similarly, the change in price is expressed as a percentage of the average of the “be-fore” and “after” prices, so that, in effect, it represents elasticity at the price halfwaybetween those two prices. That is, the price falls by $4 (from $15 to $11). Because $4is (approximately) 33 percent of the average of $14 (P0) and $10 (P1) (that is, $12), wesay that in this case a 33 percent fall in price led to a 25 percent rise in quantity ofpizza demanded.

To summarize, the elasticity formula has two basic attributes:

• Each of the changes with which it deals is measured as a percentage change.• Each of the percentage changes is calculated in terms of the average values of the be-

fore and after quantities and prices.

In addition, economists often adjust the price elasticity of demand formula in athird way. Note that when the price increases, the quantity demanded usually declines.Thus, when the price change is a positive number, the quantity change will normallybe a negative number; when the price change is a negative number, the quantitychange will normally be a positive number. As a consequence, the ratio of the twopercentage changes will be a negative number. We customarily express elasticity as apositive number, however. Hence:

• Each percentage change is taken as an “absolute value,” meaning that the calculationdrops all minus signs.2


1 The remainder of this section involves fairly technical computational issues. On a first reading, you may prefer to godirectly to the new section that begins on the next page.2 This third attribute of the elasticity formula—the removal of all minus signs—applies only when the formula is usedto measure the responsiveness of quantity demanded of product X to a change in the price of product X. Later in thechapter, we will show that similar formulas are used to measure the responsiveness between other pairs of variables.For example, the elasticity of supply uses a similar formula to measure the responsiveness of quantity supplied toprice. In such cases, it is not customary to drop minus signs when calculating elasticity. The reasons will becomeclearer later in the chapter.

We can now state the formula for price elasticity of demand, keeping all three fea-tures of the formula in mind:

In our example:

Elasticity of demand for pizzas =

Price Elasticity of Demand and the Shapes of Demand CurvesWe noted earlier that looks can be deceiving in some demand curves because theirunits of measurement are arbitrary. Economists have provided the elasticity formulato overcome that problem. Nonetheless, the shape of a demand curve does conveysome information about its elasticity. Let’s see what information some demand curveshapes give, with the aid of Figure 3.

1. Perfectly Elastic Demand Curves Panel (a) of Figure 3 depicts a horizontal de-mand curve. Such a curve is called perfectly elastic (or infinitely elastic). At any price higherthan $0.75, quantity demanded will drop to zero; that is, the comparative change inquantity demanded will be infinitely large. Perfect elasticity typically occurs when manyproducers sell a product and consumers can switch easily from one seller to another ifany particular producer raises his price. For example, suppose you and the other stu-dents in your economics class are required to buy a newspaper every day to keep up witheconomic events. If news dealer X, from whom you have been buying the newspaper,raises the price from 75 cents to 80 cents, but the competitor, Y, across the street keepsthe old price, then X may lose all her newspaper customers to Y. This situation is likelyto prevail whenever an acceptable rival product is available at the going price (75 centsin the diagram). In cases in which no one will pay more than the going price, the sellerwill lose all of her customers if she raises her price by even a penny.

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ELASTICITY: THE MEASURE OF RESPONSIVENESS 107

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FIGURE 3Demand Curves withDifferent Elasticities

2. Perfectly Inelastic Demand Curves Panel (b) of Figure 3 shows the opposite ex-treme: a completely vertical demand curve. Such a curve is called perfectly inelasticthroughout because its elasticity is zero at every point on the curve. Because quantitydemanded remains at 90 units no matter what the price, the percentage change inquantity is always zero, and hence the elasticity (which equals percentage change inquantity divided by percentage change in price) is always zero. In this case, consumerpurchases do not respond at all to any change in price.

Vertical demand curves such as the one shown in Panel (b) of Figure 3 occur whena commodity is very inexpensive. For example, you probably will not buy more rub-ber bands if their prices fall. The demand curve may also be vertical when consumersconsider the item in question to be an absolute necessity. For example, if your room-mate’s grandfather has a heart attack, the family will buy whatever medicine the doc-tor prescribes, regardless of the price, and will not purchase any more even if theprice falls.

3. (Seemingly Simple) Straight-Line Demand Curves Panel (c) of Figure 3 depicts acase between these two extremes: a straight-line demand curve that runs neither verti-cally nor horizontally. Note that, although the slope of a straight-line demand curveremains constant throughout its length, its elasticity does not. For example, the elas-ticity of demand between points A and B in Figure 3(c) is:

The elasticity of demand between points A’ and B’ is:

The general point is that:

Along a straight-line demand curve, the price elasticity of demand grows steadily smalleras you move from left to right. That is so because the quantity keeps getting larger, so thata given numerical change in quantity becomes an ever-smaller percentage change. But, si-multaneously, the price keeps going lower, so that a given numerical change in price be-comes an ever-larger percentage change. So, as one moves from left to right along the de-mand curve, the numerator of the elasticity fraction keeps falling and the denominatorkeeps growing larger; thus the fraction that is the elasticity formula keeps declining.

4. Unit-Elastic Demand Curves If the elasticity of a straight-line demand curvevaries from one part of the curve to another, what does a demand curve with the sameelasticity throughout its length look like? For reasons explained in the next section, ithas the general shape indicated in Figure 3(d). That panel shows a curve with elastic-ity equal to 1 throughout (a unit-elastic demand curve). A unit-elastic demand curvebends in the middle toward the origin of the graph—at either end, it moves closer andcloser to the axes but never touches or crosses them.

As we have noted, a curve with an elasticity greater than 1 is called an elastic de-mand curve (one for which the percentage change in quantity demanded will begreater than the percentage change in price); a curve whose elasticity is less than 1 isknown as an inelastic curve. When elasticity is exactly 1, economists say that thecurve is unit-elastic.

Real-world price elasticities of demand seem to vary considerably from product toproduct. Because people can get along without them, moderately luxurious goods, suchas expensive vacations, are generally more price elastic—people give them up morereadily when their prices rise—than goods such as milk and shirts, which are considered

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A demand curve iselastic when a given per-centage price change leadsto a larger percentagechange in quantitydemanded.

A demand curve isinelastic when a given per-centage price change leadsto a smaller percentagechange in quantitydemanded.

