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Costs

7

Introduction 7

Chapter Outline

7.1 Costs That Matter for Decision Making: Opportunity Costs

7.2 Costs That Do Not Matter for Decision Making: Sunk Costs

7.3 Costs and Cost Curves

7.4 Average and Marginal Costs

7.5 Short-Run and Long-Run Cost Curves

7.6 Economies in the Production Process

7.7 Conclusion

7Introduction

Costs and the manner in which costs are structured are key to a firm’s

production decisions.

• How much to produce?

• Whether to expand or shrink in response to changing market conditions?

• Whether to switch to producing a different product?

We began thinking about costs with the expansion path introduced in the

last chapter; now, we examine cost structures more intimately.

• Introducing different types of costs

• Differentiating between short-run and long-run

Costs That Matter for Decision

Making: Opportunity Costs 7.1

Costs are thought about differently in economics than in accounting.

• Accounting costs include the direct costs of operating a business, including

costs for raw materials.

• Economic cost is the sum of a producer’s accounting and opportunity costs.

‒ Opportunity cost is the value of what a producer gives up by using an

input.

Inclusion of opportunity cost means an economist’s interpretation of what

constitutes profit will generally be different from an accountant’s.

• Accounting profit is a firm’s total revenue minus accounting cost.

• Economic profit is a firm’s total revenue minus economic cost.

Costs That Matter for Decision

Making: Opportunity Costs 7.1

Opportunity costs occur everywhere in a production process

• By choosing to start a business, you may give up your salary at your current

position.

• When you invest in building a factory, you give up any other investment

opportunities.

• By choosing to use an office building you own, you cannot rent it to someone

else.

Why does this distinction matter?

• When firms make decisions on the use of inputs, they consider these

opportunity costs.

• Economists try to describe behavior.

‒ It is necessary to understand opportunity costs to know how firms make

decisions.

Costs That Do Not Matter for

Decision Making: Sunk Costs 7.2

While opportunity costs should be considered when making decisions,

sunk costs should be ignored.

Sunk costs are a form of fixed costs, or the cost of the firm’s fixed

inputs, independent of the quantity of the firm’s output.

• Buildings, operating permits, durable equipment

‒ These costs are partially avoidable; some money can be recovered.

Sunk costs cannot be recovered once spent.

• Licensing fees, long-term lease contracts, etc.

• Specific capital such as uniforms, menus, signs, etc.

Sunk costs cannot be recouped and therefore should not be considered if a firm

is deciding whether or not to close.



Sunk Costs and Decisions

Once incurred, sunk costs should not affect decision making

Consider a business deciding whether to close down.

• Some of the costs associated with the business are unavoidable (e.g., permits,

loss of value in kitchen equipment, uniforms).

• Others costs disappear when operations cease (e.g., wages for employees, raw

materials, phone bills).

If staying open will generate some revenue, what should the firm do?

‒ Stay open as long as operating revenues exceed operating costs.

‒ Operating revenue is the money a firm earns from selling its output.

‒ Operating cost is the cost a firm incurs in producing its output.If



Sunk Costs and Decisions

The sunk cost fallacy refers to the mistake of letting sunk costs affect a

firm’s operating decisions.

Often people and firms allow sunk costs to influence decisions.

• Usually, this means continuing down one path because of a prior investment.

Example: Going to a baseball game because you bought season tickets

even if the weather is horrible and there is something else you would rather

do.

Costs and Cost Curves 7.3

Economic analysis of costs divides operating costs into two categories:

1. Fixed cost (FC ) is the cost of the firm’s fixed inputs, independent of

the quantity of the firm’s output (e.g., office lease).

2. Variable cost (VC ) is the cost of inputs that vary with the quantity of

the firm’s output (e.g., raw materials).

The sum of fixed and variable costs is a firm’s Total Cost.


Flexibility and Fixed versus Variable Costs

• Time horizon is the chief factor determining flexibility of different input levels.

‒ Over short time horizons, many inputs are fixed costs (e.g., in a single

day for a restaurant most costs are fixed, including labor and capital).

‒ As the time horizon expands, wait staff can be hired or fired, new

capital can be purchased, and space can be expanded.

Other Factors Affecting Flexibility

• The presence (or lack) of active capital rental and resale markets allow some

capital expenditures to become variable (e.g., renting an extra crane).

