Daniel l. Rubinfeld

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134 Part 2 Producers, Consumers, and Competitive Markets Thus elasticity increases in magnitude as the price increases (and the quantity demanded falls), There is no reason to expect elasticities of demand to be . constal:t. Nevertheless, \\'e often find the isoelastic dellland Clll"Ue, in which the pnce ~lastl~itv and the income elasticity are constant, useful to work with. When \vntten 111 it~ log-linear form, the isoelastic demand curve appears as follows: 10g(Q) = a - b 10g(P) + c 10g(I) (4.6) where log ( ) is the logarithmic function and a, b, and c are the c.onsta~1ts. in the demand equation. The appeal of the log-lin,ear demand relatIonshIp IS. that the slope of the line - b is the price elasticity ot de~'nand and the constan.t L. IS the income elasticity.E Using the data in Table 4.5, tor example, we obtamed the regression line 10g(Q) = - 0.81 - 0.24log(P) + 1.46log(I) This relationship tells us that the price elasticity of deman.d.fo~ raspberries is _ 0.24 (that is, demand is inelastic) and that the income elastIcIty IS 1.46. We have seen that it can be useful to distinguish between goods that are complements and goods that are substihltes. Suppose that P 2 represents the price of a second aood-one which is belie\'ed to be related to the product we are studying, We c;n then write the demand function in the following form: 10g(Q) = a - b 10g(P) + b 2 log(P2) + C 10g(I) rather than before the acquisition. \A/hy Because after the acquisition the lost sales from consumers who 'would switch a,·vay from Grape Nuts would be recovered to the extent that they s\yitched to Shredded Wheat. TI1e extent to which a price increase will cause consumers to switch is given (in part) by the price elasticity of demand for Grape Nuts. Other things being equal, the higher the demand elasticity, the greater the loss of sales associated with a price increase. The more likely, too, that the price increase will be lmprofitable. The substitutability of Grape Nuts and Shredded Wheat can be measured by the cross-price elasticity of demand for Grape Nuts with respect to the price of Shredded Wheat. The relevant elasticities were calculated using ,",reekly data obtained from the supermarket scanning of household purchases for 10 cities over a three-year period. One of the estimated isoelastic demand equations appeared in the following log-linear form: 10g(QcrJ = 1.998 - 2.08510g(PGl'J + 0.6210g(I) + 0.14log(Psw) where QCN is the amOlmt (in pounds) of Grape Nuts sold weekly, PCN the price per pound of Grape Nuts, I real personal income, and Psw the price per pound of Shredded Wheat Spoon Size. TI1e demand for Grape Nuts is elastic (at current prices), with a price elasticity of about - L The income elasticity is 0.62: In other words, increases in income lead to increases in cereal purchases, but at less than a 1-for-1 rate. Finally, the cross-price elasticity is 0.14. TIus figure is consistent with the fact that although the two cereals are substitutes (the quantity demanded of Grape Nuts increases in response to an increase in the price of Shredded Wheat), they are not very close substitutes. & Chapter 4 Individual and Market Demand 135 When b 2 , the cross-price elasticity, is positive, the tvw goods are substitutes; when be is negative, the two goods are complements. e Post Cereals Division of Kraft General Foods acquired the Shredded Wheat cereals of Nabisco in 1995. The acquisition raised the legal and economic question of whether Post vvould raise the pri,ce of its best-selling brand, Grape Nuts, or the price of Nabisco's most successtul brand, Shredded Wheat Spoon SizeY One important issue in a lawsuit brought,by the state of ~ew York was whether the two brands \·vere close substihltes tor one another. It so, it would be more profitable for Post to increase the price of Grape Nuts after 12The naturalloaarithmic function with base c has the property that ~(log(Q)) ~Q/Q foran~ chanae in 10g(QtSimilarl\', ~(log(P)) = ~P/P for any change in 10g(P) It follows that ~(log(Q)) .-, ~Q/Q _ b~ ~(log(P))J ' - bPP/P) Therefore, (~.Q/Q)~(~P/P) =, -:- b,.whIch ,IS the pnce ela~tlClt) of demand By a similar argument, the income elastiClty ot demand LIS gl\en b} (~Q/Q)/(~L I), 13 State of New York v. Kraft Gwera/ Foods. IIlC, 926 F Supp. 321, 356 (S.D. . .N.Y 1995) , . 1. Individual consumers' demand curves for a commodity can be derived from information about their tastes for all goods and services and from their budget constraints. 2. Engel curves, which describe the relationship between the quantity of a good consumed and income, can be useful for discussions of how consumer expenditures vary with income. 3. Two goods are substitutes if an increase in the price of one leads to an increase in the quantity demanded of the other. In contrast, two goods are complements if an increase in the price of one leads to a decrease in the quantity demanded of the other. 