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Consider the maximization problem of a company that has complete flexibility to change all its factors of production. The price (p,) of its final product is 24, the price (w;) of input x1 is 1 and the price (w2) of input x2 is 4. The maximization problem is given by: 1/31/6 maxx1,x,Pyy - W,X1 - W2X2 s.a. y = x"x," a) Present the problem of maximization of the company. b) Find the first order conditions that must be solved to find the level optimal inputs. c) Show that optimal production meets the following conditions: xi = 8y* ó xi = 2(y*)? (y*)² x; = y* ó x; = %3D

Consider the maximization problem of a company that has complete flexibility to change all its factors of production. The price (p,) of its final product is 24, the price (w;) of input x1 is 1 and the price (w2) of input x2 is 4. The maximization problem is given by: 1/31/6 maxx1,x,Pyy - W,X1 - W2X2 s.a. y = x"x," a) Present the problem of maximization of the company. b) Find the first order conditions that must be solved to find the level optimal inputs. c) Show that optimal production meets the following conditions: xi = 8y* ó xi = 2(y*)? (y*)² x; = y* ó x; = %3D

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider the maximization problem of a company that has complete flexibility to change all its factors of production. The price (p,) of its final product is 24, the price (w1) of input x1 is 1 and the price (w2) of input x2 is 4. The maximization problem is given by: 1/31/6 maxxx,Pyy – W,x1 – W2X2 s.a. y = xx a) Present the problem of maximization of the company. b) Find the first order conditions that must be solved to find the level optimal inputs. c) Show that optimal production meets the following conditions: xi = 8y* ó xị = 2(y*)2 (y")2 x = y* ó x = 4
Transcribed Image Text:Consider the maximization problem of a company that has complete flexibility to change all its factors of production. The price (p,) of its final product is 24, the price (w1) of input x1 is 1 and the price (w2) of input x2 is 4. The maximization problem is given by: 1/31/6 maxxx,Pyy – W,x1 – W2X2 s.a. y = xx a) Present the problem of maximization of the company. b) Find the first order conditions that must be solved to find the level optimal inputs. c) Show that optimal production meets the following conditions: xi = 8y* ó xị = 2(y*)2 (y")2 x = y* ó x = 4
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