Question

Suppose the short run production function can be represented by Q= 60,000L^2-1000L^3. Then, determine

A) the level labor employement that maximizes the level of output

B) the level of employement that maximizes APL and the maximum APL

Answer 1

Answer (a).

The total output will be maximized when the marginal product is equal to zero.

$MPL= \frac{dQ}{dL}$

$MPL=120000L-3000L^2=0$

$L(120000-3000L)=0$

$120000-3000L=0$

$3000L=120000$

$L=40$

Answer (b):

The average product is maximized when the marginal product is equal to the average product. Average product is:

$AP=\frac{Q}{L}$

$AP=6000L-1000L^2$

$6000L-1000L^2=120000L-3000L^2$

$4000L^2=60000L$

$4000L=60000$

$L= \frac{60000}{4000}=15$

Then maximum average product is:

$AP=60000\times15-1000\times(15)^2$

$AP=900000-225000$

$AP=675000$