中级微观经济学试题2

Intermediate Microeconomics Mid-term Test 2005 (B) Name: Student No.: Class: No. 1 2 3 4 5 6 7 8 9 10 Answer No. 11 12 13 14 15 16 17 18 19 20 Answer No. 21 22 23 24 25 26 27 28 29 30 Answer Section 1 True or false.（20 points, 2 points each ） 1. Alices utility function is U(x, y) = x2y. Steves utility function is U(x, y) = x2y + 2x. Alice and Steve have the same preferences since Steves utility function is a monotonic transformation of Alices. 2. A consumer who can borrow and lend at the same interest rate should prefer an endowment with a higher present value to an endowment with a lower present value, no matter how he plans to allocate consumption over the course of his life. 3. If two assets have the same expected rate of return but different variances, a risk-averse investor should always choose the one with the smaller variance, no matter what other assets she holds. 4. Fred has a Cobb-Douglas utility function with exponents that sum to 1. Sally consumes the same two goods, but the two goods are perfect substitutes for her. Despite these differences, Fred and Sally have the same price offer curves. 5. If all prices double and income triples, then the budget line will become steeper. 6. If someone has a Cobb-Douglas utility function and no income from any source other than labor earnings, then an increase in wages will not change the amount that person chooses to work. 7. Susan is a net borrower when the interest rate is 10% and a net saver when the interest rate is 20%. A decrease in the interest rate from 20% to 10% may make Susan worse off. 8. With quasi-linear preferences, the equivalent variation and the compensating variation in income due to a price increase of one good are the same. 9. For a consumer who has an allowance to spend and no endowment of goods, a decrease in the price of a Giffen good consumed makes him better off. 10. The marginal rate of substitution measures the distance between one indifference curve and the next one. Section 2 Single Choice. (80points, 4 points each) 11. Janet consumes two commodities x and y. Her utility function is minx + 2y, y + 2x. She chooses to buy 10 units of good x and 20 units of good y. The price of good x is $1. Janets income is A. $40. B. $50. C. $30. D. $20. E. There is not enough information in the problem to determine her income because we are not told the price of good y. 12. Holly consumes x and y. The price of x is 4 and the price of y is 4. Hollys only source of income is her endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices. She plans to consume 7 units of x and 5 units of y. If the prices change to $7 for x and $7 for y, A. she is better off. B. she is worse off. C. she is neither better off nor worse off. D. she is better off if she has nonconvex preferences. E. We cant tell whether she is better off or worse off unless we know her utility function. 13. Clarissas utility function is U(r, z) = z + 120r - r 2, where r is the number of rose plants she has in her garden and z is the number of zinnias. She has 250 square feet to allocate to roses and zinnias. Roses each take up 4 square feet and zinnias each take up 1 square foot. She gets the plants for free from a generous friend. If she acquires another 100 square feet of land for her garden and her utility function remains unchanged, she will plant A. 99 more zinnias and some more roses. B. 20 more roses and 20 more zinnias. C. 25 more roses and no more zinnias. D. 100 more zinnias and no more roses. E. None of the above. Mid-term B 6-3 14. Will is paid $10 an hour for the first 40 hours per week that he works. He can also work as many hours overtime as he wishes to. He is paid $15 an hour for every hour that he works beyond 40 hours a week. Leisure is a normal good for Will and he is currently working some overtime. If his hourly wage for the first 40 hours per week that he works rises to $12 and his wages for overtime remain at $15 per hour, he will choose to work A. fewer hours per week. B. more hours per week. C. the same number of hours per week. D. more hours per week if and only if his income exceeds his labor income. E. more hours per day if and only if he works less than 20 hours overtime per week. 15. Albin has quasi-linear preferences and he loves pretzels. His inverse demand function for pretzels is p(x) = 49 - 6x, where x is the number of pretzels that he consumes. He is currently consuming 8 pretzels at a price of $1 per pretzel. If the price of pretzels rises to $7 per pretzel, the change in Albins consumer surplus is A. -$90. B. -$56. C. -$42. D. -$45. E. -$42. 16. Janes utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y . Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x. A. The bundle (1/4, 3/4) is Janes utility maximizing choice, given her budget. B. The bundle (1, 1/2) is Janes utility maximizing choice, given her budget. C. Given her budget, Jane would maximize her utility by spending all of her income on good X. D. Given her budget, Jane would maximize her utility by spending all of her income on good Y . E. None of the above. 17. When the prices were ($5, $1), Vanessa chose the bundle (x, y) = (6, 3). Now at the new prices, (px, py), she chooses the bundle (x, y) = (5, 7). For Vanessas behavior to be consistent with the weak axiom of revealed preference, it must be that A. 4py px. B. px 4py. C. 5py px. D. py = 5px. E. None of the above. 18. In an isolated mountain village, the only crop is corn. Villagers plan for two time periods. In the first time period each villager will harvest 100 bushels. In the second time period, no corn will be harvested. There is no trade with the rest of the world and no stocks of corn remain from before the first period. Corn can be stored from one time period to the next, but rats eat 25% of what is stored. The villagers all have Cobb-Douglas utility functions U(C1,C2) = C1C2 and can allocate their own corn between consumption and storage as they wish. If the introduction of cats to the village reduces the rats predations to 10% of what is stored, A. consumption in the first time period will not change. B. consumption in the first time period will increase by more than 5%. C. consumption in the first time period will increase but by less than 5%. D. consumption in the second time period will not change. E. consumption in the first time period will decrease. 19Cindy consumes goods x and y . Her demand for x is given by x(px,m) = 0.04m - 4.24px. Now her income is $322, the price of x is $2, and the price of y is $1. If the price of x rises to $3 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then A. DI = 0 and DS = -2.00. B. DI = -0.18 and DS = -0.52. C. DI = -4.06 and DS = -0.18. D. DI = -0.18 and DS = -4.06. E. DI = -0.52 and DS = -0.18. 20. In a certain kingdom, the demand function for rye bread was q = 381 - 3p and the supply function was q = 5 + 7p, where p is the price in peso and q is loaves of bread. The king made it illegal to sell rye bread for a price above 32 peso per loaf. To avoid shortages, he agreed to pay bakers enough of a subsidy for each loaf of bread so as to make supply equal demand. How much would the subsidy per loaf have to be? A. 21 peso B. 14 peso C. 8 peso D. 5.6 peso E. None of the above. 21. Ambroses brother Francis has an income of $100 and a utility function U(x1, x2) =50x11/2+x2, where x1 is his consumption of nuts and x2 is his consumption of berries. The price of nuts is $5 and the price of berries is $1. How many units of nuts will Francis demand? A. 30 B. 25 C. 20 D. 90 E. None of the above. Mid-term B 6-5 22. Bernices utility function is min x, y, where x is her consumption of earrings and y is money left for other stuff (x and y can be fractional). If he had an income of $12 and was paying a price of $4 for a pair of earrings, then if the price of earrings went up to $6, the equivalent variation of the price change would be A. $4.80. B. $3.43. C. $1.71. D. $9.60. E. $4.11. 23. Henrys utility function is x2 + 16xw + 64w2, where x is his consumption of x and w is his consumption of w. A. Henrys preferences are strictly non-convex. B. Henrys indifference curves are straight lines. C. Henry has a bliss point. D. Henrys indifference curves are hyperbolas. E. None of the above. 24. Charlies utility function is xAxB. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $2.25 and the price of bananas fell to $1.25, then in order to be able to just afford his old bundle, Charlie would have to have a daily income of A. $57.50. B. $116. C. $28.75. D. $86.25. E. $230. 25. At a large institution of higher learning, the demand for football tickets at each game is 100,000 -6,000p. If the capacity of the stadium at that university is 40,000 seats, what is the revenue maximizing price for this university to charge per ticket? A. $16.67 B. $8.33 C. $6.67 D. $10 E. None of the above. 26. A bond has a face value of 5,000 dollars. It will pay 500 dollars in interest at the end of every year for the next 45 years. At the time of the last interest payment, 45 years from now, the company will buy back the bond from its owner at a price equal to the face value of the bond. If the interest rate is 10% and is expected to remain at 10%, how much would a rational investor pay for this bond right now? A. 5,000 dollars B. 27,500 dollars C. 22,500 dollars D. More than any of the above amounts E. Less than any of the above amounts 27. If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then indifference curves A. slope downward. B. slope upward. C. may cross. D. could take the form of ellipses. E. None of the above. 28. 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 dem