The Costs of Production

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C H A P T E R

The Costs of Production

EconomicsP R I N C I P L E S O F

N. Gregory Mankiw

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13

You run General Motors. List 3 different costs you have. List 3 different

business decisions that are affected by your costs.

A C T I V E L E A R N I N G 1 Brainstorming costs

2

THE COSTS OF PRODUCTION 3

Total Revenue, Total Cost, Profit

We assume that the firm’s goal is to maximize profit.

Profit = Total revenue – Total cost

the amount a firm receives from the sale of its output

the market value of the inputs a firm uses in production


The Production Function A production function shows the relationship

between the quantity of inputs used to produce a good and the quantity of output of that good.

It can be represented by a table, equation, or graph.

Example 1: Farmer Jack grows wheat. He has 5 acres of land. He can hire as many workers as he wants.


0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qua

ntity

of o

utpu

t

Example 1: Farmer Jack’s Production Function

30005

28004

24003

18002

10001

00

Q (bushels of wheat)

L(no. of

workers)


Marginal Product If Jack hires one more worker, his output rises

by the marginal product of labor. The marginal product of any input is the

increase in output arising from an additional unit of that input, holding all other inputs constant.

Notation: ∆ (delta) = “change in…”Examples: ∆Q = change in output, ∆L = change in labor

Marginal product of labor (MPL) = ∆Q∆L


30005

28004

24003

18002

10001

00


L(no. of

workers)

EXAMPLE 1: Total & Marginal Product

200

400

600

800

1000

MPL

∆Q = 1000∆L = 1

∆Q = 800∆L = 1

∆Q = 600∆L = 1

∆Q = 400∆L = 1

∆Q = 200∆L = 1


MPL equals the slope of the production function.

Notice that MPL diminishes as L increases.

This explains why the production function gets flatter as L increases.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qua

ntity

of o

utpu

t

EXAMPLE 1: MPL = Slope of Prod Function

30005200

28004400

24003600

18002800

100011000

00

MPLQ

(bushels of wheat)

L(no. of

workers)


Why MPL Is Important Recall one of the Ten Principles:

Rational people think at the margin. When Farmer Jack hires an extra worker,

his costs rise by the wage he pays the worker his output rises by MPL

Comparing them helps Jack decide whether he would benefit from hiring the worker.


Why MPL Diminishes Farmer Jack’s output rises by a smaller and

smaller amount for each additional worker. Why? As Jack adds workers, the average worker has

less land to work with and will be less productive. In general, MPL diminishes as L rises

whether the fixed input is land or capital (equipment, machines, etc.).

Diminishing marginal product: the marginal product of an input declines as the quantity of the input increases (other things equal)


Average Product of Labor Average product is calculated by dividing the

total product produced by the total number or workers.

APP = TP/TL For Farmer Jack, when he has three workers on

the farm, his APP= 2400/3, or 800 bushels per worker.

But that doesn’t mean he’ll get 800 bushels when he hires the fourth worker. He’ll get 400 bushels.


EXAMPLE 1: Farmer Jack’s Costs Farmer Jack must pay $1000 per month for the

land, regardless of how much wheat he grows. The market wage for a farm worker is $2000 per

month. So Farmer Jack’s costs are related to how much

wheat he produces….


EXAMPLE 1: Farmer Jack’s Costs

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

Total Cost

30005

28004

24003

18002

10001

$10,000

$8,000

$6,000

$4,000

$2,000

$0

$1,000

$1,000

$1,000

$1,000

$1,000

$1,00000

Cost of labor

Cost of land

Q(bushels of wheat)

L(no. of

workers)


EXAMPLE 1: Farmer Jack’s Total Cost Curve


Total Cost

0 $1,000

1000 $3,000

1800 $5,000

2400 $7,000

2800 $9,000

3000 $11,000

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1000 2000 3000Quantity of wheat

Tota

l cos

t


Marginal Cost Marginal Cost (MC)

is the increase in Total Cost from producing one more unit:

∆TC∆QMC =


EXAMPLE 1: Total and Marginal Cost

$10.00

$5.00

$3.33

$2.50

$2.00

Marginal Cost (MC)

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

Total Cost

3000

2800

2400

1800

1000

0

Q(bushels of wheat)

∆Q = 1000 ∆TC = $2000

∆Q = 800 ∆TC = $2000

∆Q = 600 ∆TC = $2000

∆Q = 400 ∆TC = $2000

∆Q = 200 ∆TC = $2000


MC usually rises as Q rises, as in this example.

