#### Question Details

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

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**The Question**

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

Q = 10L ? 0.5L^{2}

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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DATE ANSWEREDOct 14, 2020

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