homework5 2009_last - . ) ( ) ( lim = t R t K t d) Derive...

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ECN/APEC 6000/7230 Fall 2009 Homework 5 Due 10/22/09 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:
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Unformatted text preview: . ) ( ) ( 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 overdetermined)....
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