Costs, ECON 610



Notes on Costs

Fast Track MBA, Fall 2004

Dr. Edward L. Millner

Phone: 828-1717

email: emillner@vcu.edu

URL: people.vcu.edu/~emillner/FastTrack

Learning Objectives for Costs

After finishing this section of the module you should be able to:

1. Define and calculate total cost, total variable cost, total fixed cost, average total cost, average variable cost, average fixed cost, and marginal cost.

2. State the relationships between average variable and marginal cost and between average total and marginal cost.

3. Calculate average variable cost and marginal cost when given information on wage and average and marginal product, and vice versa.

4. Use the appropriate cost information when making business decisions

5. Define long run average cost, economies of scale, minimum efficient scale, and diseconomies of scale

6. Use information on average variable cost curves and sales volume to determine the optimal scale of plant.

7. Determine whether economies of scope and cost complementarity exist.

8. Use a multi-product cost function to measure the advantages of a merger or acquisition and the disadvantages of a divestiture.

Introduction

• Costs are determined by production

• We will examine the behavior and determinants of costs in both the short and long runs

• Will maintain working assumptions of constant factor prices

Short-Run Costs

• SR is when there is at least one fixed factor

• Simplest example: Q = f(L,K) and K is fixed

Three types of total costs exist in the short run

• (Total) Fixed Cost = expense on fixed factor

o FC = r * K, where r is price for or wage to K

o FC are expenses that must be paid even if Q = 0

o Sunk costs are fixed costs that cannot be recouped

• (Total) Variable Cost = expense on variable factor

o VC = w * L, where w is price for or wage to K

o ( VC = w * ( L

o Presuming that production is efficient has two implications

▪ VC = 0 if Q = 0 because the firm will employ no L if it wants to produce no output

▪ VC increases with Q because the firm must employ more L if it wants to increase Q

• Total Cost = expense on all factors

o TC = FC + VC

o If Q=0 then TC=FC because VC=0

o TC increases with Q because VC increases

Three types of average costs exist in the short run

• Average fixed cost

o AFC = FC / Q

▪ Measures the total fixed cost incurred per unit of output

▪ FC = AFC * Q

▪ AFC decreases as Q increases

o Average variable cost

▪ AVC = VC / Q

• Measures the total variable cost incurred per unit of output

• VC = AVC * Q

▪ If L is the only variable factor then

• AVC = VC / Q = (VC / Q) (L / L) = (VC / L)(L / Q) = (w * L / L) / (Q / L) = w / APL

• AVC moves in opposite direction of APL and vice versa

o Average (total) cost

▪ ATC = TC / Q

• Measures total cost per unit of output

• TC = ATC * Q

• ATC = AFC + AVC

Short-run marginal cost

• MC = ( TC / ( Q = ( VC / ( Q

• MC measures the extra costs the firm incurs when it increases production by one unit of output, all else equal

• ( TC = ( VC = MC * ( Q

• MC may be computed for discrete changes or, with calculus, at a point for infinitesimally small changes

• If L is the only variable factor then

o ( TC = w * ( L

o w = (TC / (L

o MC = ( TC / ( Q = (( TC / ( Q) (( L / ( L) = (( TC / (L) ((L / (Q) =  w / ((Q / (L) = w / MPL

o MC moves in opposite direction of MPL and vice versa

Question #1: Conceptual and Computational Problem 6

Question #2: Conceptual and Computational Problem 4

Question #3: Add columns for FC, VC, TC, AFC, AVC, ATC, and MC to the table in Conceptual and Computational Problem 2. Complete the revised table and answer questions b and c.

Relationships between AVC, ATC, and MC

• Let AC represent either AVC or ATC

o MC > AC if and only if AC increases as Q increases (by a small amount)

o MC < AC if and only if AC decreases as Q increases (by a small amount)

o AC = MC if and only if AC is constant as Q increases (by a small amount)

When making a decision, remember to consider all opportunity costs

• Explicit costs (wages, salaries, bills)

• Risk

• Foregone income, profit, and interest payments

• Differences in risk, danger, and unpleasantness

• Economists include a “normal” profit as a cost.

o Normal profit represents the implicit cost of the resources owned by the owners that are used by the firm

o It is the minimum level of accounting profit that the owners must receive to make them indifferent between owning the firm and the next-best alternative.

