Practice Problems for Production Costs

Below are additional practice problems for issues related to production costs.

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.  Sparkle Car Wash is a profit-maximizing firm with the following production information.

a)  With which worker is the marginal product maximized?

b)  At which worker do we first see diminishing returns set in?

Number of Workers

Number of Cars Washed per Day

0 0
1 15
2 35
3 60
4 75
5 85
6 80

 

Answer to “a”:  To fill this in, note that the first worker washed 15 cars. Once the second worker is added, 35 cars are washed in total. To find the marginal cars washed by the second worker, you’ll subtract 15, the total before you added the second worker, from 35, the new total. This will reveal 20 as the marginal cars washed by the second worker. Then, you simply need to do this over and over again until you’ve run out of workers. After doing so, you see that the marginal product is maximized at 25 when you’ve added the third worker.

Answer to “b”:  Diminishing returns first sets in when the fourth worker is added. Productivity was highest at three workers (  60 /3) =  20, but went down when the fourth worker was added ( 75/4) = 18.75

3.   Fill in the table below.  Land rents for $500 per acre (total fixed cost).  Fertilizer costs $50 a ton.

Tons of Fertilizer Bushels of Wheat Average Product Marginal Product TFC TVC TC AVC ATC
1 40
2 100
3 150
4 190
5 220
6 240
7 250
8 255

 

Answer:

Tons of Fertilizer Bushels of Wheat Average Product Marginal Product TFC TVC TC AVC ATC
1 40 40 40 $500 50 $550 $1.25 $13.75
2 100 50 60 $500 100 600 1.00 6.00
3 150 50 50 $500 150 650 1.00 4.33
4 190 47.5 40 $500 200 700 1.05 3.68
5 220 44 30 $500 250 750 1.14 3.41
6 240 40 20 $500 300 800 1.25 3.33
7 250 36 10 $500 350 850 1.40 3.40
8 255 12 1 $500 400 900 1.57 3.53
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