Question

If a production is Q=250K^0.7L^0.3 determine the marginal product of capital and marginal product of labour when k=50 and L=50

Answer 1

$Q = 2 50K^{0.7} L^{0.3}$

The marginal product of labor = We will have to differentiate the above equation with respect to L

$\frac{dQ}{dL}= 0.7 × 250 K^{0.7}L^{0.3-1}$

 $\frac{dQ}{dL}= 0.7 × 250 K^{0.7}L^{-0.7}$

$\frac{dQ}{dL}=175\frac {K^{0.7 }}{L^{0.7}}$

$K=\ 50$ and $L=\ 50$

Therefore:

Marginal Product of labor= 175.

$Q=250K^{0.7} L^{0.3}$

In order to find the Marginal product of capital, we have to differentiate the equation with respect to K.

Therefore:

$Q=250\times0.7K^{0.7-1} L^{0.3}$

$=\ 175K^{-0.3} L^{0.3}$

$=\ 175\frac{L^{0.3 }}{K^{0.3}}$

Whereas the value of K and L is the same as per the equation, therefore, the Marginal product of capital will be 175