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exam07 - THE UNIVERSITY OF HONG KONG School of Economics...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG School of Economics and Finance 2006—2007 2nd Semester Examination Economics: ECON 2101 Microeconomic Theory Prof. W. Suen May 23, 2007 9:30—11:30 am. This examination consists of two sections. Answer all questions in both sections. Candidates may use any self-contained, silent, battery-operated and pocket—sized cal- culator. The calculator should have numeral-display facilities only and should be used only for the purposes of calculation. It is the candidate’s responsibility to ensure that his calculator operates satisfactorily. Candidates must record the name and type of their calculators on the front page of their examination scripts. Section 1. On the first page of your answer book, write down the correct response to each of the following multiple choice questions. (40 marks) 1. In a crowded city far away, the civic authorities decided that rents were too high. The long—run supply function of two—room rental apartments was given by q = 20+5p and the long—run demand function was given by q = 271 — 2p, where p is the rental rate in crowns per week. The authorities made it illegal to rent an apartment for more than 23 crowns per week. To avoid a housing shortage, the authorities agreed to pay landlords enough of a subsidy to make supply equal to demand. How much would the weekly subsidy per apartment have to be to eliminate excess demand at the ceiling price? A. 9 crowns B. 18 crowns C. 36 crowns D. 15 crowns E. 27 crowns 2. Touchie MacFeelie’s production function is 0.1]1/2L3/4, Where J is the number of old jokes used and L is the number of hours of cartoonists’ labor. Touchie is stuck with 1,600 old jokes for which he paid 6 dollars each. If the wage rate for cartoonists is 5 dollars, then the total cost of producing 108 comics books is A. 15,007.50 dollars. B. 5,002.50 dollars. C. 10,113 dollars. D. 10,005 dollars. E. 2,501.25 dollars. 3. A firm has a long-run cost function, C (q) = Sq2 + 72. In the long run, this firm will supply a positive amount of output, as long as the price is greater than A. $48. . $104. $96. $24. $53. snow 4. Suppose that the cost of capturing a cockatoo and transporting him to the United States is about $40 per bird. Cockatoos are drugged and smuggled in suitcases to the United States. Half of the smuggled cockatoos die in transit. Each smuggled cockatoo has a 10% probability of being discovered, in which case the smuggler is fined and the cockatoo confiscated. If the fine imposed for each smuggled cockatoo is $1,000, then the equilibrium price of cockatoos in the United States will be A. $311.11. B. $140. C. $90. D. $70. E. $222.22. 5. A profit-maximizing monopoly faces an inverse demand function described by the equation p(y) = 90 — y and its total costs are C(y) = 83/, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 8 dollars per unit of output. After the tax, the monopoly will A. increase its price by 4 dollars B. leave its price constant. C. increase its price by 8 dollars. D. increase its price by 12 dollars. E . None of the above. 6. A firm has invented a new beverage called Slops. It doesn’t taste very good, but it gives people a craving for Lawrence Welk’s music and Professor Johnson’s jokes. Some people are willing to pay money for this effect, so the demand for Slops is given by the equation q = 18 — p. Slops can be made at zero marginal cost from old-fashioned macroeconomics books dissolved in bathwater. But before any Slops can be produced, the firm must undertake a fixed cost of $86. Since the inventor has a patent on Slops, it can be a monopolist in this new industry. A. The firm will produce 9 units of Slops. B. A Pareto improvement could be achieved by having the government pay the firm a subsidy of $91 and insisting that the firm offer Slops at zero price. C. From the point of View of social efficiency, it is best that no Slops be produced. D. The firm will produce 18 units of Slops. E. None of the above. 7. The demand for Professor Bongmore’s new book is given by the function Q = 8000 —— 100p. If the cost of having the book edited and typeset is $7,000, if the marginal cost of printing an extra copy is $4, and if he has no other costs, then he would maximize his profits by A. having it edited and typeset and selling 4,000 copies. not having it edited and typeset and not selling any copies. B. C. having it edited and typeset and selling 3,800 copies. D. having it edited and typeset and selling 7,600 copies. E. having it edited and typeset and selling 1,900 copies. 