AP Krugman Microeconomics Section 3 Problem Solutions. 1.7 million million 0.2 million. (1.5 million million)/2 1.

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1 AP Krugman Economics Section 9 Problem Solutions AP Krugman Microeconomics Section 3 Problem Solutions 1. a. Using the midpoint method, the percent change in the quantity demanded by group A is 1.65 million million 0.1 million 100 = 100 = 6.25% and since the change in (1.55 million million)/2 1.6 million price is 10%, the price elasticity of demand for group A is 6.25% % =. Using the midpoint method, the percent change in the quantity demanded by 1.7 million million 0.2 million group B is 100 = 100 = 12.5% and since the (1.5 million million)/2 1.6 million change in price is 10%, the price elasticity of demand for group B is 12.5% % =. b. For group A, since the price elasticity of demand is (demand is inelastic), total revenue will decrease as a result of the discount. For group B, since the price elasticity of demand is 1.25 (demand is elastic), total revenue will increase as a result of the discount. c. If Nile.com wants to increase total revenue, it should definitely not offer the discount to group A and it should definitely offer the discount to group B. 2. a. The price elasticity of demand for Ford SUVs will increase because more substitutes are available. b. The price elasticity of demand for Ford SUVs will decrease because fewer substitutes are available. c. The price elasticity of demand for Ford SUVs will decrease because other cars are viewed as less of a substitute. d. The price elasticity of demand for Ford SUVs will increase over time because more substitutes (such as four-wheel-drive cargo vans) become available. BFW Publishers Solutions to Section 9/3 Solutions 149

2 3. a. Using the midpoint method, the percent change in the quantity supplied is 12, 000 8, 000 4, = 100 = 40% (8, ,000) / 2 10,000 and the percent change in the price is $1,100 $900 $ = 100 = 10%. The price elasticity of supply is therefore 40% 2 ($900 + $1,100) / 2 $1, % =. b. The elasticity estimate would be lower. A price change from $900 to $1,100 is a 20% price change, just as calculated in part a. Previously, when the quantity supplied changed from 8,000 to 12,000, that was a 40% change in the quantity supplied. Now that the quantity supplied at each price is higher by 1,000, the same price change would imply a change in the quantity supplied from 9,000 to 13,000, which is a 36% change using the midpoint method. The new price elasticity of supply is 36%/20% = 1.8, which is lower than in part a. c. The elasticity estimate would be unchanged. The price increase from $900 to $1,100 is a 20% increase, just as calculated in part a. But now that all quantities are 20% higher, the quantity supplied increases from 9,600 to 14,400. Using the midpoint method, this is an increase of 14, 400 9, 600 4, = 100 = 40% (9, ,400) / 2 12,000 so that the price elasticity of supply is 40% 2 20% =. Therefore the price elasticity of supply is the same as in part a. 4. a. A negative cross-price elasticity of demand implies that the two goods are complements. So airconditioning units and kilowatts of electricity are complements, as are sport-utility vehicles and gasoline. A positive cross-price elasticity of demand implies that the two goods are substitutes. So Coke and Pepsi are substitutes, as are McDonald s and Burger King burgers as well as butter and margarine. b. The larger (and positive) the cross-price elasticity of demand is, the more closely the two goods are substitutes. Since the cross-price elasticity of butter and margarine is larger than the cross-price elasticity of McDonald s burgers and Burger King burgers, butter and margarine are closer substitutes than are McDonald s and Burger King burgers. Similarly, the greater (and negative) the cross-price elasticity of demand is, the more strongly the two goods are complements. 150 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

3 c. A cross-price elasticity of 0.63 implies that a 1% increase in the price of Pepsi would increase the quantity of Coke demanded by 0.63%. Therefore, a 5% increase in the price of Pepsi would increase the quantity of Coke demanded by five times as much, that is, by % = 3.15%. d. A cross-price elasticity of 0.28 implies that a 1% fall in the price of gasoline would increase the quantity of SUVs demanded by 0.28%. Therefore, a 10% fall in the price of gasoline would increase the quantity of SUVs demanded by 10 times as much, that is, by % = 2.8%. 5. a. Suppose the average tourist income is $20,000. Using the midpoint method, the percent change in the quantity demanded is 1, 600 2, = 100 = 40 (2, ,600) / 2 2,000 and the percent change in the price is $6 $5 $1 100 = 100 = 18.2%. Dropping the minus sign, the price elasticity of ($5 + $6) / 2 $5.50 demand is therefore 40% = 2.2. Now suppose the average tourist income is $30,000. The percent 18.2% change in the quantity demanded is 3,000 4,200 1, = 100 = 33.3%. And the (4, ,000) / 2 3,600 percent change in the price is, as before, $6 $5 $1 100 = 100 = 18.2%. Dropping the ($5 + $6) / 2 $5.50 minus sign, the price elasticity of demand is therefore 33.3% % =. b. Suppose the price of a T-shirt is $4. Using the midpoint method, the percent change in the quantity demanded is 5,000 3,000 2, = 100 = 50% (3, ,000) / 2 4,000 and the percent change in income is 30, , , = 100 = 40%. The income elasticity of demand is therefore (20, ,000) / 2 25,000 50% % = BFW Publishers Solutions to Section 9/3 Solutions 151

