homework2 2009 - What about r ? 2) Assume that F ( U , V )...

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ECN/APEC 6000/7230 Fall 2009 Homework 2 Due 9/15/09 1) Consider a Solow economy with a constant returns to scale production function F ( K , AL ). Suppose that labor and capital are both paid their marginal products, so the real wage is L t L t A t K F t w = )) ( ) ( ), ( ( ) ( and the rate of return on capital is L Y Y L L = α a) The return to capital is roughly constant over time, as are the shares of output going to capital and labor. Does a Solow economy on a balanced growth path exhibit these properties? What are the growth rates of w and r on a balanced growth path? b) Suppose the economy begins with k (0) < k *. As k moves toward k *, does w grow at a rate greater than, less than, or equal to its growth rate on the balanced growth path.
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Unformatted text preview: What about r ? 2) Assume that F ( U , V ) exhibits constant returns to scale for U , V 0. a) Show that F ( U , V ) = UF U ( U , V ) + VF V ( U , V ) for all U , V 0. (Hint: Write down an equation that describes what happens if we increase U and V by a factor &gt; 0 and differentiate by .) b) Now suppose that Y = F ( K , L ). Define K Y Y K K = L Y Y L L = Show that K + L = 1. c) Show that for a Cobb-Douglas production function F ( U , V ) = U V 1-that K = ....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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