perfect competition long run overheads

Perfect Competition

Long Run

Overheads

Review of short run equilibrium

The number of firms is fixed

The firm is operating on a short-run cost curve

Some inputs are fixed

Q S ΣL

i 1yi (p , w1 ,w2 , , z)

The market or industry supply curve, QS, is the horizontal summation of the individual firm supply curves

yi yi(p , w1 , w2 , , wn , z)

Industry Supply-Demand Equilibrium

$

Output

S(p)

p0

Q0

D(p)

Demand for Individual Firm

$

Output

p0 D(p)

AVC

MC

ATC

P = 120

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0 2 4 6 8 10 12 14 16 18Output

$

Short run equilibrium

Competitive markets in the long run

The number of firms in the industry can vary

The firm is operating on its long run cost curve

Conditions for a long run equilibrium

1. No individual firm wishes to change the amount of the good it is supplying to the market

2. No individual consumer wishes to change the amount ofthe good he or she is demanding

3. No individual firm in the market has an incentive to changethe amount of any of the inputs it is usingor to exit from the market

4. No firm outside the market has any incentive to enter it

5. The aggregate supply in the market equals theaggregate demand in the market

Plant size adjustment by the firmwith no change in the market price

P = Price = $292

Short run average and marginal costs as in the table

Assumptions for example problem

The firm is operating a plant with a capacity rating of 55

SRAC SRMC SRAC SRMC SRAC SRMC SRAC SRMC y Price 5 5 9 9 15 15 18 180.00 2921.00 292 851.00 103.00 2291.00 6251.00 9041.002.00 292 479.00 112.00 1079.00 2879.00 4184.004.00 292 303.50 148.00 483.50 1203.50 1766.005.00 292 275.00 175.00 371.00 875.00 1289.006.00 292 261.00 208.00 301.00 661.00 976.00 7.00 292 256.14 247.00 256.14 7.00 513.29 757.57 8.00 292 257.75 292.00 227.75 52.00 407.75 599.00 9.00 292 264.33 343.00 211.00 103.00 331.00 481.0010.00 292 275.00 400.00 203.00 160.00 275.00 392.0011.00 292 289.18 463.00 201.91 223.00 234.64 324.6412.00 292 306.50 532.00 206.50 292.00 206.50 274.0013.00 292 326.69 607.00 215.92 367.00 188.23 7.00 236.69 14.00 292 349.57 688.00 229.57 448.00 178.14 88.00 210.2915.00 292 375.00 775.00 247.00 535.00 175.00 175.00 193.00 16.00 292 402.88 868.00 267.88 628.00 177.88 268.00 183.50 88.0017.00 292 433.12 967.00 291.94 727.00 186.06 367.00 180.76 187.0018.00 292 465.67 1072.00 319.00 832.00 199.00 472.00 184.00 292.0019.00 292 500.47 1183.00 348.89 943.00 216.26 583.00 192.58 403.0020.00 292 537.50 1300.00 381.50 1060.00 237.50 700.00 206.00 520.0022.00 292 618.09 1552.00 454.45 1312.00 290.82 952.00 245.82 772.0023.00 292 661.61 1687.00 494.65 1447.00 322.48 1087.00 271.61 907.00

Conditions for short run equilibrium

Price = MC

Price AVC

SRAC SRMC SRAC SRMC y Price 5 5 9 96.00 292 261.00 208.00 301.00 7.00 292 256.14 247.00 256.14 7.008.00 292 257.75 292.00 227.75 52.00 9.00 292 264.33 343.00 211.00 103.0010.00 292 275.00 400.00 203.00 160.0011.00 292 289.18 463.00 201.91 223.0012.00 292 306.50 532.00 206.50 292.00

