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homework6 2009 - ECN/APEC 6000/7230 Fall 2009 Homework 6...

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ECN/APEC 6000/7230 Fall 2009 Homework 6 Due 10/29/09 1) Consider the Cass-Koopmans-Ramsey model with CRRA utility and Cobb- Douglas production. Assume the share of capital α = 1/3, the growth rate of technology is g = 0.015 per annum, and the growth rate of population is n = 0.01 per annum. a) What values of the discount rate ρ and the depreciation rate δ are needed for the steady-state capital-output ratio to be 3 and the steady-state consumption- output ratio to be 0.75 for values of θ = 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0. b) For θ = 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0, what is the slope of the consumption function at k *? c) For θ = 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0, what is the rate of convergence to the steady state? d) How do the answers to (b)-(c) compare to the results that would be obtained by a consumer who follows the Solow consumption rule c ( k ) = 0.75 f ( k )? 2) Consider the Cass-Koopmans-Ramsey model with CRRA utility and Cobb- Douglas production. Assume the share of capital α = 1/3, the growth rate of technology is g = 0.015 per annum, the growth rate of population is n = 0.01 per annum, the steady-
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