Question

QUESTION 10 Acme Eggs produces eggs. Acme has estimated this production function for its eggs: Q = 10L".SK.) The marginal product of labor is given by MPL =5L-0.5 K.S and the marginal product of capital is given by MPx=520.5 -0.5 where Q = output measured in eggs, L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $15 per hour and considers the relevant rental price for capital to be $20 per hour. a. Provide an expression for the firm's isocost line associated with a total cost of $600 and calculate the slope of the isocost line (assuming labor is on the x-axis). b. Determine the optimal capital-labor ratio that Acme should use in egg production. C. Calculate the total output and the quantities of labor and capital that will be used if the firm spends $600 on production.

Answer 1

A) Isocost line :

wL + rK = C

600 = 15L + 20K

Slope = -w/r =- 15/20 = - .75

B) at eqm, MRTS = w/r = 15/20

MRTS = MPL/MPK

= K/L

At eqm, K/L = 3/4

C) for Q = 600

So, 600= 10*√KL

60= √LK

LK = 3600

So ,put K = 3L/4

L*3L/4 = 3600

L = √4800 = 69.28

K = .75*L

= 51.96