Question

You own a farm, you hire labor and capital to produce apples. The marginal product of the last unit of labor input is 15 and the marginal product of the last unit of capital input is 45. The market wage for labor is $8. If you are using the optimal combination of inputs, then the price of capital is _______.

a. $45
b. $3
c. $24
d. $360

Answer 1

C-$24

Step-by-step explanation:

At optimal combination of inputs that is at the equilibrium level the ratio of marginal productivity of labor to the marginal productivity of capital is equal to the ratio of price of labor(wage) to the price of capital(rent). That is ,

MPL/MPK = W/R

WHERE , MPL = MARGINAL PRODUCTIVITY OF LABOR

MPK = MARGINAL PRODUCTIVITY OF CAPITAL

W = WAGE

R = RENT

SO , AS GIVEN , 15/45 = 8/R

SO , R = 8*3 = $24.

SO ANSWER IS OPTION C.$24

Answer 2

c. $24

Step-by-step explanation:

At the optimal combination, the ratio between the marginal product for the last units of capital and labor must equal the ratio between the price of capital and the price of labor.

If Labor costs $8 and has a marginal product of 15, since capital has a marginal product of 45, the price of capital is:

`(45)/(15)=(C)/(\$8)\\ C=\$24`

Price of capital is $24.