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Chapter 8: Cost Curves

•A firm aims to MAXIMIZE PROFITS

•In order to do this, one must understand how to MINIMIZE COSTS

•Therefore understanding of cost curves is

essential to maximizing profits

(2)

2

Chapter 8: Costs Curves

In this chapter we will cover:

8.1 Long Run Cost Curves 8.1.1 Total Cost

8.1.2 Marginal Cost and Average Cost 8.2 Economies of Scale

8.3 Short Run Cost Curves

8.3.1 Total Cost, Variable Cost, Fixed Cost 8.3.2 Marginal Cost and Average Cost

8.4 Economies of Scope

8.5 Economies of Experience

(3)

8.1 Long Run Cost Curves

•In the long run, a firm’s costs equal zero when zero production is undertaken

•As production (Q) increases, the firm must use more inputs, thus increasing its cost

•By minimizing costs, a firm’s typical long

run cost curve is as follows:

(4)

Q (units per year) 4

L (labor services per year) K

TC ($/yr)

0 0

LR Total Cost Curve

Q0 Q1

TC0 =wL0+rK0

L0 L1 K0

K1

Q0

Q1

TC = TC1 TC = TC0

TC1=wL1+rK1

(5)

•An increase in the price of only 1 input will cause a firm to change its optimal choice of inputs

•However, the increase in input costs will always cause a firm’s costs to increase:

-(Unless inputs are perfect substitutes)

(6)

6

L K

Q0

0

B TC0/r A

TC1/r

Slope=w

1

/r

Slope=w

2

/r

C2 C1 C3

C

1

: Original isocost curve (TC = $200)

C

2

: Isocost curve after

Price change (TC = $200) C

3

: Isocost curve after

Price change (TC = $300)

(7)

Q (units/yr) TC ($/yr)

TC(Q) old TC(Q) new

Change in Input Prices ->

A Shift in the Total Cost Curve

Q 300

200

(8)

8

Let Q=2(LK)

1/2

MRTS=K/L, W=5, R=20, Q=40

What occurs to costs when rent falls to 5?

Initially:

MRTS=W/R K/L=5/20

4K=L

Q=2(LK)

1/2

40=2(4KK)

1/2

40=4K

10=K

40=L

(9)

Let Q=2(LK)

1/2

MRTS=K/L, W=5, R=20, Q=40

What occurs to costs when rent falls to 5?

After Price Change:

MRTS=W/R K/L=5/5

L=K

Q=2(LK)

1/2

40=2(LL)

1/2

40=2L

20=L

20=K

(10)

10

What occurs when rent falls to 5?

Initial: L=40, K=10 Final: W=5, R=20 Initial: TC=wL+rK

TC=5(40)+20(10) TC=400

Final: TC=5(20)+5(20) TC=200

Due to the fall in rent, total cost falls by $200.

(11)

Q (units/yr) TC ($/yr)

TC(Q) final TC(Q) initial

Change in Rent

40 400

200

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12

To calculate total cost, simply substitute labour and capital demand into your cost expression:

Q= 50L

1/2

K

1/2

(From Chapter 7:) L*= (Q

0

/50)(r/w)

1/2

K* = (Q

0

/50)(w/r)

1/2

TC = wL +rK

TC= w [(Q

0

/50)(r/w)

1/2

] +r[(Q

0

/50)(w/r)

1/2

] TC= [(Q

0

/50)(wr)

1/2

] +[(Q

0

/50)(wr)

1/2

]

TC = 2Q

0

(wr)

1/2

/50

(13)

Let Q= L

1/2

K

1/2,

MP

L

/MP

K

=K/L, w=10, r=40.

Calculate total cost.

MRTS=w/r K/L=10/40 4K=L

Q=L

1/2

K

1/2

=(4K)

1/2

K

1/2

Q=2K K=Q/2

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14

Let Q= L

1/2

K

1/2,

MRTS=K/L, w=10, r=40.

Calculate total cost.

L=4K

L=4(Q/2) L=2Q

TC = wL +rK

TC = 10(2Q) +40(Q/2)

TC = 40Q

(15)

•When the prices of all inputs change by the same (percentage) amount, the optimal input combination does not change

•The same combination of inputs are purchased

at higher prices

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16

L (labor services/yr) K (capital services/yr)

0

A

Q0

C

1

=Isocost curve before ($200)

and after ($220) a 10% increase in input prices

C1

(17)

Q (units/yr) TC ($/yr)

TC(Q) old TC(Q) new

Example: A Shift in the Total Cost Curve When Input Prices Rise 10%

Q 220

200

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18

Definition: The long run average cost function is the long run total cost function divided by

output, Q.

