Question

1) The marginal product of labor in the production of oatmeal raisin cookies is 75 cookies per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/10. What is the marginal product of capital? (5 pts)

2) A firm has a fixed production cost of $10,000 and a constant marginal cost of production of $200 per unit produced. What is the firm’s total cost function? What is its average cost function? (8 pts)

Answer 1

Answer 1 :-

Let,

Marginal rate of technical substitution of hours of labor for hours of machine capital = MRTS

Marginal product of capital = MPC

Marginal product of labor = MPL

In order to calculate MPC, we have to use following relation ;

MRTS = MPL/MPC

1/10 = 75/MPC

MPC = 75/0.1 = 750

Hence, the marginal product of capital will be 750.

Answer 2 :-

Fixed Cost (FC) = $10,000

Marginal cost (MC) = $200

Variable cost (VC) = $200Q

Total cost (TC) = FC + VC

TC = 10,000+200Q

Thus, the total cost function will be TC(Q) = 10,000 + 200Q

Now for average cost function AC(Q) ;

AC(Q) = TC(Q)/Q

AC(Q) = (10,000 + 200Q)/Q

AC(Q) = (10,000/Q) + 200

Thus the average cost function will be AC(Q) = (10,000/Q) + 200