A demand curve is unit-elastic when a givenpercentage price changeleads to the same percent-age change in quantitydemanded.

necessities. Products with close substitutes,such as Coke and Pepsi, tend to have relativelyhigh elasticities because if one soft drink be-comes expensive, consumers will switch to theother. Also, the elasticities of demand for goodsthat business firms buy, such as raw materialsand machinery, tend to be higher on the wholethan those for consumers’ goods. This is be-cause competition forces firms to buy their sup-plies wherever they can get them most cheaply.The exception occurs when a firm requires aparticular input for which no reasonable substi-tutes exist or the available substitutes are sub-stantially inferior. Table 1 gives actual statisticalestimates of elasticities for some industries inthe economy.

Aside from its role as a measure of the responsiveness of demand to a change in price,elasticity serves a second, very important purpose. As a real illustration at the end ofthis chapter will show, a firm often wants to know whether an increase in price willincrease or decrease its total revenue—the money it obtains from sales to its cus-tomers. The price elasticity of demand provides a simple guide to the answer:

If demand for the seller’s product is elastic, a price increase will actually decrease total rev-enue. If demand is exactly unit-elastic, a rise in price will leave total revenue unaffected.If demand is inelastic, a rise in price will raise total revenue. The opposite changes will oc-cur when price falls.

A corresponding story must be true about the expenditures made by the buyers ofthe product. After all, the expenditures of the buyers are exactly the same thing as therevenues of the seller.

These relationships between elasticity and total revenue hold because total revenue(or expenditure) equals price times quantity demanded, P 3 Q, and because a drop inprice has two opposing effects on that arithmetic product. It decreases P, and, if the de-mand curve is negatively sloped, it increases Q. The first effect decreases revenues by cut-ting the amount of money that consumers spend on each unit of the good. The secondeffect increases revenues by raising the number of units of the good that the firm sells.

The net effect on total revenue (or total expenditure) depends on the elasticity. Ifprice goes down by 10 percent and quantity demanded increases by 10 percent (a caseof unit elasticity), the two effects just cancel out: P 3 Q remains constant. In contrast,if price goes down by 10 percent and quantity demanded rises by 15 percent (a case ofelastic demand), P 3 Q increases. Finally, if a 10 percent price fall leads to only a 5 per-cent rise in quantity demanded (inelastic demand), P 3 Q falls.

We can easily see the relationship between elasticity and total revenue in a graph.First, note that:

The total revenue (or expenditure) represented by any point on a demand curve (any price2quantity combination), such as point S in Figure 4, equals the area of the rectangle under

PRICE ELASTICITY OF DEMAND: ITS EFFECT ON TOTAL REVENUE AND TOTAL EXPENDITURE 109

TABLE 1Estimates of Price Elasticities

Product Price Elasticity

Industrial chemicals 0.4Shoe repairs and cleaning 0.4Food, tobacco, and beverages 0.5Newspapers and magazines 0.5Data processing, precision and optical instruments 0.7Medical care and hospitalization insurance 0.8Metal products 1.1Purchased meals (excluding alcoholic beverages) 1.6Electricity (household utility) 1.9Boats, pleasure aircraft 2.4Public transportation 3.5China, tableware 8.8

SOURCES: H. S. Houthakker and Lester D. Taylor, Consumer Demand in the UnitedStates, 2d ed. (Cambridge, Mass.: Harvard University Press, 1970), pp. 153–158; andJoachim Möller, “Income and Price Elasticities in Different Sectors of the Economy—AnAnalysis of Structural Change for Germany, the U.K., and U.S.” (University of Regens-burg, December 1998).

PRICE ELASTICITY OF DEMAND: ITS EFFECT ON TOTAL REVENUE AND TOTAL EXPENDITURE

that point (the area of rectangle 0RST in the figure). This is true because the area of a rec-tangle equals its height times width, or 0R 3 RS in Figure 4. Clearly, that is price timesquantity, which is exactly total revenue.

To illustrate the connection between elasticity and con-sumer expenditure, Figure 4 shows an elastic portion of ademand curve, DD. In this figure, when price falls, quan-tity demanded rises by a greater percentage, increasing to-tal expenditure. At a price of $6 per unit, the quantity soldis four units, so total expenditure is 4 3 $6 5 $24, repre-sented by the vertical rectangle whose upper-right corneris point S. When price falls to $5 per unit, 12 units are sold.Consequently, the new expenditure ($60 5 $5 3 12), mea-sured by the rectangle 0WVU, exceeds the old expenditure.

In contrast, Figure 3(d), the unit-elastic demand curve,shows constant expenditures even though price changes.Total spending is $140 whether the price is $20 and 7units are sold (point S) or the price is $10 and 14 units aresold (point T).

This discussion also indicates why a unit-elastic de-mand curve must have the shape depicted in Figure 3(d),

hugging the axes closer and closer but never touching or crossing them. When de-mand is unit-elastic, total expenditure must be the same at every point on the curve.That is, it must equal $140 at point S and point T and point U in Figure 3(d). Sup-pose that at point U (or some other point on the curve), the demand curve were totouch the horizontal axis, meaning that the price would equal zero. Then total expen-diture would be zero, not $140. Therefore, if the demand curve remains unit-elasticalong its entire length, it can never cross the horizontal axis (where P 5 0). By thesame reasoning, it cannot cross the vertical axis (where Q 5 0). Because the slope ofthe demand curve is negative, any unit-elastic curve simply must get closer and closerto the axes as it moves away from its middle points, as illustrated in Figure 3(d). But itwill never touch either axis.

We can now see why demand elasticity is so important for business decisions. Afirm should not jump to the conclusion that a price increase will automatically add toits profits, or it may find that consumers take their revenge by cutting back on theirpurchases. For example, when Heinz’s Pet Products Company raised the price of its9-Lives cat food some years ago, its market share plummeted from 23 percent to 15percent as customers flocked to other brands. In fact, if its demand curve is elastic, afirm that raises price will end up selling so many fewer units that its total revenue willactually fall, even though it makes more money than before on each unit it sells.

Price cuts can also be hazardous—if the elasticity of demand is low. For example,among adult smokers cigarettes have an estimated price elasticity of approximately0.2, meaning that we can expect a 10 percent drop in price to induce only a 2 percentrise in demand. This relationship may explain why, when Philip Morris cut the priceof Marlboros by about 18 percent, the company’s profits dropped by 25 percentwithin months. Thus, the strategic value to a business firm of a price rise or a pricecut depends very much on the elasticity of demand for its product. But elasticity tellsus only how a price change affects a firm’s revenues; we must also consider the effectof costs on the firm’s output decisions, as we will do in Chapter 8.


