©2001ClaudiaGarcia-Szekely 1

Costs in the Long Run

When the firm can expand or contract the plant size

2

In the Long Run all inputs are variable

There are no fixed costs in the long run.Firms PRODUCE in the short run

Restricted by the size of the plant.

Firms PLAN in the long runAny plant size is available.

When firms are planning

ATC Plant 1ATC Plant 1

With this plant, we can produce any amount from zero units to 5,000.

With this plant, we can produce any amount from zero units to 5,000.

5,0005,000

The minimum ATC occurs at 2500 unitsThe minimum ATC occurs at 2500 units

2,5002,50000

$2$2

12,00012,0005,0005,000

$1$1

ATC Plant 2ATC Plant 2

With this plant, we can produce any amount from zero units to 12,000.

With this plant, we can produce any amount from zero units to 12,000.

The minimum ATC occurs at 5,000 units

The minimum ATC occurs at 5,000 units

ATC Plant 3ATC Plant 3

With this plant, we can produce any amount from zero units to 15,000.

With this plant, we can produce any amount from zero units to 15,000.

15,00015,000

The minimum ATC occurs at 10,000

units

The minimum ATC occurs at 10,000

units

10,00010,000$0.5$0.5

In the long run firms choose a plant size…

We identify the plant size with the Average Total Cost Curve.There is no single “best” plant size…Which plant is “best” depends on the volume of production.

OUTPUT PLANT 1 PLANT 2 PLANT 3

100 10 13 17

200 9 11.5 14.3

300 8.5 9.75 12.5

400 8.3 8.4 10.8

500 8.4 8.1 9.6

600 8.9 7.5 8.6

700 9.6 7.3 8.1

800 11.7 7.6 7.8

900 14.8 8.1 8

1000 17 8.9 8.3

1100 23 10.2 9

5

Building the Long Run Average Total Cost Curve (LRATC)

Match the lowest SRATC with each output level

The LRATC shows the minimum ATC for each output level.

SRATC1To produce 100 units, ATC =$4

100

6

To produce 100 units, ATC =$6

SRATC2 SRATC3

To produce 100 units, ATC =$7

4

Plant1 has the lowest cost to

produce 100 units: LRATC = $4

Plant1 has the lowest cost to

produce 100 units: LRATC = $4

7

4

2

5.7

200

2200

5.7

200

4

200

Plant 1 has the lowest ATC from

Zero to Q0

Plant 1 has the lowest ATC from

Zero to Q0

Q0

Plant1 has the lowest cost to

produce 200 units: LRATC = $2

Plant1 has the lowest cost to

produce 200 units: LRATC = $2

SRATC1

To produce 300 units, the per unit cost using plant 1 is $3

300

2

To produce 300 units, the per unit cost using plant 2 is $2

SRATC2

SRATC3

To produce 300 units, the per unit cost using plant 3 is $3

33

1

5

2.5

400

5

400

2.5

400

1

400

Plant 2 has the lowest from Q0 to

Q1

Plant 2 has the lowest from Q0 to

Q1

Q1

SRATC2 has the lowest cost of producing 300400

Q0

SRATC2SRATC3

Q1Q0

SRATC2 has the lowest cost

between Q0 and Q1

LRATC

SRATC1

SRATC3 has the lowest

cost above Q1

SRATC1 has the lowest

cost between 0 and Q0

Long Run ATC

0

LRATCThe LRATC is an envelope of SRATC curves

3 different plant sizesEach point of the LRATC tells you the lowest cost of producing a given output level when you can

change the size of the plant

The larger the number of plant size options…

The smoother the LRATC

Building the LRATC

Plant 1 has lowest cost for volumes up to 400.Plant 2 has lowest cost between 400 and 900.Plant 3 has lowest cost above 900.

LRATC

Output

Building the LRATCOUTPU

TPLANT

1PLANT

2PLANT

3 OUTPUT LRATC100 90 96 99 100 90200 84 90 93 200 84300 78 84 87 300 78400 72 78 81 400 72500 66 60 78 500 60600 72 54 75 600 54700 78 48 72 700 48800 84 42 60 800 42900 90 36 57 900 36

1000 96 30 27 1000 271100 102 36 21 1100 211200 108 42 15 1200 151300 114 48 9 1300 91400 120 54 3 1400 31500 126 60 6 1500 6

13

Increasing Returns to Scale

Economies of Scale

ATC drops as Plant Size

increaseATC drops as Plant Size

increase

Per unit costs decrease because

Fixed costs are spread out over more units of output. Variable costs decrease with the use of mass production technologies which increase labor productivity.

14

15

ATC =

Four times as much output

ATC decreases

2TC

4Q

Double Costs

4 times Output

200

10

20400

40

10

Economies of Scale: add more to the “bottom line”

Q increase by 10%

Costs increase by less

than 10%

Q increase by 20%

Costs increase by less

than 20%

20

10 40

10

Economies of Scale

ATC

ATC

SRATC1SRATC2

SRATC4

SRATC7SRATC8

SRATC3

output

LRATC

SRATC5SRATC6

Economies of scale or Increasing Returns to Scale

$8

$7

$6

$5

$4$3

$2

$1

Output increases by a larger percentage than

costs

Output increases by a larger percentage than

costs

ATC Drops

17

Constant Returns to Scale

The benefits of expanding the plant size eventually end..Further expansion leaves per unit costs the sameOutput increases by the SAME percentage as costs.

ATC =

Twice as much output

ATC Remains

the same

2TC

2Q

Double Costs

Double Output

20020

10

400

20

20

Constant Returns to Scale20

10 20

ATC ATC

19

Constant Returns to Scale

Horizontal LRATC

As the plant size increaseATC remains the same

ATC

Q

$2

20

ATC =

Twice as much output

ATC increases

3TC

2Q

Triple Costs200

20

10

600

20

30

Diseconomies of to Scale20

10 20

30 ATC ATC

Double Output

SRATC1

SRATC2

SRATC4SRATC3

SRATC7

SRATC8

SRATC6

output

LRATC3

1

2

4

SRATC5

As the plant size increase, per unit costs increaseDiseconomies of scale

A typical LRATC

Units of output

LRATCATC

Constant Returns to ScaleDise

conomies o

f Sca

leATC

decrease

ATC same

ATC Increase

Economies of Scale

SRATC1

SRATC2

SRATC3SRATC4

SRATC5

SRATC6

SRATC7

LRATC

Increasing, Constant and Decreasing returns to scale

LRATC

25

OUTPUT LRATC100 90200 84300 78400 72500 60600 54700 48800 42900 36

1000 271100 211200 211300 211400 281500 371600 431700 50

Increasing Returns to scale

Constant Returns to scale

Decreasing Returns to scale

smallest plant with lowest ATC in the long run

Only firms with plants with the lowest cost will survive in the long

run.

26

Minimum Efficient Scale (MES)

500,000

SRATC1

SRATC2

SRATC3SRATC4

SRATC5

SRATC6

SRATC7

LRATC

Total Market Demand = 3,000,000

150,000

# of Firms = 3,000,000/500,000 = 6 firms each selling 500,000

# of Firms = 3,000,000/150,000 = 20 firms each one sells 150,000

10,000

# of Firms = 3,000,000/10,000 = 300 firms each sells 10,000

The smaller the size of the MES, the more competitive the industry is.

The larger the size of the MES,

the more concentrated the industry is.

The smaller the size of the MES, the larger the number of firms

MES