4 Now suppose the price is $7. The percent change in the quantity demanded is 1, , = 100 = 76.9% ( ,800) / 2 1,300 and the percent change in income is, as before, $30, 000 $20, 000 $10, = 100 = 40%. The income elasticity of demand is therefore ($20,000 + $30,000) / 2 $25, % % =. 6. a. Supply is perfectly inelastic: the quantity of cabins on the Queen Mary 2 is fixed. As demand increases (a rightward shift in the demand curve), the price of a cabin on the Queen Mary 2 increases, without an increase in the quantity supplied. See the accompanying diagram. b. Supply is perfectly elastic. As demand changes (for instance, as demand increases in times of high electricity demand), price does not change but the quantity supplied does change. See the accompanying diagram. 152 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

5 c. Supply is inelastic. As price falls by 20%, the quantity supplied falls by 10%. This implies a price elasticity of supply of 10% = 0.5, which is inelastic. See the accompanying diagram. 20% d. Supply is elastic. As price falls by 30%, the quantity supplied falls by more than 50%. This implies a price elasticity of supply greater than 50%, that is, a price elasticity of supply 30% greater than 1.7. See the accompanying diagram. BFW Publishers Solutions to Section 9/3 Solutions 153

6 7. An increase in the amount of acreage that is cultivated results in a rightward shift in the supply of coffee. This reduces the price of coffee and increases the quantity demanded. If total revenue from coffee sales have decreased, this means that the price effect (which tends to lower total revenue) must have outweighed the quantity effect (which tends to increase total revenue). This implies that demand must be inelastic. As shown in the accompanying diagram, the price effect results in a loss of total revenue equal to the size of area A. The quantity effect (the quantity demanded increases as a result of the price fall) results in an increase in total revenue equal to the size of area B. Area A exceeds area B, so total revenue falls. 154 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

7 8. a. Leon s consumer surplus is $5. This is the difference between how much he is willing to pay ($10) and how much he does pay ($5). b. Since Alberto s willingness to pay is $10 and the price of the CD is $10, he gets zero consumer surplus. c. No trade takes place because Stacey s willingness to pay is less than the price. So no consumer surplus is created. 9. a. Gordon will receive no producer surplus since the price received for the trains is equal to his cost. b. No trade takes place because So-Hee s cost is $1,500, which is higher than the price of $1,200 she is offered. So no producer surplus is created. c. Sanjay s cost is zero. The price he is paid for his time is $80,000, so his producer surplus is $80, a. From the demand curve, you can see that with a price per ride of $5, the customer takes 10 rides. At this point her consumer surplus is 1 2 ($10 $5) 10 = $25. b. Since a consumer obtains consumer surplus of $25 from going to Fun World when each ride costs $5, that is the most that she would be willing to pay to go there. And it is therefore the maximum admission fee that Fun World could charge. (Charging consumers both an entrance fee and a price for each unit of a good bought is called a two-part tariff.) c. If Fun World charged nothing for each ride, a typical consumer would consume 20 rides, and this would give her a consumer surplus of 1 2 $10 20 = $100. This is the maximum admission fee that Fun World can charge with a price per ride of zero. 11. a. At a price of $4, the taxi driver supplies 40 rides. His producer surplus is therefore 1 2 $4 40 = $80. b. Since the taxi driver s producer surplus is $80, this is the most he is willing to pay to supply 40 rides at $4. So it is the most the city can charge him as a licensing fee. BFW Publishers Solutions to Section 9/3 Solutions 155

8 c. At a price of $8, the taxi driver supplies 80 rides, making his producer surplus 1 2 $8 80 = $320. So $320 is the most the city can charge as a licensing fee when the price per ride is $ a. The tax drives a wedge between the price paid by consumers and the price received by producers. Consumers now pay $9, and producers receive $5. So after the imposition of the tax, the quantity bought and sold will be one pizza. b. Consumer surplus is now zero (the one consumer who still buys a pizza at $9 has a willingness to pay of just $9, so that the consumer surplus is $9 $9 = $0). Compared to the situation before the imposition of the tax, where the equilibrium price was $7, consumer surplus has been reduced by $3. Similarly, the producer of the one pizza has a cost of $5, and this is the price he receives, so producer surplus is also zero: compared to the situation before, it has decreased by $3. c. Collegetown earns a tax of $4 per pizza sold, which is a total tax revenue of $4. d. Total surplus has been decreased by $6. Of that $6, the town earns $4 in revenue, but $2 of surplus is lost. That is the deadweight loss from this tax. 13. The tax should be imposed on sales of gasoline. Since both demand for and supply of gasoline are less elastic, changes in the price of gasoline will result in smaller reductions in the quantity demanded and quantity supplied. As a result, fewer transactions are discouraged by the tax in other words, less total surplus (consumer and producer surplus) is lost. Panel (a) of the accompanying diagram illustrates a tax imposed on sales of gasoline, for which both demand and supply are less elastic; panel (b) illustrates a tax imposed on sales of restaurant meals, for which both demand and supply are more elastic. As you can see, deadweight loss, the shaded triangle, is larger in panel (b) than in panel (a). 156 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

