Consider a 2x2 production economy with two firms, X andY, and two factors of production, labor L and capital K. Thetotal endowment of factors in the economy is 100 units of laborand 100 units of capital, so (L, K) = (100, 100).Firm X can produce output good X using labor and capital.The firm's technology is described by the following continuousand differentiable production function:fx(lx,kx) = alx + (1 – a)kx,where lx 2 0 is the quantity of labor and kx > 0 is thequantity of capital employed by firm X, and a e (0, 1) is aproduction parameter.Firm Y can produce output good Y using labor and capital.The firm's technology is described by the following continuousand differentiable production function:fr (ly, ky) = lk8,where ly > 0 is the quantity of labor and ky >0 is the quantityof capital employed by firm Y, and ß E (0, 1) is a productionparameter.This is a small open economy, so output prices for goods Xand Y, (px,pY) >> 0, are given. For all of the followingproblems, the price of the output good Y is 1 (i.e., Py = 1). (2) Suppose a < B. (i) Describe the set of production efficientfactor allocations and illustrate them in a Bowley box di-agram. (ii) Describe the set of production efficient outputallocation and illustrate the production possibility frontierin a diagram. (iii) Find the competitive equilibrium wagerate w, rental rate r, and allocations of factors and outputgoods for each firm, for any possible price px > 0 of theoutput good X.

decide the ideal allotment of work and capital between the two firms to augment the absolute result…

Consider a 2x2 production economy with two firms, X and Y, and two factors of production, labor L and capital K. The total endowment of factors in the economy is 100 units of labor and 100 units of capital, so (Ē, K) = (100, 100). Firm X can produce output good X using labor and capital. The firm's technology is described by the following continuous and differentiable production function: fx(lx, kx) = alx + (1 − a)kx,

Consider a 2x2 production economy with two firms, X and Y, and two factors of production, labor L and capital K. The total endowment of factors in the economy is 100 units of labor and 100 units of capital, so (Ē, K) = (100, 100). Firm X can produce output good X using labor and capital. The firm's technology is described by the following continuous and differentiable production function: fx(lx, kx) = alx + (1 − a)kx,

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

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