中级微观经济学习题.docx

1、中级微观经济学习题1 BUDGET CONSTRAINT1. A poor person who has an income of $1000 receives $100 worth of food stamps. Draw the budget constraint if the food stamp recipient can sell these coupons on the black market for less than their face value.2. Since 1979, recipients have been given food stamps. Before 1

2、979, however, people bought food stamps at a subsidized rate. For example, to get $1 worth of food stamps, a household paid about 15(the exact amount varied by household characteristics and other factors). What is the budget constraint facing an individual if that individual may buy up to $100 per m

3、onth in food stamps at 15 per each $1 coupon.3. During his first year at school, Ximing buys eight new college textbooks at a cost of $50 each. Used books cost $30 each. When the bookstore announces a 20% increase in new texts and a 10% increase in used texts next year, Ximings father offers him $80

4、 extra. Is Ximing better off, the same, or worse off after the price change? Why? 2 PREFERENCES1. Julia consumes cans of anchovies, A, and boxes of biscuits, B. Each of her indifference curves reflects strictly diminishing marginal rates of substitution. Where A = 2 and B = 2, her marginal rate of s

5、ubstitution between cans of anchovies and boxes of biscuits equals -1. Will she prefer a bundle with three cans of anchovies and a box of biscuits to a bundle with two of each? Why?2. What assumption or assumptions rule out the following phenomenon: Geoffrey has a bundle consisting of 6 apples and 8

6、 raspberries. He states that if he is given 1 more apple, he will ask for 3 more raspberries to keep him indifferent between his old bundle and the new bundle that he will have after he receives the 1 additional apple.3. Draw indifference curves for the following people:a) John says: “I get no satis

7、faction from 1 ounce of vermouth or 3 ounces of gin, but 1 ounce of vermouth and 3 ounces of gin (a martini) really turn me on.”b) Steve says: “I will not cut my hair to please my boss unless she pays me. My price is $300 plus $1 for every 1/8 inch of hair that is cut. In other words, for every $1 a

8、bove $300 that the boss pays me, I will cut 1/8 inch off my hair.”c) In Part b of this problem, what is the marginal rate of substitution between dollars and hair in the region below and above $300?d) Ann says: “I enjoy beer and pretzels, but after 12 beers, any additional beer makes me sick.”4. Jef

9、frey is five years old. He likes candy and hates spinach. He is allowed 2 candy bars a day, but his mother offers him 1 additional candy bar for every 2 ounce of spinach he eats.a) On these terms, Jeffrey eats 3 ounces of spinach and 3.5 candy bars each day. Using indifference curves, illustrate his

10、 optional choice.b) Suppose that Jeffreys mother does not give him 2 “free” candy bars each day but still gives him 1 candy bar for every 2 ounce of spinach he eats. Would his spinach consumption be greater or smaller than in Part a? Explain your answer.4 CHOICE1. Tara has a utility function U(B, Z)

11、 = ABZ, Where A, , andare constraints, B is burritos, and Z is pizzas. If the price of burritos, pB is $2 and the price of pizzas, pZ is $1, what is Taras optimal bundle?2. Assume that there are two goods in the world: apples and raspberries. Say that Geoffrey has a utility function for these goods

12、of the following type, where r denotes the quantity of raspberries and a the quantity if apples: U = ra.a) Draw an indifference curve that is defined by this utility function and has a utility level of 2500.b) What is the marginal rate of substitution between the raspberries and the apples when Geof

13、frey consumes 50 raspberries and 50 apples? What is the marginal rate of substitution between these two goods when Geoffrey consumes 100 raspberries and 50 apples?c) If the price of raspberries is $1 per unit and the price of apples is $1 per unit and Geoffrey has $100 to spend, what bundle of raspb

14、erries and apples will he buy? Is the marginal rate of substitution equal to the ratio of the prices of these goods in the optimal bundle? If not, why not?d) If the unit prices of the raspberries and the apples are $4 and $3, respectively, what bundle of raspberries and apples will Geoffrey buy with

15、 his income of $100?3. Steves utility function is U = BC, where B = veggie burgers per week and C = packs of cigarettes per week. What is his marginal rate of substitution if veggie burgers are on the vertical axis and cigarettes are on the horizontal axis? Steves income is $120, the price of a vegg

16、ie burger is $2, and that of a pack of cigarettes is $1. How many burgers and how many packs of cigarettes does Steve consume to maximize his utility? When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrate your answers in a graph.5 DEMAND1. Rogers utility funct

