2. Say we have a profit maximizing firm that produces one output good with two factor inputs. The factor prices are w;> 0 for factors i = {1,2}. The production technology is y = f(x1,₂)- a. Define the firm's short-run profit maximization problem when 21 is the fixed factor set at level 1 > 0. b. Say in the short-run profit max problem, the technology f(x1,2₂) is smooth and strictly concave and has the "increasing difference property" fi: (x) > 0. Say (a) 1 increases, (b) we decreases. Show the optimal factor demand (1,wap,w₁) increases when both (a) and (b) happen. c. Show that output in part (b) also increases when both (a) and (b) happen d. Now, use the envelope theorem to show how to construct the Long-run profit maximization problem from this short-run problem. e. Draw a picture of the long-run profit maximization problem, and explain how it relates to the cost minimization problem.
2. Say we have a profit maximizing firm that produces one output good with two factor inputs. The factor prices are w;> 0 for factors i = {1,2}. The production technology is y = f(x1,₂)- a. Define the firm's short-run profit maximization problem when 21 is the fixed factor set at level 1 > 0. b. Say in the short-run profit max problem, the technology f(x1,2₂) is smooth and strictly concave and has the "increasing difference property" fi: (x) > 0. Say (a) 1 increases, (b) we decreases. Show the optimal factor demand (1,wap,w₁) increases when both (a) and (b) happen. c. Show that output in part (b) also increases when both (a) and (b) happen d. Now, use the envelope theorem to show how to construct the Long-run profit maximization problem from this short-run problem. e. Draw a picture of the long-run profit maximization problem, and explain how it relates to the cost minimization problem.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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