# Chapter ELASTICITY - Pearson

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C h a p t e r4ELASTICITYThe total revenue test estimates the price elasticity ofdemand by noting how a change in price affects thetotal revenue spent on the product.A person’s expenditure on a good follows the samerules. If the good has an elastic demand, a price cutincreases expenditure; if it has a unit elastic demand, aprice cut does not change expenditure; and, if it has aninelastic demand, a price cut decreases expenditure.Key Concepts Price Elasticity of Demand The price elasticity of demand is a units-freemeasure of responsiveness of the quantity demandedof a good to a change in its price when all other influences on buyers’ plans remain the same.The price elasticity of demand equals the magnitude of:(percentage change in quantity demanded) Q / Q ave (percentage change in price) P / Pavewhere “ave” stands for average. When the elasticity equals 0, the good has perfectlyinelastic demand and the demand curve is vertical. When the elasticity is less than 1 and greater than 0,the good has inelastic demand. When the elasticity equals 1, the good has unit elastic demand. When the elasticity is greater than 1 and less thaninfinity, the good has elastic demand. When the elasticity equals infinity, the good hasperfectly elastic demand and the demand curve ishorizontal.Elasticity is not equal to the slope of the demand curve.Along a linear demand curve the slope ( P/ Q ) is constant but the elasticity falls in magnitude when movingdownward along the curve.Price elasticity and total revenue (P )(Q ):When demand isA price cut results inInelastic (elasticity 1) a decrease in total revenueUnit elasticno change in total revenue(elasticity 1)Elastic (elasticity 1) an increase in total revenueThe price elasticity of demand depends on three factors: Substitutability — the more close substitutes thereare for the good, the larger is its price elasticity. Necessities generally have few substitutes and so have asmall elasticity; luxuries generally have many substitutes and so have a large elasticity. Proportion of income spent on the product — thegreater the proportion of income spent on a good,the larger is its price elasticity of demand. Time elapsed since the price change — the more timethat has passed since the price changed, the greateris the price elasticity of demand. More Elasticities of DemandThe cross elasticity of demand measures the responsiveness of demand for a good to a change in the priceof a substitute or complement.The cross elasticity of demand equals:(percentage change in the quantity demanded).(percentage change in the price of a related good)The sign of the cross elasticity of demand depends onwhether the goods are substitutes or complements.WhenThenthe goods are substitutes cross-elasticity 0the goods are complements cross-elasticity 063

64CHAPTER 4The income elasticity of demand measures the responsiveness of the demand for a good to a change inincome. The income elasticity of demand is defined as:(percentage change in the quantity demanded)(percentage change in income)Whenincome elasticity 10 income elasticity 1income elasticity 0Demand isincome elastic; normalgoodincome inelastic; normalgoodinferior good Elasticity of SupplyThe elasticity of supply measures the responsiveness ofthe quantity supplied to a change in its price when allother influences on selling plans remain the same.The elasticity of supply equals:(percentage change in the quantity supplied)(percentage change in the price)The size of the price elasticity of supply depends on: the ease with which additional resources can be substituted into the production process. the time since the price change.The momentary supply curve shows the immediate response to a price change. The short-run supply curveshows how the quantity supplied responds to a changein price after some of the possible adjustments havebeen made. The long--run supply curve shows the response of the quantity supplied to a price change afterall possible adjustments have been made.Helpful Hints1. INTUITION BEHIND THE CONCEPT OF ELASTICITY : Though there are many elasticity formulasin this chapter, all of the elasticity formulas measure how strongly a relationship responds to somechange. The price elasticity of demand, for instance, indicates how strongly a change in a good’sprice affects the quantity demanded of the good,while the income elasticity of demand measureshow strongly a change in income affects the demand for a good.2. WHY ELASTICITIES USE PERCENTAGES : Percentages are a natural way to determine the importanceof a change in price, income, or quantity. For example, which seems larger: a 1 hike in the price ofa Big Mac served at the local McDonald’s or a 1increase in the price of the least expensive BMWsold at the nearest BMW dealer? The 1 rise in theprice of the Big Mac is larger because it representsapproximately a 50 percent boost. With the leastexpensive BMW selling for more than 20,000, a 1 rise in its price is minuscule, less than a 0.005percent rise. Many consumers would respond to a 1 change in the price of a Big Mac; few would to a 1 change in the price of a BMW. Thus the bestmeasure of the size of a price change is the percentage change.3. HOW TO RECALL THE ELASTICITY FORMULA :Whether the percentage change in the quantitydemanded or the percentage change in the pricegoes in the numerator for the price elasticity of demand is easy to forget. If you think of a kewpiedoll, the sort of doll that is given away at carnivalsfor a display of an otherwise fairly useless talent,you should be able to keep the formula straight.The word kewpie is pronounced q-p, thereby telling us that “q” goes first (in the numerator) andthat “p” goes second (in the denominator).4. PRICE ELASTICITY AND TOTAL REVENUE : Totalrevenue equals price times quantity. To see whythe price elasticity of demand tells us how a pricechange affects total revenue, think about a pricerise. A price hike has two separate effects on totalrevenue. First, a higher price directly raises totalrevenue. Second, consumers respond to the higherprice by decreasing the quantity they demand. Thedecrease in the quantity reduces total revenue.Which effect is larger? That depends on the priceelasticity of demand. If demand is elastic, the percentage decrease in the quantity demanded exceedsthe percentage rise in price and so the effect fromthe decreased quantity exceeds the impact from thehigher price. Total revenue falls. But if demand isinelastic, the higher price dominates the decreasedquantity and total revenue rises. Finally, if demandis unit elastic, the percentage decrease in the quantity demanded equals the percentage rise in priceso the two effects offset each other, with no changein total revenue.