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We’re back to the issue with which we began this chapter: Will a tax oncigarettes, which increases their price, effectively reduce teenage smoking? We canexpress the answer to this question in terms of the price elasticity of demand for

ISSUE REVISITED: Will a Cigarette Tax Decrease Teenage Smoking Significantly?

We said earlier in the chapter that if a cigarette tax program failed to curb teensmoking, it would benefit the government’s tax collectors a great deal. On the otherhand, if the program successfully curbed teenage smoking, then government financeswould benefit only a little. The logic of this argument should now be clear. If teencigarette demand were inelastic, the tax program would fail to make a dent in teensmoking. That would mean that many teenagers would continue to buy cigarettes andgovernment tax revenue would grow as a result of the rise in tax rate. But when elas-ticity is high, a price rise decreases total revenue (in this case, the amount of tax rev-enues collected) because quantity demanded falls by a greater percentage than theprice rises. That is, with an elastic demand, relatively few teen smokers will remainafter the tax increase, so there will be few of them to pay the new taxes. Thegovernment will “lose out.” Of course, in this case the tax seeks to change behavior,so the government would no doubt rejoice at its small revenues!

What kinds of goods have elastic demand curves, meaning that quantity demandedresponds strongly to price? What kinds of goods have inelastic demand curves? Sev-eral influences affect consumers’ sensitivity to price changes.

1. Nature of the Good Necessities, such as basic foodstuffs, normally have relativelyinelastic demand curves, meaning that the quantities consumers demand of theseproducts respond very little to price changes. For example, people buy roughly thesame quantity of potatoes even when the price of potatoes rises. One study estimatedthat the price elasticity of demand for potatoes is just 0.3, meaning that when theirprice rises 10 percent, the quantity of potatoes purchased falls only 3 percent. In con-trast, many luxury goods, such as restaurant meals, have rather elastic demand curves.One estimate found that the price elasticity of demand for restaurant meals is 1.6, sothat we can expect a 10 percent price rise to cut purchases by 16 percent.

2. Availability of Close Substitutes If consumers can easily obtain an acceptablesubstitute for a product whose price increases, they will switch readily. Thus, whenthe market offers close substitutes for a given product, its demand will be moreelastic. Substitutability is often a critical determinant of elasticity. The demand for

WHAT DETERMINES DEMAND ELASTICITY? 111

cigarettes by teenagers. If that demand elasticity is high, the tax will be effective, be-cause a small increase in cigarette taxes will lead to a sharp cut in purchases byteenagers. The opposite will clearly be true if this demand elasticity is small.

It turns out that young people are more sensitive to price increases than adultsmokers. The estimates of teenagers’ price elasticity of demand for cigarettes rangefrom about 0.7 all the way up to 1.65.3 This means that if, for example, a tax on cig-arettes raises their price by 10 percent, the number of teenage smokers will fall bysomewhere between 7 and 16.5 percent. As we just noted, adults have been found tohave a price elasticity of demand for cigarettes of just .2—their response to the 10 percent increase in the price of cigarettes will be a decrease of only 2 percent inthe number of adult smokers. So we can expect that a substantial tax on cigarettesthat resulted in a significant price increase would cause a higher percentage ofteenagers than adults to stop smoking.

3 Sources: David R. Francis, “Demographic Groups Differ in Response to Substance Abuse Policies,” The NBER Di-gest, National Bureau of Economic Research, September 1998, www.nber.org; and John Tauras, et al., “Effects ofPrices and Access Laws on Teenage Smoking Initiation: A National Longitudinal Analysis,” Impac-Teen, University ofIllinois at Chicago Health Research and Policy Centers, April 2001, www.uic.edu/orgs/impacteen; and AlexanderDing, “Youth Are More Sensitive to Price Changes in Cigarettes Than Adults,” Yale Journal of Biology and Medicine,Vol. 76, No. 3, 1 May 2003, pp. 115-124.

WHAT DETERMINES DEMAND ELASTICITY?

gasoline is inelastic because we cannot eas-ily run a car without it, but the demand forany particular brand of gasoline is extremelyelastic, because other brands will work justas well. This example suggests a generalprinciple: The demand for narrowly definedcommodities (such as romaine lettuce) ismore elastic than the demand for morebroadly defined commodities (such asvegetables).

3. Share of Consumer’s Budget The shareof the consumer’s budget represented by thepurchase of a particular item also affects itselasticity. Very inexpensive items that ab-sorb little of a consumer’s budget tend tohave inelastic demand curves. Who is goingto buy fewer paper clips if their price rises 10 percent? Hardly anyone. But many fam-ilies will be forced to postpone buying a new car, or will buy a used car instead, if autoprices go up by 10 percent.

4. Passage of Time The time period is relevant because the demand for many prod-ucts is more elastic in the long run than in the short run. For example, when theprice of home heating oil rose in the 1970s, some homeowners switched from oilheat to gas heat. Very few of them switched immediately, however, because theyneeded to retrofit their furnaces to accommodate the other fuel. So, the short-termdemand for oil was quite inelastic. As time passed and more homeowners had the op-portunity to purchase and install new furnaces, the demand curve gradually becamemore elastic.

So far we have looked only at how quantity demanded responds to price changes—that is, the price elasticity of demand. But elasticity has a more general use in measur-ing how any one economic variable responds to changes in another. From our earlierdiscussion, we know that a firm will be keenly interested in the price elasticity of itsdemand curve, but its interest in demand does not end there. As we have noted, quan-tity demanded depends on other things besides price. Business firms will be interestedin consumer responsiveness to changes in these variables as well.

1. Income ElasticityFor example, quantity demanded depends on consumer incomes. A business firm’smanagers will, therefore, want to know how much a change in consumer incomewill affect the quantity of its product demanded. Fortunately, an elasticity measurecan be helpful here, too. An increase in consumer incomes clearly raises theamounts of most goods that consumers will demand. To measure the response,economists use the income elasticity of demand, which is the ratio of the percent-age change in quantity demanded to the percentage change in income. For exam-ple, foreign travel is quite income elastic, with middle-income and higher-incomepeople traveling abroad much more extensively than poor people do. In contrast,blue jeans, worn by rich and poor alike, show little demand increase as incomeincreases.


Income elasticity ofdemand is the ratio of thepercentage change in quan-tity demanded to the per-centage change in income.

