lecture notes8

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ECO 4554 Economics of State and Local Government

Lecture Notes

PRINCIPLES OF TAX ANALYSIS

Key Points 1. The economic incidence of a tax is often different from the legal incidence. If the legal taxpayer

can reduce or avoid the tax burden by substituting lower-taxed or untaxed activities for higher-taxed activities, then the burden will be partially or fully shifted from the legal taxpayer to other individuals.

2. Suppliers bear a smaller share of a tax when supply is more elastic and demand is more inelastic.

Consumers bear a smaller share of a tax when demand is more elastic and supply is more inelastic.

3. Any tax that changes the relative price of a good, service, or activity has a substitution effect. The

substitution effect causes taxpayers to substitute less-preferred lower-taxed goods, services, or activities for the more-preferred but higher-taxed good, service, or activity. The substitution effect imposes an excess burden on taxpayers in addition to the direct burden imposed by payment of the tax.

4. The excess burden of a tax is larger the more elastic is the demand and the more elastic is the

supply. Excess burden increases exponentially as the tax increases. 5. Taxes are classified as progressive, proportional, or regressive based on how the average tax rate

(not tax liability) changes when the tax base or income changes. Even with a regressive tax, higher income individuals may pay more dollars of tax.

Synopsis

There are two major economic principles in the analysis of taxation: the incidence of a tax and the effect of a tax on economic efficiency (referred to as the excess burden or welfare cost of the tax). These principles are applicable to all taxes. We begin by distinguishing two concepts of incidence. Legal incidence refers to the individual or group that is legally responsible for paying the tax to the government. Economic incidence refers to the individual or group that bears the real burden of the tax, the individual or group whose real income is reduced by the tax. If the burden of the tax is shifted, the economic incidence is different from the legal incidence. Next, we show that economic incidence depends on substitutability as reflected in the elasticities of demand and supply. Individuals or groups that have fewer substitution possibilities also have more inelastic demands or supplies. Individuals with more inelastic demands or supplies bear the larger share of the tax. Therefore, no matter where the legal incidence is imposed, consumers bear a smaller share of the tax when demand is more elastic and supply is more inelastic. Suppliers bear a smaller share of the tax when supply is more elastic and demand is more inelastic. Any tax that changes the relative price of an economic good, service, or activity has a substitution effect. The substitution effect arises because taxpayers substitute less-preferred lower-taxed goods,

ECO 4554: Economics of State and Local Government Principles of Tax Analysis

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services, or activities for the more-preferred but higher-taxed good, service, or activity. We show that this substitution causes a loss in consumer surplus and producer surplus. The loss in surplus is greater than the tax revenue collected. This is the excess burden of a tax. The greater the substitution possibilities, the larger is the excess burden. Therefore, excess burden is greater the more elastic the demand and the more elastic the supply. Excess burden also increases exponentially as the tax is increased. Then, we introduce the concepts of average and marginal tax rates and the concepts of progressivity, proportionality, and regressivity. Finally, there are some clarifying comments about applied incidence analysis.

Lecture Notes I. Tax incidence

A. Definition: The individual or group of individuals on whom the burden of a tax rests bears the incidence of the tax.

B. Two concepts of incidence

1. Legal incidence: The individual or group of individuals that has the legal

responsibility for paying the tax to the government bears the legal incidence of the tax.

2. Economic incidence: The individual or group of individuals whose real

income (or welfare or utility) is reduced by the tax bears the economic incidence.

C. Economic incidence is independent of legal incidence

1. The individuals who bear the legal incidence may be different from those who bear the economic incidence.

2. When the economic incidence differs from the legal incidence, we say that

the burden of the tax has been "shifted". 3. The effects of a tax on the allocation of resources and on the distribution of

income depend on the economic incidence, not the legal incidence.

D. Incidence analysis is essentially hypothetical. It compares the distribution of real income (or utility) under existing policy with the distribution that would exist under a different policy, or it compares the distribution of real income under two different policies, neither of which currently exists.

