The Costs of ProductionPrinciples of Microeconomics

Boris Nikolaev

Brainstorming costs

You run Ford Motor Company. • List three different costs you have. • List three different

business decisions that are affected by your costs.

In this chapter

• What is a production function? What is marginal product? How are they related?

• What are the various costs? How are they related to each other and to output?

• How are costs different in the short run vs. the long run?

• What are “economies of scale”?

It’s business time.

• Firms are in the business of making profits.

Profit = Total Revenue (TR) – Total Cost (TC)

the amount a firm receives from the sale of its output

the market value of the inputs a firm uses in production

Sneak Preview

MR=MC

Profits

• Are profits bad?• What is the function of profits in a free market

economy?• In a competitive market profits come not from

increase in price, but from decrease in the cost of production. Why?

• Fortune 500 most profitable companies [see here]

The Weed Trail [read here]

Profits and Insurance

• Recollect risk-aversion & uncertainty.

Corporate Profits after tax

CP/GDP

Marxist View

• The stagnating wages since the 1970s– Technology– World war II– Outsourcing– Women in the labor force– Immigration

• Problem of effective demand– Work more hours– Borrowing binge (mortgage debt, credit cards)

• Greatest profit boom (in the history of the world)– Marginal productivity, wages, and profits

Productivity vs Wages

What do you do with the profits?

• CEO salaries [Forbes list]• Mergers & Acquisitions• Lend to employees (e.g. GM, IBM, etc.)

Costs

• Resources are scarce, productive, and have alternative uses.

Explicit costs are the direct cash payments you make to use resources you don’t own such as wages, rent, insurance, taxes, etc.

Implicit costs is the opportunity cost of the resource you own (the benefit you could have extracted from it from its next best use). Do not require direct cast payments.

Example

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

• Case 1: borrow $100,000– explicit cost = $5000 interest on loan

• Case 2: use $40,000 of your savings, borrow the other $60,000– explicit cost = $3000 (5%) interest on the loan– implicit cost = $2000 (5%) foregone interest you

could have earned on your $40,000.

Economic vs Accounting Profit

• Accounting profit = total revenue minus total explicit costs

• Economic profit= total revenue minus total costs (including explicit

and implicit costs)• Accounting profit ignores implicit costs,

so it’s higher than economic profit.

Example 1

The equilibrium rent on office space has just increased by $500/month. Determine the effects on accounting profit and economic profit if:

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

Answers

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.

Practice QuestionYour current job pays $50K/year. You have $20K savings that earn you $3K interest a year. You own a garage, which you rent for $12K/ year. You decide to invest your savings and use your garage to start your own business.

Did you make a good economic decision?

Total Revenue $105KExplicit Costs

labor $21Kfood $20K

Total Cost $41K

Accounting Profit _____

Implicit Costssalary _____interest _____rent _____

Total Implicit Cost _____

Economic Profit / Loss______

Production in the Short Run

Q= f(L,K)

A production function shows the relationship between the quantity of inputs used to produce a good and the quantity of output of that good.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qu

anti

ty o

f o

utp

ut

EXAMPLE 1: Production Function

30005

28004

24003

18002

10001

00

Q (bushels of wheat)

L(no. of

workers)

Marginal Product (MP)

• If you hire one more worker, your 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

Q (bushels of wheat)

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

Qu

anti

ty o

f o

utp

ut

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 you hire an extra worker, – your costs rise by the wage he pays the worker– your output rises by MPL

• Comparing them helps you decide whether he should hire the worker.

Class demonstration

The Law of Diminishing Marginal Returns

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

• Why does it decline?

Practice Question# fishermen Fish caught MP of labor MRP

1 152 353 584 805 956 1057 1088 105

Input (L) TP = f(L)

Assume that only one input (L) is relevant in production.The wage / worker = $175 and one pound of fish is selling for $10

Let’s go back to our farm example…

• You must pay $1000 per month for the land, regardless of how much wheat you grow.

• The market wage for a farm worker is $2000 per month.

• Your cots are related to how much wheat you produce…

EXAMPLE 1: Your 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: Total Cost Curve

Q (bushels of wheat)

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 3000

Quantity of wheat

To

tal c

ost

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

gin

al C

ost

($)

Why MC Is Important

• You are rational and want to maximize your profits. To increase profit, should you produce more or less wheat?

• To find the answer, you need to “think at the margin.”

• If MC > MR then producing one more unit will decrease profits.

Fixed and Variable Costs

• Fixed costs (FC) do not vary with the quantity of output produced. – In our example, FC = $1000 for land– Other examples:

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

– In our example, VC = wages you pay workers– Other example: cost of materials

• Total cost (TC) = FC + VC

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

Co

sts

FC

VC

TC

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∆Q

MC =

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

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 7

Q

Co

sts

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

Co

sts

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

Co

sts

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

Co

sts

Calculating costsFill 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

AnswersUse 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

EXAMPLE 2: ATC and MC

ATCMC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

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.

Cost in the Long Run

• Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC.

• Long run: All inputs are variable (e.g., firms can build more factories or sell existing ones).

EXAMPLE 3: LRATC with 3 factory sizes

ATCSATCM ATCL

Q

AvgTotalCost

Firm can choose from three 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.

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

Sources of Economies of Scale

• Spread of “overhead,” fixed cost over bigger

production.

• Labor specialization.

• Technology.

• Learning by doing.

• Agglomeration economies.

Note on International Trade• What goods are produced and where?

• David Ricardo (1800’s) – comparative advantage.

• Heckscher & Ohlin (1920-30’s) – differences in factor endowments. Example: Developed countries export more capital intensive goods (cars, airplanes, etc…) and import from developing countries more labor intensive goods (clothing, agricultural products, etc…)

• Empirical studies.

Krugman’s Model

Uses economies of scale to explain international trade.

1. Mass production decreases average cost (ES)

2. Consumers prefer diversity of products

Each country specializes and then trades. This is how countries with similar factor endowments engage in trade (e.g. Japan sells Toyota to US, US sells GM to Germany, etc…)