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# Calculating average and marginal costs

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Policy Associates, Inc. (PA) is a policy analysis firm that produces policy reports hiring analysts who scrutinize datasets. Its production function is :

Q(D,L)=(0.10)D^(1/2)L^(3/4)

Where Q is the number of policy reports it produces, L is the number of policy analysts it hires, and D is the number of datasets purchased.

A) Are the returns to scale of PA increasing, decreasing, or constant?
B) What is the marginal product of labor (L) used by the firm? Does this marginal product increase/decrease/ remains constant when L increases? Provide a brief explanation for your result.
C) What is the marginal product of datasets (D) used by the firm? Does this marginal product increase/decrease/remain constant when D increases? Provide a brief explanation for your result.

Assume that the price of each dataset is \$1 and the wage of each unit of policy analyst labor is \$2. Further assume that the firm has available 100 datasets and its managers do not plan to buy any other datasets in the near future. They are, however, willing to hire public policy graduates as analysts.

D) Write expressions to illustrate:
i) How many policy analysts should PA hire in order to produce 100 policy reports?
ii) What is PA's total cost as function of its output, Q?
iii) What is PA's short run average cost?
iv) What is PA's short run marginal cost?
v) What is PA's short run average fixed cost?
vi) What is PA's short run average variable cost?

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#### Solution Preview

a) Q(D,L)=0.10*D^(1/2)*L^(3/4)=0.10*D^0.5*L^0.75
Sum of exponents=0.5+0.75=1.25
Sum of exponents is greater than 1, we can say that firm is experiencing increasing returns to scale.

b) Q(D,L)= 0.10*D^0.5*L^0.75
Marginal Product of labor=MPL=dQ(D,L)/dL
=0.10*0.75*D^0.5*L^(0.75-1)
=0.075*D^0.5*L^(-0.25)
=0.075*D^0.5/L^0.25

As is clear from the above expression marginal ...

#### Solution Summary

Solution describes the steps to calculate marginal product, average and marginal costs in the given case.

\$2.19