Question

Suppose a firm’s production function is Y=f(K,L) and has the following:

Output = 5,000

Wage rate = 40

Marginal product of labor = 5

Labor = 100

Rental rate = 250

Capital = 75

Marginal Product of capital = 20

Price = 10

A. What is the firm’s total revenue?

B. What is the firm’s total cost?

C. What is the profit for the firm?

D. What is the real wage rate for this firm?

E. What is the real rental rate?

F. Suppose the firm is deciding whether or not to expand its factors of production. Do you recommend they hire another worker and/or add another unit of capital? What justification can you show to justify your answers? (Hint: I am looking for a yes or no for each factor and a mathematical justification for why you came to that conclusion)

Answer 1

A) Total revenue = Output * Price = 5,000 * 10 = 50,000

B) Total Cost = Labor Cost + Capital Cost = Wage rate * labor + rental Rate * Capital

= 40*100 + 250*75 = 22,500

C) Total Profit = Total revenue - Total cost = 50,000 - 22,500 = 27250

D) Real Wage Rate = Wage Rate/ Price = 40/10 = 4

E) Real rental rate = Rental rate/Price = 250/10 = 25

F) Ratio of Marginal Product of labor (MPL) to Marginal Product of capital (MPK) = 5/20 = 0.25

Ratio of Capital employed to Labor employed = 75/100 = 0.75

Therefore MPL/MPK < Capital Labor ratio. Therefore firm should hire more capital as capital is underemployed in relation to the employed.

So Hire Capital: Yes

Hire Labor = NO