ELASTICITY655. WHY ONLY THE PRICE ELASTICITY OF DEMANDUSES THE MAGNITUDE OF THE PERCENTAGECHANGES : The price elasticity of demand uses theabsolute value of the percentage change in quantitydemanded divided by the percentage change inprice. However, neither the income elasticity northe cross elasticity take the absolute value. Why thedifference? Because the sign of the last two elasticities is important. The price elasticity of demand always is negative. The income elasticity, however,can be either negative or positive. A negative income elasticity indicates that the product is an inferior good and a positive income elasticity signifiesthat the product is a normal good. The sign of thecross elasticity also is important. A negative crosselasticity indicates that the two goods are complements and a positive cross elasticity means that thetwo goods are substitutes. Because the signs of theincome elasticity and cross elasticity convey information, we retain the sign rather than discard.Questions10. Your local Domino’s Pizza outlet estimates that theprice elasticity of demand for its pizzas is 4.00, so ifit raises the price it charges for its pizza, its totalrevenue will increase.More Elasticities of Demand11. The cross elasticity of demand between hot dogsand hot dog buns is negative.12. A product that has an elastic demand if its incomeelasticity of demand exceeds 1.0.13. An inferior good has an income elasticity that isnegative; a normal good has an income elasticitythat is positive.Elasticity of Supply14. The elasticity of supply equals the change in thequantity supplied divided by the change in price.15. If a good has a vertical supply curve, its elasticity ofsupply equals 0. Multiple Choice QuestionsPrice Elasticity of Demand True/False and ExplainPrice Elasticity of Demand11. The price elasticity of demand is the same as theslope of the demand curve.12. The price elasticity of demand ranges from 0 to .13. The more demanders respond to a price change,the larger the price elasticity of demand.14. If the price elasticity of demand is positive, the demand is elastic.15. Exxon gasoline is likely to have an elastic demand.16. Moving along a linear demand curve to lowerprices and increased quantities, the price elasticityof demand does not change.17. People spend more on rent than on soap, so theprice elasticity of demand for housing is likely to belarger than the price elasticity of demand for soap.18. The price elasticity of demand for food is largest inpoor nations.19. As more time passes after a price change, the priceelasticity of demand becomes smaller.11. Suppose that a 10 percent hike in the price of atextbook decreases the quantity demanded by 2 percent. Then the price elasticity of demand for textbooks isa. 0.2.b. 2.0.c. 5.0.d. 10.0.TABLE 4.1Multiple Choice Question 2Price per volleyball(dollars)Quantity demanded1955214512. Two points on the demand curve for volleyballs areshown in Table 4.1. What is the price elasticity ofdemand between these two points?a. 2.5.b. 2.0.c. 0.5.d. 0.4.

