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Public Finance
by John E. Anderson
Chapter 10
Efficiency Effects of
Taxes and Subsidies
Introduction

Taxes and subsidies can cause
inefficiencies or correct for inefficiencies
in the market.

In this chapter we learn how to analyze
taxes and subsidies for their efficiency
effects.
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3
Excess Burden of Taxes and
Subsidies

Whenever a tax is placed on a good, service, or
form of income, people in the economy are
burdened.

Not only do they have to pay the tax, which is the
first form of burden, but they also are induced to
change their behavior as a result of the tax.

That change of behavior causes a second form of
burden that we call the excess burden of the tax.
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Excess Burden

The excess burden of a tax refers to the
welfare loss caused by imposition of the
tax, over and above the revenue the tax
generates.

In this chapter we consider the causes of
excess burden and consider ways to
minimize the size of excess burdens
resulting from taxation.
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Excess Burden With Demand
Curves

The simplest way to show excess burden
is with a demand curve,

Although a special type of demand curve is
needed called a compensated demand
curve.

This type of demand curve takes out the
income effects of price changes and only
shows the substitution effects.
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Figure 10.1: Ordinary and Compensated Demand
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Figure 10.2: Excess Burden of a Tax
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Excess Burden Formula
EBx  (1 / 2)x xpxt x
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2
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Figure 10.3: Excess Burden When Tax Is Doubled
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Marginal Excess Burden

It is important to consider how the excess
burden of a tax changes when there is a
change in the tax rate.

This concept is known as the marginal
excess burden (MEB) of a tax.
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Figure 10.4: Marginal Excess Burden of a Tax Increase
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Excess Burden of a Subsidy

Subsidies also create excess burden.

The excess burden is the cost of the
subsidy in excess of the welfare
improvement created by the subsidy.
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Figure 10.5: Excess Burden of a Subsidy
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Adding the Supply Side to the
Story

So far, we have assumed that the supply
curve is perfectly elastic (horizontal).

If we assume that the supply curve is
upward sloping, we can generalize the
formula for excess burden.

Assuming that the elasticity of supply is
denoted x we can write the generalized
excess burden formula as follows:
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Figure 10.6: Excess Burden With Upward Sloping Supply
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Generalized Excess Burden
Formula
EBx  (1 / 2) xpx t x / (1 /  x  1 /  x )
2
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Generalized Excess Burden
Formula [continued]

Notice that as the elasticity of supply
becomes infinite, (x approaches infinity)
the generalized formula collapses to the
simple formula first presented.

Also notice that excess burden is directly
related to both elasticities.

The larger the elasticity of demand or
supply, the larger the excess burden.
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The Special Cases of Inelastic
Demand and Supply

The generalized excess burden formula
also indicates that the smaller the
elasticity of demand or supply, the
smaller the excess burden of a tax.

Consider the cases of zero elasticities of
demand and supply in Figure 7.
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Figure 10.7: Excess Burden When Demand or Supply is
Inelastic
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Determinants of Excess Burden

From the formula for excess burden, we
know its determinants include:

Elasticities of demand and supply.

Price of the good (which determines
quantity).

Tax rate applied to the good.
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Optimal Taxation

What if we could tax commodities or
income in such a way as to minimize the
excess burden, or the efficiency loss due
to the tax?

So-called optimal taxation is an attempt
to do this.
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Optimal Commodity Taxation

Suppose we have two goods X and Y.

We want to know the ad valorem taxes to apply to
these goods that will minimize excess burden.

A British economist named Frank Ramsey solved
this problem.

He developed the so-called inverse elasticity rule
that commodity taxes should be inversely
proportional to the good’s elasticity of demand.
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Ramsey Rule
tx / t y   y / x
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Ramsey Rule
[continued]

An implication of the Ramsey Rule is that
the taxes should reduce demand
proportionately for all goods.

That is, the percentage reduction in
market-clearing quantity should be the
same for all commodities.

This does not mean equal proportionate
price increases.
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Figure 10.8: Illustration of the Ramsey Rule
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Implications of the Ramsey Rule

Tax commodities that have inelastic demand
at relatively high rates.

Examples: gasoline, cigarettes, coffee.

Tax commodities that have elastic demand
at relatively low rates.

Examples: durable goods, appliances,
automobiles, fine china and stemware.
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Optimal Income Taxation

In an income tax context, optimal taxation
has a slightly different implication.

Optimal taxation refers to designing an
income tax combining equity and efficiency
concerns.

Labor supply issues are important as an
income tax affects work effort.
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