Production and Cost in the Long Run
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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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Production and Cost in the Long Run Overheads

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Production and cost in the long run overheads

Production and Cost in the Long Run

Overheads


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


Production and cost in the long run overheads

Cost minimization assumption

For any given level of output,

the firm will choose the input combination

with the lowest cost


Production and cost in the long run overheads

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?


Production and cost in the long run overheads

For any output level, there are are

usually several different input

combinations that can be used

Each combination will have a different cost


Production and cost in the long run overheads

Consider the hay problem

x1x2 TPPAPP A MPPMPPTFCTVCTCAFCAVCATCAMCMC

8.01.01536.0192.00 262.00 256.00 20.0 48.00 68.00 0.0130.0310.0440.0230.023

9.01.01782.0198.00 246.00 234.00 20.0 54.00 74.00 0.0110.0300.0420.0240.026

10.01.02000.0200.00 218.0 200.00 20.0 60.00 80.0 0.0100.0300.0400.0280.030

11.01.02178.0198.00 178.0 154.00 20.0 66.00 86.0 0.0090.0300.0390.0340.039

12.01.02304.0192.00 126.0 96.00 20.0 72.00 92.0 0.0090.0310.0400.0480.063

13.01.02366.0182.00 62.0 26.00 20.0 78.00 98.0 0.0080.0330.0410.0970.231

14.01.02352.0168.00 -14.0 -56.00 20.0 84.00 104.0 0.0090.0360.044

4.02.01345.0336.25 406.00 424.00 40.0 24.00 64.00 0.0300.0180.0480.0150.014

5.02.01783.0356.60 438.00 450.00 40.0 30.00 70.00 0.0220.0170.0390.0140.013

6.02.02241.0373.50 458.00 464.00 40.0 36.00 76.00 0.0180.0160.0340.0130.0137.02.02707.0386.71 466.00 466.00 40.0 42.00 82.00 0.0150.0160.0300.0130.013

8.02.03169.0396.13 462.00 456.00 40.0 48.00 88.00 0.0130.0150.0280.0130.013

9.02.03615.0401.67 446.00 434.00 40.0 54.00 94.00 0.0110.0150.0260.0130.014

10.02.04033.0403.30 418.0 400.00 40.0 60.00 100.0 0.0100.0150.0250.0140.015

11.02.04411.0401.00 378.0 354.00 40.0 66.00 106.0 0.0090.0150.0240.0160.017

12.02.04737.0394.75 326.0 296.00 40.0 72.00 112.0 0.0080.0150.0240.0180.020

14.02.05185.0370.36 224.0 144.00 40.0 84.00 124.0 0.0080.0160.0240.0270.042

16.02.05281.0330.06 48.0 -56.00 40.0 96.00 136.0 0.0080.0180.026

18.02.04929.0273.83 -176.0 -304.00 40.0 108.00 148.0 0.008


Production and cost in the long run overheads

There are many ways to produce

2,000 bales of hay per hour

WorkersTractor-WagonsTotal CostAverage Cost

101800.04

6.451.6671.94.03597

5.48272.86580.0364

3.667382.00150.041

2.636495.81670.0479

1.97865111.872.0559


Production and cost in the long run overheads

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


Production and cost in the long run overheads

OutputWorkersTractor-WagonsCostAverage Cost

5003.701.0743.620.087

1,0004.911.2754.890.055

1,5005.781.4763.990.043

2,0006.451.6671.940.03597

2,5007.031.8579.140.03165

3,0007.542.0385.780.02859

4,0008.422.3797.900.02448

5,0009.162.70108.890.0217781

7,00010.383.32128.610.01837

10,00011.854.17154.540.0154543

20,00015.306.67225.130.0112564

30,00017.778.85283.600.00945317

50,00021.5112.73383.710.00767416

75,00025.1317.11493.000.00657338

100,00028.1821.22593.500.00593498

150,00033.4829.17784.200.00522799

200,00038.4137.36977.580.00488791

244,00042.9945.521168.260.00478795

245,00043.1045.721173.060.00478798

250,00043.6746.771197.510.00479003

275,00046.8652.801337.080.00486212

290,00049.3957.691450.070.00500025

300,00052.1363.141575.650.00525218

301,00052.6464.171599.250.00531311


Production and cost in the long run overheads

Long run average cost of production

LRATC


Production and cost in the long run overheads

Examples

y = 2000

y = 100000


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

Consider the following data where the short run costs

hold wagons fixed at the long run least cost level

OutputLACAC - 1000AC - 5000AC - 50000

5000.08723330.08809

1,0000.054880.05488

1,5000.04266270.04296

2,0000.03597130.038930.03929

2,5000.031650.03351

3,0000.028590.02959

3,5000.026290.02678

4,0000.024480.02467

4,5000.0230030.02305

5,0000.02177830.021778

6,0000.01984390.020018

7,0000.018370.019202

10,0000.01545430.027668

20,0000.01125640.0149885

30,0000.009453170.0107744

40,0000.008392010.00872874

50,0000.007674160.00767416

52,5000.007528350.00757569


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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.


Production and cost in the long run overheads

400

350

300

250

200

150

100

50

0

0

5

10

15

20

25

30

35

Another Example


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

Economies of size and the shape of LRATC

We measure the relationship between average cost

and output by the elasticity of scale (size)


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

Why do economies of scale occur?

Gains from specialization

More efficient use of lumpy inputs

blast furnace

combine

X-ray machine

receptionist


Production and cost in the long run overheads

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


Production and cost in the long run overheads

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


Production and cost in the long run overheads

Why do diseconomies of scale occur?

Changes in the quality of inputs

Supervision and motivation problems

Externalities or congestion in production


Production and cost in the long run overheads

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


Production and cost in the long run overheads

Why do constant returns to scale occur?

Duplication of processes

Fixed production proportions and replication

Economies and diseconomies balance out


Production and cost in the long run overheads

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


Production and cost in the long run overheads

The End


Production and cost in the long run overheads

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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