Question

 A firm has a Cobb-Douglas production function given as

q=L^0.6K^0.2

Suppose that in the Short run, the mill’s capital (K) is fixed at 32 units and that it can only increase output q by increasing the amount of labour (L)

a. Determine the firms’ SR production function

b. If the firms’ competitive output price is ₵50 find its labour demand curve

c. How many workers does the firm hire if the wage rate is ₵15?

d. What is the MRPL between the 31st and 32nd worker who is hired at the competitive price?

Answer 1

a. In the short run, the mill's capital is fixed at 32 units. So, short-run production function:

$q=L^{0.6}\times K^{0.2}=2L^{0.6}$

b. Labour demand curve is given by $MPL=\frac{W}{P}$

$MPL=\frac{dq}{dL}=1.2L^{-0.4}. \\P=50. So,\\ W=1.2\times50\times L^ {-0.4}=60L^{-0.4}$

c. Wage rate$=MPL\times P$

With $W=15 \space and\space P=50, 60L^{-0.4}=15$

or, L^(0.4)=4

or, L=32.

d. MRPL between the 31st and 32nd worker is $60\times32^{-0.4}=15.$