Problem_Set_1_Solutions

Problem_Set_1_Solutions - Economics W3213 Spring 2010 Bruce...

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Economics W3213 Spring 2010 Bruce Preston Problem Set 1 Solutions Textbook Questions Short Answer Questions Indicate whether you think the following statements are true, false or uncertain. Support your answer by giving all necessary reasoning and calculations. 1. With a Cobb-Douglas production function, the elasticity of the marginal product of labor (i.e. labor demand) with respect to changes in total factor productivity is independent of the quantity of available capital and labor in the economy. Solution : True To determine the verity of the statement, apply the de±nition of an elasticity discussed in class. In this context we have = @MPN @A A MPN as the elasticity of the marginal product of labor with respect to changes in total factor productivity. Now MPN = (1 ± ± ) AK N for Cobb-Douglas technology. Hence @MPN @A = (1 ± ± ) K N : Substituting these two last equations into the formula for the elasticity gives = (1 ± ± ) K N A (1 ± ± ) AK N = 1 : It follows that the elasticity is independent of the quantity labor and capital inputs. 2. In the Solow Growth model a policymaker can increase steady state output, capital and consumption per worker by reducing population growth. But there are limits to the ef- fectiveness of this policy as steady state capital per worker may eventually exceed the Golden Rule level of capital. 1
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Solution: False In class it was shown that under the assumption of Cobb-Douglas production the Solow model predicts that steady state capital-labor ratio is determined by k ss = sA n + ± 1 1 : The Golden Rule level of capital is given by k gr = ±A n + ± 1 1 : Hence the two will coincide when ± = s . It is then immediate that no matter what the choice of n (or for that matter) the Golden rule level of capital will always be greater ± > s . Hence there are no policy limitations
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This note was uploaded on 02/27/2011 for the course ECONOMICS 201 taught by Professor P during the Spring '11 term at Columbia College.

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Problem_Set_1_Solutions - Economics W3213 Spring 2010 Bruce...

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