# 401ps7-10 - ECON 401 Autumn 2010 PROBLEM SET VII(for...

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ECON 401 Hartman Autumn 2010 PROBLEM SET VII (for Thursday, December 2) 1. In each period a firm uses capital to produce output according to the production function () tt Yf K where Y t is output in period t and K t is the capital input in that period. The firm makes changes in the level of capital through investment. If I t denotes investment in period t , then capital accumulates according to K I K t 1 1 where is the depreciation rate. (Note that investment in a period does not affect the capital stock until the next period.) The output ptice for period t is t p , and the purchase price for a unit of the investment good in period t is t q . The firm maximizes the net present value of its cash flows, 0 (1 ) ttt t t t pfK qI r where K 0 is fixed by past decisions and r is the interest rate. Substitute for I t , and derive the first order conditions for the choice of K t for some typical time period t . Interpret this condition. What is the user cost of capital for period t ?
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## This note was uploaded on 04/04/2011 for the course ECON 401 taught by Professor Staff during the Spring '08 term at University of Washington.

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