Consider the following production function: q=L1/2q=L1/2

Accounting Dec 07, 2020

Consider the following production function: q=L1/2q=L1/2. Derive the marginal product of labor, average cost, and marginal cost when LL = 9 and wage is $8.

Expert Solution

Given: q=L0.5L=9w=$8q=L0.5L=9w=$8

The marginal product of labor (MPL) is:

MPL=∂q∂L=0.5L−0.5=12L0.5MPLL=9=0.16MPL=∂q∂L=0.5L−0.5=12L0.5MPLL=9=0.16

The average cost is:

AC=TCq=wLq=8LL0.5=8(9)0.5=24AC=TCq=wLq=8LL0.5=8(9)0.5=24

The total cost is:

TC=AC×q=24L0.5TC=AC×q=24L0.5

The marginal cost is:

MC=∂TC∂q=12L−0.5=12(9)0.5=4MC=∂TC∂q=12L−0.5=12(9)0.5=4

Average Cost:

Average cost is the cost which is per unit cost of a good. It is a sum of both the average variable cost and average fixed cost. The curve of average cost is U-shaped.

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