P = 292

SRMC 5

SRAC 5

MC = $292 y* = 8

Short Run Equilibrium 1

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Profit 274.00

MC = $292 y* = 12

SRAC 9SRMC 9

SRAC 5SRMC 5


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P = 292

Profit 1026

SRAC 9SRMC 9


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$

P = 292

SRAC 15SRMC 15

Profit 1828.98

MC = $292 y* = 16.25

Profit 1944

MC = $292 y* = 18

SRAC 18SRMC 18


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P = 292

SRAC 15SRMC 15

Profits are higher with the size 18 plantthan with the size 15 plant

With a price of $292, a size 18 plantmakes more sense than a size 15 plant

SRAC SRMC SRAC SRMC SRAC SRMC y Price 15 15 18 18 23 230.00 2921.00 292 6251.00 9041.00 14891.00 5.00 292 875.00 1289.00 2219.00 6.00 292 661.00 976.00 1701.00 8.00 292 407.75 599.00 1067.75 9.00 292 331.00 481.00 864.33 10.00 292 275.00 392.00 707.00 12.00 292 206.50 274.00 486.50 13.00 292 188.23 7.00 236.69 409.77 14.00 292 178.14 88.00 210.29 349.57 15.00 292 175.00 175.00 193.00 303.00 16.00 292 177.88 268.00 183.50 88.00 267.88 17.00 292 186.06 367.00 180.76 187.00 242.53 18.00 292 199.00 472.00 184.00 292.00 225.67 19.00 292 216.26 583.00 192.58 403.00 216.26 103.00 20.00 292 237.50 700.00 206.00 520.00 213.50 220.0021.00 292 262.43 823.00 223.86 643.00 216.71 343.0022.00 292 290.82 952.00 245.82 772.00 225.36 472.00 23.00 292 322.48 1087.00 271.61 907.00 239.00 607.00 25.00 292 395.00 1375.00 333.80 1195.00 279.80 895.00

SRAC 18SRMC 18


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$

P = 292

SRAC 23SRMC 23

Profit 1591.39

MC = $292 y* = 20.59

Profits are lower with the size 23 plantthan with the size 18 plant

We would not want the size 23 plant withprices of $292

SRAC 23SRMC 23

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$P = 607

SRAC 18SRMC 18

When is the big plant optimal?Profit 8464

MC = $607 y* = 23

SRMC 15

SRAC 15

SRAC 9SRMC 9

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$ P = 175

What about lower prices? Profit 0.00

MC = $175 y* = 15

The long run cost curve

The long run average total cost curve (LRATC)is an envelope curve that touches all the short runaverage total cost curves (SRATC) from below

For any given price (or output) , there isan “optimal” plant size that gives thelowest level of costs (highest level of profits)

Consider the family of short run cost curves

SRAC 18SRMC 18

SRAC 9SRMC 9

SRAC 5SRMC 5

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SRAC 15SRMC 15

SRAC 23SRMC 23

SRAC 18SRMC 18

SRAC 9SRMC 9

SRAC 5SRMC 5

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SRAC 15SRMC 15

SRAC 23SRMC 23ATCMC

We bound the short run curves with the long run curve

SRMC = LRMC at “optimal” plant size

SRAC 5SRMC 5

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ATCMC


SRMC = LRMC SRAC = LRAC

SRAC 9SRMC 9

SRAC 5SRMC 5

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$

ATCMC



SRAC 18SRMC 18

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$

ATCMC



SRAC 18SRMC 18

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$

SRAC 15SRMC 15

ATCMC


SRMC = LRMC = SRAC = LRAC

A less cluttered view

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ATCMC

SRAC 18SRMC 18

SRAC 5SRMC 5

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$Some clutter, some detail

SRAC 23SRMC 23ATCMC

Profit and Loss, Entry and Exit

In a competitive market, economic profit and lossare the forces driving long run change

The expectation of continued economic profitcauses outsiders to enter the market;

