03 cost curves

Bellringer Chapter 141. Calculate the TC, FC, VC, MC

2. What do you think AFC, AVC and ATC stand for?

Averages

Do you guys bring up or down the GPA of all of Flowing Wells high school?

Does the cross country team bring up or down the average weight of Flowing Wells High School?

Does a high average cost of living mean that everyone spends a lot to live in California? What do homeless people do to the average? What type of person brings up the average?

Average Costs

Average Fixed Costs = FC/Q

Average Variable Costs = VC/Q

ATC = TC/Q

Hot dogs per hour

FC VC TotalCost

AFC AVC ATC MC

0 $ 3 $ 0 ------

1 $0.30

2 $0.80

3 $1.50

4 $2.40

5 $3.50

6 $4.80

7 $6.30

8 $8.00

9 $9.90

10 $12.00

SHORT RUN Cost Curves

THE COSTS OF PRODUCTION 7


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

Qu

anti

ty o

f o

utp

ut

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

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 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)


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 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∆Q

MC =


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 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.


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

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


$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE 2: Why ATC Is Usually U-Shaped

As Q rises:

Initially, falling AFC pulls ATC down.

Eventually, rising AVC pulls ATC up.

Efficient scale:The quantity that minimizes ATC.


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

Costs

Check mark?Bowed up L shapeSmileBowed down L shape


EXAMPLE 2: ATC and MC

ATCMC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Costs

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 Round up If MC is higher than AVC, does MC increase or

decrease?

Why does the AFC curve slope down forever as a firm produces more?

Which curve looks like a check mark?

Which curve has the most extreme upward slope?

Which is the only average curve that decreases over time?

Which curve is the above the other average curves?

Costs assignment1

2

Costs assignment1

2

Costs assignment1

2

03 cost curves

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