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# HW2 - Graduate Macro II Homework 2 Jonathan Heathcote Due...

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Graduate Macro II, Homework 2 Jonathan Heathcote Due in class on Thursday February 16th 2006 Consider the neoclassical growth model in discrete time. In the two exam- ples below, you are asked to solve for e cient allocations by considering social planner’s problems. 1. Assume the planner’s preferences are given by T P t =0 β t u ( c t ) where u ( c t ) = ln( c t ) , and the technology is c t + i t = y t t 0 y t = k θ t t 0 k t +1 = (1 δ ) k t + i t t 0 c t 0 , k t 0 t 0 k 0 given (a) Describe a set of equations that implicitly de fi nes a solution to this planning problem. (b) Assume the following parameter values: β = 0 . 96 , T = 100 , θ = 0 . 36 , δ = 0 . 08 . Assume k 0 = 1 . Solve for the e cient allocation { c t , k t } T t =0 . I suggest you use the following “shooting method”: i. Guess bounds such that c 1 l c 0 c 1 h , and make an initial guess for c 0 , denoted c 1 0 , where c 1 0 = 0 . 5 ¡ c 1 l + c 1 h ¢ ii. Use the set of equations de fi ning a solution to the problem to compute k T +1 given c 1 0 and k 0 iii. Use “bisection" to update the guess for

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HW2 - Graduate Macro II Homework 2 Jonathan Heathcote Due...

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