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Public Finance Public Finance by John E. Anderson

Power Point Slides to Accompany:

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Chapter 10

Efficiency Effects of Taxes and Subsidies

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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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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

2)2/1( xxxx txpEB

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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

EB xp tx x x x x ( / ) / ( / / )1 2 1 12

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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

xyyx tt //

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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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