Suppose that a firm's production function of output $Q$ is a function of only two inputs, labor (L) and capital $( K )$ and can be written $Q = 25 L K$ with marginal products $M P _ { L } = 25 K$ and $M P _ { K } =$ 25L. Let the wage rate for labor be $w = 1$ and the rental rate of capital be $r = 1$. If the firm produces 100 units of output, how many units of labor will it use?
A)1
B)2
C)3
D)4

Question

Quizplus · Accepted Answer

To produce 100 units, set $Q = 25LK = 100$. With $w = 1$ and $r = 1$, the cost-minimizing condition is $\frac{MPL}{w} = \frac{MPK}{r}$, which simplifies to $K = L$. Substituting $K = L$ into $25LK = 100$ gives $25L^2 = 100$, so $L^2 = 4$, thus $L = 2$.

Suppose That a Firm's Production Function of Output QQQ Is a Function of Only Two Inputs, Labor (L) and a Function

Suppose That a Firm's Production Function of Output $Q$ Is a Function of Only Two Inputs, Labor (L) and a Function