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Question: Consider a firm producing output y with two inputs x_1 and x_2. The technology is represented b, ...

Show transcribed image text Consider a firm producing output y with two inputs x_1 and x_2. The technology is represented b, a production function y = 0.3 In (x_1) + 0.7 In (x_2). The marginal products are MP_1 = 0.3/x_1 and MP_2 = 0.7/x_2. Suppose that output price is p and input prices are w_1 and w_2. a. Consider the problem of short-term profit maximization where x_2is a fixed input Write and interpret the condition for profit maximization. b. Obtain and interpret the short-term optimal demand function for x_1. c. Obtain and interpret the short-term optimal supply function. d. Obtain and interpret the short-term optimal profit function.

Consider a firm producing output y with two inputs x_1 and x_2. The technology is represented b, a production function y = 0.3 In (x_1) + 0.7 In (x_2). The marginal products are MP_1 = 0.3/x_1 and MP_2 = 0.7/x_2. Suppose that output price is p and input prices are w_1 and w_2. a. Consider the problem of short-term profit maximization where x_2is a fixed input Write and interpret the condition for profit maximization. b. Obtain and interpret the short-term optimal demand function for x_1. c. Obtain and interpret the short-term optimal supply function. d. Obtain and interpret the short-term optimal profit function.