Question

1. A firm is using 650 units of labor and 150 units of capital to produce 10,000 units of output.  At this combination the marginal product of labor is 20 and the marginal product of capital is 25. The price of labor is $10 and the price of capital is $15.  

a) The MP per dollar of labor is _________ and the MP per dollar of capital is _________.

b) The firm can increase labor by one unit and decrease capital by _________ units while keeping output constant.  This will ____________ (increase, decrease, not change) cost by _________.

c) If the firm increases labor and reduces capital the marginal product of labor will ____________ (rise, fall, remain the same), while the marginal product of capital will ____________ (rise, fall, remain the same).

d) To produce the current output at the minimum cost the firm will increase ____________ and decrease ____________ until the MP_L/MP_Kequals _________.

Answer 1

a. The MP per dollar of labor is = marginal product of labor /  price of labor = 20/ 10 =$2

The MP per dollar of capital is = marginal product of capital/  price of capital = 25/15 = 1.67

b.  The firm can increase labor by one unit and decrease capital by 0.8 units [20/25].

This will decrease cost by 2[ 15*0.8 -10].

c.If the firm increases labor and reduces capital the marginal product of labor will increase. [ Assuming a stage of increasing returns]

while the marginal product of capital will fall.

d. To produce the current output at the minimum cost the firm will increase labor and decrease capital until MPL/ MPK equals 0.67 [ 10/15]