That is, the LRAC function tells us the firm’s cost per unit of output…

Q Q Q TC

AC ( )

)

( 

(19)

Definition: The long run marginal cost function is rate at which long run total cost changes with a change in output

The (LR)MC curve is equal to the slope of the (LR)TC curve

Q Q Q TC

MC

  ( ) )

(

(20)

20

Q (units/yr) TC ($/yr)

TC(Q) post

Average vrs. Marginal Costs

Q0 TC0

Slope=LRMC

Slope=LRAC

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21

When marginal cost is less than average cost, average cost is decreasing in quantity. That is, if MC(Q) < AC(Q), AC(Q) decreases in Q.

When marginal cost is greater than average cost, average cost is increasing in quantity. That is, if MC(Q) > AC(Q), AC(Q) increases in Q.

When marginal cost equals average cost, average cost is at its minimum. That is, if MC(Q) = AC(Q),

AC(Q) is at its minimum.

(22)

Q (units/yr)22

AC, MC ($/yr)

0

MC AC

AC at minimum when AC(Q)=MC(Q)

“typical” shape of AC, MC

(23)

If average cost decreases as output rises, all else equal, the cost function exhibits

economies of scale.

-large scale operations have an advantage If average cost increases as output rises, all else equal, the cost function exhibits

diseconomies of scale.

-small scale operations have an advantage

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24

Why Economies of scale?

-Increasing Returns to Scale for Inputs -Specialization of Labour

-Indivisible Inputs (ie: one factory can produce up to 1000 units, so increasing output up to

1000 decreases average costs for the factory)

(25)

Why Diseconomies of scale?

-Diminishing Returns from Inputs -Managerial Diseconomies

-Growing in size requires a large expenditure on managers

-ie: The owner is very passionate, but can

only manage 1 or two branches

(26)

26

0 Q (units/yr)

AC ($/yr)

Q*

AC(Q)

Typical Economies of Scale

Economies of scale Diseconomies of scale

Minimum Efficient Scale – smallest

Quantity where LRAC curve reaches

Its min.

(27)

Production Function Cost Function Increasing returns to

scale Economies of Scale

Decreasing returns to

scale Diseconomies of Scale

Constant Returns to

Scale Neither economies nor

diseconomies of scale

Production functions and cost functions are related:

(28)

28

Example: Returns to Scale and Economies of Scale CRS IRS DRS

Production Function Q = L Q = L

2

Q = L

1/2

Labor Demand L*=Q L*=Q

1/2

L*=Q

2

Total Cost Function TC=wQ wQ

1/2

wQ

2

Average Cost Function AC=w w/Q

1/2

wQ

Economies of Scale none EOS DOS

(29)

•Economies of Scale are also related to marginal cost and average cost:

If MC < AC, AC must be decreasing in Q.

Therefore, we have economies of scale.

If MC > AC, AC must be increasing in Q.

Therefore, we have diseconomies of scale.

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30

Let Cost=50+20Q

2

MC=40Q

IF Q=1 or Q=2, determine economies of scale

(Let Q be thousands of units)

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31

TC=50+20Q

2

MC=40Q

AC=TC/Q=50/Q+20Q Initially: MC=40(1)=40

AC=50/1+20(1)=70

MC<AC – Economies of Scale Finally: MC=40(2)=80

AC=50/2+20(2)=65

MC>AC – Diseconomies of Scale

(32)

32

8.3 Short-Run Cost Curves

•In the short run, at least 1 input is fixed (ie: (K=K*)

•Total fixed costs (TFC) are the costs associated with this fixed input (ie: rk)

•Total variable costs (TVC) are the costs associated with variable inputs (ie:wL)

•Short-run total costs are fixed costs plus variable costs:

STC=TFC+TVC

(33)

Q (units/yr) TC ($/yr)

TVC(Q, K*)

TFC rK*

STC(Q, K*) rK*

Short Run Total Cost, Total Variable

Cost and Total Fixed Cost

(34)

34

Short Run Costs

Example:

Minimize the cost to build 80 units if Q=2(KL)

1/2

and K=25. If r=10 and

w=20, classify costs.

Q=2(KL)

1/2

80=2(25L)

1/2

80=10(L)

1/2

8=(L)

1/2

64=L

(35)

Short Run Costs

Example:

K*=25, L=16. If r=10 and w=20, classify costs.

TFC=rK*=10(25)=250

TVC=wL=20(64)=1280

STC=TFC+TVC=1530

(36)

36

The firm can minimize costs better in the long run because it is less

constrained.

Hence, the short run total cost curve lies above the long run total cost

curve almost everywhere.

(37)

L K

TC0/w TC1/w TC2/w TC2/r

TC1/r TC0/r

Q0

Long Run Expansion path

0

A C

B Q1

Q0 K*

Only at point A is short run minimized as well as long run

Short Run

Expansion path

(38)

38

Q (units/yr) TC ($/yr)

LRTC(Q) A

STC(Q)

rK*

(39)

Definition: The short run average cost function is the short run total cost function divided by

output, Q.