• Labor contracts may lead to stickiness in labor inputs; it may be difficult to

fire workers, and firms may become reluctant to hire unless absolutely

necessary.


Deriving Cost Curves

• A cost curve is the mathematical relationship between a firm’s production

costs and output.

‒ Curves associated with fixed, variable, and total costs will have

different shapes.

‒ Costs can be represented by a table or a graph.

Consider Fleet Foot, a shoe company that produces running shoes.


Figure 7.1 Fixed, Variable, and Total Costs

Cost($/week)

$300

250Total cost (TC )

200Variable cost (VC )

150

100

50Fixed cost (FC )

0 1 2 3 4 5 6 7 8

Quantity of shoes (pairs)

9 10 11 12

TC is the sum of VC and FC


The Fixed Cost Curve is horizontal.

• Costs do not vary with output; they are $50 per week regardless of production.

Variable costs change with the amount of output, and the Variable Cost Curve

is therefore not constant.

• The slope of the variable cost curve is always positive.

• In this example, the curve becomes flatter as output rises from 0 to 4 pairs, then

becomes steeper as the number of pairs produced per week increases.

The Total Cost Curve is the sum of variable cost and fixed cost.

• The total cost curve will have the same shape as the variable cost curve, but it will

be shifted up at each level of output by the amount of fixed costs.

Average and Marginal Costs 7.4

Understanding the cost structure of firms is important, but to understand

how costs affect production decisions, we must introduce two related

measures: Average cost and Marginal cost.

Average cost is simply cost divided by output:

• Average Fixed Cost (AFC )

• Average Variable Cost (AVC )

• Average Total Cost (ATC )

Returning to the shoe example:

QFCAFC /

QVCAVC /

QVCFCQTCATC //

AVCAFCQVCQFC //


Figure 7.2 Average Cost Curves

Average cost($/pair)

$70

60 Average total cost (ATC )

50

Average fixed cost (AFC )40

30Average variable cost (AVC )

20

10

0 1 2 3 4 5 6 7 8


9 10 11 12

AFC always falls as quantity rises. This is because it is being averaged

across more and more units.


Marginal cost is another deciding factor in firms’ production decisions

• The additional cost of producing an additional unit of output

Returning to the previous table:

QTCMC /


Figure 7.3 Marginal Cost

Marginal cost($/pair)

$80

70Marginal cost (MC )

60

50

40

30

20

10

0 1 2 3 4 5 6 7 8


9 10 11 12

MC falls at first because AFC is falling. Eventually MC rises.


Relationships Between Average and Marginal Costs

• Since fixed costs do not change when a firm expands output, marginal cost

only depends on variable cost.

What happens when marginal cost is less than average total cost?

For example, consider your overall GPA. What happens to your 3.0

average when you get a 2.5 for the semester?

‒ It drops below 3.0.

• The same holds with costs; when marginal cost is less than the average total

cost, producing another unit will reduce average total cost, and vice versa.

This observation helps to determine when average total costs are

minimized.

• Average total costs are minimized when ATC = MC .

‒ This explains why ATC and AVC have a “U” shape.

QTCQVCMC / /


Figure 7.4 The Relationship Between Average and Marginal

Costs

Average costand marginalcost ($/unit)

MCATC

Minimum AVCATC

MinimumAVC

Quantity

MC always crosses AVC and ATC at their minimums.

Short-Run and Long-Run Cost

Curves 7.5

We now analyze how the time horizon affects the cost structure facing a

firm.

• Remember, in the short run, the amount of capital is assumed to be fixed.

Short-Run Production and Total Cost Curves

A firm’s short-run total cost curve describes the total cost of producing

various quantities of output when the amount of capital available for use

is fixed.

• An easy way to see this concept in action is with a graph.

• Consider the production of engines.


Curves 7.5

0Labor(L)

Capital (K)

XQ = 20

C = 100

0Quantity of engines

Total Cost ($)

$100

Q = 10C = 180 C = 300

Q = 30

Long-Run Expansion Path

10 20 30

TCLR

Capital and labor are used to produce engines (quantities are per week)

Y

Z

X′ Z′

C = 120

C = 360

Short-Run Expansion Path

( 𝑲 = 𝟔)6

$300

$180

X

X′$120

$360

Y

Z

Z′

TCSR

Figure 7.6Figure 7.5


Curves 7.5

Short-Run Versus Long-Run Average Total Cost Curves

Figure 7.6 shows that the short-run total cost curve will never fall below the long-

run total cost curve.

