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CHAPTER 15 | Market Demand TRUE-FALSE Difficulty: 3 Correct Answer: True 12. If a rational consumer must consume either zero or one unit of a good, then an increase in the price of that good with no change in income or in other prices can never lead to an increase in the consumer’s demand for it. Difficulty: 1 Correct Answer: False 13. In the reservation price model, either aggregate demand is zero or everyone demands one unit of the good. Difficulty: 1 Correct Answer: False 14. The Laffer effect occurs only if there is a backward- bending labor supply curve. Difficulty: 2 Correct Answer: True 15. If the demand curve were plotted on graph paper with logarithmic scales on both axes, then its slope would be the elasticity of demand. Difficulty: 1 Correct Answer: True 16. The market demand curve is simply the horizontal sum of the individual demand curves. Difficulty: 1 Correct Answer: False 17. The demand curve is inelastic for inferior goods and elastic for normal goods. Difficulty: 1 Correct Answer: True 18. Marginal revenue is equal to price if the demand curve is horizontal. Difficulty: 2 Correct Answer: False 19. If the amount of money that people are willing to spend on a good stays the same when its price doubles, then demand for that good must have a price elasticity of demand smaller in absolute value than 1. Difficulty: 1 Correct Answer: True 20. If the price elasticity of demand for a normal good is constant, then a price increase of .10¢ will reduce demand by more if the original price is $1 than if the original price is $2. Difficulty: 1 Correct Answer: True 21. The demand function for potatoes has the quantity q = 1,000 - 10p. As the price of potatoes changes from .10¢ to .20¢, the absolute value of the price elasticity of demand for potatoes increases. Difficulty: 1 Correct Answer: True 22. If the demand curve for a good is given by the equation q = 2/p, where q is quantity and p is price, then at any positive price, the elasticity of demand will be -1. MULTIPLE CHOICE 26. Given his current income, Rico’s demand for bagels is related to the price of bagels by the equation Q = 540 - 16P. Rico’s income elasticity of demand for bagels is known to be equal to 0.5 at all prices and incomes. If Rico’s income quadruples, his demand for bagels will be related to the price of bagels by the equation a. Q = 540 - 16P. b. Q = 2,160 - 64P. c. Q = 540 - 32P. d. Q = 1,080 - 32P e. Q = 1,080 - 16P. Difficulty: 2 Correct Answer: b 27. Given his current income, Rico’s demand for bagels is related to the price of bagels by the equation Q = 520 - 12P. Rico’s income elasticity of demand for bagels is known to be equal to 0.5 at all prices and incomes. If Rico’s income quadruples, his demand for bagels will be related to the price of bagels by the equation a. Q = 520 - 24P. b. Q = 1,040 - 24P. c. Q = 2,080 - 48P. d. Q = 520 - 12P. e. Q = 1,040 - 12P. Difficulty: 3 Correct Answer: e 28. A person with a quasilinear utility function will a. have a price elasticity of demand equal to zero for some goods. b. have an income elasticity of demand equal to one for some goods. c. necessarily consume zero quantity of some good. d. necessarily consume positive amounts of every good. e. None of the above. Difficulty: 2 Correct Answer: c 29. In the village of Frankfurter, the demand function for sausages per person is D(p) = 20 - 1.5p, where p is the price of a single sausage. The present population of Frankfurter is 100 persons. Suppose that 10 more people move into town, each of whom has the same demand function as the old residents. At a price of $2, the price elasticity of demand for sausages in Frankfurter is a. increased by 10%. b. decreased by 10%. c. unchanged. d. increased by 15%. e. None of the above. Difficulty: 1 Correct Answer: b 30. A firm faces a demand function D(p), for which the revenue- maximizing price is $16. The demand function is altered to 2D(p). What is the new revenue-maximizing price? a. $8 b. $16 c. $32 d. There is insufficient information to determine this. e. None of the above. Difficulty: 1 Correct Answer: c 31. A firm faces a demand function D(p), for which the revenue- maximizing price is $10. The demand function is altered