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ELASTICITY AS A GENERAL CONCEPT

2. Price Elasticity of SupplyEconomists also use elasticity to measure other responses. For example, to measurethe response of quantity supplied to a change in price, we use the price elasticity of sup-ply—defined as the ratio of the percentage change in quantity supplied to the percent-age change in price, for example, by what percent the supply of wheat increases whenthe price (at the time of planting) goes up by, say, 7 percent. The logic and analysis ofall such elasticity concepts are, of course, perfectly analogous to those for price elas-ticity of demand.

3. Cross Elasticity of DemandConsumers’ demands for many products are substantially affected by the quantitiesand prices of other available products. This brings us to the important concept calledcross elasticity of demand, which measures how much the demand for product X is af-fected by a change in the price of another good, Y.

This elasticity number is significantly affected by the fact that some products makeother products more desirable, but some products decrease consumer demand forother products. There are some products that just naturally go together. For exam-ple, cream and sugar increase the desirability of coffee, and vice versa. The same istrue of mustard or ketchup and hamburgers. In some extreme cases, neither productordinarily has any use without the other—automobiles and tires, shoes and shoelaces,and so on. Such goods, each of which makes the other more valuable, are calledcomplements.

The demand curves of complements are interrelated. That is, a rise in the price ofcoffee is likely to reduce the quantity of sugar demanded. Why? When coffee pricesrise, people drink less coffee and therefore demand less sugar to sweeten it. The op-posite will be true of a fall in coffee prices. A similar relationship holds for other com-plementary goods.

At the other extreme, some goods make other goods less valuable. These productsare called substitutes. Ownership of a motorcycle, for example, may decrease one’sdesire for a bicycle. If your pantry is stocked with cans of tuna fish, you are less likelyto rush out and buy cans of salmon. As you may expect, demand curves for substitutesare also related, but in the opposite direction. When the price of motorcycles falls,people may desire fewer bicycles, so the quantity of bicycles demanded falls. Whenthe price of salmon goes up, people may eat more tuna.

Economists use cross elasticity of demand to determine whether two productsare substitutes or complements. This measure is defined much like the ordinary priceelasticity of demand, except that instead of measuring the responsiveness of the quan-tity demanded of, say, coffee, to a change in its own price, cross elasticity of demandmeasures how quantity demanded of one good (coffee) responds to a change in theprice of another, say, sugar. For example, if a 20 percent rise in the price of sugar re-duces the quantity of coffee demanded by 5 percent (a change of minus 5 percent inquantity demanded), then the cross elasticity of demand will be:

Obviously, cross elasticity is important for business firms, especially when rivalfirms’ prices are concerned. American Airlines, for example, knows all too well that itwill lose customers if it does not match price cuts by Continental or United. Coke andPepsi provide another clear case in which cross elasticity of demand is crucial. Butfirms other than direct competitors may well take a substantial interest in cross elas-ticity. For example, the prices of DVD players and DVD rentals may profoundly af-fect the quantity of theater tickets that consumers demand.

Percentage change in quantity of coffee demandedPercentage change in sugar price

52 5%20%

5 2 0.25

ELASTICITY AS A GENERAL CONCEPT 113

Two goods are calledcomplements if anincrease in the quantityconsumed of one increasesthe quantity demanded ofthe other, all other thingsremaining constant.

Two goods are calledsubstitutes if an increasein the quantity consumedof one cuts the quantitydemanded of the other, allother things remainingconstant.

The cross elasticity ofdemand for product X to achange in the price of an-other product, Y, is the ratioof the percentage change inquantity demanded of X tothe percentage change inthe price of Y that bringsabout the change in quan-tity demanded.

The cross elasticity of demand measure underlies the following rule about comple-ments and substitutes:

If two goods are substitutes, a rise in the price of one of them tends to increase the quan-tity demanded of the other; so their cross elasticities of demand will normally be positive.If two goods are complements, a rise in the price of one of them tends to decrease thequantity demanded of the other item so their cross elasticities will normally be negative.Notice that, because cross elasticities can be positive or negative, we do not customarilydrop minus signs as we do in a calculation of the ordinary price elasticity of demand.

This result is really a matter of common sense. If the price of a good rises and buy-ers can find a substitute, they will tend to switch to the substitute. If the price ofJapanese-made cameras goes up and the price of American-made cameras does not, atleast some people will switch to the American product. Thus, a rise in the price ofJapanese cameras causes a rise in the quantity of American cameras demanded. Bothpercentage changes are positive numbers and so their ratio—the cross elasticity of de-mand—is also positive.

However, if two goods are complements, a rise in the price of one will discourageboth its own use and use of the complementary good. Automobiles and car radios areobviously complements. A large increase in automobile prices will depress car sales,and this in turn will reduce sales of car radios. Thus, a positive percentage change inthe price of cars leads to a negative percentage change in the quantity of car radiosdemanded. The ratio of these numbers—the cross elasticity of demand for cars andradios—is therefore negative.

In practice, courts of law often evaluate cross elasticity of demand to determinewhether particular business firms face strong competition that can prevent them fromovercharging consumers—hence, the quotation from the U.S. Supreme Court at thebeginning of this chapter. The quotation is one of the earliest examples of the courtsusing the concept of cross elasticities. It tells us that if two substitute (that is, rival)products exhibit a high cross elasticity of demand (for example, between McDonald’sand Burger King), then neither firm can raise its price much without losing customersto the other. In such a case, no one can legitimately claim that either firm has a mo-nopoly. If a rise in Firm X’s price causes its consumers to switch in droves to a FirmY’s product, then the cross elasticity of demand for Firm Y’s product with respect tothe price of Firm X’s product will be high. That, in turn, means that competition isreally powerful enough to prevent Firm X from raising its price arbitrarily. This rela-tionship explains why cross elasticity is used so often in litigation before courts orgovernment regulatory agencies when the degree of competition is an important is-sue, because the higher the cross-elasticity of demand between two products, thestronger must be the competition between them. So cross elasticity is an effectivemeasure of the strength of such competition.

The cross elasticity issue keeps coming up whenever firms are accused of actinglike monopolists. For example, in 1997 a dispute arose between Litton and Honey-well, the two main manufacturers of the mechanisms that guide the flight of aircraft.In 1998, the issue reappeared in a lawsuit in which Rolite, an ash recycling firm, suedWaste Management, a waste removal company, charging monopolistic behavior bythe latter. (See “How Large Is A Firm’s Market Share? Cross Elasticity as a Test,” onpage 115, for more on cross elasticity.)