66CHAPTER 413. The quantity of new cars increases by 5 percent. Ifthe price elasticity of demand for new cars is 1.25,the price of a new car willa. fall by 4 percent.b. fall by 5 percent.c. fall by 6.25 percent.d. fall by 1.25 percent.19. Moving upward along a linear demand curve, as theprice rises and the quantity demanded decreases, theprice elasticity of demanda. falls.b. does not change.c. rises.d. first rises and then falls.14. Along a perfectly vertical demand curve, the priceelasticity of demanda. equals 0.b. is greater than 0 but less than 1.0.c. equals 1.0.d. is negative.10. If the price elasticity of demand equals 1.0, then asthe price falls thea. quantity demanded decreases.b. total revenue falls.c. quantity demanded does not change.d. total revenue does not change.15. Perfectly elastic demand is represented by a demandcurve thata. is vertical.b. is horizontal.c. has a 45 slope.d. is a rectangular hyperbola.11. A rise in the price of a product increases the totalrevenue from the product if thea. income elasticity of demand exceeds 1.b. good is an inferior product.c. product has an inelastic demand.d. product has an elastic demand.16. The demand for a good is more price inelastic ifa. its price is higher.b. the percentage of income spent on it is larger.c. it is a luxury good.d. it has no close substitutes.12. By reviewing its sales records, IBM economists discover that when it lowers the price of its personalcomputers, the total revenue IBM obtains from thesale of its personal computers rises. Hencea. supply of IBM personal computers is elastic.b. demand for IBM personal computers is elastic.c. supply of IBM personal computers is inelastic.d. demand for IBM personal computers is inelastic.17. Which of the following is likely to have the largestprice elasticity of demand?a. An automobileb. A new automobilec. A new Ford automobiled. A new Ford Mustang18. Business people often speak about price elasticitywithout actually using the term. Which statementdescribes a good with an elastic demand?a. “A price cut won’t help me. It won’t increase mysales, and I’ll just get less money for each unit.”b. “I don’t think a price cut will help my bottomline any. Sure, I’ll sell a bit more, but I’ll morethan lose because the price will be lower.”c. “My customers are real shoppers. After I cut myprices just a few cents below those my competitors charge, customers have been flocking to mystore and sales are booming.”d. “The economic expansion has done wonders formy sales. With more people back at work, mysales are taking off!”13. If a 4 percent rise in the price of peanut buttercauses total revenue from sales of peanut butter tofall by 8 percent, then peanut butter has a(n)a. elastic demand.b. inelastic demand.c. unit elastic demand.d. There is not enough information given to determine whether the demand for peanut butter iselastic, unit elastic, or inelastic.14. When the price of a hot dog rises 10 percent, yourexpenditure on hot dogs increases. Hence, it is certain thata. hot dogs are a normal good for you.b. hot dogs are an inferior good for you.c. your demand for hot dogs is elastic.d. your demand for hot dogs is inelastic.