9 14. a. Al has increasing marginal utility of economics classes. Each additional class adds more to his total utility than the previous class. b. Al has constant marginal utility of volume of music. His total utility increases by 5 utils for each additional notch of volume, so his marginal utility is constant at 5 utils. c. Al has diminishing marginal utility of Friends episodes. Although additional episodes increase his total utility, they do so less and less. That is, his marginal utility declines. d. Al has diminishing marginal utility of marshmallows. For a certain range, additional marshmallows add to his total utility, so total utility increases. But total utility increases by less and less. In fact, total utility eventually begins to decline. In other words, his marginal utility becomes smaller and smaller and eventually becomes negative. 15. After you have taken the first newspaper, the marginal utility of the second newspaper is zero: you don t learn any more news by having two copies of the same paper instead of just one. So once you have paid for the vending machine to open, you will take only one paper. For soda, on the other hand, marginal utility is positive: after you have drunk the first soda, the second will still give you more utility. It will give you less utility than the first soda that is, there is diminishing marginal utility but the marginal utility of the second soda is still positive. If the vending machine allowed you to take more than one soda BFW Publishers Solutions to Section 9/3 Solutions 157

10 at a time after paying for only one, you would. So the soda vending machine has to be designed to prevent you from taking more than one soda, and it does so by dispensing only one soda at a time. 16. a. If Brenda consumes 2 cups of coffee, the consumption bundles that are relevant are those in the accompanying table. The first two columns are the bundles, and the third column shows the total utility of each bundle. The fourth column calculates her marginal utility of bagels. b. The accompanying diagram shows Brenda s marginal utility of bagels. Since Brenda s marginal utility curve of bagels slopes downward, she has diminishing marginal utility of bagels. 158 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

11 17. a. Bernie can consume the following bundles if he spends all his income: 0 notebooks, 5 CDs 2 notebooks, 4 CDs 4 notebooks, 3 CDs 6 notebooks, 2 CDs 8 notebooks, 1 CD 10 notebooks, 0 CDs The accompanying diagram shows Bernie s budget line. b. The accompanying table shows the marginal utility for each notebook and for each CD, the marginal utility per dollar spent on notebooks, and the marginal utility per dollar spent on CDs. Note that the utility numbers for notebooks are given in increments of 2: for instance, going from 4 notebooks to 6, utility increases by 50 utils (from 130 utils to 180 utils). Per notebook, this is a marginal utility of 25 utils. BFW Publishers Solutions to Section 9/3 Solutions 159

12 c. The optimal consumption rule states that the optimal bundle, from all those on a consumer s budget line, is the one at which the marginal utility per dollar spent on each good is equal. The accompanying diagram shows the marginal utility per dollar spent on notebooks and the marginal utility per dollar spent on CDs. When Bernie consumes 4 notebooks and 3 CDs, the marginal utility per dollar spent on notebooks is the same as the marginal utility per dollar spent on CDs, so this is the optimal consumption bundle. It is also the only bundle from all the bundles he can consume (that is, from all the bundles on his budget line) for which the marginal utility per dollar is equal for the two goods. 160 Section 9/3: Behind the Demand Curve: Consumer Choice BFW Publishers

13 18. a. This bundle lies on Lakshani s budget line, but the marginal utility per dollar for sneakers and for sweaters is not equal. The marginal utility per pair of sneakers is equal to her marginal utility per sweater. However, since sneakers cost $50 and sweaters cost only $20 (that is, sneakers are 2.5 times as expensive as sweaters), Lakshani s marginal utility per dollar spent on sweaters is 2.5 times greater than her marginal utility per dollar spent on sneakers. That is, she would improve her level of utility if she spent more money on sweaters and less on sneakers. b. This bundle lies on Lakshani s budget line. The marginal utility per pen is five times as great as the marginal utility per pencil. However, pens are also five times as expensive as pencils, so her marginal utility per dollar spent on pens is just equal to her marginal utility per dollar spent on pencils. So this is her optimal bundle. c. Although Lakshani s marginal utility per dollar spent on soccer tickets is equal to her marginal utility per dollar spent on football tickets, this bundle is not optimal: it does not lie on her budget line. She could buy more of both goods and probably will. But for a precise answer about how many football tickets and how many soccer tickets she will actually buy, we would need more information about her utility at other consumption bundles. BFW Publishers Solutions to Section 9/3 Solutions 161