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homework7 2009 solutions

# homework7 2009 solutions - ECON 7240 Spring 2009 Homework 7...

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ECON 7240 Spring 2009 Homework 7 Solutions 1) a) The capital map is ) 1 )( 1 ( ) 1 ( 1 g n k s k t t + + - = + α α where ρ + = 2 1 s . If n increases by n , the k t +1 ( k t ) map shifts down everywhere by the factor 2 ) 1 ( n n + . Meanwhile, α α - + + - = 1 1 ) 1 )( 1 ( ) 1 ( * g n s k . 0 ) 1 ( 1 ) 1 ( 1 1 * 1 1 1 1 1 < + + - - - = - - - - α α α α n g s n k Thus steady state capital decreases as the rate of population growth increases. b) The map shifts down by B everywhere with ) 1 )( 1 ( ) 1 ( 1 g n k s B k t t + + - = + α α . Meanwhile, α α - + + - = 1 1 ) 1 )( 1 ( ) 1 ( * g n Bs k

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ECON 7240 Spring 2009 . 0 ) 1 )( 1 ( ) 1 ( 1 1 * 1 1 1 + + - - = - - - α α α α α B g n s B k Thus if productivity decreases, steady-state capital decreases. c) If the share of capital decreases, this has two effects. k t α will be flatter for most k t but get steeper for k t close to zero. At the same time, the smaller share of capital will increase the amount of output going to wages so k t +1 ( k t ) will shift upward by the percent that 1 - α increases everywhere.
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