PRODUCTION AND COSTS
Practice problems -- Answer Key

1. The "Greasy Wrench" shop specializing in auto repairs rents a building at the corner of 77th and Moonawalker. In the short run, it can vary its output (the number of cars fixed) only by varying the number of mechanics it employs. Each Greasy Wrench employee is paid a fixed wage.
Over the years, Wu Wei, the owner of "Greasy Wrench", has tried hiring different numbers of workers. The data about the average productivity of each worker (also known as the Average Product of Labor) for each number of workers are given in the table below.
Number of workers
Average productivity
Total Product
Marginal Product
1
5
5
5
2
7
14
9
3
10
30
16
4
11
44
14
5
10
50
6
6
9
54
4

a. Complete the table by calculating the Total Product of Labor (total output of the firm) and Marginal Product of Labor corresponding to each number of workers.

See the table. TP = (AP) times (Number of workers); MP is the difference between two successive numbers in the TP column.

b. At which worker does the Law of Diminishing Marginal Returns start working? How do you know?

Law of DMR starts working when MP starts decreasing. As we can see from the table, it happens when the firm hires the fourth worker (an alternative answer - "after the firm hires the third worker"; phrasing it either way is fine).

c. Using the Greasy Wrench example, explain why every firm, as it hires more people in an attempt to increase its output, will sooner or later hit the range of diminishing marginal returns.

Law of DMR is present only in the short run, when some of the firm's inputs are fixed. Greasy Wrench has limited space (and probably fixed amount of equipment). As a result, as more workers are hired, there will eventually be shortage of space, or equipment, to work with. The capital-labor ratio will no longer be optimal, and the increase in the output attributed to an additional worker starts to decrease.

d. When Mr. Wei's son looked at the table, he said to his dad: "Hiring 5th and 6th person makes no sense!" Do you agree? Explain.

The fifth worker does not add as much to the output as the fourth worker does. However, this does not necessarily mean that hiring him is a bad idea. Once again, everything will depend on how much a worker costs and what is the dollar value of his marginal product. So Mr. Wei Junior may be wrong.

e. Currently, "Greasy Wrench" employs 3 workers, each of whom is paid $200 a day. Determine the average labor cost of repairing a car.

3 workers cost the firm 3 times $200 = $600. That is our total labor cost. To determine the average cost, we need to divide total cost by the number of cars fixed. With three workers employed, 30 cars are fixed daily. The average labor cost of fixing a car = $600/30 = $20.

2. The information about the costs of a firm is given below.

Output
AFC, $
AVC, $
1
50.00
100.00
2
25.00
80.00
3
16.67
66.67
4
12.50
65.00
5
10.00
68.00
6
8.37
73.33
7
7.14
80.00
8
6.25
87.50

Answer the following questions:

a. What is the firm's fixed cost?

FC = AFC x Q, and it doesn't matter which row of the table we take data from. For instance, $50 x 1 = $50, and $6.25 x 8 = $50.

b. If the firm produces five units, what is the average total cost?

ATC = AFC + AVC. For 5 units of output, ATC =$10 + $68 = $78.

c. What is the total cost of producing four units?

TC = ATC x Q = (AFC+AVC) x Q. For 4 units of out put, TC = ($12.50 + $65) x 4 = $310.
Another way would be to calculate VC = $65 x 4 = $260 and it to FC = $50 obtained in part a to get TC = $310.

d. If the firm closes down and produces no output, what will be its total cost?

No output - no variable cost. The firm's cost will then be limited to its fixed cost, TC = FC = $50.

e. If the firm decides to increase its output from 6 to 7 units, by how much will its total cost increase?

One way is to calculate the total cost of 6 units and of 7 units following any of the procedures in part c and then find the difference. A somewhat shorter way is to recognize that FC does not depend on output, and calculate the marginal cost of the 7th unit as MC(7) = VC(7) - VC(6) = AVC(7) x 7 - AVC(6) x 6 = $80 x 7 - $73.33 x 6 = $560 - $440 = $120.

3. Imagine a firm using only one variable input. When the Marginal Product of using every next unit of this input is decreasing, the Marginal Cost (MC) of every next unit of output will be necessarily increasing. -- True or False?

True. MC = (Price of Input)/MP - see slide 134. Since the price of input is constant, a decrease in MP will cause MC to increase.

4. Which of the following will cause the average fixed cost curve of making cigarettes to shift?
a) A $5 million penalty charged to each cigarette maker.
b) A $1 per pack tax on cigarettes.
c) A $3 per hour wage increase in tobacco industry.
d) An increase in the demand for cigarettes.

5. True or False? The short run is the time period in which the level of output is fixed.

False. In the short run, some inputs are fixed while some are variable. A change in the amount of variable inputs used will cause the output to increase.
Another way to look at it is: if everything is fixed and we cannot change it, why worry about it and study it?

 



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