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400exam1-10

# 400exam1-10 - ECON 400 Winter 2010 MIDTERM EXAMINATION 1...

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ECON 400 Hartman Winter 2010 MIDTERM EXAMINATION 1. A firm uses two inputs, labor and capital, to produce its output. The production function is 1/4 1/4 8 Q L K where Q , L , and K denote the firms output and its inputs of labor and capital, respectively. The firm is a price taker in all of its markets and and it chooses L and K to maximizes its profit, 1/4 1/4 8 p L K wL rK , where p , w , and r denote the output price, and the prices of the labor and capital inputs, respectively. a. What are the first order conditions for profit maximization? b. What are the (sufficient) second order conditions? Are the second order conditions satisfied? c. Solve for the profit-maximizing factor demand functions, * ( , , ) L w r p and * ( , , ) K w r p . d. Find the firm's supply function, * ( , , ) Q w r p . e. Are * ( , , ) L w r p , * ( , , ) K w r p , and * ( , , ) Q w r p homogeneous of degree zero in w , r , and p ? Does this imply that the production function is homogeneous of degree one? f. What is the elasticity of labor demand with respect to the price of the capital input, i . e ., what is Lr
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