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Chapter 7: Q2. (page 280)

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 firm has a fixed production cost of \(5000 and a constant marginal cost of production of \)500 per unit produced.

  1. What is the firm鈥檚 total cost function? Average cost?

  2. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.

You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q = 5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r = \(10,000 per week, and each team costs w = \)5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design.

  1. What is the cost function for your plant鈥攏amely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output?

  2. How many teams are required to produce 250 engines? What is the average cost per engine?

  3. You are asked to make recommendations for the design of a new production facility. What capital/ labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q?

Joe quits his computer programming job, where he was earning a salary of \(50,000 per year, to start his own computer software business in a building that he owns and was previously renting out for \)24,000 per year. In his first year of business he has the following expenses: salary paid to himself, \(40,000; rent, \)0; other expenses, $25,000. Find the accounting cost and the economic cost associated with Joe鈥檚 computer software business.

Suppose that a firm鈥檚 production function is q = 10L1/2K1/2. The cost of a unit of labor is \(20 and the cost of a unit of capital is \)80.

  1. The firm is currently producing 100 units of output and has determined that the cost-minimizing quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines.

  2. The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this graphically and find the firm鈥檚 new total cost.

  3. Graphically identify the cost-minimizing level of capital and labor in the long run if the firm wants to produce 140 units.

  4. If the marginal rate of technical substitution is K/L, find the optimal level of capital and labor required to produce the 140 units of output.

In the average cost curve, there is a point where production reaches a minimum. What is that minimum called?
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