Handout 7 Key

Handout 7 Key - Econ 3140 Fall 2009 Handout #7 with answers...

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Econ 3140 Fall 2009 Handout #7 with answers 1. (a) First, we transform the production function into per worker term Y t N t = AK 1 = 2 t N 1 = 2 t N t , y t = f ( k t ) = k 1 = 2 Second, we use the steady state condition s f ( k t ) = ( n + d ) k t () 1 4 k 1 = 2 t = 1 10 k t () k 1 = 2 t = 10 4 () k t = 100 16 = 6 : 25 Plugging k t = 6 : 25 into the prod. fn y t = f ( k t ) = 100 16 ± 1 = 2 = 10 4 () y t = 10 4 = 2 : 5 (b) To calculate the steady state value of per capita consumption we might use either c t = (1 ± s ) y t or c t = f ( k t ) ± ( n + d ) k t . c t = 3 4 10 4 ± = 30 16 = 1 : 875 (c) Since the production function is CRS ( + ± = 1) and assuming productivity ( A ) remains constant, the steady state growth rate will equal ( n + d ) = 10% . (Also, since f 0 ( k t ) = ( n + d ) ). (d) Recalling the Golden Rule condition (maximize welfare): @c t @k t = 0 and using the consumption function c t = f ( k t ) ± ( n + d ) k t : @c t @k t = f 0 ( k t ) ± ( n
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This note was uploaded on 03/10/2010 for the course ECON 3140 taught by Professor Mbiekop during the Spring '07 term at Cornell.

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Handout 7 Key - Econ 3140 Fall 2009 Handout #7 with answers...

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