• This further implies that the short-run average total cost curve will never fall

below the long-run average total cost curve.

• This fact holds true for all short-run average total cost curves.

‒ Each of which corresponds to a different fixed capital level.

This property means that the long-run ATC curve will envelop all of the

short-run ATC curves.


Curves 7.5

Figure 7.8 The Long-Run Average Total Cost Curve

Envelops the Short-Run Average Cost Curves

Average ATCSR,10 ATCSR,30total cost($/unit) ATCSR,20 ATCLR

X′ Z'$12

X Y Z9

0 Quantity10 20 30of engines


Curves 7.5

Short-Run versus Long-Run Marginal Cost Curves

Just as with average costs,

• Short-run marginal cost is the cost of producing an additional unit of

output when capital is fixed.

• Long-run marginal cost is the cost of producing an additional unit of

output when both capital and labor are variable.

What does this imply for the shape of the marginal cost curves?

‒ In general, the long-run marginal cost curve will be flatter than

the short-run marginal cost curve.


Curves 7.5

Figure 7.9 Long-Run and Short-Run Marginal Costs

Average cost ATCSR,10 MCLRATCSR,30and marginalATCSR,20cost ($/unit)

$12

B

Y9

A

MCSR,10 MCSR,30MCSR,20

0 Quantity10 20 30of engines

Note that each short run MC curve

intersects each ATCcurve at its minimum.

Economies in the Production

Process 7.6

What happens to the long-run ATC curve as a firm grows?

• The answer reveals information about economies in the production process.

• Similar to returns to scale, but focused on the cost side.

Economies of Scale: Costs rise more slowly than production.

Constant economies of Scale: Costs rise at the same rate as output.

Diseconomies of Scale: Costs rise more quickly than production.


Process 7.6

Given these relationships, what does the common “U-shape” of

the long-run ATC curve imply for production?

‒ At first, average cost per unit produced falls (economies of

scale).Eventually, as output rises considerably, diseconomies of scale

take hold.

What factors might cause diseconomies of scale to set in?

‒ Overcrowding, overutilization of capital, organizational complexity, etc.

Not the same as returns to scale!

• Returns to scale describes how production changes when all inputs are

changed by a common factor.

• Economies of scale does not impose this “common factor” rule in input

proportions.


Process 7.6

Economies of Scope

A related concept is the idea of economies of scope.

• Refers to the simultaneous production of multiple products at a lower cost

than if a firm made each separately.

Why might a firm observe economies of scope?

1. Flexible inputs or production processes

‒ For instance, oil refineries can produce many different petroleum

products at the same time through distillation at a much lower

aggregate cost than if each were produced separately.

2. Expertise is translatable across several products/services

‒ For instance, life and auto insurance

Conclusion 7.7

We have now linked cost to production.

• Opportunity costs, fixed costs, variable costs, sunk costs

• Marginal and average costs

• Short- and long-run costs

In the next chapters, we introduce market conditions to a firm’s

production decision.

We begin with the case of a perfectly competitive market in

Chapter 8.

In-text

figure it out

Cooke’s Catering is owned by Dan Cooke. For the past year, Cooke’s

Catering had the following statement of revenues and costs

Revenues $500,000

Supplies $150,000

Electricity and water $15,000

Employee salaries $50,000

Dan’s salary $60,000

Dan has the option of closing his business and renting out the building he

owns for $100,000 per year. In addition, Dan could go work for another

catering company for $45,000 per year or for a high end restaurant for

$75,000.

Answer the following questions:

a. What is Cooke’s Catering’s accounting cost?

b. What is Cooke’s Catering’s economic cost?

c. What is Cooke’s Catering’s economic profit?

In-text

figure it out

a. Accounting cost is the direct cost of operating a business,

including supplies, utilities, and salaries.

Accounting cost = $150,0000 + $15,000 + $50,000 + $60,000 = $275,000

1.

b. Economic cost includes the opportunity cost of ownership.

In this case, the opportunity costs include the forgone rent

($100,000) and the difference between Cooke’s current salary

and what his would earn if he took the restaurant job ($15,000).