to 2D(p). What is the new revenue-maximizing price? a. $5 b. $20 c. $10 d. There is insufficient information to determine this. e. None of the above. Difficulty: 1 Correct Answer: c 32. If the supply curve for x is given by x = 100p2, then the inverse supply curve is given by a. 100/p2. b. x2/100. c. x1/2/10. d. p-2/100. e. None of the above. Difficulty: 1 Correct Answer: c 33. Ed has 100 tons of manure. The lowest price at which he is willing to sell it is $10 per ton. Fred wants to buy 100 tons of manure. The most he is willing to pay is $8 per ton. The federal government offers to subsidize manure sales at a rate of $1 per ton. If Ed and Fred are the only people who deal in manure, then the deadweight loss caused by the subsidy is a. $100. b. $50. c. $0. d. $200. e. None of the above. Difficulty: 2 Correct Answer: e 34. Fred’s price elasticity of demand for milk is -2 at today’s prices when we measure price in dollars and quantity of milk in quarts. If the price per quart of milk stays the same but we measure quantity of milk in gallons and price in dollars, then what will be the elasticity of demand for gallons of milk? (A gallon is four quarts.) a. -1 b. -1/2 c. -8 d. -4 e. -2 Difficulty: 2 Correct Answer: d 35. In a small Kansas town, there are two kinds of gasoline consumers: 100 Buick owners and 50 Dodge owners. Each Buick owner has the demand function Db(p) = max{0, 20 - 5p} and each Dodge owner has the demand function Dd = max{0, 15 - 3p}. In this town, the market demand curve has a. no kinks but gets steeper as price rises. b. no kinks but gets flatter as price rises. c. constant slope since individual demand curves have constant slope. d. a kink at p = 4 and another at p = 5. e. a kink at p = 35/8. PROBLEMS Difficulty: 2 1. Suppose that the inverse demand function for wool is p = A/q for some constant A. Suppose that 1/4 of the world’s wool is produced in Australia. a. If Australian wool production increases by 1% and the rest of the world holds its output constant, what will be the effect on the world price of wool? b. How does the marginal revenue to Australia from an extra unit of wool relate to the price of wool? Answer: a. Price will fall by about 0.25%. b. Marginal revenue is 75% of price. Difficulty: 2 2. Bart Wurst runs the only hot-dog stand in a large park in a large boring town. On Sundays people in this town all sit in the park and sunbathe. For any t between 0 and 30, the number of people who are sitting within t minutes of Bart’s stand is 10t2. People in Bart’s town are lazy and hate to walk. They think that every minute of walking they do is as bad as spending $.10. Everybody in the park has a reservation price of $1 for a hot dog, where the cost of a hot dog includes the subjective cost of walking as well as the money price they have to pay when they get there. (Nobody has ever thought of fetching a hot dog for someone else.) Find a formula for the demand curve for Bart’s hot dogs. Explain how you got it. Answer: If Bart charges p, where 0 < p < 1, his extensive margin is the customers who are at distance t* from Bart where p + .10t* = 1. Then t* = 10 - p and the demand for hot dogs at prices p is the number (10 - p)2 of people within t* of Bart. Difficulty: 3 3. In Tassel, Illinois (pop. 20,000), there are two kinds of families, those who like swimming pools and those who don’t. Half of the population is of each type. Families who like swimming pools are willing to spend up to 5% of their income each year on a swimming pool. Families who don’t like them would pay nothing for a swimming pool. Nobody wants more than one swimming pool and nobody has thought of sharing a swimming pool. Incomes in Tassel range between $10,000 and $110,000. For incomes M in this range, the number of families in Tassel with income greater than M is about 22,000 - .2M. (The two types of families have the same income distribution.) Find the aggregate demand function for swimming pools in Tassel (demand for swimming pools as a function of the annual cost of having one). Answer: The number of people willing to pay at least p is half of the number who have income at least $20p. Therefore the aggregate demand function is 11,000 - 2p.

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