Question

Suppose capital and labour are perfect substitutes for producing widgets and that it takes 1 unit of capital or 3 units of labour to produce one widget. If the price of labour is $4 and the price of capital is $16, how much labour and capital should a firm use to produce 30 widgets? Explain.

Answer 1

Answer

The production function is the form of

Q=K+L/3

K=1 and L=0 then Q=1

K=0 and L=3 then Q=1

As provided in the information given.

The firm uses the input with the higher marginal product per dollar.

MPK=1 and MPL=1/3

Marginal product per dollar =MP/price of MP

MPK per dollar =1/16

MPL per dollar =(1/3)/4=1/12

So the marginal product per dollar is higher from labor, and the firm only use labor to produce the output

Q=K+L/3

K=0 and Q=30

30=0+L/3

L=30*3

L=90

the firm will employ 90 labors and zero capital units.