• Note, the catering offer is irrelevant because opportunity cost

measures the value of the next best alternative, which is working

at the high end restaurant.

‒ Economic Cost = Accounting cost + Opportunity cost

Economic cost = $275,000 + $100,000 + ($75,000 − $60,000) = $390,000

In-text

figure it out

c. Economic profit is simply revenues minus economic cost,

Economic profit = $500,000 – $390,000 = $110,000

Both accounting and economic profit are positive, so Cooke

should continue operating his catering business.

Additional

figure it out

Jim’s Consulting is owned by James Smith. For the past year, Jim’s

Consulting had the following revenues and costs

Revenues $600,000

Supplies $20,000

Electricity and water $10,000

Employee salaries $300,000

James’s salary $250,000

James has the option of shutting down and renting out the building he owns

for $60,000 per year. Additionally, James could go work for a larger

consulting house for $275,000 per year.


a. What is Jim’s Consulting’s accounting cost?

b. What is Jim’s Consulting’s economic cost?

c. What is Jim’s Consulting’s economic profit?

Additional

figure it out

a. Accounting cost is the direct cost of operating a business,

including supplies, utilities, and salaries.

Accounting cost = $20,000 + $10,000 + $300,000 + $250,000 = $580,0001.

b. Economic cost includes the opportunity cost of ownership.

In this case, the opportunity costs include the forgone rent

($60,000) and the difference between James’s current salary

and what he would earn if he took another job ($25,000)

Economic cost = $580,000 + $60,000 + $25,000 = $665,000

c. Economic profit is simply revenues minus economic cost,

Economic profit = $600,000 – $665,000 = –$65,000

While accounting profit is positive, economic profit is negative,

and James could do better by shutting down his business and

taking his outside opportunities.

In-text

figure it out

Fields Forever is a small farm that grows strawberries to sell to local

farmers. It produces strawberries using 5 acres of land that it rents for

$200 per week. They can hire labor at a price of $250 per week per

worker. The table below shows how the output of strawberries

(measured in truckloads) varies with the number of workers hired:

Calculate the marginal cost of 1 to 5 truckloads of strawberries for

Fields Forever (assume labor to be the only variable cost).

Labor(Workers per Week)

Strawberries(Truckloads)

0 0

1 1

3 2

7 3

12 4

18 5

In-text

figure it out

The simplest way to solve this is to add several columns to the

previous table representing fixed, variable, and total costs.

Marginal cost is simply 𝑀𝐶 = ∆𝑇𝐶/∆𝑄output and is measured in dollars

Fixed

Cost

Variable Cost Total

Cost

$200 $250 × 0 = $0 $200

$200 $250 ×1 = $250 $450

$200 $250 × 3 = $750 $950

$200 $250 × 7 = $1,750 $1,950

$200 $250 × 12 = $3,000 $3,200

$200 $250 × 18 = $4,700 $4,700

Marginal

Cost

—

$250

$500

$1,000

$1,250

$1,500

Labor(Workers per

Week)

Strawberries(Truckloads)

0 0

1 1

3 2

7 3

12 4

18 5

Additional

figure it out

Frame de Art is an art framing shop in a small town. Frame de Art has

one storefront ($500 per week), and can hire workers for $300 per week

per worker. The table below shows how output of framed art (in

hundreds-per-week) varies with the number of workers.

Calculate the marginal cost of 100 to 500 framing jobs for Frame

de Art (assume labor to be the only variable cost).

Labor(Workers per

Week)

Framed Art(Hundreds per Week)

0 0

1 1

3 2

6 3

11 4

20 5

Additional

figure it out

Labor(Workers per

Week)

Framed Art(Hundreds per

Week)

0 0

1 1

3 2

6 3

11 4

20 5

The simplest way to solve this is to add several columns to the

previous table representing fixed, variable, and total costs.

Marginal cost is simply 𝑀𝐶 = ∆𝑇𝐶/∆𝑄output and is measured in dollars.

