2. Say we have a profit maximizing firm that produces one output goodwith two factor inputs. The factor prices are w> 0 for factors i = {1,2}. Theproduction technology is y = f(x1.₂).a. Define the firm's short-run profit maximization problem when 1 is thefixed factor set at level 1 > 0.b. Say in the short-run profit max problem, the technology f(1, ₂) issmooth and strictly concave and has the "increasing difference property" f12(x) >0. Say (a) #1 increases, (b) we decreases. Show the optimal factor demand(1, Waip, w1) increases when both (a) and (b) happen.c. Show that output in part (b) also increases when both (a) and (b) happend. Now, use the envelope theorem to show how to construct the Long-runprofit maximization problem from this short-run problem.e. Draw a picture of the long-run profit maximization problem, and explainhow it relates to the cost minimization problem.

Short-run production function shows the output by using one factor of the production variable and…

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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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