The expectation of continued economic lossescauses firms in the market to exit

Q D 670 P P 670 Q D

Demand for the example market

Assumptions about the industry structure

21 identical firms

Each firm operates a size 18 plant

Pricey* Supply Cost AC

17 187.00 3073.00 180.76

Optimal output at various prices -- Plant size = 18

18 292.00 3312.00 184.00 19 403.00 3659.00 192.58 20 520.00 4120.00 206.00 21 643.00 4701.00 223.86 22 772.00 5408.00 245.82

16.9410 181.00 3062.16 180.75

17.2046 208.00 3113.41 180.96 17.6068 250.00 3205.48 182.06

Supply is equal to MC above the minimum of AVC

Pricey* Supply Cost AC16.9410 181.00 3062.16 180.75 17 187.00 3073.00 180.76 17.2046 208.00 3113.41 180.96 17.6068 250.00 3205.48 182.06 18 292.00 3312.00 184.00 19 403.00 3659.00 192.58 20 520.00 4120.00 206.00 21 643.00 4701.00 223.86 22 772.00 5408.00 245.82

Optimal output at various prices -- Plant size = 18

Supply for One Firm with Plant Size = 18

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Supply - 1

Individual Firm SupplySupply is equal to MC above the minimum of AVC

Aggregate SupplyQ S L y(p , w1 ,w2 , , z)

Supply for 21 Firms with Plant Size = 18

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Supply - 1Supply - 21

Supply PriceQ y* 21 Firms AC355.76 16.941074 181.00 180.75 357.00 17 187.00 180.76 361.30 17.204651 208.00 180.96 369.74 17.606817 250.00 182.06 378.00 18 292.00 184.00 399.00 19 403.00 192.58 420.00 20 520.00 206.00 441.00 21 643.00 223.86 462.00 22 772.00 245.82

Market and Individual Firm Supply,Price, and Average Cost

Putting supply and demand together

P = $292QS = 378

yi = 18

i = $19440

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Supply - 21D

In equilibrium, at a given quantity, supply and demand price must be equal

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Supply - 21D

NOPE

P = $292QS = 378

yi = 18

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Supply - 21D

In equilibrium, at a given quantity, supply and demand price must be equal

Supply Price DemandQ y* 21 Firms AC Price355.76 16.941074 181.00 180.75 314.24 357.00 17 187.00 180.76 313.00 361.30 17.204651 208.00 180.96 308.70 369.74 17.606817 250.00 182.06 300.26 378.00 18 292.00 184.00 292.00 399.00 19 403.00 192.58 271.00 420.00 20 520.00 206.00 250.00 441.00 21 643.00 223.86 229.00 462.00 22 772.00 245.82 208.00

Market and Individual Firm Supply,Supply Price, Average Cost and Demand Price

Supply Price DemandQ y* 21 Firms AC Price355.76 16.941074 181.00 180.75 314.24 357.00 17 187.00 180.76 313.00 361.30 17.204651 208.00 180.96 308.70 369.74 17.606817 250.00 182.06 300.26 378.00 18 292.00 184.00 292.00 399.00 19 403.00 192.58 271.00 420.00 20 520.00 206.00 250.00 441.00 21 643.00 223.86 229.00 462.00 22 772.00 245.82 208.00

What about profits?Looks good!

With high profits, other firms will want to enter

Let the number of firms increase to 26

Plant Size 18Number of firms 26

Price PriceQ y* Supply - 26 AC Demand440.47 16.941 181.00 180.75 229.53 442.00 17 187.00 180.76 228.00 450.33 17.320 220.00 181.18 219.67 468.00 18 292.00 184.00 202.00 494.00 19 403.00 192.58 176.00 520.00 20 520.00 206.00 150.00 546.00 21 643.00 223.86 124.00 572.00 22 772.00 245.82 98.00

Market and Individual Firm Supply,Supply Price, Average Cost and Demand Price

Supply and Demand for 26 Firms, Plant Size = 18

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Supply - 26D

P $220, QS 450

Notice that price falls from $292 to $220

Firms will want to cut output and change plant size

Suppose plant size declines to size 15

P $257, QS 413

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Supply - 26D

Plant Size 15Number of Firms 26

Price PriceQ y* Supply - 26 ACDemand390.00 15 175.00 175.00 280.00 397.72 15.297 202.00 175.26 272.28 413.01 15.885 257.00 177.26 256.99 416.00 16 268.00 177.88 254.00 422.45 16.248 292.00 179.43 247.55 442.00 17 367.00 186.06 228.00 468.00 18 472.00 199.00 202.00 494.00 19 583.00 216.26 176.00 520.00 20 700.00 237.50 150.00

What about profits?

