Question

Suppose short run production function of a firm is given by Q = 600L2 - L where Q is the level of output and L is the number of labours employed.

a. Compute optimum labour use for a profit maximizing firm.

b. Over what range of labour does this firm experience increasing marginal product?

C. Over what range of labour does this firm experience diminishing marginal product?

d. Over what range of labour does this firm experience a negative marginal product?

Answer 1

(a)

$q=600l^2-l^3$

Output is maximized when$MPL=\frac{dq}{dl}=0$

$MPL=\frac{dq}{dl}=1200l-3l^2=0.$

$3l\times(400-l)=0$

Either $l=0$ or $(400-l)=0$

$l=0$ or $l=400$

When $l=0,$ $q=0$

When $l=400,$ $q=600\times(400)2-(400)3$

$=32000000$

(b)

Increasing MPL occurs when $\frac{dMPL}{dl}>0$

Setting $\frac{dMPL}{dl}=0$ we get:

$1200-6l=0$

$6l=1200$

$l=200$

$\therefore$ when $0<l<200$ , increasing MPL sets in. In this range, total product increases at an increasing rate with increase in labor.

(c)

Diminishing MPL sets in when $\frac{dMPL}{dl}<0.$ Since $\frac {dMPL}{dl}=0$ when $l=200$ , when $l>200$ , diminishing MPL sets in. In this range, total product increases at a decreasing rate, with increase in labor.

(d)

When $MPL=0, l=400$ , MPL becomes negative. In this range, total product decreases with increase in labor.