ELASTICITYMore Elasticities of Demand15. For which of the following pairs of goods is the crosselasticity of demand positive?a. Tennis balls and tennis racketsb. Videotapes and laundry detergentc. Airline trips and textbooksd. Beef and chicken16. A 10 percent increase in the price of a Pepsi increases the demand for a Coca Cola by 50 percent.Thus the cross elasticity of demand between Pepsiand Coca Cola isa. 50.0.b. 10.0.c. 5.0.d. 0.2.17. A fall in the price of a paperback book from 6 to 4 causes a decrease in the quantity of magazinesdemanded from 1,100 to 900. What is the crosselasticity of demand between paperback books andmagazines?a. 0.5b. –0.5c. 2.0d. Without information about what was the changein income, it is not possible to calculate the crosselasticity of demand.18. Suppose that the income elasticity of demand forapartments is –0.2. This value indicates thata. the demand for apartments is price inelastic.b. the demand for apartments is unit elastic.c. a rise in the rent for apartments lowers the totalrevenue from renting apartments.d. apartments are an inferior good.19. Beans are an inferior good; chicken is a normalgood. When people’s incomes rise, the demand forbeans and the demand for chicken .a. increases; increasesb. increases; decreasesc. decreases; increasesd. decreases; decreases6720. A 10 percent hike in income increases the demandfor coffee by 3 percent. Then the income elasticityof demand for coffee isa. –0.3.b. 3.3.c. 0.3.d. 10.021. All normal goods havea. income elasticities of demand greater than 1.0.b. price elasticities of demand greater than 1.0.c. negative price elasticities of demand.d. positive income elasticities of demand.Elasticity of Supply22. Suppose that the price elasticity of supply for oil is0.1. Then, if the price of oil rises by 20 percent, thequantity of oil supplied will increasea. by 200 percent.b. by 20 percent.c. by 2 percent.d. by 0.2 percent.23. When the price of a CD is 13 per CD, 39,000,000CDs per year are supplied. When the price is 15per CD, 41,000,000 CDs per year are supplied.What is the elasticity of supply for CDs?a. 2.86b. 0.35c. 0.14d. 0.0524. If the long-run supply of rice is perfectly elastic, thena. as people’s incomes rise, the quantity of rice supplied decreases.b. as the price of corn falls, the quantity of rice demanded decreases.c. in the long run, a large rise in the price of ricecauses no change in the quantity of rice supplied.d. in the long run, an increase in the demand forrice leaves the price of rice unchanged.25. The elasticity of supply does NOT depend ona. resource substitution possibilities.b. the fraction of income spent on the product.c. the time elapsed since the price change.d. None of the above because all of the factors listedaffect the elasticity of supply.

68CHAPTER 4 Short Answer ProblemsFIGURE 4.2FIGURE 4.1Price (dollars per unit)Short Answer Problem 214Short Answer Problem 5Price (dollars per tape)1. Assume that the price elasticity of demand for oil is0.2 in the short run and 0.8 in the long run. Toraise the price of oil by 10 percent in the short run,what must be the decrease in the quantity of oil? Inthe long run, to have a 10 percent rise in the priceof oil, what must be the decrease?S321121008203040506070Quantity (millions of tapes per year)6DA4DB201010203040506070Quantity (units per month)2. In Figure 4.1 which demand is more elastic between prices 10 and 8?3. Why is the price elasticity of demand for foodlarger in poor nations than in rich nations?4. Explain what perfectly elastic demand means.Sketch an example of a demand curve for a goodwith perfectly elastic demand. When will perfectlyelastic demand occur? Be sure to use the notion ofsubstitutes in your answer.5. The supply curve for audio tapes is illustrated inFigure 4.2. Perhaps because of a rise in wages, thesupply of tapes decreases so that for every possiblequantity, the new supply curve lies above the oldsupply curve by 1.a. Suppose the demand for tapes is perfectly elasticand is such that the initial equilibrium price is 2 for a tape. After the decrease in supply, byhow much does the price of a tape rise? Draw afigure to illustrate your answer.b. Suppose the demand for tapes is perfectly inelastic and is such that the initial equilibriumprice of a tape is 2. In this case, by how muchdoes the price of a tape rise? Draw a figure toillustrate this situation.c. Based on your answers to parts (a) and (b),when will an increase in costs raise the price of aproduct the most: When demand is elastic orwhen it is inelastic? When will it decrease thequantity the most? When demand is elastic orinelastic? Is there any situation under which theprice does not change?TABLE 4.2The Demand for BurritosPrice(dollars perburrito)Quantity demanded(burritos per week)Total revenueper week(dollars) 830 740 650 560 470 380 290 110016. Table 4.2 gives eight points on a demand curve forburritos.a. Graph this demand curve.b. Calculate the price elasticity of demand between 1 and 2; 2 and 3; 3 and 4; 4 and 5; 5 and 6; 6 and 7; and 7 and 8.

