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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:

C_L = $10 / unit                  MP_L = 25

C_M = $2 / unit                   MP_M = 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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Oct 14, 2020

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