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A firm has the following short-run production function (where L = Labor and Q = Output):

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A firm has the following short-run production function (where L = Labor and Q = Output):

Q = 10L ? 0.5L2

Suppose that the output can be sold for $10 per unit. Further assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.

a) Determine the marginal revenue function (5 points)

b) Determine the value of L that maximizes profits (5 points)

A company uses two variable inputs, labor (L) and materials (M), to produce its output. At the company?s current level of output:

CL = $10 / unit                  MPL = 25

CM = $2 / unit                   MPM = 4

a) Determine whether the firm is operating efficiently, given that its objective is to minimize the cost of producing the given the level of output (5 points)

b) Determine what changes (if any) in the relative proportions of labor and materials are needed to operate efficiently (5 points)

A company has a cost structure described in the table below. Using your knowledge of the types of costs involved in a production process, fill in the blanks in the table.

Quantity produced

Total Cost

Total Fixed Cost

Total Variable Cost

Average Total Cost

Average Fixed Cost

Average Variable Cost

Marginal Cost

0

100

0

-

-

-

-

1

160

2

80

3

65

4

10

5

120

6

40

7

180

8

30

9

421

10

100

 


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A firm has the following short-run production function (where L = Labor and Q = Output):

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