Question #4: Consider two otherwise similar jobs: Job A where the accounting ( is $60K and you would work 40 hours per week or Job B where the accounting ( is $61K and you would work 80 hours per week. Which job would you choose? Why?

Question #5: Consider two otherwise similar investment opportunities: Firm A where the accounting ( is $100 per year and you would be required to put up $100 and Firm B where the accounting ( is $200 per year and you would be required to put up $10,000. Which investment would you choose? Why?

Question #6: Problem and Application 14

When making a decision, an analyst should focus on incremental costs and incremental revenue

• Ignore sunk costs when deciding whether or not to exit an industry

• Ignore fixed costs when deciding whether to increase or decrease production in the short run

Question #7: Problem and Application 15

Question #8: Imagine that you are nearing graduation and are trying to decide what to do for the next year. (You have been accepted and will attend law school one year after graduation.) Your discount rate for financial investments is 10% per year. You have prepared yourself to sell frozen food products for the year. You have purchased a refrigerated truck suitable for the task for $25,000 six months ago that you could now resell for $24,000. The only time you would use the truck is for the frozen food business. You believe that after using the truck for a year, you will be able to resell it for $20,000. The following table contains your projected revenues and out-of-pocket expenses.

|Total Revenue |$60,000 |

|Gasoline and Maintenance for Truck |$3,000 |

|Cost of Items Sold |$20,000 |

|Insurance |$3,500 |

|Rent Paid for Freezer Space |$2,000 |

 

You plan to use one-half of a spare bedroom in your apartment for your office. The room is used for storage and you are planning to stack the items on one side of the room to give you room for a desk on the other side. The apartment costs $600 per month and the bedroom accounts for about 20% of the total square footage. Your rental agreement specifies that you are unable to sublet the spare bedroom. Your uncle has now offered you a position as a sales associate in his sports shop.

a. If non-monetary aspects and tax implications of the two jobs are identical, what is the smallest salary your uncle could offer that would induce you to work for him (and not sell frozen foods for the year)?

b. Would your answer to part a differ if the apartment lease allowed you to sublet the spare bedroom? Explain briefly.

c. Would your answer to part a differ if the non-monetary aspects of the two jobs were not identical?

Question #9: Ann Jones is thinking about buying a franchise for a carpet cleaning company. The expected revenues for the company are $250,000 per year. The franchiser has told her to anticipate the following expenses each year: $100,000 in labor expenses, $50,000 for supplies, $10,000 in rent for office and storage space, and $30,000 for trucks and maintenance. Ann can purchase the franchise without paying an initial franchise fee, but must pay 10% of her revenues to the franchiser each year. She cannot sell the franchise but can relinquish her rights to the franchise at any time.

a. Assuming that the figures above are true and complete, what is the anticipated accounting profit for the carpet cleaning business?

b. Assuming that the figures above are true and complete, list four or five additional pieces of information that you would like to know before you advise Ann on whether or not she should buy the franchise.

Question #10: Self-checking is being introduced by several retailers. For example, at least one local Target and Kroger’s have lines in which customers scan their own purchases and pay for purchases by swiping credit or debit cards.

a. What are the incremental benefits of self-checking?

b. What are the major incremental costs of self-checking?

c. Why does a local Target that uses self-checking for most merchandise require the assistance of a salesperson for camera purchases?

d. Why is self-checking much more prominent now than it was 5 years ago?

 

Question #11: Price discounts are common in many wholesale transactions. The executives at Atkins Cheesecake, Inc. are trying to decide whether to agree to a discount to a potential new customer, Sam’s Club. Atkins is currently selling 1,000 boxes of cakes a week for a total revenue of $70,000 per week. The total cost of producing 1,000 boxes of cakes a week is $50,000 per week. Sam’s Club has offered to pay $65 per box for 100 boxes of cakes per week. The Vice-President in charge of sales for Atkins, Pat Atkins, has met with the officials at Sam’s Club and is convinced that $65 is the highest price that Sam’s will accept. The Executive Board must now decide whether or not to agree to the offer. To help make the decision, the executives have examined the impact on sales of accepting the offer. The executives has decided that the extra revenue generated from selling to Sam’s would not affect sales to their current customers sales in any way; the current customers will continue to pay $70,000 per week to buy 1,000 of boxes of cakes. Therefore, accepting the contract will increase unit sales from 1,000 per week to 1,100 and the revenue from the sales to Sam’s will be extra revenue for Atkins. The executives have also learned that total cost and average cost will rise if the firm sells 1,100 boxes per week instead of 1,000 boxes per week. The following table contains the cost projections.

