Question

Problem 05-01 A firm can manufacture a product according to the production function: Q=F(K.L) = 3/4 1/4 a. Calculate the average product of labor, AP, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. Instruction: Round your responses to 3 decimal places. What is the average product of labor when the firm uses 256 units of labor? b. Find an expression for the marginal product of labor, MP4, when the amount of capital is fixed at 81 units. Instruction: The second response is the exponent on L in the expression. Round your responses to 2 decimal places. MPL = D O Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. Instruction: Round your responses to 3 decimal places. MPL when L = 16:D MPL when L = 81: D C. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labor at $50 per unit, how many units of labor should the firm hire in order to maximize profits? Instruction: Enter your response as a whole number.

Answer 1

Q = F(K, L) = k 3/4 '' 314 when k=81 L=16 APL = (817% (16) 3/4 - [883%4 124) = 33 23 APL = 27 = 3.375

when L=256 k=8 I APL = (81) 314 (256) 3/4 = (3) 3/4 (4") 3/4 = 1393 u3 = 2.7 64 APL = oual MPL = da TP het 12h17 4 = Au N

when L=81 MPL = 27 1817-4 = 27 & 3") -34 27 A 1 u 27 MPL = 0.25 Waso P=200 =81 APL = 27. 1314 an optimal condition of Labor hiring MPL + P = wage rate 27 314 x 200 = so. 27x200 - L3/4 uxso

27 x200 200 1314 = 27 L = (27) 9/3 L = [(3²) 37" L = [3 ] L =81 Firm hould hire Hence 81 units of Labor,