课程名称︰个体经济学二 课程性质︰必修 课程教师︰江淳芳 开课学院：社会科学院 开课系所︰经济系 考试日期（年月日）︰2013/06/20 考试时限（分钟）：9:20-12:00 试题 : Microeconomics Final Exam Time: 9:20-12:00 1. (7%) Consider a market of risk-averse decision makers, each with a utility function U = √I. Each decision maker has an income of $900,000, but faces the possibility of a loss of %50,000 in income. Each decision maker can purchase an insurance policy that fully compensates her for her loss. This insurance policy has a cost of $5,900. Suppose each decision maker potentially has a different probability q of exeriencing the loss. (a) What is the smallest value of q so that a decision maker purchases insurance? (b) What would happen to this smallest value of q if the insurance company were to raise the insurance premium from $5,900 to $27,500? 2. (7%) The village of Sky Fall has 700 residents. They have a single public good, the happy farm. Everyone's utility function is U_i(X_i,Y) = X_i - 121/Y, where X is the amount of money spent on private consumption, and Y is the size of the happy farm in square meters. The cost of the happy farm is $7 per square meter. Everyone has an aincome of $5,000. What is the Oareto efficient size for the happy farm? 3. (20%) Suppose that Robinson and Friday have the following production possibility frontiers for good x and good y. Robinson: x^2 + y^2 = 100, Friday : x^2 + y^2 = 100, x,y ≧ 0 Their preferences for good x and good y can be expressed as : Robinson: u = xy^2, Friday : u = x^2y Please answer the following question: (a) Robinson is in Happy Island alone. He has to produce x and y for himself. How much units of good x and good y will he produce? (Hint: The MRT = x/y for the production possibility frontiers x^2 + y^2 = k) (b) Both Robinson and Friday are in Happy Island. But both of them are sick and cannot produce anything. Fortunately Robinson finds 8 good x and 10 good y on the ground and Friday finds 8 good x and 4 good y on the ground. Is this allocation Pareto efficient? Can you come up a way to improve their welfare? (c) Both Robinson and Friday are in Happy Island. They are health and are able to produce good x and good y. Robinson decides to produce 6 units of good x and 8 units of good y. Friday decides to purduce 8 unit of good x and 6 units of good y. They will exchange to improve their utilities after production. Is their production plan efficient? Can you come up a way to improve their welfare? (d) In the general equilibrium, will Robinson be the seller of x? Explane why. 4. (24%) The town of Steeleville has three steel factories, each of which produces air pollution. There are 10 citizens of Steeleville, each of whose marginal benefits from reducing air pollution is represented by the curve P(Q) = 5 - Q/10, where Q is the number of units of polutants removed from the air. The reduction of pollution is a public good. For each of the three source of air pollution, the following table lists the current amount of pollution being produced with the constant marginal cost of reducing it. Units of Pollution MC of pollution Source Currently Being Produced Reduction ────────────────────────── Factory A 20 $10 Factory B 40 $20 Factory C 60 $30 (a) On a graph, illustrate marginal benefits ("demand") and the marginal costs ("supply") of reducing pollution.What is the efficient amount of pollution reduction? Which factories should be the ones to reduce polution, and what would the total costs of pollution reduction be? In a private market, would and units of this public good be provided? (b) The Steeleville City Council is currently considering the following policies for reducing pollution: i. Requiring each factory to reduce pollution by 10 units. ii. Requiring each factory to produce only 30 units of pollution. iii. Reequiring each factory to reduce pollution by one fourth. Calculate the total costs of pollution reduction associated with each policy. Compare the total costs and amount of pollution reduction to the efficient amount you found in part (a). Do any of these policies creat a deadweight loss? (c) Another policy option would create pollution permits, to be allocated and, if desired, traded among the firms. If each factory has a permit allowing it to produce 30 units if pollution, which factories, if any, would trade them? (Assume zero transactions cost.) If they do trade, at what prices would the permits be traded? How does your answer in part (c) relate to in part (a)? 5.(18%) Suppose that low-productivity workers all have marginal products of 6 and high-productivity workers all have marginal products of 12. The community has equal numbers of each type of worker. The local community college offers four-year college education. The cost of college education for a high-productivity worker is 1 and the cost of college education for a low-productivity worker is 2. The reserve utility (the utility of no working and no education) is 0 for all workers. (a) Will there be a separating equilibrium? Please describe the choices made by firms and workers in the equilibrium. Explain. (b) Suppose now the reserve utility is 10 for high-productivity workers. Please describe the choices made by firms and workers in the equilibrium. (c) Suppose now the reserve utility is 10 for high-productivity workers, and the local college offers a training program. High-productivity worker think finishing the program is as bad as a wage cut of 5. Will there be a separating equilibrium? Please describe the choices made by firms and workers in the equilibrium. Explain. 6. (24%) There are two types of drivers in an island: careless drivers and careful drivers. A careless driver's car will be stolen with probability 0.5. A careful driver's car will be stolen with probability 0.2. Geico, a car insurance firm, cannot distinguish between careless drivers and careful drivers. The CEO of Geico designed two insurance policies. Policy A offers fair insurance for careful drivers(i.e., the premium rate is 0.2) and policy B offers fair insurance for careless drivers(i.e., the premium rate is 0.5). Both can be purchased in unlimited quantities. Tom is a careless driver/ His utility function of consumption is u(c) and he is risk averse. Without insurance, Tom has $1,000 worth of assets (C_g = 1,000) if his car is not stolen and has $250 worth of assets (C_b = 250) if his car is stolen. Tom's indifference curves over C_g and C_b can be depicted in the following graph. Graph: http://ppt.cc/Ci7z (a) (4%) Please write down Tom's expected utility function. Please derive the MRS when C_g = C_b. (b) (4%) Please plot the budget line associated with the purchase of insurance policy A and the budge line associated with the purchase of insurance policy B on a graph. (c) (4%) If policy A is not available, how much insurance will Tom buy? Explain. (d) (4%) When both policy A and policy B are both available, which policy will Tom choose? What type of information problem does the insurance company face? (e) (8%) Now a new CEO would like to solve the infomation problem. The new CEO decides to keep policy B unchanged, but add a limitation in policy A: in policy A, the pruchase amount of insurance cannot be exceed X. Will the change be able to solve the information problem? If so, how should the new CEO decide X? --

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