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# hw_2_2 - EC640 Fall 2011 Ke Pang Problem Set#2 Part 2 Due...

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EC640 Fall 2011 Ke Pang Problem Set #2 - Part 2 Due: Monday, October 17 in class Be sure to show your work and the reasoning used to obtain your answer. 1. Consider the following overlapping generations economy. N t young agents (generation t ) are born in period t , t = 1 , 2 , · · · . Each generation lives for two periods. Population grows at a constant rate g N . The representative agent of generation t has a lifetime utility function given by u ( c 1 ,t , c 2 ,t +1 ) = ln ( c 1 ,t ) + βln ( c 2 ,t +1 ) . Let e 1 and e 2 denote this representative agent’s endowments in the first and second periods of his life. The initial old (generation 0) are endowed with e 2 and consume c 2 , 1 in period 1. (a) Solve for the competitive equilibrium. (b) Solve for the social planner’s problem in this economy. (c) Explain in which case the economy is dynamically efficient (i.e. Pareto efficient or Pareto optimal) and in which case the economy is not dynamically efficient. 2. Consider the following overlapping generations economy. N young agents (generation t ) are born in period t , t = 1 , 2 , · · · . Each generation lives for two periods. There is no population growth. Suppose there are two types of agents within a generation. In particular, a fraction

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hw_2_2 - EC640 Fall 2011 Ke Pang Problem Set#2 Part 2 Due...

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