|Q |TC |ATC |

|1,000 |50000 |50 |

|1,100 |57200 |52 |

 

The discussion is heated. One group argues that Atkins should walk away from the deal because it generates less revenue per box ($65) than the firm is getting ($70) and will increase average total cost. Another side argues that Atkins should accept the contract because the price offered, $65, is greater than $52, the average total cost of producing 1,100 boxes per week. What would you recommend? Why? Explain fully!

Long-run costs

• All factors are variable

• Realistic when plans are being drawn

• LRAC is the minimum ATC possible when all factors are variable

• Cost is minimized at a given level of output when MPL / w = MPK / r

• Firm is experiencing economies of scale if LRAC decreases as Q increases (by a small amount)

• Minimum efficient scale is the lowest quantity at which LRAC is minimized

• Firm experiencing diseconomies of scale if LRAC increases as Q increases (by a small amount)

• Often said that the firm is experiencing constant returns to scale if LRAC remains constant as Q increases (by a small amount)

o Constant returns to scale more properly applies to long-run production

o Firm experiences increasing, constant, or decreasing returns to scale if the percentage increase in output is greater than, equal to, or less than X% when all inputs are increased by X%

• Improvements in long-run average cost is often a motivation for mergers and acquisitions

Question #12: In the mid 1980’s Whirlpool was producing 150,000 dishwashers per year and KitchenAid was producing 50,000. Suppose that the minimum efficient scale was 100,000. Approximately 400,000 dishwashers were sold in the US each year.

a. Would Whirlpool benefit from a merger? Why or why not?

b. Would KitchenAid benefit from a merger? Why or why not?

c. How many efficient competitors could exist in the market?

Question #13: Problem and Application 16

Costs and multi-product firms

• Most firms produce more than one product

• Costs of producing one product are often affected by production levels of other products

• Economies of scope

o Total cost of producing two or more goods by a single firm is less than the sum of the total costs of all firms specializing in the production of the goods individually, holding output constant

o TC(Q1, 0) + TC(0, Q2) > TC(Q1, Q2)

• Cost complementarity occurs when the marginal cost of producing one product is reduced when the production of another product is increased

o MC1 = ( TC / ( Q1

o MC2 = ( TC / (Q2

o Cost complementarity occurs when (MC1 / (Q2 < 0 or (MC2 / (Q1 < 0

• When the multiproduct cost function is quadratic, cost complementarity guarantees that economies of scope exist but economies of scale do not guarantee cost complementarity exist.

• The ability for a single firm to produce two products more efficiently than when two firms specialize in the production of the two products individually is a basis for synergies and mergers

• The ability for a single firm to produce two products more efficiently than when two firms specialize in the production of the two products individually sometimes justifies continued ownership of an unprofitable division.

Question #14: Conceptual and Computational Problem 7

Question #15: Suppose that a firm operates two divisions, each division produces a different product, C = 200 - Q1 Q2 + 2 Q12 + 0.5 Q22, Q1 = Q2 = 10, costs have been allocated evenly between the two products, and total revenue at the two divisions is $400 and $200, respectively.

a. Do cost complementarities exist?

b. Do economies of scope exist?

c. An investor is interested in purchasing the second division. What is the lowest price the firm should accept if it sells the division? Use a discount rate of 10% and an infinite time horizon. Assume that all outputs, prices, and cost structures will forever remain constant.

(Click here to see an answer.)

(Note to Millner – Change values next time)

Answers

Answer to Minimum Price to Sell Division Question

Q1 |Q2 |C |C1 |C2 |TR1 |TR2 |TR |Pro1 |Pro2 |Pro | |10 |10 |350 |175 |175 |400 |200 |600 |225 |25 |250 | |10 |0 |400 |400 |0 |400 |0 |400 |0 |0 |0 | | | | | | | | | | | | | |Incremental Cost |50 | | | | | | | | | |Incremental Revenue |-200 | | | | | | | | | |Incremental Profit |-250 | | | | | | | | | |PV | |-2500 | | | | | | | | | |Min. Price | |2500 | | | | | | | | | |

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