Question

2. Mike's Tires produces tires according to the following production function: q E /2K1/, Suppose the hourly wage is $10 and the rental rate of capital is $20. The price of a tire is $50 a. In the short run, the capital stock is fixed at Ko 1600. How much employment should Mike's Tires choose in the short run? b. What is Mike's Tires profit in the short runi?

Answer 1

(a)

When K = 1600,

q = E^1/2(1600)^1/2

q = 40 x E^1/2

Hiring is optimized when (Output price x MPE) = Wage rate

MPE = dq/dE = 40 x (1/2) / E^1/2 = 20 / E^1/2

50 x (20 / E^1/2) = 10

1000 / E^1/2 = 10

E^1/2 = 100

Squaring,

E = 10,000

(b)

When E = 10,000, q = 40 x 100 = 4,000

Revenue (R) = Output price x q = $50 x 4,000 = $200,000

Cost (C) = wL + rK = 10 x 10,000 + 20 x 1,600 = 100,000 + 32,000 = $132,000

Profit ($) = R - C = 200,000 - 132,000 = 68,000