That is, the SAC function tells us the firm’s cost per unit of output…

Q

Q Q STC

SAC ( )

)

( 

(40)

40

Definition: The short run marginal cost function is rate at which short run total cost changes with a change in input

The SMC curve is equal to the slope of the STC curve

Q

Q Q STC

SMC

  ( )

)

(

(41)

In the short run, 2 additional average costs exist:

average variable costs (AVC) and average fixed costs (AFC)

Q

Q Q TVC

AVC

Q

Q Q TFC

AFC

) ) (

(

) ) (

(

(42)

AVC

42

AFC SAC

Therefore

Q TVC Q

TFC Q

STC

TVC TFC

STC Note

:

:

(43)

43

To make an omelet, one must crack a fixed number of eggs (E) and add a

variable number of other ingredients (O).

Total costs for 10 omelets were $50. Each omelet’s average variable costs were

$1.50. If eggs cost 50 cents, how many eggs in each omelet?

AC=AVC+AFC TC/Q=AVC+AFC 50/10=$1.50+AFC

$3.50=AFC

(44)

44

To make an omelet, one must crack a fixed number of eggs (E) and add a

variable number of other ingredients (O).

Total costs for 10 omelets were $50. Each omelet’s average variable costs were

$1.50. If eggs cost 50 cents, how many eggs in each omelet?

$3.50=AFC

$3.50=P

E

(E/Q)

$3.50=0.5 (E/Q) 7=E/Q

There were 7 eggs in each omelet.

(45)

Q (units per

$ Per Unit

0

AFC

Average fixed cost is

constantly decreasing, as

fixed costs don’t rise with

output.

(46)

Q (units per46

year)

$ Per Unit

0

AVC

AFC

Average variable cost generally

decreases then increases due to economies of

scale.

(47)

Q (units per

$ Per Unit

0

SAC AVC

AFC

SAC is the vertical sum of AVC and AFC

Equal

(48)

Q (units per48

year)

$ Per Unit

0

SMC

SAC AVC

AFC

SMC intersects SAC and

AVC at their minimum

points

(49)

49

Often a firm produces more than one product, and often these products are related:

-Pepsi Cola makes Pepsi and Diet Pepsi -HP makes Computers and Cameras

-Denny’s Serves Breakfast and Dinner

Often a firm benefits from economies of scope by producing goods that are related; they share

common inputs (or good A is an input for good

B). Efficiencies often exist in producing related

products (ie: no shipping between plants).

(50)

50

If a firm can produce 2 products at a lower total cost than 2 firms each producing their own

product:

TC(Q

1

,Q

2

)<TC(Q

1

,0)+TC(0,Q

2

)

That firm experiences economies of scope.

(51)

51

If the cities maintains local roads, it costs are $15 million a year. If a private firm covers park

maintenance, it costs are $12 million a year. If the city does both, it costs $25 million a year.

TC(Q

1

,Q

2

)=$25 million

TC(Q

1

,0)+TC(0,Q

2

)=$15 million + $12 million TC(Q

1

,0)+TC(0,Q

2

)=$27 million

TC(Q

1

,Q

2

)<TC(Q

1

,0)+TC(0,Q

2

)

Economies of scope exist.

(52)

52

Often with practice a firm “gets better” at

producing a given output; it cuts costs by being able to produce the good faster and with fewer defects.

Ie: The first time you worked on elasticities, each question took you 10 minutes and 10% were

wrong. By the end of the course you’ll be able to calculate elasticities in 4 minutes with only 5%

error (for example).

(53)

Economies of experience are efficiencies (cost advantages) resulting from accumulated

experience (learning-by-doing).

The experience curve shows the relationship between average variable cost and cumulative production volume.

-As more is produced (more experience is

gained), average cost decreases.

(54)

54

AVC

Eventually the curve Flattens out

The Experience Curve

Cumulative Output

(55)

Economies of experience occur once, while economies of scale are ongoing.

A large producer benefiting from economies of scale will increase average costs by decreasing production.

A large producer benefiting from economies of

experience may safely decrease production

(56)

56

Chapter 8 Key Concepts

Long-Run Costs:

TC=wL+rK (if labor and capital are the only inputs

AC=TC/Q

MC=∆TC/ ∆ Q

Economies of scale summarize how average cost changes as Q increases

Economies of scale = AC decreases as Q increases

Diseconomies of scale = AC increases as

Q increases

(57)

Chapter 8 Key Concepts

Short-Run Costs

TFC=All costs of the FIXED input

TVC=All total costs of the VARIABLE input

STC=TFC+TVC

SAC=STC/Q

SMC=∆STC/ ∆Q

AFC=TFC/Q

AVC=TVC/Q

SAC=AFC+AVC

(58)

58

Chapter 8 Key Concepts

If one firm has lower costs producing two goods than two firms producing the goods individually, that firm enjoys ECONOMIES OF SCOPE

If AC decreases as cumulative output

increases, a firm enjoys ECONOMIES OF EXPERIENCE

This effect decreases over time

Calculators are important in Econ 281

References

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