econ 204 hw7 - ECON 204 STUDY QUESTIONS 7 Firm Supply,...

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Unformatted text preview: ECON 204 STUDY QUESTIONS 7 Firm Supply, Industry Supply 1. Suppose that a firm uses three inputs to produce its output: capital (K), labor (L), and materials (M). The firm’s production function is given by Q(K; L; M) = g G/¡ ¢ G/¡ £ G/¡ . The prices of capital, labor, and materials are r = 1, w = 1, and m = 1, respectively. a) Provide expressions for the marginal products of capital, labor, and materials. Does this production function exhibit increasing, decreasing, or constant returns to scale? b) What is the solution to the firm’s long-run cost minimization problem given that the firm wants to produce Q units of output? c) What is the solution to the firm’s short-run cost minimization problem given that the firm wants to produce Q units of output and capital is fixed at g ¤ ? d) Verify that when Q = 4 and g ¤ ? = 4, which is the long-run cost minimizing quantity of capital when Q = 4, the short-run and long-run quantities of labor and materials are the same....
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