Question

A firm has an MPL=(K^0.5)/(L^0.5). Given K=100, L=121, Wages = 10, price of output=2
1. Is the firm operating efficiently
2. What is the optional rate of labor

Answer 1

1. The firm is operating efficiently if

$MPL/w = MPK/r,$

where r is rate of capital, MPK is marginal product of capital.

In our case

$MPL/w = \frac{100^{0.5}}{121^{0.5}}÷10 = 0.09.$

So, the firm is operating efficiently if MPK/r = 0.09.

2. To find out if the amount of labor is optimal we need to know MPK and r.