Fixed

Cost

Variable Cost Total

Cost

$500 $300 × 0 = $0 $500

$500 $300×1 = $300 $800

$500 $300 × 3 = $900 $1,400

$500 $300 × 6 =$1,800 $2,300

$500 $300 × 11 = $3,300 $3,800

$500 $300 × 20 = $6,000 $6,500

Marginal

Cost

—

$300

$600

$900

$1,500

$2,700

In-text

figure it out

Suppose a firm’s total cost curve is

and marginal cost


a. Find expressions for the firm’s fixed cost, variable cost,

average total cost, and average variable cost.

b. Find the output level that minimizes average total cost.

c. Find the output level that minimizes average variable cost.

45815 2 QQTC

830 QMC

In-text

figure it out

a. Find the firm’s fixed cost, variable cost, average total cost,

and average variable cost.

Fixed cost does not vary with output, so solve for total cost when output

equals zero.

Variable cost is the portion that does vary with output:

Average total cost is simply total cost divided by output:

And the same applies to Average variable cost:

45454508015 2 FCTC

QQVCQQTC 81545815 2

Fixed2

QQATC

Q

QQATC

45815

45815 2

815815 2

QAVCQ

QQAVC

In-text

figure it out

b. Minimum average total cost occurs when marginal cost is

equal to average total cost.

So, ATC is minimized when Q = 1.732.

c. Finally, average variable cost is minimized when marginal

cost is equal to average variable cost.

And AVC is minimized when production ceases.

83045815 2

QQ

QQMCATC

0015830815 2

QQQQ

QQMCAVC

QQ

QQ

QQQ

Q 1545

3045

1583045

815

732.14515 2 QQ

Additional

figure it out

Suppose a firm’s total cost curve is

and marginal cost


a. Find expressions for the firm’s fixed cost, variable cost,

average total cost, and average variable cost.

b. Find the output level that minimizes average total cost.

c. Find the output level that minimizes average variable cost.

60610 2 QQTC

MC = 20Q+6

Additional

figure it out

a. Find the firm’s fixed cost, variable cost, average total cost,

and average variable cost.

Fixed cost does not vary with output, so solve for total cost when output

equals zero.

Variable cost is the portion that does vary with output.

Average total cost is simply total cost divided by output.

And the same applies to Average variable cost,

60606006010 2 FCTC

QQVCQQTC 61060610 2

Fixed

2

QQATC

Q

QQATC

60610

60610 2

610610 2

QAVCQ

QQAVC

Additional

figure it out

b. Minimum average total cost occurs when marginal cost is

equal to average total cost.

So, ATC is minimized when Q = 2.45.

c. Finally, average variable cost is minimized when marginal

cost is equal to average variable cost,

and AVC is minimized when production ceases.

62060610 2

QQ

QQMCATC

0620610 2

QQQ

QQMCAVC

45.26

601062060610 222

Q

QQQQQ

In-text

figure it out

Steve and Sons Solar Panels has a production function:

The wage rate (w) is $8 per hour, and the rental rate on

capital (r) is $10 per hour.


a. In the short run, capital is fixed at 𝐾 = 10. What is the cost of producing

200 solar panels?

b. What will the firm wish to do in the long run to minimize the cost of

producing Q = 200 solar panels? How much will the firm save?

‒ Find the cost minimizing combination of K and L (hint, review

Chapter 6).

‒ Show what this combination will cost and compare it to the short

run cost.

LMPKMPKLQ KL 4 ;4 ;4

In-text

figure it out

a. If capital is fixed at 10 units, the amount of labor needed to produce

200 solar panels is found by plugging in 10 for K and solving for L:

Total cost is therefore given by

b. From Chapter 6, we know that costs are minimized when the MRTS

of labor for capital is equal to the ratio of the costs of labor to

capital,

3

The ratio of capital to labor that should be used to minimize costs

should be 0.8, or for every 1 worker they employ they should employ

0.8 unit of capital.

10

8;

4

4

R

W

L

K

L

K

MP

MP

R

WMRTS

K

LLK

LLKorL

K8.0

10

8

10

8

140$58$1010$ wLrKTC

5)10(4200 LL

In-text

figure it out

To solve for the cost minimizing combination of capital and labor, substitute

the expression for K into the production function. This yields:

To minimize the cost of producing 200 solar panels, the firm should

employ 7.91 units of labor.

Solving for the amount of capital used yields:

To minimize the cost of producing 200 solar panels, the firm should

employ 6.33 units of capital.

Finally, total costs are given by

Cost is $13.42 ($140 − $126.58) less in the long run than the short run.

