1 Chapter 11 APPLIED COMPETITIVE ANALYSIS. 2 Economic Efficiency and Welfare Analysis The area...

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Chapter 11

APPLIED COMPETITIVE ANALYSIS

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Economic Efficiency and Welfare Analysis

• The area between the demand and the supply curve represents the sum of consumer and producer surplus– measures the total additional value

obtained by market participants by being able to make market transactions

• This area is maximized at the competitive market equilibrium

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Quantity

Price

P *

Q *

S

D

Consumer surplus is thearea above price and belowdemand

Producer surplus is thearea below price andabove supply

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At output Q1, total surpluswill be smaller


Quantity

Price

P *

Q *

S

D

Q1

At outputs between Q1 andQ*, demanders would valuean additional unit more thanit would cost suppliers toproduce

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• Mathematically, we wish to maximize

consumer surplus + producer surplus =

Q Q

dQQPQUdQQPPQPQQU0 0

)()(])([])([

• In long-run equilibria along the long-run supply curve, P(Q) = AC = MC

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• Maximizing total surplus with respect to Q yields

U’(Q) = P(Q) = AC = MC

– maximization occurs where the marginal value of Q to the representative consumer is equal to market price

• the market equilibrium

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Welfare Loss Computations

• Use of consumer and producer surplus notions makes possible the explicit calculation of welfare losses caused by restrictions on voluntary transactions– in the case of linear demand and supply

curves, the calculation is simple because the areas of loss are often triangular

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• Suppose that the demand is given by

QD = 10 - P

and supply is given by

QS = P - 2

• Market equilibrium occurs where P* = 6 and Q* = 4

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• Restriction of output to Q0 = 3 would create a gap between what demanders are willing to pay (PD) and what suppliers require (PS)

PD = 10 - 3 = 7

PS = 2 + 3 = 5

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The welfare loss from restricting outputto 3 is the area of a triangle


Quantity

Price

S

D

6

4

7

5

3

The loss = (0.5)(2)(1) = 1

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• The welfare loss will be shared by producers and consumers

• In general, it will depend on the price elasticity of demand and the price elasticity of supply to determine who bears the larger portion of the loss– the side of the market with the smallest

price elasticity (in absolute value)

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Price Controls and Shortages

• Sometimes governments may seek to control prices at below equilibrium levels– this will lead to a shortage

• We can look at the changes in producer and consumer surplus from this policy to analyze its impact on welfare

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Quantity

PriceSS

D

LS

P1

Q1

Initially, the market isin long-run equilibriumat P1, Q1

Demand increases to D’

D’

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Quantity

PriceSS

D

LS

P1

Q1

D’

Firms would begin toenter the industry

In the short run, pricerises to P2

P2

The price would endup at P3

P3

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Quantity

PriceSS

D

LS

P1

Q1

D’

P3

There will be a shortage equal toQ2 - Q1

Q2

Suppose that thegovernment imposesa price ceiling at P1

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This gain in consumersurplus is the shadedrectangle


Quantity

PriceSS

D

LS

P1

Q1

D’

P3

Q2

Some buyers will gain because they can purchase the good for a lower price

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The shaded rectangletherefore represents apure transfer fromproducers to consumers


Quantity

Price

D

P1

Q1

D’

SS

LSP3

Q2

The gain to consumers is also a loss to producers who now receive a lower price

No welfare loss there

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This shaded trianglerepresents the value of additional consumer surplus that would have been attained without the price control


Quantity

PriceSS

D

LS

P1

Q1

D’

P3

Q2

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This shaded trianglerepresents the value of additional producer surplus that would have been attained without the price control


Quantity

PriceSS

D

LS

P1

Q1

D’

P3

Q2

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This shaded arearepresents the total value of mutually beneficial transactions that are prevented by the government


Quantity

PriceSS

D

LS

P1

Q1

D’

P3

Q2

This is a measure of the pure welfare costs of this policy

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Disequilibrium Behavior• Assuming that observed market

outcomes are generated by

Q(P1) = min [QD(P1),QS(P1)],

suppliers will be content with the outcome but demanders will not

• This could lead to a black market

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Tax Incidence

• To discuss the effects of a per-unit tax (t), we need to make a distinction between the price paid by buyers (PD) and the price received by sellers (PS)

PD - PS = t

• In terms of small price changes, we wish to examine

dPD - dPS = dt

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Tax Incidence

• Maintenance of equilibrium in the market requires

dQD = dQS

or

DPdPD = SPdPS

• Substituting, we get

DPdPD = SPdPS = SP(dPD - dt)

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Tax Incidence

• We can now solve for the effect of the tax on PD:

DS

S

PP

PD

ee

e

DS

S

dt

dP

• Similarly,

DS

D

PP

PS

ee

e

DS

D

dt

dP

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Tax Incidence• Because eD 0 and eS 0, dPD /dt 0

and dPS /dt 0

• If demand is perfectly inelastic (eD = 0), the per-unit tax is completely paid by demanders

• If demand is perfectly elastic (eD = ), the per-unit tax is completely paid by suppliers

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Tax Incidence

• In general, the actor with the less elastic responses (in absolute value) will experience most of the price change caused by the tax

S

D

D

S

e

e

dtdP

dtdP

/

/

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Tax Incidence

Quantity

PriceS

D

P*

Q*

PD

PS

A per-unit tax creates awedge between the pricethat buyers pay (PD) andthe price that sellers receive (PS)

t

Q**

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Buyers incur a welfare lossequal to the shaded area