Demand is a complex phenomenon. We have studied in detail the dependence ofquantity demanded on price, and we have noted that quantity demanded depends alsoon other variables such as consumers’ incomes and the prices of complementary andsubstitute products. Because of changes in these other variables (which we formerly


CHANGES IN DEMAND: MOVEMENTS ALONGTHE DEMAND CURVE VERSUS SHIFTS IN THE DEMAND CURVE

held constant when we studied only the effect of changes in price), demand curves of-ten do not keep the same shape and position as time passes. Instead, they shift about.Chapter 4 showed that shifts in demand curves affect both quantity and pricepredictably.

Public policy and business discussions often make vague references to “changes indemand.” By itself, this expression does not mean anything. Recall from our discus-sion in Chapter 4 that we must distinguish between a response to a price change—which shows up as a movement along the demand curve—and a change in the relationshipbetween price and quantity demanded—which produces a shift in the demand curve (ineffect, it moves the curve itself).

When price falls, quantity demanded generally rises. This change represents amovement along the demand curve. In contrast, an effective advertising campaign mayresult in people buying more goods at any given price. This case involves a rightwardshift of the demand curve. Such a shift can be caused by a change in the value of anyof the variables other than price that affect quantity demanded. Although the distinc-tion between a shift in a demand curve and a movement along it may at first seemtrivial, the difference is very significant in practice. Let us pause for a moment to con-sider how changes in some of these other variables shift the demand curve.

Demand ShiftersAs an example, consider the effect of a change in consumer income on the demandcurve for sweaters. In Figure 5(a), the black curve D0D0 is the original demand curve

CHANGES IN DEMAND: MOVEMENTS ALONG THE DEMAND CURVE VERSUS SHIFTS IN THE DEMAND CURVE 115

How Large Is a Firm’s Market Share? Cross Elasticity as a Test

A firm’s “market share” is often a crucial element in antitrust law-suits (see Chapter 13) for a simple reason. If the firm supplies nomore than, say, 20 percent of the industry’s output, courts and reg-ulators presume that the firm is not a monopoly, as its customerscan switch their business to competitors if the firm tries to chargetoo high a price. On the other hand, if the defendant firm in thelawsuit accounts for 90 percent of the industry’s output, courts mayhave good reason to worry about monopoly power (which we coverin Chapter 11).

Such court cases often provide lively debates in which the de-fendant firms try to prove that they have very small market shares,and the plaintiffs seek to establish the opposite. Each side knowshow much the defendant firm actually produces and sells, so whatdo they find to argue about? The dispute is about the size of the to-tal relevant market, which clearly affects the magnitude of thefirm’s market share. Ambiguity arises here because different firmsdo not produce identical products. For instance, are Rice Krispies inthe same market as Cheerios? And how about Quaker Oatmeal,which users eat hot? What about frozen waffles? Are all of theseproducts part of the same market? If they are, then the overall mar-ket is large, and each seller therefore has a smaller share. If theseproducts are in different markets, the opposite will be true.

Many observers argue, as the Supreme Court did in the famousDuPont cellophane case (and, more recently, as was argued whenRolite sued Waste Management in 1998), that one of the proper cri-teria for determining the borders of the relevant market is crosselasticity of demand. If two products have a high and positive cross

elasticity, they must be close enough substitutes to compete closely;that is, they must be in the same market. But how large must thecross elasticity be before the court decides that two products are inthe same market? Although the law has not established a clear elas-ticity benchmark to determine whether a particular firm is in a rel-evant market, several courts have determined that a very high crosselasticity number clearly indicates effective competition betweentwo products, meaning that the two items must be in the samemarket.

SOU

RCE:

© La

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Dwig

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for sweaters. Now suppose that parents start sending more money to their needy sonsand daughters in college. If the price of sweaters remains the same, those students arelikely to use some of their increased income to buy more sweaters. For example, if theprice remains at $35, quantity demanded might rise from 40,000 sweaters (point R) to60,000 (point S). Similarly, if price had been $28 and remained at that level, the risein income might produce a corresponding change from T to U. In other words, wewould expect the rise in income to shift the entire demand curve to the right fromD0D0 to D1D1. In exactly the same way, a fall in consumer income can be expected tolead to a leftward shift in the demand curve for sweaters, as shown in Figure 5(b).

We can analyze other variables that affect quantity demanded in the same way. Forexample, increased television advertising for sweaters may lead to a rightward (out-ward) shift in the demand curve for sweaters, as in Figure 5(a). The same thing mightoccur if the price of a substitute product, such as jackets, increased, because it wouldput sweaters at a competitive advantage. If two goods are substitutes, a rise in theprice of one of them will tend to shift the demand curve for the other one outward (tothe right). Similarly, if a complementary product (perhaps matching pants to go withthe sweaters) became more expensive, we would expect the demand curve for sweatersto shift to the left, as in Figure 5(b). In summary:

We expect a demand curve to shift to the right (outward) if consumer incomes rise, iftastes change in favor of the product, if substitute goods become more expensive, or ifcomplementary goods become cheaper. We expect a demand curve to shift to the left (in-ward) if any of these influences changes in the opposite direction.

One more important feature of a demand curve does not show up on a graph. A de-mand curve indicates, at each possible price, the quantity of the good that is de-manded during a particular time period. That is, all of the alternative prices consideredin a demand curve must refer to the same time period. Economists do not compare aprice of $10 for commodity X in January with a price of $8 in September.

This feature imparts a peculiar character to the demand curve and complicates statis-tical calculations. For obvious reasons, actual observed data show different prices andquantities only for different dates. Statistical data may show, for example, the one pricethat prevailed in January and another that occurred at a later date, when that price had


40 60

28

$35

Price

Quantity of Sweaters in Thousands(a)

D0

D0

T

R

D1

S

U

Price

Quantity of Sweaters(b)

D0

D0

D2

D2

D1

FIGURE 5Shifts in a DemandCurve

THE TIME PERIOD OF THE DEMAND CURVE AND ECONOMIC DECISION MAKING

changed. Why, then, do economists adopt the apparently peculiar approach of dealingin a demand curve only with the prices that may conceivably occur (as alternative possi-bilities) in one and the same time period? The answer is that the demand curve’s strictlydefined time dimension arises inescapably from the logic of decision making and at-tempts to reach an optimal decision—the decision that moves the decision maker asclose to her goal as is possible under the circumstances she faces.

