Problem 2: Production economy Consider a production economy with two firms, X and Y, and two factors of production, labor and capital. Firm X produces the output good X with a technology that can be de- scribed by the following production function: fx(lx.kx) = lx+kx, where lx is the quantity of labor and ky is the quantity of capital. Firm Y produces the output good Y with a technology that can be de- scribed by the following production function: fy(ly, ky)=√√√√ky. where ly is the quantity of labor and ky is the quantity of capital. The economy has a total endowment of labor L > 0 and a total endowment of capital K = L. The price of the good X is p > 0 and the price of good Y is q = 1. These output prices are determined on international markets and are not affected by the supply decisions of the firms. (a) Find the set of production efficient allocations in this economy. Illus- trate the set of efficient factor allocations in a Bowley box diagram. Describe and illustrate the production possibility frontier. (b) For all possible values of p>0, find the competitive equilibrium wage and rental rates, as well as the competitive equilibrium allocations of the output goods and the factors labor and capital.

Problem 2: Production economy Consider a production economy with two firms, X and Y, and two factors of production, labor and capital. Firm X produces the output good X with a technology that can be de- scribed by the following production function: fx(lx.kx) = lx+kx, where lx is the quantity of labor and ky is the quantity of capital. Firm Y produces the output good Y with a technology that can be de- scribed by the following production function: fy(ly, ky)=√√√√ky. where ly is the quantity of labor and ky is the quantity of capital. The economy has a total endowment of labor L > 0 and a total endowment of capital K = L. The price of the good X is p > 0 and the price of good Y is q = 1. These output prices are determined on international markets and are not affected by the supply decisions of the firms. (a) Find the set of production efficient allocations in this economy. Illus- trate the set of efficient factor allocations in a Bowley box diagram. Describe and illustrate the production possibility frontier. (b) For all possible values of p>0, find the competitive equilibrium wage and rental rates, as well as the competitive equilibrium allocations of the output goods and the factors labor and capital.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

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