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 ()ttYfKwhere Ytis output in period tand Ktis the capital input in that period. The firm makes changes in the level of capital through investment. If Itdenotes investment in period t, then capital accumulates according to KIKt11where 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 tis tp, and the purchase price for a unit of the investment good in period tis tq. The firm maximizes the net present value of its cash flows, 0(1)ttttttpfKqIrwhere K0is fixed by past decisions and ris the interest rate. Substitute for It, and derive the first order conditions for the choice of Ktfor 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.