Answer to Question #230615 in Microeconomics for Epherem teketel

Question #230615
Suppose the production function is given by Q(L,K)=L^1/2K^1/2 Assuming capital is fixed ,find APL and MPL.
1
Expert's answer
2021-09-02T10:46:02-0400

Given,

Production function:

Q(L,K)=L12K12Q(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=QLAPL=L12K12LAPL=K12L12APL=(KL)12APL=\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=QLMPL=12L12K12MPL=K122L12MPL=\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.


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