When a business seeks to price one of its products for, say, the following sixmonths, it must consider the range of alternative prices available for that six-monthperiod and the consequences of each of these possible prices. For example, if manage-ment is reasonably certain that the best price for the six-month period lies somewherebetween $3.50 and $5.00, it should perhaps consider each of four possibilities—$3.50,$4.00, $4.50, and $5.00—and estimate how much it can expect to sell at each of thesepotential prices during that given six-month period. The result of these estimates mayappear in a format similar to that of the following table:

This table supplies managers with the informa-tion that they need to make optimal pricing deci-sions. Because the price that will be selected willbe the one at which goods are sold during the periodin question, all the prices considered in that deci-sion must be alternative possible prices for thatsame period. The table therefore also containsprecisely the information an economist uses todraw a demand curve.

The demand curve describes a set of hypothetical quantity responses to a set of potentialprices, but the firm can actually charge only one of these prices. All of the points on thedemand curve refer to alternative possibilities for the same time period—the period forwhich the decision is to be made.

Thus, a demand curve of the sort just described is not just an abstract notion that isuseful primarily in academic discussions. Rather, it offers precisely the informationthat businesses or government agencies need to make rational decisions. However,the fact that all points on the demand curve are hypothetical possibilities for the sameperiod of time causes problems for statistical estimation of demand curves. Theseproblems are discussed in the appendix to this chapter.

Let’s look at an example from the real world to show how the elasticity concept helpsto resolve a concrete problem rather different from those we have been discussing. In1989, a lengthy trial in a U.S. district court resulted in a judgment against the photo-graphic products manufacturing company Eastman-Kodak for patent infringement oftechnology that rival firm Polaroid had designed. The court then set out to determinethe amount of money Kodak owed Polaroid for its patent infringement during theten-year period 1976 to 1986, when Kodak had sold very similar instant cameras andfilm. The key issue was how much profit Polaroid had lost as a result of Kodak’s entryinto the field of instant photography, because that would determine how much Kodakwould be required to pay Polaroid. Both price elasticity of demand and cross elastic-ity of demand played crucial roles in the court’s decisions.

The court needed accurate estimates of the price elasticity of demand to determinewhether the explosive growth in instant camera sales between 1976 and 1979 wasmainly attributable to the fall in price that resulted from Kodak’s competition, or wasattributable to Kodak’s good reputation and the resulting rise in consumer confidence

REAL-WORLD APPLICATION: POLAROID VERSUS KODAK 117

An optimal decision isone that best serves the ob-jectives of the decisionmaker, whatever those ob-jectives may be. It is se-lected by explicit or implicitcomparison with the possi-ble alternative choices. Theterm optimal connotes nei-ther approval nor disap-proval of the objective itself.

Potential Six-Month Expected QuantityPrice Demanded

$3.50 75,0004.00 73,0004.50 70,0005.00 60,000

4 Here it should be pointed out that William Baumol was a witness in this court case, testifying on behalf of Kodak.

REAL-WORLD APPLICATION: POLAROID VERSUS KODAK4


in the quality of instant cameras. If the latter were true, then Polaroid might actuallyhave benefited from Kodak’s entry into the instant camera market rather than losingprofits, because Kodak’s presence in the market would have increased the total num-ber of potential customers aware of and eager to try instant cameras.

After 1980, instant camera and film sales began to drop sharply. On this issue, thecross elasticity of demand between instant and conventional (35-millimeter) cameras andfilm was crucial to the explanation. Why? Because the decline in the instant cameramarket occurred just as the prices of 35-millimeter cameras, film, developing, andprinting all began to fall significantly. So, if the decline in Polaroid’s overall sales wasattributable to the decreasing cost of 35-millimeter photography, then Kodak’s instantphotography activity was not to blame. And, in that case, the amount that Kodakwould be required to pay to Polaroid would decrease significantly. But if the crosselasticity of demand between 35-millimeter photography prices and the demand forinstant cameras and film was low, then the cause of the decline in Polaroid’s salesmight well have been Kodak’s patent-infringing activity—thus adding to the damagecompensation payments to which Polaroid was entitled.

On the basis of its elasticity calculations, Polaroid at one point claimed that Kodakwas obligated to pay it $9 billion or more. Kodak, however, claimed that it owed Po-laroid something in the neighborhood of $450 million. A lot of money was at stake.The judge’s verdict came out with a number very close to Kodak’s figure.

In this chapter, we have continued our study of the demand side of the market. Ratherthan focusing on what underlies demand formation, as we did in Chapter 5, we ap-plied demand analysis to business decisions. Most notably, we described and analyzedthe economist’s measure of the responsiveness of consumer demand to changes inprice, and we showed how this assessment determines the effect of a firm’s pricechange on the revenues of that enterprise. We illustrated how these concepts throwlight not only on business sales and revenues, but also on a number of rather differentissues, such as smoking and health, the effectiveness of competition among businessfirms as studied by courts of law, and the determination of penalties for patent in-fringement. In the next chapter, we turn to the supply side of the market and move astep closer to completing the framework we need to understand how markets work.

IN CONCLUSION

SUMMARY

1. To measure the responsiveness of the quantity demandedto price, economists calculate the elasticity of demand,which is defined as the percentage change in quantity de-manded divided by the percentage change in price, afterelimination of the minus sign.

2. If demand is elastic (elasticity is greater than 1), then a risein price will reduce total expenditures. If demand is unit-elastic (elasticity is equal to 1), then a rise in price will notchange total expenditures. If demand is inelastic (elasticityis less than 1), then a rise in price will increase total expen-diture.

3. Demand is not a fixed number. Rather, it is a relationshipshowing how quantity demanded is affected by price andother pertinent influences. If one or more of these othervariables change, the demand curve will shift.

4. Goods that make each other more desirable (hot dogs andmustard, wristwatches and watch straps) are called com-plements. When two goods are such that when consumersget more of one of them, they want less of the other (steaksand hamburgers, Coke and Pepsi), economists call thosegoods substitutes.

5. Cross elasticity of demand is defined as the percentagechange in the quantity demanded of one good divided bythe percentage change in the price of another good. Twosubstitute products normally have a positive cross elasticityof demand. Two complementary products normally have anegative cross elasticity of demand.

6. A rise in the price of one of two substitute products can beexpected to shift the demand curve of the other product tothe right. A rise in the price of one of two complementary

goods tends to shift the other good’s demand curve tothe left.

7. All points on a demand curve refer to the same time period—the time during which the price that is under considerationwill be in effect.

