CHAPTER

7 Analysis of Costs CHAPTER OVERVIEW AND TEACHING TIPS

This chapter brings into focus the wide range of cost measures used by economists: total cost, fixed cost, variable cost, average total cost, average fixed cost, average variable cost, and marginal cost.

Minimum production costs for a firm are represented along a total cost schedule, which is a function of the level of output. Inputs used in their least-cost combination link the production function with the cost curves, and it is the ability to adjust the employment of inputs that provides the distinction between the two components of short-run total cost: variable cost and fixed cost. The major objective here is for students to obtain a solid understanding of an economist’s perspective of cost accounting, so that subsequent descriptions of market structure will make sense. The student is expected to use tables and diagrams to develop an understanding of both specific examples and more general representa- tions of cost concepts.

Chapter 7 also provides a brief introduction to accounting practices. The introduction here is short, covering only two basic tools—the balance sheet and the income statement. The balance sheet is a snapshot of financial health; it reflects the economic condition of an economic entity at some prescribed point in time. The income statement, by way

of contrast, is a motion picture, reflecting growth over a given period of time; it describes the path a firm takes between two different balance sheets.

LEARNING OBJECTIVES

1. Define and describe total cost, fixed cost, variable cost, marginal cost, and average cost, explaining what these measures of cost are designed to reflect and how they are related to one another.

2. Derive the associated average and marginal cost statistics from total, fixed, and variable cost.

3. Explain the link between productivity and cost.

4. Demonstrate precisely why marginal cost always intersects average cost at the minimum of any U-shaped average cost curve.

5. Demonstrate why production costs are minimized when inputs are hired in combinations such that the ratios of their marginal products to their prices are all equal.

6. Explain carefully the information that a balance sheet is intended to convey. List the major categories appearing on the two sides of a balance sheet, and indicate the meaning (or definition) of each of those categories.

7. List the major items appearing on an income statement. Indicate the information that an income statement is intended to convey.

8. Explain the role of depreciation and opportunity cost in the correct and accurate construction of an income statement.

9. Define the term opportunity cost and apply it to management decisions made by firms and individuals

SUGGESTED ANSWERS TO QUESTIONS IN THE TEXT

1. a. .344 b. At the end of 1959 his average was .346. His average for 1960 was .316. Since his average in 1960 was below his lifetime average the 1960 average pulled his lifetime average down. 2. MC and AVC do not change; TC, AC, and AFC shift up. Minimum occurs where MC = AC = $60 at 5 units.

29

30 CHAPTER 7: ANALYSIS OF COSTS 3. AC above (below) MC means that the next increment lowers (increases) the average; i.e., AC is falling (climbing).

Only when MC = AC is AC neither rising nor falling; i.e., it is at its minimum.

4. With a volunteer army the government must be concerned about attracting soldiers. People will agree to enlist

only when the wages they are paid cover their opportunity costs. If service is compulsory, the government has no such constraints on its wage scheme.

5. a. Fixed cost equals 15 ? $12 = $180. MC is the cost of the labor required for each unit increase in output: $30,

$25, $20, $30, $50, $70, $90. Variable cost is total labor times the wage: $30, $55, $65, $l05, $l55, $225, $315. b. Doubling the wage increases AC and MC (doubles, in fact, MC but not AC).

c. Doubling productivity cuts MC and AC in half. (Factor prices and productivity both influence cost curves.)

6. a. Average costs are minimized when marginal cost equals average cost; AC is falling where MC is minimized. b. AFC = FC/output; FC is fixed so as output increases AFC falls.

c. AC is rising whenever MC>AC, but AC is falling when MC<AC, even if MC is rising.

d. The absence of a market does not imply the absence of value.

e. The least-cost rule collapses to this only in very special circumstances. The firm minimizes costs when the

ratios of marginal product to input price are equal for all inputs.

7. The income statement would look something like:

Net sales $10 million

Less: costs $9

million Net income $1

million Less: dividends $0

Addition to retained earnings $1 million

8.

Assets Liabilities and net worth

1999 2000 1999 2000

Liabilities 0 Net worth $50 $51 Total $50 $51 Total $50 $51

DISCUSSION QUESTIONS

1. Explain what is meant by the terms fixed cost, variable cost, marginal cost, and average cost.

2. Define the following concepts of costs and discuss how they are related to one another: TC, VC, FC, MC, AC, AFC,

AVC.

3. Why is it that the MC curve always intersects the AC curve at the minimum point of the AC curve? Why is this

important?

