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 maximazes the level of output

B) the level of employment that maximazes APL and the maximum APL

Answer 1

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

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

$MPL=\dfrac{dQ}{dL}\\[0.3cm] MPL = 120,000L– 3000L^2=0\\[0.3cm] L(120,000– 3000L)=0\\[0.3cm] 120,000– 3000L=0\\[0.3cm] 3000L=120,0000\\[0.3cm] L^*=\dfrac{120,000}{3000}=40$

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

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

The average product is;

$AP=\dfrac{Q}{L}\\[0.3cm] AP=60,000L-1000L^2$

Therefore;

$60,000L-1000L^2=120,000L-3000L^2\\[0.3cm] 4000L^2=60000L\\[0.3cm] 4000L=60000\\[0.3cm] L=\dfrac{60000}{4000}=15$

The maximum average product is equal to;

$AP=60,000(15)-1000(15)^2\\[0.3cm] AP=675,000$