# Answer to Question #73964 in Microeconomics for Zulfiqar Ali

Question #73964

Given the production function

Q = AKaLpNb

where Q is the rate of output and K, L, and N represent inputs of capital, labor, and land, respectively, determine

a. The specific conditions (i.e., values of a, p\ and b) under which returns to scale would be increasing, constant, and decreasing.

b. The equation for the marginal product function for each input

Q = AKaLpNb

where Q is the rate of output and K, L, and N represent inputs of capital, labor, and land, respectively, determine

a. The specific conditions (i.e., values of a, p\ and b) under which returns to scale would be increasing, constant, and decreasing.

b. The equation for the marginal product function for each input

Expert's answer

Q = A*K^a*L^p*N^b.

a. The specific conditions (i.e., values of a, p and b) under which returns to scale would be: - increasing: a, p, b > 1,

- constant: a, p, b = 1,

- decreasing: a, p, b < 1.

b. The equations for the marginal product functions for each input are:

MPK = Q'(K) = a*A*K^(a - 1)*L^p*N^b,

MPL = Q'(L) = p*A*K^a*L^(p - 1)*N^b,

MPN = Q'(K) = b*A*K^a*L^p*N^(b - 1).

a. The specific conditions (i.e., values of a, p and b) under which returns to scale would be: - increasing: a, p, b > 1,

- constant: a, p, b = 1,

- decreasing: a, p, b < 1.

b. The equations for the marginal product functions for each input are:

MPK = Q'(K) = a*A*K^(a - 1)*L^p*N^b,

MPL = Q'(L) = p*A*K^a*L^(p - 1)*N^b,

MPN = Q'(K) = b*A*K^a*L^p*N^(b - 1).

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