Assume that a firm produces output using one fixed input, capital, and one variable input, labor. The firm can sell all of the output it produces at a market price of $3 each, can hire all of the workers it wants at a market wage rate $11 each, and has fixed costs of $10. It faces the following production schedule.

Number of Employees Total Output
0 0
1 14
2 26
3 35
4 42
5 46
6 48

(a) In what kind of market structure does this firm sell its output? How can you tell?
(b) In what kind of market structure does this firm hire its employees? How can you tell?
(c) Using marginal revenue product analysis, how many employees should this firm hire to maximize short-run profits? How can you determine that?
(d) Based on your answer in part (c), how many units of output will this firm produce?
(e) At the level of output you identified in part (d), is the firm earning an economic profit, a normal profit, or suffering a loss? How can you tell?

a) perfectly competitive market

b) perfectly competitive market

c) 5 workers

d) 46 units

e) Profit of $73

Explanation:

a) The firm sells its output at the present market price, the firm has control of the market prices therefore this is a perfectly competitive market.

b) The firm can hire all of the workers it wants at a market wage rate, this means that the labor market is also perfectly competitive.

c) We have to first calculate the marginal revenue product (MRP) of each worker. The marginal revenue product of the last worker must be equals his wage rate in order to maximize profits. Hiring new workers as every additional employee adds less to the total revenue than to the costs of the firm.

MRP = Marginal product × Price.

Price = $3

Number of       Total         Marginal             Marginal Revenue

Employees      Output    Product (MP)       Product $ (MRP = MP * P)

0                          0

1                           14                 14                                 52

2                          26                12                                 36

3                           35                9                                  27

4                           42                7                                   21

5                           46                4                                   12

6                            48               2                                    6

The MRP of each of the first 5 employees is higher than their wage rate ($11). The firm should hire 5 workers to maximize profit

d) The output of 5 workers is 46 units

e) Fixed cost = $10

Variable cost = number of workers × wage rate = 5 × $11 = $55

Revenue = output × price per unit = 46 × $3 = $138

Profit = Revenue - variable cost - fixed cost = $138 - $55 - $10 = $73

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