Price PriceQ y* Supply - 26 ACDemand390.00 15 175.00 175.00 280.00 397.72 15.297 202.00 175.26 272.28 413.01 15.885 257.00 177.26 256.99 416.00 16 268.00 177.88 254.00 422.45 16.248 292.00 179.43 247.55 442.00 17 367.00 186.06 228.00 468.00 18 472.00 199.00 202.00 494.00 19 583.00 216.26 176.00 520.00 20 700.00 237.50 150.00

Now should the firm consider expanding again?

Prices are up

Profits are good

The plant is too small

Maybe??

But with positive profits, other firmswill keep entering the market

Long run equilibriumLong run equilibrium

If there are profits, firms will enterand supply will increaseIf the firm does not have the optimal size plant,it will modify plant size so that it is producingusing the “optimal” long run technology.

This will go on until there are no profitsand all firms have their optimal plant size

This implies that long and short runmarginal costs will be equal

What if price is $292 and plant size is variable?

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P = 292

ATCMC

The firm produces 18 units of output

The optimal long run plant size is 18

SRAC 18SRMC 18

SRMC = LRMC

What about profits?

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P = 292

ATCMC

The firm produces 18 units of output

The optimal long run plant size is 18

SRAC 18SRMC 18

Lots of profits

Why not a bigger plant?

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SRAC 18SRMC 18SRAC 23SRMC 23

P = 292

ATCMC

Cost > Min

What if price drops to $256?

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SRAC 5SRMC 5

SRAC 18SRMC 18

P = 292P = 256

ATCMC

The firm could reduce size to a smaller plantTry size 5

What about profits with this smaller plant?

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SRAC 5SRMC 5

SRAC 18SRMC 18

P = 292P = 256

ATCMC

Profit = 0

Not a good decisionP = SRAC LRMCP = SRMC

P = 256

ATC

MC

0

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5 10 15 20 25

SRAC 18

SRMC 18

SRAC 5

SRMC 5

SRMC = LRM

CInstead pick a plant where SRMC = LRMC

Is a size 5 plant a good choice with P = 256?

P = 292

ATC

MC

0

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400

5 10 15 20 25

SRAC 5

SRMC 5

SRAC 18

SRMC 18

SRAC 5

SRMC 5

SRMC LRM

C

Pick a plant where SRMC = LRMC

A size 5 plant is not optimal with P = 256

ATC

MC

SRAC 17.21

SRMC 17.21

0

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SRAC 18

SRMC 18

SRAC 5

SRMC 5

SRMC = LRM

C

SRMC LRM

C

Pick a plant where SRMC = LRMC

ATC

MC

SRAC 17.21

SRMC 17.21

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5 10 15 20 25

But with a price of $256, there are still profits

Profit

P = 175

Only with a price of $175are long run profits zero

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SRAC 15SRMC 15

ATCMC

LRMC = SRMC = LRAC

Long Run Equilibrium

Q Q

S1

IndustryFirm

q̂1

PS0

Consider a firm with long run average cost LRAC

LRAC

Is the plant size PS0 an equilibrium size for the firm?

D

Suppose demand is given by D and industry supply is S1

NO!!

Optimal Plant Size with Supply = S1

Q Q

S1

IndustryFirm

q1

PS1 LRAC

Q Q

S1

IndustryFirm

q1

PS1 LRAC

Profits are high and so firms will want to enter the market

What about Profits?