This is obtained by utilizing less units of capital and more units of

labor.

91.710

8200

10

84200 2

LLLLQ

33.6)91.7(10

8

10

8 KLK

58.126$91.78$33.610$ wLrKTC

Additional

figure it out

Suppose a wind turbine producer faces a production function

The wage rate (w) is $12 per hour, and the rental rate on

capital (r) is $22 per hour.


a. In the short run, capital is fixed at 8. What is the cost of producing 200

turbines?

b. What should the firm do in the long run to minimize the cost of producing

200 turbines?

‒ Find the cost minimizing combination of K and L.

‒ Show what this combination will cost and compare it to the short

run cost. Are the costs of producing 200 turbines in long run

more or less than in the short run?

LMPKMPKLQ KL 25.0 ;25.0 ;25.0

Additional

figure it out

a. If capital is fixed at 8 units, the amount of labor needed to produce

200 turbines is found by plugging in 8 for K and solving for L.

Total cost is therefore given by

b. From Chapter 6, we know that costs are minimized when the MRTS

of labor for capital is equal to the ratio of the costs of labor to

capital,

The ratio of capital to labor that should be used to minimize costs

should be 𝟏𝟐

𝟐𝟐, or for every 1 worker they employ they should employ

0.545 units of capital.

200 0.25 8 100L L

22

12;

25.0

25.0

R

W

L

K

L

K

MP

MP

R

WMRTS

K

LLK

LKorL

K

22

12

22

12

376,1$10012$822$ wLrKTC

Additional

figure it out

To solve for the cost minimizing combination of capital and labor, substitute

the expression for K into the production function. This yields:

To minimize the cost of producing 200 turbines, the firm should

employ 38.3 workers.

Solving for the amount of capital used yields:

To minimize the cost of producing 200 turbines, the firm should

employ 20.89 units of capital.

Finally, total costs are given by

Cost is $456.82 ($1,376 − $919.18) less in the long run than the short

run. This is obtained by utilizing more machines and less workers.

3.3822

3200

22

1225.0200 2

LLLLQ

89.20)3.38(22

12

22

12 KLK

18.919$3.3812$89.2022$ wLrKTC

In-text

figure it out

Suppose the long-run total cost function for a firm is

𝐿𝑇𝐶 = 32,000𝑄 − 250𝑄2 + 𝑄3, and its long-run marginal cost

function is 𝐿𝑀𝐶 = 32,000 − 500𝑄 + 3𝑄2.

Answer the following question:

a. At what levels of output will the firm face economies of scale?

Diseconomies of scale?

‒ Hint: these cost functions yield a typical U-shaped long-run

average cost curve.

In-text

figure it out

a. We know that when LMC < LATC, long-run average total cost is

falling, and when LMC = LATC, long-run average total costs are

minimized.

First, derive the equation for LATC

Set LMC = LATC to find the quantity that minimizes the LATC:

Long-run average total cost is minimized at 125 units of output.

Therefore, at output levels below 125, the firm is experiencing

economies of scale, and output above 125 they are experiencing

diseconomies of scale.

232

250000,32250000,32

QQQ

QQQ

Q

LTCLATC

125

2250

3500000,32250000,32

2

22

Q

QQ

QQQQ

Additional

figure it out

Suppose the long-run total cost function for a firm is LTC = 15,000Q – 200Q2 + Q3 and its long-run marginal cost function

is LMC = 15,000 – 400Q + 3Q2.

Answer the following question:

a. At what levels of output will the firm face economies of scale?

Diseconomies of scale?

‒ Hint: these cost functions yield a typical U-shaped long-run

average cost curve.

Additional

figure it out

a. We know that when LMC < LATC, long-run average total cost is

falling, and when LMC = LATC, long-run average total costs are

minimized.

First, derive the equation for LATC:

Set LMC = LATC to find the quantity that minimizes the LATC:

Long-run average total cost is minimized at 100 units of output.

Therefore, at output levels below 100, the firm is experiencing

economies of scale, and at output above 100 they are experiencing

diseconomies of scale.

232

200000,15200000,15

QQQ

QQQ

Q

LTCLATC

15,000 - 200Q+Q2 =15,000 - 400Q+3Q2

200Q = 2Q2

Q =100

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