Tax Incidence

Quantity

PriceS

D

P*

Q*

PD

PS

Q**

But some of this loss goesto the government in theform of tax revenue

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Sellers also incur a welfareloss equal to the shaded area

Tax Incidence

Quantity

PriceS

D

P*

Q*

PD

PS

Q**

But some of this loss goesto the government in theform of tax revenue

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Therefore, this is the dead-weight loss from the tax

Tax Incidence

Quantity

PriceS

D

P*

Q*

PD

PS

Q**

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Deadweight Loss and Elasticity

• All nonlump-sum taxes involve deadweight losses– the size of the losses will depend on the

elasticities of supply and demand

• A linear approximation to the deadweight loss accompanying a small tax, dt, is given by

DW = -0.5(dt)(dQ)

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• From the definition of elasticity, we know that

dQ = eDdPD Q0/P0

• This implies that

dQ = eD [eS /(eS - eD)] dt Q0/P0

• Substituting, we get

00

2

0

50 QPeeeeP

dtDW DSSD )]/([.

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• Deadweight losses are zero if either eD or eS are zero

– the tax does not alter the quantity of the good that is traded

• Deadweight losses are smaller in situations where eD or eS are small

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Transactions Costs• Transactions costs can also create a

wedge between the price the buyer pays and the price the seller receives– real estate agent fees– broker fees for the sale of stocks

• If the transactions costs are on a per-unit basis, these costs will be shared by the buyer and seller– depends on the specific elasticities involved

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Gains from International Trade

Quantity

Price

S

D

Q*

P*

In the absence ofinternational trade,the domesticequilibrium price would be P* andthe domesticequilibrium quantitywould be Q*

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Quantity

Price

Q*

P*

S

D

Quantity demanded willrise to Q1 and quantitysupplied will fall to Q2

Q1Q2

If the world price (PW)is less than the domesticprice, the price will fallto PW

PW

Imports = Q1 - Q2

imports

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Consumer surplus rises

Producer surplus falls

There is an unambiguouswelfare gain


Quantity

Price

Q*

P*

S

D

Q2Q1

PW

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Effects of a Tariff

Quantity

Price

S

D

Q1Q2

PW

Quantity demanded fallsto Q3 and quantity suppliedrises to Q4

Q4 Q3

Suppose that the governmentcreates a tariff that raisesthe price to PR

PR

Imports are now Q3 - Q4

imports

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Consumer surplus falls

Producer surplus rises

These two triangles represent deadweight loss

The government getstariff revenue

Effects of a Tariff

Quantity

Price

S

D

Q1Q2

PW

Q4 Q3

PR

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Quantitative Estimates of Deadweight Losses

• Estimates of the sizes of the welfare loss triangle can be calculated

• Because PR = (1+t)PW, the proportional change in quantity demanded is

DDW

WR teeP

PP

Q

QQ

1

13

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The areas of these twotriangles are

Quantitative Estimates of Deadweight Losses

Quantity

Price

S

D

Q1Q2

PW

Q4 Q3

PR

))((. 311 50 QQPPDW WR

12

1 50 QPetDW WD.

))((. 242 50 QQPPDW WR

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2 50 QPetDW WS.

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Other Trade Restrictions• A quota that limits imports to Q3 - Q4

would have effects that are similar to those for the tariff– same decline in consumer surplus– same increase in producer surplus

• One big difference is that the quota does not give the government any tariff revenue– the deadweight loss will be larger

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Trade and Tariffs• If the market demand curve is

QD = 200P-1.2

and the market supply curve is

QS = 1.3P,

the domestic long-run equilibrium will occur where P* = 9.87 and Q* = 12.8

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Trade and Tariffs• If the world price was PW = 9, QD would

be 14.3 and QS would be 11.7

– imports will be 2.6

• If the government placed a tariff of 0.5 on each unit sold, the world price will be PW = 9.5

– imports will fall to 1.0

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Trade and Tariffs• The welfare effect of the tariff can be

calculated

DW1 = 0.5(0.5)(14.3 - 13.4) = 0.225

DW2 = 0.5(0.5)(12.4 - 11.7) = 0.175

• Thus, total deadweight loss from the tariff is 0.225 + 0.175 = 0.4

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Important Points to Note:• The concepts of consumer and producer

surplus provide useful ways of analyzing the effects of economic changes on the welfare of market participants– changes in consumer surplus represent

changes in the overall utility consumers receive from consuming a particular good

– changes in long-run producer surplus represent changes in the returns product inputs receive

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Important Points to Note:

• Price controls involve both transfers between producers and consumers and losses of transactions that could benefit both consumers and producers

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Important Points to Note:• Tax incidence analysis concerns the

determination of which economic actor ultimately bears the burden of a tax– this incidence will fall mainly on the actors

who exhibit inelastic responses to price changes

– taxes also involve deadweight losses that constitute an excess burden in addition to the burden imposed by the actual tax revenues collected

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Important Points to Note:• Transaction costs can sometimes be

modeled as taxes– both taxes and transaction costs may affect

the attributes of transactions depending on the basis on which the costs are incurred

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Important Points to Note:• Trade restrictions such as tariffs or

quotas create transfers between consumers and producers and deadweight losses of economic welfare– the effects of many types of trade

restrictions can be modeled as being equivalent to a per-unit tariff

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