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hw_2_1 - EC640 Fall 2011 Ke Pang Problem Set#2 Part 1 Due...

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EC640 Fall 2011 Ke Pang Problem Set #2 - Part 1 Due: Monday, October 17 in class Be sure to show your work and the reasoning used to obtain your answer. 1. Consider the following closed economy. The representative agent maximizes her utility MAX { c 1 , c 2 } u ( c 1 ) + βu ( c 2 ) subject to her intertemporal budget constraint, and u ( c t ) = c 1 - σ t - 1 1 - σ , t = 1 , 2. Let y t denote the exogenous endowment of goods received in period t, t = 1 , 2. Goods are perishable. (a) For what values of σ is the period utility increasing and concave? What is the elasticity of intertemporal substitution and how does it relate to σ ? (b) Write down the intertemporal budget constraint and find the first-order conditions of the representative agent’s problem. (c) Define a competitive equilibrium allocation and price system. Solve for the competitive equilibrium. (d) What is the impact of an increase in σ on the real rate of interest? Explain the intuition. 2. Consider the following closed economy with two types of agents. Type A agent receives a
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