Thank you! a. Demonstrate that the production functions satisfy the conditions formonotonically increasing, diminishing return to labor, and constant returns toscale.b. If labor markets are perfectly competitive, in each sector the value of the marginalproduct of labor will be equal to the wage rate. Write these two conditions. Makesure to base your answer on the provided production functions.c. Combine the two conditions above to get the relationship between the relativeprice of corn and potatoes, and the allocation of labor to the two sectors (Lc, Lp).If the relative price of corn decreases, what happens to the allocation of laborbetween the two sectors? 3) 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 thefollowing Cobb-Douglas production functions:1-aQc= Ac K“ LcªQp = Ap T Lp'8Where 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 andTerra are denoted by Rx and RT, respectively. Wage of labor is W.The allocation of labor and capital to the two industries is subject toconstraintsresourceLc + Lp = Lwhere 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.

a. Constant returns to scale refers to when a growth in total output is proportional to an increase…

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. c. Combine the two conditions above to get the relationship between the relative price of corn and potatoes, and the allocation of labor to the two sectors (Lc, LP). If the relative price of corn decreases, what happens to the allocation of labor between the two sectors?

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. c. Combine the two conditions above to get the relationship between the relative price of corn and potatoes, and the allocation of labor to the two sectors (Lc, LP). If the relative price of corn decreases, what happens to the allocation of labor between the two sectors?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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