homework4 2009 - risk aversion θ ≠ 1(The result holds...

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ECN/APEC 6000/7230 Fall 2009 Homework 4 Due 10/1/09 1) Consider N firms each with the constant returns to scale production function Y = F ( K , AL ) or (in intensive form) Y = ALf ( k ). Assume f > 0 and f ′′ < 0. All firms can hire labor at the wage W and rent capital at the cost r , and all firms have the same A . a) Consider the problem of a firm trying to produce Y units of output at minimum cost. Show that the cost-minimizing level of k is uniquely defined and independent of Y . b) Show that the total output of the N cost-minimizing firms equals the output that a single firm with the same production function has if it uses all the labor and capital used by the N firms. 2) Consider an individual who lives for two periods and who has CRRA utility with
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Unformatted text preview: risk aversion θ ≠ 1. (The result holds for = 1 but needs to be derived differently.) Let P 1 and P 2 denote the prices of consumption in the two periods, and let W denote the value of lifetime income. Thus the budget constraint is . 2 2 1 1 W C P C P = + a) What are the utility-maximizing choices of C 1 and C 2 as a function of W , P 1 , and P 2 ? b) The intertemporal elasticity of substitution is the elasticity of substitution between consumption in the two periods, defined as . ) / ln( ) / ln( 2 1 2 1 P P C C ∂ ∂-Show that the elasticity of substitution is -1 ....
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