The manager of a national retailing outlet recently hired an economist to estima
ID: 1251698 • Letter: T
Question
The manager of a national retailing outlet recently hired an economist to estimate the firm's production function. Based on the economist's report, the manager now knows that the firm's production function is given by Q=K^(1/2) L^(1/2) and that capital is fixed at 1 unit.a. Calculate the average product of labor when 9 units of labor are utilized.
b. Calculate the marginal product of labor when 9 units of labor are utilized.
c. Suppose the firm can hire labor at a wage of $10 per hour and output can be sold at a price of $100 per unit. Determine the profit-maximizing levels of labor and output.
d. What is the maximum price of capital at which the firm will still make nonnegative profits?
Explanation / Answer
A. Q=K^(1/2) L^(1/2) Q=1^(1/2) 9^(1/2) Q = 3 B. Q=K^(1/2) L^(1/2) MPL = (1/2)*(K/L)^(1/2) MPL = (1/2)*(1/9)^(1/2) MPL = 1/6 C. For profit maximization: MPL/w = MPK/r [(1/2)*(K/L)^(1/2)]/[(1/2)*(L/K)^(1/2)] = w/r (K/L)^(1/2)/(L/K)^(1/2) = 10/r K/L = 10/r 1/L = 10/r L = r/10 Q=K^(1/2) L^(1/2) Q=(r/10)^(1/2) D. Let's call profit V. V = P*Q - C C = wL + rK C = 10*(r/10) + r C = 2r V = 100*(r/10)^(1/2) - 2r > 0 100*(r/10)^(1/2) > 2r (r/10)^(1/2) > r/50 50/(10^(1/2)) > r/(r^1/2) 50/(10^(1/2)) > r^(1/2) r < (50^1/2)/(10^(1/4)) r < 14.058Related Questions
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