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Production and Cost in the Long Run Overheads. The long run. In the long run, there are no fixed inputs or fixed costs; all inputs and all costs are variable. The firm must decide what combination of inputs to use in producing any level of output. Cost minimization assumption.

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slide2

The long run

In the long run, there are no fixed inputs or fixed costs;

all inputs and all costs are variable

The firm must decide what combination of inputs to use

in producing any level of output

slide3

Cost minimization assumption

For any given level of output,

the firm will choose the input combination

with the lowest cost

slide4

The cost minimization problem

Pick y; observe w1, w2, etc;

choose the least cost x’s

Why not just pick 0 for all the x’s?

slide5

For any output level, there are are

usually several different input

combinations that can be used

Each combination will have a different cost

slide6

Consider the hay problem

x1 x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC

8.0 1.0 1536.0 192.00 262.00 256.00 20.0 48.00 68.00 0.013 0.031 0.044 0.023 0.023

9.0 1.0 1782.0 198.00 246.00 234.00 20.0 54.00 74.00 0.011 0.030 0.042 0.024 0.026

10.0 1.0 2000.0 200.00 218.0 200.00 20.0 60.00 80.0 0.010 0.030 0.040 0.028 0.030

11.0 1.0 2178.0 198.00 178.0 154.00 20.0 66.00 86.0 0.009 0.030 0.039 0.034 0.039

12.0 1.0 2304.0 192.00 126.0 96.00 20.0 72.00 92.0 0.009 0.031 0.040 0.048 0.063

13.0 1.0 2366.0 182.00 62.0 26.00 20.0 78.00 98.0 0.008 0.033 0.041 0.097 0.231

14.0 1.0 2352.0 168.00 -14.0 -56.00 20.0 84.00 104.0 0.009 0.036 0.044

4.0 2.0 1345.0 336.25 406.00 424.00 40.0 24.00 64.00 0.030 0.018 0.048 0.015 0.014

5.0 2.0 1783.0 356.60 438.00 450.00 40.0 30.00 70.00 0.022 0.017 0.039 0.014 0.013

6.0 2.0 2241.0373.50 458.00 464.00 40.0 36.00 76.00 0.018 0.016 0.034 0.013 0.0137.0 2.0 2707.0 386.71 466.00 466.00 40.0 42.00 82.00 0.015 0.016 0.030 0.013 0.013

8.0 2.0 3169.0 396.13 462.00 456.00 40.0 48.00 88.00 0.013 0.015 0.028 0.013 0.013

9.0 2.0 3615.0 401.67 446.00 434.00 40.0 54.00 94.00 0.011 0.015 0.026 0.013 0.014

10.0 2.0 4033.0 403.30 418.0 400.00 40.0 60.00 100.0 0.010 0.015 0.025 0.014 0.015

11.0 2.0 4411.0 401.00 378.0 354.00 40.0 66.00 106.0 0.009 0.015 0.024 0.016 0.017

12.0 2.0 4737.0 394.75 326.0 296.00 40.0 72.00 112.0 0.008 0.015 0.024 0.018 0.020

14.0 2.0 5185.0 370.36 224.0 144.00 40.0 84.00 124.0 0.008 0.016 0.024 0.027 0.042