DISCUSSION QUESTIONS 119

KEY TERMS

(Price) elasticity of demand 105

Elastic, inelastic, and unit-elasticdemand curves 108

Income elasticity of demand 112

Complements 113

Substitutes 113

Cross elasticity of demand 113

Optimal decision 117

TEST YOURSELF

1. What variables other than price and advertising are likelyto affect the quantity demanded of a product?

2. Describe the probable shifts in the demand curves for:a. Airplane trips when airlines’ on-time performance

improvesb. Automobiles when airplane fares increasec. Automobiles when gasoline prices increased. Electricity when the average temperature in the United

States rises during a particular year (Note: The demandcurve for electricity in Maine and the demand curve forelectricity in Florida should respond in different ways.Why?)

3. Taxes on particular goods discourage their consumption.Economists say that such taxes “distort consumer de-mands.” In terms of the elasticity of demand for the com-modities in question, what sort of goods would you chooseto tax to achieve the following objectives?a. Collect a large amount of tax revenueb. Distort demand as little as possiblec. Discourage consumption of harmful commoditiesd. Discourage production of polluting commodities

4. Give examples of commodities whose demand you wouldexpect to be elastic and commodities whose demand youwould expect to be inelastic.

5. A rise in the price of a certain commodity from $15 to $20reduces quantity demanded from 20,000 to 5,000 units.Calculate the price elasticity of demand.

6. If the price elasticity of demand for gasoline is 0.3, and thecurrent price is $1.20 per gallon, what rise in the price ofgasoline will reduce its consumption by 10 percent?

7. Which of the following product pairs would you expect tobe substitutes, and which would you expect to be comple-ments?a. Shoes and sneakersb. Gasoline and sport utility vehiclesc. Bread and butterd. Instant camera film and regular camera film

8. For each of the product pairs given in Test Yourself Ques-tion 7, what would you guess about the products’ crosselasticity of demand?a. Do you expect it to be positive or negative?b. Do you expect it to be a large or small number? Why?

DISCUSSION QUESTIONS

1. Explain why elasticity of demand is measured in percent-ages.

2. Explain why the elasticity of demand formula normallyeliminates minus signs.

3. Explain why the elasticity of a straight-line demand curvevaries from one part of the curve to another.

4. A rise in the price of a product whose demand is elastic willreduce the total revenue of the firm. Explain.

5. Name some events that will cause a demand curve to shift.6. Explain why the following statement is true: “A firm with a

demand curve that is inelastic at its current output levelcan always increase its profits by raising its price and sell-ing less.” (Hint: Refer back to the discussion of elasticityand total expenditure/total revenue on pages 104–110.)


APPENDIX How Can We Find a Legitimate Demand Curve from Historical Statistics?

The peculiar time dimension of the demand curve, inconjunction with the fact that many variables other thanprice influence quantity demanded, makes it surprisinglydifficult to derive a product’s demand curve from histori-cal statistical data. Specialists can and often do derivesuch estimates, but the task is full of booby traps and usu-ally requires advanced statistical methods and interpreta-tion. This Appendix seeks to warn you about the boobytraps. It implies, for example, that if you become themarketing manager of a business firm after you graduatefrom college, and you need demand analysis, you willneed experts to do the job. This Appendix will also showyou some mistakes to look for as you interpret the re-sults, if you have reason to doubt the qualifications of thestatisticians you hire to calculate or forecast your demandcurve. It also gives an intuitive explanation of the legiti-mate ways in which demand curves may be determinedfrom the statistics.

The most obvious way to go about estimating a de-mand curve statistically is to collect a set of figures onprices and quantities sold in different periods, like thosegiven in Table 2. These points can then be plotted on adiagram with price and quantity on the axes, as shown in

Figure 6. We can then draw a line (the dashed line TT)that connects these points (labeled Jan., Feb., and so on),and connects them reasonably well, to represent theprices and quantities sold in the months indicated. Thisline may appear to approximate the demand curve, butunfortunately line TT, which summarizes the data fordifferent points of time, may bear no relationship to thetrue demand curve. Let us see why, and what can be doneabout it.

You may notice at once that the prices and quantitiesrepresented by the historical points in Figure 6 refer todifferent periods of time, and that each point on thegraph represents an actual (not hypothetical) price andquantity sold at a particular period of time (for example,one point gives the data for January, another for Febru-ary, and so on). The distinction is significant. Over theentire period covered by the historical data (Januarythrough May), the true demand curve, which is what aneconomist really needs to analyze decision problems,may well have shifted because of changes in some of theother variables affecting quantity demanded.

The actual events may appear as shown in Figure 7. InJanuary, the demand curve was given by JJ, but by Feb-

ruary the curve had shifted to FF, by March toMM, and so on. This figure shows a separateand distinct demand curve for each of the rel-evant months, and none of them needs to re-semble the plot of historical data, TT.

In fact, the slope of the historical plotcurve, TT, can be very different from the

TABLE 2Historical Data on Price and Quantity

January February March April May

Quantity Sold 95,000 91,500 95,000 90,000 91,000Price $7.20 $8.00 $7.70 $8.00 $8.20

FIGURE 6

May

Feb.

March

Jan.

April R

S

T

T

$8.20

8.00

7.80

7.60

7.40

7.20

7.00

0 90 91 92 93 94 95 96 97 98

Quantity Demanded in Thousands

Ave

rage

Pri

ce

FIGURE 7 Plot of Historical Data and TrueDemand Curves for January,February, and March

Feb.

March

Jan.

RS

W

$8.20

8.00

7.80

7.60

7.40

7.20

7.00

0 90 91 92 93 94 95 96 97

Quantity Demanded in Thousands

Ave

rage

Pri

ce

FJ

M

F

98

T

M

T

J

Plot of Historical Data on Price and Quantity

slopes of the true underlying demand curves, as is thecase in Figure 7. As a consequence, the decision makercan be seriously misled if she selects her price on the ba-sis of the historical data. She may, for example, think thatdemand is quite insensitive to changes in price (as lineTT seems to indicate), so she may conclude that a pricereduction is not advisable. In fact, the true demandcurves show that a price reduction would increase quan-tity demanded substantially, because they are much moreelastic than the shape of the estimated curve in Figure 6would suggest.

For example, if the decision maker were to charge aprice of $7.80 rather than $8.00 in February, the histori-cal plot would lead her to expect a rise in quantity de-manded of only 1,000 units. (Compare point R, withsales of 91,500 units, and point S, with sales of 92,500units, in Figure 6.) The true demand curve for February(line FF in Figure 7), however, indicates an increase insales of 2,500 units (from point R, with sales of 91,500units, to point W, with sales of 94,000 units). A managerwho based her decision on the historical plot, rather thanon the true demand curve, might be led into serious er-ror. Nevertheless, it is astonishing how often peoplemake this mistake in practice, even when using appar-ently sophisticated techniques.