4. The effect of a price change on the quantity demanded of a good can be broken into two parts: a substitution effect, in which satisfaction remains constant while price changes, and an income effect, in Which the price remains constant while satisfaction changes. Because the income effect can be positive or negative, a price change can have a small or a large effect on quantity demanded. In the unusual case of a so-called Giffen good, the quantity demanded may move in the same direction as the price change, thereby generating an upward-sloping individual demand curve. 5. The market demand curve is the horizontal summation of the individual demand curves of all consumers in the market for a good. It can be used to calculate how much people value the consumption of particular goods and services. 6. Demand is price inelastic when a 1-percent increase in price leads to a less than 1-percent decrease in quantity demanded, thereby increasing the consumer's expenditure. Demand is price elastic when a 1-percent increase in price leads to a more than 1-percent decrease in quantity demanded, thereby decreasing
1136 Part 2 Producers, Consumers, and Competitive Markets Individual and Market Demand the consumer's expenditure. Demand is unit elastic when a I-percent increase in price leads to a I-percent decrease in quantity demanded. 7. The concept of consumer surplus can be useful in determinina the benefits that people recei\'e from the consumption of a product Consumer surplus is the difference between the maximum amolmt a consumer is willing to pay for a good and what he actually pays when buving it. 8. A netw~rk externality occurs when one person's demand is affected directly by the purchasing decisions of other consumers, A positive network externalitv, the bandwagon effect, occurs when a typical cons~lmer's quantity demanded increases because she 1. How is an individual demand curve different from a market demand curve Which curve is likely to be more price elastic (Hint: Assume that there are no network externalities,) 2. Is the demand for a particular brand of product, such as Head skis, likely to be more price elastic or price inelastic than the demand for the aggregate of all brands of downhill skis Explain. 3. Tickets to a rock concert sell for 510 .. At that price, however, the demand is substantially greater than the available number of tickets .. Is the value or marginal benefit of an additional ticket greater than, less than, or equal to S10 How might you determine that value 4. Suppose a person allocates a giwn budget between two goods, food and clothing, If food is an inferior good, can vou tell whether clothing is inferior or normal Explain. 5. \'Vhich of the following combinations of goods are complements and which are substitutes Could any of them be either in different circumstances Discuss, a. a mathematics class and an economics class b. telmis balls and a tennis racket c. steak and lobster d. a plane trip and a train trip to the same destination e. bacon and eggs 6. Which of the follOWing events would cause a movement along the demand curve for US-produced clothing Which would cause a shift in the demand curve 1. The ACME Corporation determines that at current prices, the demand for its computer chips has a price elasticity of - 2 in the short run. The price elasticity for its disc drives is - L considers it stylish to buv a product that others have purchased C~nversely, ~ negati\'e network externality, the snob effect, occurs when the quantity d~manded increases when fewer people OInt the LTood. 9. A number of methods can be used to obtain information about consumer demand, These include inter \'iew and experimental approaches, direct marketing experiments, and the more indirect statistical approaclL The statistical approach can be wry powerful in its application, but it is necessary to determine the appropriate \'ariables that affect demand before the statistical work is done. a. the removal of quotas on the importation of foreign clothes b. an increase in the income of US citizens c. a cut in the industry's costs of producing domestic clothes that is passed on to the market in the form of lower prices 7. For which of the following goods is a price increase likelv to lead to a substantial income (as well as substitution) effect a. salt b. housing c. theater tickets d. food 8. Suppose that the a\'erage household in a state consumes 500 gallons of gasoline per yeaL A 10-cent gasoline tax is introduced, coupled with a 550 alUmal tax rebate per household. Will the household be better or worse off after the new program is introduced 9. Which of the following three groups is likely to have the most and which the least price-elastic demand for membership in the Association of Business Economists a. students b. junior executives c. senior executi\'es a. If ACME decides to raise the price of both products by 10 percent, what will happen to its sales To its sales revenue b. Can you tell from the available information which product will generate more re\'enue If yes, which one If not, what additional information would vou need 2. Refer to Example -1.3 on the aggregate demand for wheat in 1998. Consider 1996, at which time the domestic demand cun'e was QDD 1560 - 60P" The export demand ClUTe, however, was about the same as in 1998, i .. e., QDE = 15+! - 176P. Calculate and draw the aggregate demand curve for wheat in 1996. 