8. An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has an initial endowment of 3 apples and 12 bananas. Doris has an initial endowment of 6 apples and 6 bananas. Charlie’s utility function is U (Ac, BC) 2 ACBC, where Ac is his apple consumption and BC is his banana consumption. Doris’s utility function is U (A DaBD) = ADBD, where AD is her apple and B D her banana consumption. At every Pareto optimal allocation, A. tacos: Charlie consumes the same number of apples as Doris. Charlie consumes 9 apples for every 18 bananas that he consumes. Doris consumes equal number of apples and bananas. Charlie consumes more bananas per apple than Doris does. Doris consumes 6 apples for every 6 bananas that she consumes. 9. Al and Bill are the only workers in a small factory that makes geegaws and doodads. Al can make 5 geegaws per hour or 10 doodads per hour. Bill can make 4 geegaws per hour or 24 doodads per hour. Assuming that neither of them finds one task more odious than the other, A. B. C. D. E. Bill has a comparative advantage in producing geegaws and Al has a comparative advantage in producing doodads. Bill has a comparative advantage in producing both geegaws and doodads. Al has a comparative advantage in producing geegaws and Bill has a comparative advantage in producing doodads. Al has a comparative advantage in producing both geegaws and doodads. both have a comparative advantage in producing doodads. 10. On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There are 1,000 acres of land. An acre of land will produce either 3 units of milk or 7' units of wheat. Some citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions of the form U (M, W) = MW. At every Pareto optimal allocation, A. scam the number of units of milk produced equals the number of units of wheat pro— duced. all citizens consume the same commodity bundle. . total milk production is 1,500 units. every consumer’s marginal rate of substitution between milk and wheat is —1. None of the above is true at every Pareto optimal allocation. Section 2. Start a new page on your answer book to answer each ofthe following questions. You must explain your answers in order to get full credit. (60 marks) QUESTION 1. An economy consists of two regions. The production function in region 1 is A1F (X 1, L1), where X1 is the number of farmers working in region 1 and L1 is the (fixed) amount of land available in the region. The parameter A1 is an index of productivity. The production function in region 2 is given by A2F(X2, L2), where the variables are similarly defined. The function F exhibits diminishing marginal product to each input. (a) Suppose farmers and land are complements in the production function. If A1 = A2 and X1 = X2, but region 1 has more land than region 2, will farmers’ wages be higher in region 1 or in region 2? (b) Let the total number of farmers in this economy be fixed at Y, but farmers are free to migrate between the two regions, so that X1 + X2 = Y. Also assume that farmers and land are complements in the production function. (i) If A1 = A2 and L1 > L2, will there be more farmers in region 1 or region 2? (ii) Suppose A1 increases while A2 remains unchanged. Analyze what will happen to farmers’ wages and to the distribution of farmers across the two regions. Also analyze the effects on land rents in the two regions. QUESTION 2. Suppose each student disrupts the classroom with probability 1— p. Then in a classroom of size n, learning takes place with probability p". (a) If there are 16 good students with p = pa and 8 bad students with p 2 p3, where 190 > mg. The school may either assign classes by (1) putting 12 good students in one classroom and the remaining 4 good students and 8 bad students in another classroom; or (2) putting 8 good students and 4 bad students in each of the two classrooms. Which method of assigning classes will produce a higher amount of total learning? Why? (b) Now assume all students have the same value of p. The school has a total of Z students. It wants to maximize its profits by choosing the appropriate class size n. The total value of educational output (total revenue) is ZVp”, where V is the value of one unit of learning. If W is the cost of operating one classroom, total cost for the school is WZ/n. Use a revealed preference argument to Show that optimal class size is larger when the cost of operating a classroom is higher. QUESTION 3. (a) Your utility function is given by U (cc, y) = “i? — %. Are your preferences monotonic and convex? Are your preferences homothetic? (b) Suppose the prices of goods :1: and y are pm 2 1 and py = 4, respectively. Also suppose your money income is m = 18 dollars. Find your optimal consumption bundle. (0) Consider two alternative scenarios. (1) Your grandmother gives you a cash gift of 12 dollars. (2) Your grandmother gives you an in—kind gift of 12 units of :5 (which cannot be resold). Under which of the two scenarios would you attain a higher level of utility? Under which of the two scenarios would you consume more units of m? [For this part, you do not need to calculate the exact numbers. A clear verbal or diagrammatic analysis will suffice for full credit, though numerical answers (with explanations) are also acceptable] — END OF PAPER — ...
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