CROSS PRICE ELASTICITY AND INCOME ELASTICITYOF DEMAND: ARE YOUR STUDENTS CONFUSED?

by Philip E. Graves* and Robert L. Sexton**

Abstract

TTie authors demonstrate that most textbooks are ambiguous at best in their treatment of cross priceand income elasticity of demand. There is also no discussion of what initiates a price increase in dis-cussions of substitutes and complements in the textbooks examined. The authors offer a remedy forthese deficiencies.

Introduction

We examined a large sampling of top sellingmicroeconomics textbooks (principles and interme-diate): Arnold (20()8), Baumöl and Blinder (2009),Besanko and Braeutigatn (2(X)8), Case and Fair(2004). Frank and Bennanke (2007). Hall andLieberman (2008), Hubbard atid O'Brien (2008),Pindyck and Rubinfeld (2005), Lipsey, Ragan andStorer (2(X)8), Mankiw (2007). McConnell andBrue (2008), Miller (2008) and Parkin (2008),Perloff (2009), Sexton (2008) and Schiller (pp.404-07). In each of these texts, in the chapter onsupply and demand, it clearly states that if adecrease (an increase) in the price of one goodcauses a decrease (an increase) in the demand foranother good, buyers view these two goods as sub-stitutes. And. if a decrease (an increase) in the priceof one good causes an increa.se (a decrease) in thedemand for another good, buyers view these twogoods as complements. However, it is al.so true thatin almost every principles and intennediate eco-nomics textbook the deftnition of cross price elas-ticity is written as follows: the percentage change inthe quantity demanded for a good that results froma given percentage change in the price of anothergood. The problem is the use (or abuse) of theterms demand and quantity demanded. In one chap-ter, students are taught that substitutes and comple-ments are the relationship between the price of onegood and the demand for another and now in a dif-ferent chapter they are taught that substitutes andcomplements are the relationship between the priceof one good and the quantity demanded for another.

without explanation. McEachem (2009) was theonly text that we surveyed that was correct.

Of eourse, the problem stems from economistsemploying convenient two-dimensional graphs todescribe n-dimensional phenomena. The problemdisappears in more advanced discussions where it isseen that the demand relationship is a mapping fromRn to R1+, and a change in any independent vari-able causes a change in the dependent variable,desired quantity. Whether one calls this "change indemand" or "change in quantity demanded" isimmaterial in the n-dimensionaJ setting. However, atthe principles level, and in some intermediate treat-tnents, there is great potential for cottiusion as weshow here.

Cross Price Elasticity of Demand

With regard to cross price elasticities. Pindyckand Rubinfeld (2005, p. 34-35) write, " . . . the crossprice elasticity will be positive because the goods aresubstitutes: Because they compete in the market, arise in the price of margarine, which makes buttercheaper relative to margarine. leads to an increase inthe quantit>' demanded (Becau.se the demand curvefor butter will shift to the right, the price of thebutter will rise). Some gmxls are cotnplements . . . Ifthe price of gasoline goes up the quantity of gasoUnefalls and motorists will drive less. And because thep»eople are driving less, the demand for motor oilalso falls (the entire demand curve for mortor oilshifts to the left). Thus, the cross price elasticity ofmotor oil with respect to gasoline is negative." It is

* Department of Economics. University of Colorado Boulder, CO 80309.• * Distinguished Professor of Economics Pepperdine University Malibu. California 90263.4

Vol. 54, No. 2 (Fall 2009) 107

clear that students could easily be confused withwhat they leamed in the supply and demand chap-ter—Pindyck and Rubinleld (2005, p. 22) write.". . . we will use the phrase change in demand torefer to shifts in the demand curve and reserve thephrase change In quantity demanded to apply tomovements along the demand curve. However, theydefine complements and substitutes to be when achange in the price leads to a change in the quantitydemanded. This would suggest to a student that theyare saying that there is not a shift in the detnandcurve when the price of a related g(X)d changes. Wecontend that the failure to consistently use "changein demand" and "change in quantity demanded'' islikely to lead to confusion among students.

Besanko and Braeutigam (2iX)8, p. 49) vmte. "thecross price elasticity of demand for chicken withrespect to beef is positive indicates that as the priceof beef goes up, the quantity of chicken demandedgoes up . . . As the price of breakfast cereal goesup consumers will buy less cereal and thus will needless milk to pour on top of their cereal.Consequently, the demand for the milk will fall"This is likely to be confusing to students because theauthors use quantity demanded of chicken (incor-rectly) in the substitute example and the demand formilk (correctly) in the complements example.

Lipsey, Ragan and Storer (2008) is the least con-fusing of the books we examined. They define crossprice elasticity as "the responsiveness of demand tochanges in the price of another product is called thecross elasticity of demand." However, then the>'write the cross price elasticity formula as the per-centage change in quantity demanded divided bythe percentage change in the price of Good Y. Thisleads to the sanie confusion between demand andquantity demanded seen earlier. Why not call it wbatit is. namely the percentage change in demand?They follow by correctly stating, "The change in theprice of good Y causes the demand curve for GoodX to shift. If X and Y are substitutes, an increase inthe price of Y leads to an increase In the demand forX. If X and Y are complements, an increase in theprice of Y leads to a reduction in the demand for X.in either case, we are holding the price of X con-stant. Therefore, we measure the change in quan-tity demanded of X at its unchanged price bymeasuring the shift for the demand curve for X.(authors' bold for emphasis)

See figure I. where an increase in the price ofbutter increases the demand for the substitute mar-

Qg Q3 Qi Margarine

FIGURE 1 The Case of Substitute Goods

garine. We are interested in measuring the percent-age shift in the demand curve for margarine, i.e.the difference between Q^ and Q, divided by QQ.The important point is that the cross price elastic-ity of demand is the measurement of the percent-age shift in the demand curve for the substitute orcomplementary good. We need to avoid the usageof the expression "change in quantity demanded"when demand curves are shifting, saving thatexpression for movements along a demand curveresulting from own-price changes. We propose thatthe cross price elasticity definition be written asthe impact the price of one good will have on thedemand for another good in percentages, otherthings equal.