Firms will enter and supply will increase to S2

Q Q

S1

S2

IndustryFirm

q1

PS1 LRAC

Prices in the market will fall

The firm will want a slightly smaller plant in the long run Firm level output will fall

Profits are still quite good

Q Q

S1

S2

IndustryFirm

q1

PS1 LRAC

More firms will enter the market

Long Run Equilibrium Occurs When SRMC = LRMC

Q Q

S1

S2

S*

IndustryFirm

q1

PS1

q*

LRAC

And there is no incentive for entry or exit -- profits are zero

With supply = S2, there are still profits

Supply will increase until Price is equal to LRAC

Long Run Equilibrium Occurs whenthere is no incentive for entry or exit

Q Q

S1

S2

S*

IndustryFirm

q1

PS1

PS*

q*

LRAC


Price =LRAC

In the long run, the firm will have zero profits and will operate at the minimum on the long run average cost curve

Long Run Equilibrium Occurs when there is no incentive for entry or exit


What have we learned?

1. In the long run, every competitive firm will earn normal profit, that is, zero profit

2. In the long run, every competitive firm will produce where price (P) is equal to marginal cost (MC), P = MC.

3. In the long run, every competitive firm will produce where price (P) is equal to the minimum of short run average cost (SRAC), P = SRAC. This implies zero economic profit.

Summary

4. In the long run, every competitive firm will produce where price (P) is equal to the minimum of long run average cost (LRAC = ATC), P = minimum LRAC.This implies that no identical firms will want to enter or exit.

5. Putting it all together:

P = MC = min SRAC = min LRAC

Summary (continued)

P = MR = Demand

SRACSRMC

q*

LRMC

LRAC

Q

$


The End

SRAC 18SRMC 18

SRAC 9SRMC 9

SRAC 5SRMC 5

Long Run Equilibrium ??

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P = 292

SRAC 15SRMC 15

SRAC 23SRMC 23ATCMC

1944.00 Profit

SRMC 15

SRAC 15

SRAC 23SRMC 23

SRAC 9SRMC 9

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$P = 607

SRAC 18SRMC 18

P = 175


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SRAC 5SRMC 5 SRAC 15SRMC 15SRAC 18SRMC 18SRAC 23SRMC 23ATCMC

P = 175

P = 292P = 256

SRAC 17.21

SRMC 17.21

ATC

MC

0

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5 10 15 20 25

SRAC 5

SRMC 5

SRAC 18

SRMC 18

SRAC 5

SRMC 5

SRAC 15

SRMC 15

P = 175

Only with a price of $175are long run profits zero

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SRAC 5SRMC 5 SRAC 15SRMC 15SRAC 18SRMC 18SRAC 23SRMC 23

P = 292P = 256

ATCMC

The short run and long run equilibrium for an individual firm with a price of 292 is output and a plant size of 18. Here the long and short run marginal cost curves are equivalent. But this price and output combination gives large profits. A larger plant size of 23 will give positive but smaller profits.

If price drops to $256, then the firm will want to cut output. If it cuts all the way back to a size 5 plant, it will have zero profits and no firms will want to enter. But with a price of $256, the firm would prefer a larger plant so that SRMC = LRMC. If the firm increases to a size 18 plant it will have zero profits with a price of 175.

Long Run Equilibrium Occurs whenthere is no incentive for entry or exit

Q Q

S1

S2

S*

IndustryFirm

q1

PS1

PS*

q*

LRAC

Supply will increase until Price is equal to LRAC



Q Q

S1

S2

S*

IndustryFirm

q1

PS1

q̂1

PS0

q2

PS*

q*

Consider a firm with long run average cost LRAC

LRAC

Suppose the industry supply is S1. If the plant size is PS0 and the firm produces qhat_1, the firm is not in an equilibrium position because this is not the best plant size for the market price.

perfect competition long run overheads

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