answerstohomework4spring2005

answerstohomework4spring2005 - Economics 302 Spring 2005...

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Economics 302 Spring 2005 Answers to Homework #4 Due March 30, 2005 1. Consider the Solow growth model with population growth where labor’s share of output is ¾, the savings rate is 15%, the depreciation rate is 7%, and the population growth rate is 3%. a. Find the steady state level of capital per worker and output per worker. (There are exponents involved. Do not use your calculator to reduce them.) The steady state is defined by 0 = k . The law of motion is then k k f ) 3 . 7 (. ) ( 15 . 0 + - = . This can be rearranged to give 5 . 1 ) ( = k f k The production function is 4 / 3 4 / 1 L K Y = . Dividing this by L and noting that L K k / = we have that 4 / 1 ) ( k k f = . By substituting this into the above equation and simplifying we find that 3 / 4 5 . 1 = k which is the steady state level of capital per worker. To get output per worker in the steady state just put the steady state level of capital per worker into 4 / 1 ) ( k k f = to get 3 / 1 5 . 1 = y . b. What is total labor income in the steady state? Each worker receive an income of y, the amount of output per worker. By assumption ¾ of this income comes from wages. Therefore each worker’s wage is 3 / 1 5 . 1 ) 4 3 ( ) 4 3 ( = = y wage . There are L workers so the total labor income is 3 / 1 5 . 1 ) 4 3 ( L . c. Using the model discuss how the steady state level of capital per worker and output per worker would change for increases in the savings rate, the depreciation rate, population growth rate, or labor’s share of income.
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