ECON 400 Hartman 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 abQK Lwhere 0Kand 0Ldenote the firm's inputs of capital and labor, respectively, Qdenotes its output, and 0aand 0bare constants. The firm is a price taker in both input markets; the prices of the capital and labor inputs are rand w, respectively. The firm's objective is to minimize the cost of producing some specified level of output, Q., i.e., the firm chooses 0Kand 0Lto minimize rKwLsubject to the constraint abQK L. 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 3. Solve the first order conditions for the conditional factor demand functions, ˆ( ,,)K r w Q
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