homework6 2009 solutions

# homework6 2009 solutions - ECN/APEC 6000/7230 Fall 2009...

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Unformatted text preview: ECN/APEC 6000/7230 Fall 2009 Homework 6 Solutions 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) In the steady state, * ) ( * * k g n y c δ + +-= . * g r θ ρ + = Thus we must have . * * ) ( 1 * * y k g n y c + +-= . 0583 . 015 . 01 . 3 25 . * * * * 1 =--=---= g n y k y c-= 1 *) ( * * k y k . 196 . 5 3 * * * 2 / 3 1 1 = = =-y k k 732 . 1 196 . 5 *) ( * 3 / 1 = = = k y . 299 . 1 ) 732 . 1 )( 75 . ( * = = c =-=-=--0583 . ) 196 . 5 ( 3 1 *) ( * 3 / 2 1 k r 0.0528 Thus g r-= * ECN/APEC 6000/7230 Fall 2009 b) In class, we derived that the slope of the consumption function is , *) ( ' ' * 4 2 1 2 -+ = θ β k f c m CKR where = ρ-n-(1 -) g = r * -n-g . 2 *) )( 1 ( *) ( ' '--= α k k f . *) ( * 4 ) 1 ( 2 1 2 2 -+ + =-k c m CKR c) In class, we derived that the rate of convergence is . * *) )( 1 ( *) ( ' ' * 2 μ CKR CKR CKR m c k m k f c--=-= For the designated values of , the results are THETA RHO M MU 0.5 0.045278 0.206839 0.179062 1 0.037778 0.150679 0.122901 2 0.022778 0.111111 0.083333 3 0.007778 0.093674 0.065897 4-0.00722 0.083333 0.055556 5-0.02222 0.076312 0.048534 d) In the Solow model, . 08333 . ) 0583 . 0528 . )( 75 . ( ) * )( 1 ( = + = +-= δ r s m S Thus for < 4, we have that m CKR > m S . In the Solow model, . 0556 . ) 0583 . 015 . 01 . ( 3 2 ) )( 1 ( = + + = + +-= g n s Again for <4, we have CKR > m S . 2) ECN/APEC 6000/7230 Fall 2009 a) With CRRA utility and risk aversion θ ≠ 1, utility starting from T for a balanced growth path where per capita consumption is C ( t ) = c * e gt is ....
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homework6 2009 solutions - ECN/APEC 6000/7230 Fall 2009...

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