Answer to Question #230615 in Microeconomics for Epherem teketel

Question

Suppose the production function is given by Q(L,K)=L^1/2K^1/2 Assuming capital is fixed ,find APL and MPL.

Answer 1

Given,

Production function:

$Q(L,K)=L^{\frac{1}{2}}K^{\frac{1}{2}}$

To find: APL and MPL

APL (Average product of labor): APL refers to the average number of goods produced by each worker.

$APL=\frac{Q}{L}\\APL=\frac{L^{\frac{1}{2}}K^{\frac{1}{2}}}{L}\\APL=\frac{K^{\frac{1}{2}}}{L^{\frac{1}{2}}}\\APL=(\frac{K}{L})^{\frac{1}{2}}$

The above equation shows the APL.

MPL: Marginal product of labor refers to the addition to the total output due to an increase in the labor by one unit.

$MPL=\frac{∂Q}{∂L}\\MPL=\frac{1}{2}L^{\frac{−1}{2}}K^{\frac{1}{2}}\\MPL=\frac{K^{\frac{1}{2}}}{2L^{\frac{1}{2}}}$

The above equation shows the MPL.