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

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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 a b Q K L 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 a b Q K 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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