47509-midterm

47509-midterm - ECO 475, Fall 2009, Midterm Exam Jay H....

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Unformatted text preview: ECO 475, Fall 2009, Midterm Exam Jay H. Hong Oct 21, 2009 This exam has 3 questions, for a total of 100 points. You have 3 hours. Manage your time wisely. Feel free to make an appropriate assumption if needed. Good luck!! 1. Computing the equilibrium (32 points) Consider an island where two individuals ( i = 1 , 2) live forever who maximize their lifetime utility given by ∞ X t =0 β t ln( c i t ) , where c i t is the consumption choice of an agent i at time t . Each consumer is given a type-, time-specific endowment process of non-storable consumption goods, e i t , such that e 1 t = ( 6 if t = even 2 if t = odd e 2 t = ( 2 if t = even 4 if t = odd (a) (5 points) Define carefully a competitive equilibrium. You can choose any definition of competitive equilibrium we’ve studied so far. (b) (6 points) Solve the competitive equilibrium defined above directly. (c) (7 points) Using the Negishi’s method, compute the competitive equilibrium for this econ- omy. Verify that the equilibrium derived using Negishi’s method is identical to the equi- librium you obtained in (b). What is the planner’s weight on agent 1? (d) (5 points) Suppose the Social Planner tries to improve the social welfare by introducing a lumpsum tax/transfer ( τ i t ) so that the effective endowment of an individual is e i t- τ i t . Discuss whether it is welfare-improving in Pareto sense to introduce the tax/transfer policy. Why or why not? The Social Planner of the island has a new machine called “refrigerator” in which 1 unit of consumption goods can be stored today and gets 1 units of goods tomorrow. (e) (9 points) Assume that β is high enough ( β > 3 / 4). Discuss whether it is welfare- improving in Pareto sense to introduce that tax/transfer policy if the refrigerator is avail- able. Why or why not? Given the same planner’s weight on agent 1, (from (c) Negishi’s method), characterize the allocation of consumption, tax/transfer, and the optimal level of storage (if there is any)....
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This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.

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47509-midterm - ECO 475, Fall 2009, Midterm Exam Jay H....

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