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Updated: 09 Oct 2007

ECON 635: PUBLIC ECONOMICS

Lecture 3Topics to be covered:a. Tax Revenue, Excess Burden and Tax Incidenceb. Incremental Excess Burdenc. Concluding Commentsd. Taxes in more than One Market

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• The supply price (Ps) is the price received by the producer/seller, while the demand price (Pd) is the price paid by the consumer/purchaser.

• An ad valorem tax (t) is usually expressed as a percentage of the supply price.

Pd = (1+t) Ps

• A specific (or ad rem) tax (T) is expressed in terms of so many dollars or cents per unit.

Pd = Ps + T

ECONOMIC PRINCIPLES: TAX REVENUE, EXCESS BURDEN AND TAX INCIDENCE

(CONT’D)

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P1d = P1

s + T

Tax Revenue, Excess Burden, and Tax Incidence

Producers tax incidence

Consumers’ tax incidence

The tax revenue, excess burden and tax incidence are:Tax Revenue: This is given by the area Pd

1AEPs1.

Excess Burden: This is represented by the area ABE.Tax Incidence: Consumers lose Pd

1ABPo and producers lose PoBEPs1.

(a) Tax burden is shifted forward to the consumer (b) Part is shifted backward to the producer.

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Algebraic Formulation• In order to quantify the effects of the tax we need to find the new

market equilibrium defined by Q1, Pd1 and Ps

1. We do this by first finding Ps = Ps

1 - Po, as follows:

s = price elasticity of supply d = price elasticity of demand.

• T = Pd - Ps

Pd = T + Ps Therefore,

• Tax Revenue: TQ1

• Excess Burden: ½ T(Q0 – Q1)• Tax Incidence: Cost borne by consumers is

s s d s

s s d d

sd

s d

ds d

P P T)

P ) = T

P T

P T

(

(

s

(P P )(Q Q

2)1

d0

0 1

dS QQQQQ 01

0

0

0

0 11QP

PP

QQP

PP

Q dd

dSS

S

ddSS PP

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• If the tax is ad valorem rather than specific then this equation becomes:

From these equations, we may draw the following conclusions:• Higher (absolute) values of either d or s imply a lower tax revenue. In other

words, if demand and/or supply is more elastic then tax revenue will be lower, ceteris paribus.

• An elastic demand means that consumers will shift quickly to other goods if the price rises; they are thus able to "run away" from a tax relatively easily.

• As the tax rate (t) rises, total tax revenue will first rise, reach a maximum and then fall! The idea is that eventually the tax rate becomes so high that it scares away a large number of consumers and the tax revenue declines.

• Often the tax rate does not have to be very high for this to happen. For instance, if supply is perfectly elastic (s ) and demand is unit elastic (d = -1) then tax revenues are maximized when the tax rate is 50%. If the tax rate exceeds 50%, revenues will begin to fall.

Total Tax RevenueTTR = TQ0 ( )1

0

TP

s d

s d

TTR =tP Q t P Q0 02

0 0

( ( )

( ))

d s

s d t1

1

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Algebraic FormulationTotal Tax Revenue

TTR 11 QtP S )( 0SPPt )( 0

SQQ

))1(

( 00 t

tPPt dS

d

))1(

( 00 t

tQQ dS

dS

2

003

002

00)1(

)()1(

)1(2

t

QPtt

QPtQtP

dS

d

dS

Sd

)1()1(00

2

00 tQPt

QtP dS

Sd

Since 0tPT , TTR )1(0

0 dS

dS

PTTQ

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Excess Burden• The expression for excess burden (EB) for a specific tax is as follows:

• and for an ad valorem tax, EB is:

It is noteworthy that:• The Excess Burden rises with the square of the tax rate; that is, if the tax

rate is doubled the excess burden will be quadrupled. • Thus high tax rates have a disproportional effect in reducing efficiency. • It follows that lower tax rates levied on a broader base will be less

inefficient and may bring the same amount of revenue.• The Excess Burden increases as demand and supply become more

elastic. • This also argues for taxing broad categories of goods (low demand

elasticities) rather than particular products (often high demand elasticities).

EB - T QP

( )12

2 0

0

s d

s d

EB - t P Q ((1 t)

)12

20 0

s d

s d

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Algebraic FormulationExcess Burden

SS QtPEB 1)21(

SS QPPtEB )()21( 0

)1()

)1(()

21( 00

0 ttQ

ttP

PtEB dS

dS

dS

d

22

003

002

)1()

21(

)1()

21(

t

QPtt

QPtEBdS

S

dS

dS

)1()

21( 00

2

tQPtEB dS

dS

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• Although the excess burden triangles may look small on a diagram, it is important to realize that they often represent a high proportion of the tax collected. Assuming that supply is infinitely elastic:

Excess Burden (Cont’d)

Elasticity of demand

t -0.5 -1 -2

20%33%50%

5.6%10.0%16.7%

12.5%25.0%50.0%

33.3%100.0%

Note: Excess Burden is given as a fraction of total tax revenue

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• Following figure shows the extra excess burden as a fraction of extra tax revenue following a small increase in the tax rate:

• In other words, if the tax rate is 20%, and the elasticity of demand is -1, then the efficiency cost of a small increase in the tax rate is 33 cents for each extra $1 raised in tax revenue. Thus the efficiency costs of increases in the tax rates can be large.