EXAMPLE 1: The Marginal Cost Curve

$11,000

$9,000

$7,000

$5,000

$3,000

$1,000

TC

$10.00

$5.00

$3.33

$2.50

$2.00

MC

3000

2800

2400

1800

1000

0

Q(bushels of wheat)

$0

$2

$4

$6

$8

$10

$12

0 1,000 2,000 3,000Q

Mar

gina

l Cos

t ($)


$0

$2

$4

$6

$8

$10

$12

0 1,000 2,000 3,000Q

Mar

gina

l Cos

t ($)


Why MC Is Important Farmer Jack is rational and wants to maximize

his profit. To increase profit, should he produce more or less wheat?

To find the answer, Farmer Jack needs to “think at the margin.”

If the cost of additional wheat (MC) is less than the revenue he would get from selling it, then Jack’s profits rise if he produces more.


Revenue and Profit Revenue

TR = P x Q

Profit TR – TC, or P*Q – TC

As more output is sold (at a constant price), TR increases, but so does TC (at a different rate!)

The goal is to find the level of output where profit is maximized.

THE COSTS OF PRODUCTION

Max’s Lemonade Stand ($2 a cup)

OutputIn Cups

Total Revenue(P*Q)

Total Cost$

Profit$

0 0 1.00 -$1.00

1 2 1.25

2 1.75

3 2.50

4 3.50

5 4.75

6 6.25

7 8.00

8 10.00

9 12.25

10 14.75

Find the total number of cups Max should sell to make the most profit

21.


Do Now Get a book – sharing P. 286, #7


Fixed and Variable Costs Fixed costs (FC) do not vary with the quantity of

output produced. For Farmer Jack, FC = $1000 for his land Other examples:

cost of equipment, loan payments, rent Variable costs (VC) vary with the quantity

produced. For Farmer Jack, VC = wages he pays workers Other example: cost of materials

Total cost (TC) = FC + VC


EXAMPLE 2 Our second example is more general,

applies to any type of firm producing any good with any types of inputs.


EXAMPLE 2: Costs

7

6

5

4

3

2

1

620

480

380

310

260

220

170

$100

520

380

280

210

160

120

70

$0

100

100

100

100

100

100

100

$1000

TCVCFCQ

$0

$100

$200

$300

$400

$500

$600

$700

$800

0 1 2 3 4 5 6 7

Q

Cos

ts

FCVCTC


Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:

Usually, MC rises as Q rises, due to diminishing marginal product.

Sometimes (as here), MC falls before rising.

(In other examples, MC may be constant.)

EXAMPLE 2: Marginal Cost

6207

4806

3805

3104

2603

2202

1701

$1000

MCTCQ

140

100

70

50

40

50

$70∆TC∆QMC =

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7Q

Cos

ts


EXAMPLE 2: Average Fixed Cost

1007

1006

1005

1004

1003

1002

1001

14.29

16.67

20

25

33.33

50

$100

n/a$1000

AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output:

AFC = FC/Q

Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7Q

Cos

ts


EXAMPLE 2: Average Variable Cost

5207

3806

2805

2104

1603

1202

701

74.29

63.33

56.00

52.50

53.33

60

$70

n/a$00

AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output:

AVC = VC/Q

As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7Q

Cos

ts


EXAMPLE 2: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

n/a

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

74.2914.29

63.3316.67

56.0020

52.5025

53.3333.33

6050

$70$100

n/an/a

AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:

ATC = TC/Q

Also,

ATC = AFC + AVC


Usually, as in this example, the ATC curve is U-shaped.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

EXAMPLE 2: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

n/a

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

TCQ


EXAMPLE 2: The Various Cost Curves Together

AFCAVCATC

MC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

A C T I V E L E A R N I N G 3 Calculating costs

32

Fill in the blank spaces of this table.

210

150

100

30

10

VC

43.33358.332606

305

37.5012.501504

36.672016.673

802

$60.00$101

n/an/an/a$500

MCATCAVCAFCTCQ

60

30

$10

A C T I V E L E A R N I N G 3 Answers

33

Use AFC = FC/QUse AVC = VC/QUse relationship between MC and TCUse ATC = TC/QFirst, deduce FC = $50 and use FC + VC = TC.

210

150

100

60

30

10

$0

VC

43.33358.332606

40.003010.002005

37.502512.501504

36.672016.671103

40.001525.00802

$60.00$10$50.00601

n/an/an/a$500

MCATCAVCAFCTCQ

60

50

40

30

20

$10


$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

EXAMPLE 2: Why ATC Is Usually U-ShapedAs Q rises:

Initially, falling AFC pulls ATC down.

Eventually, rising AVC pulls ATC up.

Efficient scale:The quantity that minimizes ATC.


EXAMPLE 2: ATC and MCATCMC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Cos

ts

When MC < ATC,ATC is falling.

When MC > ATC,ATC is rising.

The MC curve crosses the ATC curve at the ATC curve’s minimum.