17、ion is U = B1/4Z3/4, his income is Y, the price of B is pB, and the price of Z is pZ. Derive his demand curves.2. Derive Rogers Engel curve for B for the utility given in problem 2.7 CONSUMERS SUPPLUS1. If the inverse demand function is p = a bQ, what is the consumer surplus if price is a/2? 2. If t

18、he supply function is Q = Ap, what is the producer surplus if price is p*?9 EQUILIBRIUM1. In 1998, a virus killed more than half the oysters used to produce pearls in the worlds busiest undersea factory. Use a diagram to indicate why the price of pearls rose 18%. How did the equilibrium quantity cha

19、nge?2. Increasingly, instead of advertising in newspapers, individuals and firms use Web sites that offer free classified ads, such as R, J, M, and portals like Yahoo and America Online. Using a supply-and-demand model, explain what will happen to the equilibrium levels of newspaper advertising as t

20、he use of the Internet grows. Will the growth of the Internet affect the supply curve, the demand curve or both? Why?3. The U.S. supply of frozen orange juice comes from Florida and Brazil. What is the effect of a freeze that damages oranges in Florida on the price of frozen orange juice in the U.S.

21、 and on the quantities of orange juice sold by Floridian and Brazilian firms?4. The supply of corn by the U.S. is Qa= a + bp, and the supply by the rest of the world is Qr = c + ep. What is the world supply? 5. A rent control law limits the price of an apartment. What is the likely effect of such a

22、law in the short run? What is the likely effect of the law in the long run? Be sure to discuss the quantity and quality of apartments available for rent.6. The government wants to drive the price of soybeans above the equilibrium price, p1 to p2. It offers growers a payment of x to reduce their outp

23、ut from Q1 (the equilibrium level) to Q2, which is the quantity demanded by consumers at p2. How large must x be for growers to reduce output to this level? What are the effects of this program on consumers, farmers, and total welfare? Compare this approach to (a) offering a price support of p2, (b)

24、 offering a price support and a quota set at Q1, and (c) offering a price support and a quota set at Q2.10 TECHNOLOGY1. Michelles business produces ceramic cups using labor, clay, and a kiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process illus

25、trate diminishing returns to scale or diminishing marginal returns to scale? What is the likely explanation for why output doesnt increase proportionately with the number of workers? 2. Suppose that the production function is q = L3/4K1/4.a. What is the average product of labor，holding capital fixed

26、 at?b. What is the marginal product of labor?c. Does this production function have increasing, constant, or decreasing returns to scale?3. A good recipe for a French dish called ceviche requires 16 ounces of fillet of red snapper, 3 ounces of lime juice, 1 ounce of coriander, and 8 ounces of Bermuda

27、 onion. This combination of inputs is expressed in the following production function:In this production function, z1 is fillet of red snapper, z2 is lime juice, z3 is coriander, and z4 is Bermuda onion. The unit of measure for each input is the ounce, and the unit of measure for ceviche (the output)

28、 is the quantity produced by the recipe. If a restaurant has on hand 32 ounces of snapper, 9 ounces of lime juice, 5 ounces of coriander, and 48 ounces of onion, how many “units” of ceviche can it produce?4. Construct a total product curve for a function that exhibits diminishing marginal product th

29、roughout. Then construct another total product curve for a function that exhibits initially constant and subsequently diminishing marginal product. Below the graphs of these two total products curve, derive the corresponding average and marginal functions. Check to see that the curves you have drawn

30、 are consistent with what you know about the relationship between the average and marginal product curves.11 PROFIT MAXIMIZATION1. You have 60 minutes to take an exam with two questions. You want to maximize your score. Toward the end of the exam, the more time you spend on either question, the fewe

31、r extra points per minutes you get for that question. How should you allocate time between the two questions?(Hint: Think about producing an output of a score on the exam using inputs of time spent on each of the problem) 2. A competitive firms production function is y = L + 2LK + K. What is its mar

32、ginal revenue product of labor?3. A firms production function is y = ALK. What is the firms marginal revenue product of labor? 4. A competitive firm has the production of function Q = 20L L2, where Q is the number of units of output produced and L is the number of units of labor (the only input) used. The output price is $2, the wage rate is $1, and the firm faces a fixed cost of $100.a) What is the profit-maximizing quantity of labor demanded by the firm?b) What is the firms profit in the short run?c) If, in the long run, the