Excess Burden (Cont’d)

Elasticity of demand

t -0.5 -1 -2

20%33%50%

12%25%50%

33%100%

200%

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• It can be shown that the proportion of tax borne by consumers is given by

• A few observations are in order:

• The incidence of the tax depends only on the relative size of the demand and supply elasticities, and not on the tax rate.

• In other words, the fraction of the burden borne by consumers will not change if the tax rate is increased or lowered.

• As demand becomes more elastic (i.e. d rises absolutely) consumers bear less of the burden, as they "run away” from the tax.

• Conversely, as supply becomes more elastic, consumers bear more of the burden. An important case is that of taxes on trade.

• Since the supply curve for imports is perfectly elastic, it follows that consumers bear the entire burden of import tariffs.

Tax Incidence

PT

d

s

s d d

s

1

1 ( )

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Algebraic Formulation Tax Incidence

dS QQ 0

0

0

0 11QP

PP

QQP

PP

Q dd

dSS

S

SdSd PP )/(

SS tPTPTt 11 ,/ )(, 01

SSSd PPttPPPT )( 0

SSd PPtPP SSSdS PttPPP 0)/(

0)1/( tPtP dSS 0)1(tP

tP ds

dS

0tPT

Tt

P dS

ddSd

)1()/(

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• This analysis does not include the cost of administering the taxes, or the cost of compliance borne by the taxpayers.

• These expenses should, in principle, be counted as part of excess burden.

• This analysis is in a partial equilibrium framework.

• For instance, it does not take into account the effect of the tax on the revenue from an existing tax on a substitute or a complement.

• A more general analysis is often possible and is now being used increasingly.

• Nevertheless, even the partial equilibrium analysis is quite powerful and helps understand the different aspects of taxation.

Concluding Comments

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1. A low tax rate on a broad base is generally preferable to a high tax rate on a narrow base. This is because as t rises the excess burden (inefficiency) rises rapidly, and tax revenue rises less quickly.

2. Other things being equal, put a lower tax on goods with very elastic demand and supply curves. Since imports often have a highly elastic supply, this usually argues against taxes on imports.

3. An understanding of tax incidence is one of the keys to understanding the politics of taxation, since it helps us identify who the winners and losers are likely to be.

Concluding Comments (Cont’d)

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• It was brought out above that the excess burden due to taxes depends on the price elasticity of demand and supply. If the demand and supply are inelastic, the excess burden is minimum.

• As different products have different elasticities of demand and supply, the taxes which would reduce excess burden would be different. But in practice, it is difficult to get information regarding price elasticities of demand and supply for all commodities measured consistently.

• It will also be impractical to administer a tax system which has a large set of different rates imposed on a wide range of products.

• In practice, administrative convenience favors a uniform rate of tax, even though an optimal approach would call for differentiation among products.

• Tax system should be stable, easy to understand.

Concluding Comments (Cont’d)

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Taxes in More Than One Market Considered

Tax Revenue = Area Py1 Py0 B CExcess Burden = Area ABCResources BAY0Y1 move from market of Y to market of X (FEX1X0).NNP after tax = X1 × Px0 + Y1 × Py1

= Y1 × 1.2 + X1 × 1

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Taxes in More Than One Market Considered (Cont’d)

When a 10% tax is introduced on X, the change in EB is:EB = ½×0.10×(X1 – X2) – 0.2 × (Y2 – Y1)

1.101.00 1.00

1.20

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Taxes in More Than One Market Considered (Cont’d)

• The change in excess burden is negative if the second term is larger.• Then, the EB in both markets combined can be reduced by putting a tax

on market X.• The net EB in both markets after putting taxes in both markets is

EBnet= ½ × 0.2 × (Y0 – Y1) + ½ × 0.1 × (X1 – X2) – 0.2 × (Y2 – Y1)• If the net excess burden is negative, there is welfare gain. In practice, a

tax on services, when there are already taxes on goods, may result in a welfare gain.

• Specific taxes induce distortions in the market and result in efficiency costs.

• Lump sum taxes which do not affect producers nor consumers behavior do not create distortions in the market.

• Efforts are made by different countries to develop tax systems which minimize efficiency cost, increase and stabilize tax revenue over a reasonable time horizon of 10 years or more.

• The cost of the tax administration and the simplicity are also important factors which are considered while structuring the tax system.