homework2 2009 solutions

homework2 2009 solutions - ECN/APEC 6000/7230 Fall 2009...

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ECN/APEC 6000/7230 Fall 2009 Homework 2 Solutions 1) a) On a balanced growth path, k ( t ) = k *, so r ( t ) = f ( k *) - δ for all t , so the rate of return is constant. The share of output paid to labor is . )) ( ( ))] ( ( ' ) ( )) ( ( )) ( ( ) ( ) ( ))] ( ( ' ) ( )) ( ( )[ ( ) ( ) ( ) ( ) ( t k f t k f t k t k f t k f t L t A t k f t k t k f t L t A t Y t L t w - = - = Thus on a balanced growth path, , *) ( *) ( ' * 1 ) ( ) ( ) ( k f k f k t Y t L t w - = which is constant. The share of output going to capital is , *) ( *) ( ' * ) ( ) ( ) ( k f k f k t Y t K r = + which is also constant. The wage is w ( t ) = A ( t )[ f ( k *) - k * f ( k *)], which grows at g , the same rate as A ( t ). b) The wage is ))]. ( ( ' ) ( )) ( ( )[ ( ) ( t k f t k t k f t A t w - = From (1-1a), . ) ( )) ( ( ' ' ) ( ) ( ) ( ) ( ))] ( ( ' ' ) ( )) ( ( ' )) ( ( ' [ )) ( ( ' ) ( )) ( ( 1 ) ( ) ( 1 ) ( ) ( 1 dt t dk t k f t k t w t A g dt t dk t k f t k t k f t k f t k f t k t k f dt t dA t A dt t dw t

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homework2 2009 solutions - ECN/APEC 6000/7230 Fall 2009...

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