AN ILLUSTRATION: DID THEADVERTISING PROGRAM WORK?

Some years ago, one of the largest producers of packagedfoods in the United States conducted a statistical study tojudge the effectiveness of its advertising expenditures,which amounted to nearly $100 million per year. A com-pany statistician collected year-by-year figures on com-pany sales and advertising outlays and discovered, to hisdelight, that they showed a remarkably close relationshipto one another: Quantity demanded rose as advertisingrose. The trouble was that the relationship seemed justtoo perfect. In economics, data about demand and anyone of the elements that influence it almost never showsuch a neat pattern. Human tastes and other pertinentinfluences are just too variable to permit such regularity.

Suspicious company executives asked one of the au-thors of this book to examine the analysis. A littlethought showed that the suspiciously close statistical re-lationship between sales and advertising expenditures re-sulted from a disregard for the principles just presented.The investigator had, in fact, constructed a graph of his-torical data on sales and advertising expenditure, analo-gous to TT in Figures 6 and 7 and therefore not neces-sarily similar to the truly relevant relationship.

It transpired, after study of the situation, that the sta-bility of the relationship actually arose from the fact that,in the past, the company had based its advertising spend-ing on its sales, automatically allocating a fixed percent-

age of its sales revenues to advertising. The historical re-lationship between advertising and demand therefore de-scribed only the company’s budgeting practices, not theeffectiveness of its advertising program. If the firm’smanagement had used this curve in planning future ad-vertising campaigns, it might have made some regret-table decisions. The moral of the story: Avoid the use ofpurely historical curves like TT in making economicdecisions.

HOW CAN WE FIND A LEGITIMATEDEMAND CURVE FROM THESTATISTICS?

The trouble with the discussion so far is that it tells youonly what you cannot legitimately do. But business execu-tives and economists often need information about de-mand curves—for example, to analyze a pricing decisionfor next April. How can the true demand curves befound? In practice, statisticians use complex methodsthat go well beyond what we can cover in an introduc-tory course. Nevertheless, we can (and will) give you afeeling for the advanced methods used by statisticians viaa simple illustration in which a straightforward approachhelps to locate the demand curve statistically.

The problem described in this Appendix occurs be-cause demand curves and supply curves (like other curvesin economics) shift from time to time. They do not shiftfor no reason, however. As we saw in the chapter, theyshift because quantity demanded or supplied is influ-enced by variables other than price, such as advertising,consumer incomes, and so forth. Recognizing this rela-tionship can help us track down the demand curve—if wecan determine the “other things” that affect the demandfor, say, widgets, and observe when those other thingschanged and when they did not, we can infer when thedemand curve may have been moving and when it prob-ably wasn’t.

Consider the demand for umbrellas. Umbrellas arerarely advertised and are relatively inexpensive, so nei-ther advertising nor consumer incomes should havemuch effect on their sales. In fact, it is reasonable to as-sume that the quantity of umbrellas demanded in a yeardepends largely on two influences: their price and theamount of rainfall. As we know, a change in price willlead to a movement along the demand curve without shift-ing it. Heavy rains will shift the demand curve outward, be-cause people will need to buy more umbrellas, whereasthe curve will shift inward in a drought year. Ideally, wewould like to find some dates when the demand curvestayed in the same position but the supply curve shifted, so thatwe can obtain a number of different equilibrium points,all of which lie on or near the same demand curve.

Suppose that rainfall in St. Louis was as given in Table3 for the period 1993–2001 and that prices and quantities

APPENDIX 121

of umbrellas sold in those years were as indicated by thedots in Figure 8. Notice, first, that in years in which rain-fall was highest, such as 1997 and 2001, the dots in thegraph lie farthest to the right, whereas the dots for low-rain years lie toward the left, meaning that in rainieryears more umbrellas were sold, as our hypothesis aboutthe effect of rain on sales suggests. More important forour purposes, for the four years 1993, 1995, 1996, and2000, rainfall was about the same—nearly 27 inches.Thus, the demand curve did not shift from one of theseyears to the next. It is reasonable to conclude that thedots for these four years fell close to the same true de-mand curve.

But the dots for those four years are quite far apartfrom one another. This separation means that in thoseyears, with the demand curve in the same position, thesupply curve must have been shifting. So, if we wish, we

can check this suppositionstatistically, by observing thatthe supply curve can be ex-pected to shift when there isa change in the cost of theraw materials that go into theproduction of umbrellas—

cloth, steel for the ribs, and plastic for the handles.Changes in this cost variable can be expected to shift thesupply curve but not the demand curve, because con-sumers do not even know these cost numbers. So, just asthe rainfall data indicated in what years the demandcurve probably moved and when it did not, the inputprice data can give us such information about the supplycurve.

To see this, imagine that we have a year-by-year tablefor those input costs similar to the table for rainfall (thecost table is not shown here); and suppose it tells us thatin the four years of interest (1993, 1995, 1996, and 2000),those costs were very different from one another. We caninfer that the supply curves in those years were quite dif-ferent even though, as we have just seen, the demandcurve was unchanging in the same years. Accordingly, thegraph shows line DD drawn close to these four dots, withtheir four supply curves—SS93, SS95, SS96, and SS00—also going through the corresponding points, which arethe equilibrium points for those four years. We cantherefore interpret DD as a valid statistical estimate ofthe true demand curve for those years. We derived it byrecognizing as irrelevant the dots for the years withmuch higher or much lower rainfall amounts, in whichthe demand curve can be expected to have shifted, and bydrawing the statistical demand curve through the rele-vant dots—those that, according to the data on the vari-ables that shift the curves, were probably generated bydifferent supply curves but a common demand curve.

The actual methods used to derive statistical demandcurves are far more complex. The underlying logic, how-ever, is analogous to that of the process used in thisexample.


TABLE 3Hypothetical Annual Rainfall in St. Louis, 1993–2001

Year 1993 1994 1995 1996 1997 1998 1999 2000 2001

Inches of rain 26 18 28 29 35 20 32 27 34

FIGURE 8 Legitimate Demand CurveEstimation from Statistical Data

Quantity of Umbrellas Sold

Price

D

DS

1994

S

S

S

S00

2000

19931996

1995

1999

2001 1997

S93S96

S951998

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