3. Judy has decided to allocate exactly 5500 to textbooks at college e\'ery year, even though she knows that the prices are likely to increase by from 5 to 10 percent per vear and that she will be getting a substantial monetary gift from her grandparents next year. What is Judy's price elasticity of demand for textbooks What is her income elasticity 4. Vera has decided to upgrade the operating system on her new PC She hears that the new Linux operating system is teclmologically superior to the Windows operating system and is substantially lower in price c However, when she asks her friends, it turns out they all use PCs with Windows. They agree that Linux is more appealing but add that they see relatively few copies of Linux on sale at local retail software stores .. Based on what she learns and observes, Vera chooses to upgrade her PC with Windows. Can you explain her decision 5. Suppose you are in charge of a toll bridge that is essentially cost free. The demand for bridge crossings Q is given by P 12 - 2Q. a. Draw the demand curve for bridge crossings" b. How many people would cross the bridge if there were no toll c. What is the loss of consumer surplus associated with the charge of a 56 toll 6. a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate priceconsumption cun-e (for a variable price of orange juice) and income-consumption curve. b. Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-consumption curves. 7. Heather'S marginal rate of substihltion of movie tickets for video rentals is the same no matter how many \-ideos she wants. Draw Heather's income consumption curve and her Engel CLUTe for videos. 8. You are managing a 5300,000 city budget in which monies are spent on schools and public safety only You are about to receive aid from the federal government to support a special antidrug program. Two programs are available: (1) a 5100,000 grant that must be spent on law enforcement; and (2) a 100-percent matching grant, in which each dollar of local spending on law enforcement is matched bv a dollar of federal money The federal matching program limits payment to each city to a maximum of 5100,000. a. Complete the table below with the amounts c1\-ailable for safet\' SAFETY (NO GOvr. SAFETY SAFETY SCHOOl.S ASSISTANCE) 1) ,~~.IAM SO 50,000 100,000 150,000 200,000 250,000 300,000 b. Suppose that you allocate S50,000 of the 5300,000 to schools. Which program would you (the manager) choose if you wish to maximize citizen satisfaction What if you allocate 5250,0007 c. Draw the budget constraints for the three options: no aid, program 1, or program 2. 9. By obselYing an individual's behador in the situations outlined below, determine the rele\'ant income elasticities of demand for each good (Leo., whether the good is normal or inferior) If you cannot determine the income elastiCity, what additional information might you need a. Bill spends all his income on books and coffee. He finds 520 while rummaging through a used paperback bin at the bookstore .. He immediately buys a new hardcm-er book of poetry b. Bill loses 510 with which he was going to buy a double espresso" He decides to sell his new book at a discount and use the money to buy coffee c. Being bohemian becomes the latest teen fad. As a result, coffee and book prices rise by 25 percent. Bill lowers his consumption of both goods by the same percentage" d. Bill drops out of art school and gets an MB.A. instead. He stops reading books and drinking coffee .. Now he reads the Wall Street Journal and drinks bottled mineral water. 10. Suppose the income elasticity of demand for food is 05 and the price elasticity of demand - La. Suppose also that Felicia spends 510,000 a year on food, that the price of food is 52, and that her income is 525,000. a. If a £2 sales tax on food were to cause the price of food to double, what would happen to Felicia's consumption of food (Hillt: Because a large price change is im'oh-ed, .'lOll should assume that the price elasticity measures an arc elasticity rather than a point elasticity)
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Daniel l. Rubinfeld

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