Advanced Micro II
Midterm Exam
Winter 2019
高级微观经济Midterm代写 A natural gas company owns pipelines running underneath a new housing development. The company can invest $u to maintain the pipes.
Welcome! Before you begin, write your name below. You will need to turn in this paper at the end of the test. You will have 80 minutes to complete this test. The test is also worth 80 points, so plan your time so that you spend one minute per point. You will get partial credit so it is very costly to leave a question completely blank. The points per question are listed in parentheses.
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1 True, False, or Uncertain 高级微观经济Midterm代写
Are the following statements True, False, or Uncertain? Whatever your answer, to get credit you must provide a justification.
- (5 points) The Second Theorem of Welfare Economics states that all Pareto allocations are social welfare maxima.
Suggested Solution:
- (5 points) Every allocation of goods in a one good world is efficient.
- (5 points) If a monopolist is producing a harmful externality, taxing the monopolist will result in a welfare gain to consumers.
- (5 points) If supply is more inelastic than demand, then a per-unit tax on sellers of a good will yield less deadweight loss than the same per-unit tax on buyers of that good.
2 Long problems 高级微观经济Midterm代写
- (10 points total) Consider a pharmaceutical company, Gouth, which is making the decision about whether or not to develop a cancer fighting drug. The company is an expected profit maximizer. It knows that the R&D cost of creating the drug and getting approval to market the drug is R > The cost of making each additional unit of the cancer-fighting drug is c. Gouth expects demand will be linear in price, so that it can summarize the demand curve using the formula P = a – bQ.
(a)(3 points) Why do we not draw supply curves for monopolists?
(b)(3 points) Consider the following cases:
i.If c > a how many units will Gouth produce?
ii.If c < a how many units will Gouth produce?
(c)(4 points) Suppose that the government forces Gouth to price at P = c. Why would the govern ment choose this price? What must be true of Gouth’s profits from making the drug?
2.(10 points total) Suppose that 2 individuals live in a pure exchange economy with two goods—coconuts and water. Person 1 is endowed with 10 coconuts and no water. Person 2 is endowed with 10 liters of water and no coconuts.
(a)(5 points) Draw the Edgeworth box for this economy, labeling the endowment.
(b)(5 points) Suppose that utility of person 1 is u(c, w) = 2c + w and the utility of person 2 is u(c, w) = 2c + 2w where c = number of coconuts and w =liters of water. What are the Pareto efficient allocations in this economy?
3.(25 points total) Robinson and Crusoe live on an isolated island. They each consume coconuts, a private good, and need to use latrine pits. Latrine pits are a public good. Both have preferences representable by a utility function of the form Ui(Xi, Y) = X1-aYawhere Xi is i’s own consumption of coconuts and Y is the number of latrine pits. Normalize the price of coconuts to 1. Latrine pits can be dug at the cost of p per unit. Although preferences don’t differ, incomes do. Robinson has an income of WR and Crusoe has an income of WC .
(a)(10 points) Show that in the Lindahl equilibrium, the share of the cost of latrine pit digging paid by Robinson is increasing in his wealth (holding the wealth of Crusoe fixed). 高级微观经济Midterm代写
(b)(5 points) Assume that a government is established on Robison and Crusoe’s island which wants to start a latrine digging project for the benefit of Robinson and Crusoe. They know nothing about Robinson and Crusoe’s utility or wealth. Suppose they decide to build latrine pits based on the following rule: ask Robinson and Crusoe how much each of them value an additional latrine pit, if the sum of their reported valuations is greater than zero, build the pit. In this case (assuming Robinson and Crusoe can’t collude), will the number of latrine pits built be the same as in the Lindahl equilibrium?
(c)(8 points) Now suppose the government states the if a latrine pit is built, Robinson will receive a transfer equal to Crusoe’s reported value of the pit, denoted Vc,and Crusoe will receive a transfer equal to Robinson’s reported value of the pit, denoted Vr. Assuming there can be no collusion, show that the optimal report of each agent is their true valuation.
(d)(2 points) In the situation above, explain intuitively why Robinson and Crusoe have incentive to collude, if possible.
4.(15 points) A natural gas company owns pipelines running underneath a new housing development. The company can invest $u to maintain the pipes. The company would like to maintain the pipes because it loses less gas when pipes are well maintained. The value of lost gas is given by 1for a level of maintenance u. However, more maintenance also means less damage to the land above the pipes. Assume the damage to the land above the pipes is given by 1 for a level of maintenance u.
(a)(5 points) What level of maintenance would the social planner choose?
(b)(5 points) What level of maintenance is chosen by the natural gas company, assuming it owns none of the land above the pipes and what is the associated deadweight loss?
(c)(5 points) What could the government do to achieve the socially optimal outcome?
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