You are an efficiency expert hired by a firm in the clothing industry that uses

Question

You are an efficiency expert hired by a firm in the clothing industry that uses machines (K) and workers (L) as inputs. The firm has estimated that the marginal product of labor is MPL = 120 - 6 L, while the marginal product of capital is MPK = 50 - 5 K. The firm is currently using 16 units of L and 7 units of K. If w = $20, r = $15 then..

a. the firm is minimizing the cost of producing the given quantity of output.

b. the firm should use less L and more K to minimize the cost of producing the given quantity of output.

c. the firm should use less K and more L to minimize the cost of producing the given quantity of output   

d.; the firm is profit maximizing but not cost minimizing

Explanation / Answer

a. the firm is minimizing the cost of producing the given quantity of output.

as MPL = 120 - 6 L , after L=16 , MPL =24 ,that is > wage rate = $20, for L=17,MPL =18 that is less than what have u paid to the 17th man,
and MPK = 50 - 5 K ,at K=7 ,MPK =15,exactly equals to rent = $15, after that greater K will have MPK less than rent,
so
COST =wl+rk =16*20+15*7=425 is minimzed   

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