400ps7-11 - ECON 400 Winter 2011 Problem Set VII (due...

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E C O N 4 0 0 H a r t m a n Winter 2011 Problem Set VII (due Wednesday, February 23) A firm uses two inputs, capital and labor, to produce its output. The production function is ab QKL where 0 K and 0 L denote the firm's inputs of capital and labor, respectively, Q denotes its output, and 0 a and 0 b are constants. The firm is a price taker in both input markets; the prices of the capital and labor inputs are r and w , respectively. The firm's objective is to minimize the cost of producing some specified level of output, Q ., i . e ., the firm chooses 0 K and 0 L to minimize rK wL subject to the constraint . 1. What are the first order conditions for this optimization problem? 2. What is the (sufficient) second order condition? (The second order condition is satisfied for all values of 0 a and 0 b . You do not need to show this, but you may want to for your own satisfaction. A fair bit of algebra is involved.) 3. Solve the first order conditions for the conditional factor demand functions, ˆ (, , ) KrwQ and ˆ
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This note was uploaded on 04/04/2011 for the course ECON 400 taught by Professor Ellis,g during the Spring '08 term at University of Washington.

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