Costs in the Short Run & Long Run

Short run: The short run isn’t a specific time period

Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC. Once you sign a lease you can’t get out of it for

several years.


Costs in the Short Run & Long Run

• Long run: All inputs are variable After a few years you can expand your space or lease a smaller one

• In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (e.g., the factory size with the lowest ATC).


EXAMPLE 3: LRATC with 3 factory Sizes

ATCS ATCM ATCL

Q

AvgTotalCost

Firm can choose from 3 factory sizes: S, M, L.

Each size has its own SRATC curve.

The firm can change to a different factory size in the long run, but not in the short run.


EXAMPLE 3: LRATC with 3 factory Sizes

ATCS ATCM ATCL

Q

AvgTotalCost

QA QB

LRATC

To produce less than QA, firm will choose size S in the long run. To produce between QA and QB, firm will choose size M in the long run. To produce more than QB, firm will choose size L in the long run.


A Typical LRATC Curve

Q

ATCIn the real world, factories come in many sizes, each with its own SRATC curve.

So a typical LRATC curve looks like this:

LRATC


How ATC Changes as the Scale of Production Changes

Economies of scale: ATC falls as Q increases.

Constant returns to scale: ATC stays the same as Q increases.

Diseconomies of scale: ATC rises as Q increases.

LRATC

Q

ATC


How ATC Changes as the Scale of Production Changes

Economies of scale occur when increasing production allows greater specialization: workers more efficient when focusing on a narrow task. More common when Q is low.

Diseconomies of scale are due to coordination problems in large organizations. E.g., management becomes stretched, can’t control costs. More common when Q is high.


Costs: Explicit vs. Implicit Explicit costs require an outlay of money,

e.g., paying wages to workers. Implicit costs do not require a cash outlay,

e.g., the opportunity cost of the owner’s time. Remember one of the Ten Principles:

The cost of something is what you give up to get it.

This is true whether the costs are implicit or explicit. Both matter for firms’ decisions.


Explicit vs. Implicit Costs: An Example

You need $100,000 to start your business. The interest rate is 5%.

Case A: borrow $100,000 explicit cost = $5000 interest on bank loan

Case B: use $100,000 of your savings explicit cost = $0 No loan, no interest paid to

bank implicit cost = $5000 (5%) foregone interest you

could have earned on your $100,000.

In both cases, total (exp + imp) costs are $5000.


Economic Profit vs. Accounting Profit

Your revenues for Year 1 are $103,000 Accounting profit = total revenue minus total

explicit costs In Case A, your accountant reports a profit!

Economic profit = total revenue minus total costs (including explicit and implicit costs) In Case B, your economist reports a loss!

WHY??


Accountants ignore opportunity costs

Accounting profit ignores implicit costs, so it’s higher than economic profit.

Accountant EconomistRevenue $103,000 $103,000

Labor and Materials (explicit)

-95,000 -95,000

Interest on Bank Loan (explicit)

-5,000 0

Foregone Interest (implicit)

-5,000

Foregone Salary (implicit)

-75,000

Profit $3,000 -$72,000

The equilibrium rent on office space has just increased by $500/month.

Compare the effects on accounting profit and economic profit if

a. you rent your office spaceb. you own your office space

A C T I V E L E A R N I N G 2 Economic profit vs. accounting profit

47

The rent on office space increases $500/month. a. You rent your office space.

Explicit costs increase $500/month. Accounting profit & economic profit each fall $500/month.

b.You own your office space.Explicit costs do not change, so accounting profit does not change. Implicit costs increase $500/month (opp. cost of using your space instead of renting it), so economic profit falls by $500/month.

A C T I V E L E A R N I N G 2 Answers

48


CONCLUSION Costs are critically important to many business

decisions, including production, pricing, and hiring.

This chapter has introduced the various cost concepts.

The following chapters will show how firms use these concepts to maximize profits in various market structures.

CHAPTER SUMMARY

Implicit costs do not involve a cash outlay, yet are just as important as explicit costs to firms’ decisions.

Accounting profit is revenue minus explicit costs. Economic profit is revenue minus total (explicit + implicit) costs.

The production function shows the relationship between output and inputs.

50

CHAPTER SUMMARY

The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly.

Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper.

Variable costs vary with output; fixed costs do not.

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CHAPTER SUMMARY

Marginal cost is the increase in total cost from an extra unit of production. The MC curve is usually upward-sloping.

Average variable cost is variable cost divided by output.

Average fixed cost is fixed cost divided by output. AFC always falls as output increases.

Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.

52

CHAPTER SUMMARY

The MC curve intersects the ATC curve at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises.

In the long run, all costs are variable. Economies of scale: ATC falls as Q rises.

Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.

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The Costs of Production

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