16.0 2.0 5281.0 330.06 48.0 -56.00 40.0 96.00 136.0 0.008 0.018 0.026

18.0 2.0 4929.0 273.83 -176.0 -304.00 40.0 108.00 148.0 0.008

slide7

There are many ways to produce

2,000 bales of hay per hour

Workers Tractor-Wagons Total Cost Average Cost

10 1 80 0.04

6.45 1.66 71.94 .03597

5.48 2 72.8658 0.0364

3.667 3 82.0015 0.041

2.636 4 95.8167 0.0479

1.9786 5 111.872 .0559

slide8

Long run total cost

By minimizing total cost of production for

various output levels with all inputs variable,

the firm determines the

long run total cost of production

slide9

Output Workers Tractor-Wagons Cost Average Cost

500 3.70 1.07 43.62 0.087

1,000 4.91 1.27 54.89 0.055

1,500 5.78 1.47 63.99 0.043

2,000 6.45 1.66 71.94 0.03597

2,500 7.03 1.85 79.14 0.03165

3,000 7.54 2.03 85.78 0.02859

4,000 8.42 2.37 97.90 0.02448

5,000 9.16 2.70 108.89 0.0217781

7,000 10.38 3.32 128.61 0.01837

10,000 11.85 4.17 154.54 0.0154543

20,000 15.30 6.67 225.13 0.0112564

30,000 17.77 8.85 283.60 0.00945317

50,000 21.51 12.73 383.71 0.00767416

75,000 25.13 17.11 493.00 0.00657338

100,000 28.18 21.22 593.50 0.00593498

150,000 33.48 29.17 784.20 0.00522799

200,000 38.41 37.36 977.58 0.00488791

244,000 42.99 45.52 1168.26 0.00478795

245,000 43.10 45.72 1173.06 0.00478798

250,000 43.67 46.77 1197.51 0.00479003

275,000 46.86 52.80 1337.08 0.00486212

290,000 49.39 57.69 1450.07 0.00500025

300,000 52.13 63.14 1575.65 0.00525218

301,000 52.64 64.17 1599.25 0.00531311

slide11

Examples

y = 2000

y = 100000

slide12

LAC

Graphically we can plot LRATC (LAC)

as

Long Run Average Cost

0.09

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

0

50000

100000

150000

200000

250000

300000

Output - y

slide13

Long run costs are less than or equal

to short run costs for any given output level

Why?

If we are free to vary all inputs in the long run,

we can match any short run least cost combination

slide14

Consider the following data where the short run costs

hold wagons fixed at the long run least cost level

Output LAC AC - 1000 AC - 5000 AC - 50000

500 0.0872333 0.08809

1,000 0.05488 0.05488

1,500 0.0426627 0.04296

2,000 0.0359713 0.03893 0.03929

2,500 0.03165 0.03351

3,000 0.02859 0.02959

3,500 0.02629 0.02678

4,000 0.02448 0.02467

4,500 0.023003 0.02305

5,000 0.0217783 0.021778

6,000 0.0198439 0.020018

7,000 0.01837 0.019202

10,000 0.0154543 0.027668

20,000 0.0112564 0.0149885

30,000 0.00945317 0.0107744

40,000 0.00839201 0.00872874

50,000 0.00767416 0.00767416

52,500 0.00752835 0.00757569

slide15

LAC

AC - 50000

Consider long and short run average cost when

wagons are at the 50,000 bale minimum cost

Long And Short Run Average Cost

0.09

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

0

10000

20000

30000

40000

50000

60000

Output - y

slide16

LAC

AC - 5000

Consider long and short run average cost when

wagons are at the 5,000 bale minimum cost

Long and Short Run Average Cost

0.027

Cost

0.025

0.023

0.021

3400

3800

4200

4600

5000

Output - y

slide17

LAC

Consider long and short run average cost when

wagons are at the 1,000 bale minimum cost

Long and Short Run Average Cost

0.09

Cost

0.08

0.07

AC - 1000

0.06

0.05

0.04

0.03

400

600

800

1000

1200

1400

1600

1800

2000

2200

Output - y

slide18

LAC

AC 2 Wagons

Because non-integer values for wagons are not typically

feasible, we might consider alternative wagon levels instead

0.07

Cost

0.06

0.05

0.04

0.03

0.02

500

1500

2500

3500

4500

5500

Output - y

slide19

AC 1 Wagon

LAC

AC 2 Wagons

AC 3 Wagons

Consider 1, 2 and 3 wagons

0.09

Cost

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

1500

2500

3500

4500

5500

6500

Output - y

slide20

AC 1 Wagon

LAC

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

Consider 1, 2, 3 and 5 wagons

0.09

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

5500

10500

15500

20500

25500

30500

Output - y

slide21

AC 1 Wagon

LAC

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

AC 10 Wagons

Now add 10 wagons

0.09

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

5500

10500

15500

20500

25500

30500

Output - y

slide22

Long-run

average cost

$

ATC1

ATC3

ATC2

Output per period

The long run average total cost curve (LRATC) is an envelope

curve that touches all the short run average total cost curves

(SRATC) from below.

