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a. Fill in the blanks in the table below.

Units of Output
Fixed Cost
Variable Cost
Total Cost
Marginal Cost
Average Fixed Cost
Average Variable Cost
Average Total Cost
0

100



1

125



2

145



3

157



4

177



5

202



6

236



7

270



8

326



9

398



10

490



b. Draw a graph that shows marginal cost, average variable cost, and average total cost, with cost on the vertical axis and quantity on the horizontal axis.

Short Answer

Expert verified

a. The missing values from the table are given below:

Units of Output
Fixed Cost
Variable Cost (=TC-100)
Total Cost
Marginal Cost
Average Fixed Cost (=FC/Units of output)
Average Variable Cost (=VC/Units of output)
Average Total Cost (=TC/Units of Output)
01000100
---
1100
2512525 (= 125-100)
10025125
2100
4514520 ( = 145-125)
5022.572.5
3100
5715712 ( = 157-145)
33.331952.33333333
4100
7717720( = 177-157)
2519.2544.25
5100
10220225 ( = 202-177)
2020.440.4
6100
13623634 ( = 236-202)
16.66722.66666667
39.33333333
7100
17027034 ( = 270-236)
14.28571429
24.28571429
38.57142857
8100
22632656 ( = 326-270)
12.528.2540.75
9100
29839872 ( = 398-326)
11.11111111
33.11111111
44.22222222
10100
39049092 ( = 490-398)
103949

b. The marginal cost, the average variable cost, and the average total cost curves are as follows:

Step by step solution

01

The calculation for missing values of the table

The total cost for any number of outputs is the aggregate of fixed and variable costs.

TC = FC + VC

The fixed cost does not variate with the units of output. It remains constant in the short run even if the output produced is zero or larger鈥攆or example, the amount invested in capital. The capital does not change in the short run, even if the firm stops producing suddenly or expands its production.

The variable cost depends on the output produced. Suppose the firm increases its production, the variable cost will increase, and vice-versa.

Marginal cost is the change in total cost by an additional unit. For instance, if the total cost of producing 5 units is $100 and 6 units is $120. The marginal cost of producing the 6th unit is $20 (= $120 - $100).

The average fixed cost, average variable cost, and average total cost are per unit of output. As the units of output increase, the average costs decline.

The values for all the costs at successive units of output are given below.

Units of Output
Fixed Cost
Variable Cost (=TC-100)
Total Cost
Marginal Cost
Average Fixed Cost (=FC/Units of output)
Average Variable Cost (=VC/Units of output)
Average Total Cost (=TC/Units of Output)
01000100
---
1100
2512525 (= 125-100)
10025125
2100
4514520 ( = 145-125)
5022.572.5
3100
5715712 ( = 157-145)
33.331952.33333333
4100
7717720( = 177-157)
2519.2544.25
5100
10220225 ( = 202-177)
2020.440.4
6100
13623634 ( = 236-202)
16.66722.66666667
39.33333333
7100
17027034 ( = 270-236)
14.28571429
24.28571429
38.57142857
8100
22632656 ( = 326-270)
12.528.2540.75
9100
29839872 ( = 398-326)
11.11111111
33.11111111
44.22222222
10100
39049092 ( = 490-398)
103949
02

The marginal cost, the average variable cost, and the average total cost curves

As the output increases, the marginal cost, the average total cost, and the average variable cost eventually decline but ultimately increase. Thus, all the cost curves are non-linear in shape.

Also, the marginal cost increases rapidly at higher levels of output.

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Most popular questions from this chapter

A chair manufacturer hires its assembly-line labor for \(30 an hour and calculates that the rental cost of its machinery is \)15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. If the firm is currently using 3 hours of labor for each hour of machine time, is it minimizing its costs of production? If so, why? If not, how can it improve the situation? Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital.

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output.

  1. How does this tax affect the firm鈥檚 fixed, marginal, and average costs?

  2. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm鈥檚 fixed, marginal, and average costs?

Suppose the long-run total cost function for an industry is given by the cubic equation TC = a + bq + cq2 + dq3. Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of a, b, c, and d.

Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm鈥檚 expansion path.

In a famous article (J. Viner, 鈥淐ost Curves and Supply Curves,鈥 Zeitschrift fur Nationalokonomie 3 (Sept. 1931): 23鈥46), Jacob Viner criticized his draftsman who could not draw a family of short-run ATC curves whose points of tangency with the U-shaped LAC curve were also the minimum points on each SAC curve. The draftsman protested that such a drawing was impossible to construct. Whom would you support in this debate, and why? Include a diagram in your answer.

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