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Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions.

Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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a. Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. b. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions.
Transcribed Image Text:a. Demonstrate that the production functions satisfy the conditions for monotonically increasing, diminishing return to labor, and constant returns to scale. b. If labor markets are perfectly competitive, in each sector the value of the marginal product of labor will be equal to the wage rate. Write these two conditions. Make sure to base your answer on the provided production functions.
Specific Factors Model: Consider an economy with two goods – corn (C) and potatoes (P) – both produced using labor. The technologies for the two sectors are given by the following Cobb-Douglas production functions: 1-a Qc= Ac K“ Lc Qp = Ap T Lp'B Where 0 <a < 1, 0< ß < 1, and Capital (K) and Land (T, stands for terra) are fixed (specific factors), while labor can freely move across sectors. Prices of corn and potatoes are denoted by Pc and Pp, respectively. Prices for Capital and Terra are denoted by Rk and RT, respectively. Wage of labor is W. The allocation of labor and capital to the two industries is subject to the resource constraints Lc + Lp = L where L is the aggregate endowment of labor. The representative household's preferences are given by the utility function U(Cc, Cp) = log Cc + log CP.
Transcribed Image Text:Specific Factors Model: Consider an economy with two goods – corn (C) and potatoes (P) – both produced using labor. The technologies for the two sectors are given by the following Cobb-Douglas production functions: 1-a Qc= Ac K“ Lc Qp = Ap T Lp'B Where 0 <a < 1, 0< ß < 1, and Capital (K) and Land (T, stands for terra) are fixed (specific factors), while labor can freely move across sectors. Prices of corn and potatoes are denoted by Pc and Pp, respectively. Prices for Capital and Terra are denoted by Rk and RT, respectively. Wage of labor is W. The allocation of labor and capital to the two industries is subject to the resource constraints Lc + Lp = L where L is the aggregate endowment of labor. The representative household's preferences are given by the utility function U(Cc, Cp) = log Cc + log CP.
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