70CHAPTER 4Answers Multiple Choice AnswersPrice Elasticity of Demand True/False AnswersPrice Elasticity of Demand11. F The slope of the demand curve equals P/ Q,whereas the price elasticity of demand equals( Q Q ave ) ( P Pave ) .12. T The smallest value for the price elasticity of demand, 0, reflects perfectly inelastic demand; thelargest, , indicates perfectly elastic demand.13. T The stronger the response to a price change, thelarger is the elasticity.14. F Demand is elastic when the price elasticity ofdemand exceeds 1.0.15. T Other brands of gasoline, such as Shell orAmoco, are close substitutes for Exxon, so thedemand for Exxon gasoline is likely to be elastic.16. F Moving downward along a linear demand curve,the price elasticity of demand falls.17. T Generally, the larger the total budget share spenton a product, the greater is the price elasticity ofdemand.18. T In poor nations food takes a larger portion ofconsumer spending, so the price elasticity of demand is larger.19. F As more time passes, more changes in demandcan occur, so demand becomes more elastic.10. F The demand for Domino’s Pizza is elastic, sorising the price decreases the quantity by somuch that total revenue declines.More Elasticities of Demand11. T Hot dogs and hot dog buns are complements, sothe cross elasticity of demand is negative.12. F To be elastic, the price elasticity of demand mustexceed 1.0.13. T An increase in income decreases the demand forinferior goods and increases it for normal goods.Elasticity of Supply14. F The price elasticity of supply equals the percentage change in the quantity supplied divided bythe percentage change in price.15. T When the elasticity of supply equals zero, thesupply is perfectly inelastic.11. a The price elasticity of demand is equal to (2percent)/(10 percent) 0.2.12. b The price elasticity of demand between twopoints equals ( Q Q ave ) ( P Pave ) . In this casewe get (10/50)/( 2/ 20) 2.13. a Rearranging the formula for the price elasticityof demand gives (percentage change in price) (percentage change in quantity demanded)/(elasticity of demand). So, the percentage change inprice equals (5 percent)/(1.25) 4 percent.14. a When a product has a perfectly inelastic demand, the price elasticity of demand equals zeroand the demand curve is vertical.15. b “Perfectly elastic” means that a very small rise inthe price means that the quantity demanded decreases to 0, which is the situation with a horizontal demand curve.16. d If there are no close substitutes, demanders continue to buy the product even if its price isboosted substantially, which means that the demand is inelastic.17. d There are many more substitutes for a new FordMustang than for the other goods. This answeris an example of the proposition that the morenarrowly defined a good, the larger is its priceelasticity of demand.18. c This statement describes a situation whereby asmall cut in price increased the quantity demanded substantially, which means that the demand is elastic.19. a Moving upward along a linear demand curve,the price elasticity of demand falls in value.10. d If demand is unit price elastic, a change in theprice of the product creates an offsetting changein the quantity demanded so that total revenuedoes not change.11. c If the demand is inelastic, the percentage rise inprice exceeds the percentage decrease in thequantity demanded, so total revenue from salesof the good increases.12. b When the demand is elastic, the percentage increase in the quantity demanded exceeds thepercentage fall in the price, so total revenue rises.13. a When demand is elastic, a rise in the price of theproduct decreases the quantity demanded by