slide23

400

350

300

250

200

150

100

50

0

0

5

10

15

20

25

30

35

Another Example

slide24

Plant size and economies of scale

Economists often refer to the collection of

fixed inputs at a firm’s disposal as its plant

Restaurant

building

fixtures

kitchen items

Corn farmer

land

machinery

breeding stock

Dentist

office

drill

slide25

Choosing the optimal plant size

AC 1 Wagon

AC 2 Wagons

For different output levels, different plants are appropriate

Short Run Average Cost

0.09

Cost

0.08

0.07

0.06

0.05

0.04

0.03

500

750

1000

1250

1500

1750

2000

Output - y

slide26

AC 1 Wagon

AC 2 Wagons

AC 3 Wagons

Consider plant sizes of 1, 2 and 3 wagons

Short Run Average Cost

0.09

Cost

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

1500

2500

3500

4500

5500

Output - y

slide27

AC 1 Wagon

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

AC 6 Wagons

AC 7 Wagons

We can add 5, 6 and 7 wagons

Short Run Average Cost

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

5500

10500

15500

Output - y

slide28

AC 1 Wagon

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

AC 7 Wagons

AC 10 Wagons

AC 15 Wagons

Or 1, 2, 3, 5, 7, 10 and 15 wagons

Short Run Average Cost

0.08

0.07

Cost

0.06

0.05

0.04

0.03

0.02

0.01

0

500

8000

15500

23000

30500

38000

45500

Output - y

slide29

AC 1 Wagon

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

AC 7 Wagons

AC 10 Wagons

AC 15 Wagons

AC 20 Wagons

AC 40 Wagons

And all the way up to 40 wagons

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

10500

20500

30500

40500

50500

60500

70500

Output - y

slide30

5 Wagons

7 Wagons

10 Wagons

15 Wagons

20 Wagons

40 Wagons

LAC

40 wagons is only efficient at over 200,000 bales

Long and Short Run Average Costs

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

0

40000

80000

120000

160000

200000

Output - y

slide31

Economies of size and the shape of LRATC

We measure the relationship between average cost

and output by the elasticity of scale (size)

slide32

If AC > MC, then the cost curve is downward

sloping and S > 1

If MC > AC, then the cost curve is upward

sloping and S < 1

slide33

AC > MC S > 1

LRAC

MC

Long Run Average & Marginal Cost Curves

LRAC is downward sloping

80

70

60

50

40

30

20

10

0

0

10

20

30

40

y

slide34

AC < MC S < 1

LRAC

MC

Long Run Average & Marginal Cost Curves

LRAC is upward sloping

80

70

60

50

40

30

20

10

0

0

10

20

30

40

y

slide35

Economies of scale (size)

When average cost is falling as output rises, we say

the firm experiences economies of scale

or increasing returns to size

When long run total cost rises proportionately less

than output, production is characterized by economies

of scale and the LRATC curve slopes downward

slide36

AC > MC S > 1

LRAC

Economies of Size/Scale

MC

Long Run Average & Marginal Cost Curves

80

70

60

50

40

30

20

10

0

0

10

20

30

40

y

slide37

Why do economies of scale occur?

Gains from specialization

More efficient use of lumpy inputs

blast furnace

combine

X-ray machine

receptionist

slide38

Diseconomies of scale (size)

When average cost rises as output rises, we say

the firm experiences diseconomies of scale

or decreasing returns to size

When long run total cost rises more than in proportion

to output, production is characterized by diseconomies

of scale and the LRATC curve slopes upward

slide39

AC > MC S > 1

LRAC

Diseconomies of Size

MC

Long Run Average & Marginal Cost Curves

80

70

60

50

40

30

20

10

0

0

10

20

30

40

y

slide40

Why do diseconomies of scale occur?

Changes in the quality of inputs

Supervision and motivation problems

Externalities or congestion in production

slide41

Constant returns to scale (size)

When average cost does not change as output rises,

we say the firm experiences constant returns

to size or scale

When both output and long run total cost rise by the

same proportion, production is characterized by

constant returns to scale and the LRATC is flat

slide42

Why do constant returns to scale occur?

Duplication of processes

Fixed production proportions and replication

Economies and diseconomies balance out

slide43

LRAC

General shape of the LRAC curve

40

36

32

Cost

28

24

20

16

12

8

4

0

0

5

10

15

20

25

30

Output - y

slide45

AC 1 Wagon

LAC

AC 2 Wagons

AC 3 Wagons

AC 5 Wagons

AC 10 Wagons

0.09

0.08

Cost

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

500

5500

10500

15500

20500

25500

30500

Output - y

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