Income Elasticity of Demand

The same problem occurs with income elasticityfor all the authors cited above. For example,McConnell (2008) in the supply and demand chap-ter writes, "for most products a rise in incomecauses an increase in demand." This is the normalgood scenario seen in every principles text. Goodswhose demand varies inversely with money incomeare called inferior goods. However, moving to thechapter on elasticity McConnell writes, "normal andinferior goods are deñned as the percentage changein quantity demanded divided by the percentagechange in income." Again, we see a potentially

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cotifusing failure to distinguish between dematid andquantity demanded. Consistent u.sage would requirethat the income elasticity of demand be defined asthe responsivetiess of the change in demand to achange in income in percentage terms.

What Caused the Price Increase?

There is another source for possible confusionthat the formal definition may pose to students if thecause of the initial price increase is not specified.

For example, assume that peanut butter andjelly are complementary goods. This would meanthat a change in the price of peanut butter wouldbe inversely related to a change in demand forjelly. The logic would seem straightforward-a.s aresult of a higher price for peanut butter fewerpeople will purchase peanut butter and conse-quently there would be less demand for jelly. Thiswould hold true if the price increase in peanutbutter was caused by a supply shift. However, thiswould not necessarily be the ca.se if the increase inthe price of peanut butter was caused by anincrease in demand. If the higher price of peanutbutter was demand induced, say a new medicaldiscovery that peanut butter was a longevityenhancing substance; then the outcome would be alarger quantity of peanut butter bought at thehigher price and hence, a greater demand for jelly.And, if a decrease in demand for peanut butter, amedical discovery that many people now realizethey are actually allergic to peanuts would causethe demand curve for peanut butter to fall and asthe price for peanut butter fell there would befewer jars of peanut butter purchased and thereforea lower, not higher demand for jelly.

The same caution is also relevant for substitutegoods. If. for example. Chevron gas and Shellgas are substitutes, then one would expect to seean increase in the relative price of Chevron tolead to an increase In demand for Shell. Thiswould, of course, be true if the increase in theprice was caused by a reduction in the supplycurve of Chevron. If, on the other hand, the demandfor Chevron increased, say through effectiveadvertising—say a new improved cleaner burningfuel, and this caused the price increase: the quan-tity of Chevron would actually increase and hencecustomers would be substituting away from theother product, Shell. Alternatively, if the price of

Chevron fell, the student would be led to believethat there would be a reduction in demand forShell. However, if demand fell for Chevron, theprice and quantity of Chevron would fall, implyingthat there would now be less of Chevron and pre-sumably more of Shell purchased despite thelower relative price of the substitute.

Conclusion

In discussions of substitutes and complementsand of cross price and income elastiticities—both in class and on e x a m s ^ t is important toinform students to consistently employ "changein demand" (supply) and "change in quantitydemanded" in all contexts/chapters. The additionaltime spent here will lead to greater clarity and muchless student confusion in the application of supplyand demand.

References

Arnold, R. 2008. Economics, 8*̂ ed. Mason. Ohio:Thomson South-Westem.

Baumöl, W. and A. BlinderBesanko. D. and R Braeutigani. 2008.

Microeconomics, 3"̂ ed. Hoboken, NJ: John Wileyand Sons, Inc.

Case, K and R. Fair 2004. Principles ofMicroeconomics, 7"" ed. Upper Saddle River,NJ: Pearson Prentice Hall

Frank. R. and B. Bemanke. 2007. Principles ofMicroeconomics. 3"̂ ed. New York: McGraw-Hill/Irwin.

Hall and Lieberman. 2008. Economics, S'^ ed.Mason, Ohio: Thomson South-Westem.

Hubbard, R.G. and A. O'Brien. 2008. Economics,2"'' ed. Upper Saddle River, NJ: Pearson PrenticeHall.

Lipsey, R, Ragan, C and P Storer 2008.Microeconomics, 13'^ ed., Boston: PearsonEducation, Inc.

Mankiw, G. 2009. Principles of Microeconomics,5^^ ed. Mason, Ohio: Thomson South-Westem.

McConnell. C. and S. Brue. 2008. Microeconomics,17''' ed. New York: McGraw-Hill/Irwin.

McEachem, W (2009) Economics: A ContemporaryApproach, 8"̂ ed. Mason, Ohio: Thomson South-Westem.

Vol. 54, No. 2 (Fall 2009) 109

Miller. R.L. 2008. Microeconomics Today, M"* ed.Boston: Pearson Education. Inc.

Parkin, M. 2008. Microeconomics, 8th ed. Boston:Pearson Education, Inc.

Pindyck, R. and D. Rubinfeld. 2009.Microeconomics, 7"̂ ed. Upper Saddle River, NJ:Pearson Prentice Hall.

Perioff, J. 2009, Microeconomics 5'*̂ ed. Boston:Pearson Education, Inc.

Schiller, B. 2008, Economics II"' ed. New York:McGraw-Hill/I rw in.

Sexton, R.L.. 199!. "Demand Induced PriceChanges—Substitutes and Complements: ACautionary Comment." Atlantic EconomicJournal, Vol. 19. Issue 2, p68.

Sexton, R.L. 2008. Exploring Microeconomics,4"* ed. Mason, Ohio: Thomson South-Western.

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