homework5 2009 - overdetermined). 2) Consider the...

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ECN/APEC 6000/7230 Fall 2009 Homework 5 Due 10/15/09 1) Consider the Cass-Koopmans model but with the quadratic period utility function 2 ) ( 2 1 ) ( C M C u - - = , where the constant M > 0 is known as the bliss point. a) Write down the Hamiltonian for the household’s problem. b) Write down Hamilton’s equations for the household’s problem. c) Solve for the optimal path of consumption. You may assume that C ≤ 0 is allowed and that there is no free disposal, so the budget constraints must hold with equality and the no-Ponzi condition also must hold with equality: . 0 ) ( ) ( lim = t R t K t d) Derive and interpret an expression for dC ( t )/ dt . e) Derive equations of motion for capital per effective labor k and consumption per effective labor c . f) Assume the growth rate of technology g > 0. Show that the equations of motion for k and c have a steady state solution with positive capital at finite times only for a set of measure zero of the parameter space (i.e. if the parameters are
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Unformatted text preview: overdetermined). 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, 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 = 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0, what is the slope of the consumption function at k *? ECN/APEC 6000/7230 Fall 2009 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 )?...
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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homework5 2009 - overdetermined). 2) Consider the...

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