ELASTICITYMore Elasticities of Demand15. d The cross elasticity of demand is positive forsubstitutes. Beef and chicken are substitutes, sotheir cross elasticity of demand is positive.16. c The cross elasticity of demand equals the percentage change in the quantity of Coca Cola divided by the percentage change in the price of aPepsi. Hence the cross elasticity of demandequals (50 percent)/(10 percent) 5.0.17. a The cross elasticity of demand is calculated as( Q Q ave ) ( P Pave ) , in which the “quantity”refers to magazines and the “price” to paperbackbooks. Using the formula for the cross elasticitygives (–200/1,000)/(– 2/ 5) 0.5.18. d If the income elasticity is negative, the product isan inferior good.19. c For an inferior good an increase in income decreases demand; for a normal good an increase inincome increases demand.20. c The income elasticity of demand equals in thiscase equals (3 percent)/(10 percent) or 0.3.21. d An increase in income increases the demand fora normal good.Elasticity of Supply22. c Rearranging the formula for the price elasticityof supply gives (percentage change in quantitysupplied) (price elasticity of supply) (percentage change in price) (0.1) (20 percent) 2 percent.23. b Analogous to the price elasticity of demand, theelasticity of supply is ( Q Q avg ) ( P Pavg ), or(2,000,000/40,000,000)/( 2/ 14) 0.35.24. d When the supply is perfectly elastic, an increasein demand has no effect on the equilibriumprice. This result is illustrated in Figure 4.3, inwhich the increase in demand from D0 toD 1 leaves the price constant at 50 a ton.25. b The proportion of income spent on the productaffects the price elasticity of demand, not theprice elasticity of supply.FIGURE 4.3Multiple Choice Question 24Price (dollars per ton of rice)proportionally more, so that total revenue fallswhen the price is boosted.14. d When an increase in the price of a product increases your expenditure on the product, yourdemand for the product is tity (tons of rice per year) Answers to Short Answer Problems1. Rearranging the formula for the price elasticity ofdemand gives (price elasticity of demand) (percentage change in price) (percentage change inquantity). The price rise is 10 percent, so theamount by which the quantity must be restricted inthe short run is (0.2) (10 percent) 2 percent.In the long run, the price elasticity of demand is0.8, so the decrease in the quantity is (0.8)(10 percent) 8 percent. To raise the price by 10 percent,the long-run decrease in the quantity must be fourtimes the short-run decrease.2. The demand represented by D A is more elastic thanthe demand given by DB . To see why, recall theformula for the price elasticity of demand(percentage change in quantity demanded)(percentage change in price)Along both demand curves, the percentage changein the price from 10 to 8 is the same. But Figure4.4 (on the next page) shows that the percentagechange in the quantity demanded is greater alongD A where the quantity demanded increases from30 to 50, a 50 percent increase, whereas along DBthe quantity demanded increases to 40, only a 29percent increase. Because the percentage increase inthe quantity demanded is greater along D A theprice elasticity of demand over this price range ishigher for D A .

72CHAPTER 4ple, consider corn grown by one farmer. Otherfarmers’ corn is a perfect substitute for the firstfarmer’s corn. If there are perfect substitutes for theproduct, even the smallest rise in the price of theproduct leads the quantity demanded to decrease to0. The horizontal demand curve in Figure 4.5 indicates that any rise in the price above 4 a bushel willdecrease the quantity demanded to 0.FIGURE 4.4141210FIGURE 4.68DA64DB2010203040506070Quantity (units per month)3. The larger the fraction of their income that consumers spend on a product, the greater the priceelasticity of demand. People in poor nations spend alarger proportion of their income on food than dopeople in wealthy nations, so the price elasticity ofdemand for food is larger in poor nations.Short Answer Problem 5 (a)Price (dollars per tape)Price (dollars per unit)Short Answer Problem 2SBSA32D1010203040506070Quantity (millions of tapes per year)FIGURE 4.5Price (dollars per bushel of corn)Short Answer Problem 47654D321010203040506070Quantity (thousands of bushels of corn per year)4. A perfectly elastic demand is illustrated in Figure4.5. Demand is perfectly elastic when demanderscan find perfect substitutes for a product. For exam-5. a. In Figure 4.6 the rise in costs shifts the supplycurve from S A to S B . The arrow indicates 1,the amount by which the new supply curve liesabove the old supply curve. The price stays at 2; in other words, the price does not rise. Thequantity, however decreases from 40 million to20 million per year.b. In Figure 4.7 (on the next page), the supplycurve again shifts from S A to S B and the lengthof the arrow again indicates 1. In this case,when the demand is perfectly inelastic, the pricerises by the full amount indicated by the arrow;that is, the price climbs from 2 to 3 a tape,which is a rise of exactly 1. The quantity, however, remains constant at 40 million tapes.c. As Figures 4.6 and 4.7 show, the rise in costsincreases the price the most when demand isinelastic. When demand is perfectly inelastic, theprice goes up by the full amount of the rise incosts. Then, as demand becomes more elastic,the price rises by less. At the other extreme,

Price Elasticity of Demand 11.The price elasticity of demand is the same as the slope of the demand curve. 12.The price elasticity of demand ranges from 0 to . 13.The more demanders respond to a price change, the larger the price elasticity of demand. 14.If the price elasticity of demand is positive, the de-mand is elastic.

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