4. “Opportunity cost is a construction of academia that has no relevance to the daily life of a firm, an entrepreneur, or

the average individual.” Discuss this statement and provide examples to illustrate your arguments.

5. What is the purpose of the income statement? What steps are necessary to translate a figure for sales into a figure

for net earnings after taxes? A figure for sales to a figure for retained earnings? Explain.

6. What is depreciation? Outline several ways in which it might be computed for accounting purposes and for tax pur-

poses. Can different tax accountings actually favor more rapid growth for a firm? Explain.

7. Does an income statement always provide a true summary of a firm’s cash transactions? Why or why not?

8. What does a balance sheet show? Describe how the fundamental accounting identity comes into play.

9. “The law of diminishing returns is a production principle; hence it has nothing to do with the cost curves.” Is this

statement true? Discuss.

10. What are the opportunity costs of a new parking garage that your university is considering building? Explain.

11. Is it true that in the long run fixed costs are always zero? Explain why or why not.

ESSAY QUESTIONS

1. Suppose that it is known that FC = $10 and that TVC = 0, 1, 5, 8, 15 for Q = 0, 1, 2, 3, and 4, respectively. Derive a

production table with columns depicting TC, FC, VC, MC, AC, AFC and AVC.

CHAPTER 7: ANALYSIS OF COSTS

31

2. Draw a U-shaped AC curve and then draw its corresponding MC curve. Describe the relationship between these

two curves. If marginal cost is rising, must it be above average costs?

3. Define the term marginal cost. What is the relationship between diminishing returns and the marginal cost curve?

Explain.

4. How is AC computed? How do AFC and AVC differ? Illustrate these relationships graphically.

5. Why should price equal opportunity costs in a well-functioning market?

6. “The concept of marginal cost has great importance for welfare economics. The resources of

society are being efficiently allocated and used only if there is an equality of marginal costs across goods produced everywhere in the country.” Discuss why this statement is true.

7. a. What is a balance sheet? Explain what it means for a balance sheet to balance.

b. What is an income statement? How, if at all, is it related to the balance sheet?

c. Does a year-end addition to earnings retained in a business necessarily imply an equal

increase in the company’s cash? Why or why not?

8. The balance sheet of Simplified Corporation contains the following items: common stock $8000, inventory $700,

cash $500, accounts payable $1000, plant and equipment (less allowance for depreciation) $7000, bonds payable $3000.

a. Calculate retained earnings (the only item missing above).

b. What other information would you need to calculate Simplified Corporation’s net earnings after taxes?

c. Arrange these items in proper balance-sheet form.

9. An oil company buys a tanker at a cost of $200 million. It is estimated that the tanker will be obsolete in 8 years

and will have a scrap value of $1.6 million.

a. If the straight-line method of depreciation is used, how much depreciation will be charged each year on the income statement?

b. How will this asset be shown on the balance sheet at the end of 5 years?

10. Particular Engines Ltd. is incorporated as of January 1, 1985. It sells 10,000 shares of common stock at

$100 per share. It buys new a plant and equipment worth $500,000 and pays $250,000 for a small engine-manufacturing company whose net assets, consisting only of plant and equipment, are valued at $200,000. During the year, the company purchases $200,000 of material, pays wages of $100,000, and makes sales of $500,000-all in cash. It depreciates its plant and equipment on an assumed average life of 10 years. At year end, its inventory is valued at

$50,000, and a dividend is paid of $50,000.

Draw up (a) an income statement for 1985 for Particular Engines Ltd. and (b) a balance sheet as of December 31, 1985.

11. a. Arrange the following items into a balance sheet, under the appropriate headings and subheadings. (Figures

refer to thousands of dollars.)

Accounts Payable = 80 Accounts receivable = 120

Cash = 40 Common stock = 150

Inventories = 60 Plant and equip = 200

Depreciation allowance = 70 Retained earnings = ?

Bonds payable = 50

b. What is the net worth of the company?

c. No dividend was paid during the last year. A stockholder suggested that retained earnings being what they were, a dividend of $50 should be declared. Comment.

d. Bond interest of $5 was paid during this last year. Another stockholder suggested that if dividends were being passed over, then bond interest ought not to have been paid either. Comment on this suggestion.

12. Discuss the sense in which depreciation allowances on the asset side of the balance sheet do or do not represent

an available pool of liquid assets to retire debt or replace equipment. Compare and contrast a sinking fund to retire debt with an allowance for depreciation.

13. Explain the relationship between MC and AC. Explain what happens when MC equals AC.

14. Explain what happens to AC when MC is greater than AC.

15. Is it possible for AC to be falling and MC to be increasing?