Suppose for a particular production function that $$M P _ { L } = 36 \left( \frac { K } { L } \right) M P _ { X } = 36 \left( \frac { L } { K } \right)$$ If the price of capital is $5 per unit and the price of labor is $125 per unit, at the cost-minimizing combination of capital and labor the firm should employ:
A)five times as much labor as capital.
B)five times as much capital as labor.
C)125/36 units of capital and 5/36 units of labor.
D)36/125 units of capital and 36/5 units of labor.

Question

Quizplus · Accepted Answer

To minimize costs, a firm should set the ratio of the marginal product of labor to the price of labor equal to the ratio of the marginal product of capital to the price of capital. Given $MP_L = 36(K/L)$ and $MP_K = 36(L/K)$, and the prices of labor and capital, setting $MP_L/P_L = MP_K/P_K$ leads to $36(K/L)/125 = 36(L/K)/5$. Simplifying this equation shows that the firm should employ five times as much capital as labor to minimize costs.

Suppose for a Particular Production Function That MPL=36(KL)MPX=36(LK)M P _ { L } = 36 \left( \frac { K } { L } \right) M P _ { X } = 36 \left( \frac { L } { K } \right)MPL​=36(LK​)MPX​=36(KL​)

Suppose for a Particular Production Function That $M P _ { L } = 36 \left( \frac { K } { L } \right) M P _ { X } = 36 \left( \frac { L } { K } \right)$