II. Incidence depends on elasticities

A. Incidence and the elasticity of supply

1. General proposition: For any fixed elasticity of demand, the more inelastic is the supply the greater the share of the tax borne by suppliers and the smaller the share borne by consumers.


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2. Examples: Suppose an excise tax of $0.50 per gallon is imposed on gasoline. Without the tax, the equilibrium price of gasoline would be $1.50 per gallon and the equilibrium quantity would be 5000 gallons.

a. Perfectly inelastic supply (vertical supply curve) See PowerPoint

Slides Figure 8-1.

(1) Neither equilibrium price and nor equilibrium quantity are changed by the tax. The equilibrium price is $1.50 and the equilibrium quantity is 5000 gallons with the tax or without the tax.

(2) Economic incidence and legal incidence are the same.

Because the equilibrium price is unchanged, the net price received by the suppliers decreases to $1.00 per gallon. Suppliers bear the full burden of the tax. Their net revenue is reduced by exactly the amount of the tax. The tax burden is distributed among all the sellers in proportion to their sales revenues.

Price

SupplyDemand

Quantity

5000

$1.50

$1.00

Tax

(3) Consumers bear none of the tax burden because the price of

gasoline doesn’t change. The burden of the tax is not shifted.

b. Perfectly elastic supply (horizontal supply curve reflecting constant marginal costs) See PowerPoint Slides Figure 8-2.

(1) The tax increases suppliers’ costs by $0.50, the amount of

the tax. Supply decreases (the supply curve rises by the amount of the tax). Equilibrium price rises from $1.50 to $2.00, and equilibrium quantity decreases from 5000 gallons to 2000 gallons.


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(2) Economic incidence and legal incidence are entirely different. The full tax burden is shifted from suppliers to consumers through higher prices. Each consumer's real income is reduced in proportion to her/his pre-tax expenditure on gasoline.

Price

Supply without tax

Demand

Quantity

5000

$2.00

$1.50

Tax

Supply with tax

2000

c. Intermediate case (positively-sloped supply curve)

(1) Supply decreases (the supply curve shifts up by $0.50, the full amount of the tax). Price increases.

(2) The higher price provides an incentive for consumers to

reduce their purchases of gasoline. The equilibrium price with the tax is higher than the price without the tax, but the difference is less than the full amount of the tax. Equilibrium quantity decreases.

(3) Consumers bear part of the tax burden in higher gasoline

prices. Suppliers also bear part of the tax burden in lower sales revenues.

(4) The amount of the tax that can be shifted to consumers

depends on the elasticity of supply. If supply is more inelastic (closer to vertical), suppliers bear more of the tax. If it is more elastic (closer to horizontal), consumers bear more of the tax.

B. Incidence and the elasticity of demand


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1. General proposition: For any fixed elasticity of supply, the more inelastic is the demand the greater the share of the tax borne by consumers and the smaller the share borne by suppliers.

2. Examples

a. Perfectly elastic demand (horizontal demand curve) See PowerPoint Slides Figure 8-3.

(1) The tax increases suppliers’ costs by $0.50, the amount of

the tax. Supply decreases (the supply curve shifts up or left by the amount of the tax). Equilibrium price is unchanged but equilibrium quantity decreases from 5000 gallons to 2500 gallons.

Price

Supply without tax

Demand

Quantity

5000

$1.50

$1.00

Tax

Supply with tax

2500

(2) Economic incidence and legal incidence are the same. Because the equilibrium price is unchanged, the net price received by the suppliers decreases to $1.00 per gallon. Suppliers bear the full burden of the tax. Their net revenue is reduced by exactly the amount of the tax. The tax burden is distributed among all the sellers in proportion to their sales revenues.

(3) Consumers bear none of the tax burden because the price of

gasoline doesn’t change. The burden of the tax is not shifted.

b. Perfectly inelastic demand (vertical demand curve) See PowerPoint Slides Figure 8-4.

(1) The tax increases suppliers’ costs by $0.50, exactly the

amount of the tax. Supply decreases (the supply curve shifts up by the amount of the tax). When supply decreases,


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equilibrium price rises from $1.50 to $2.00. Equilibrium quantity is unchanged at 5000.

Price

Supply without tax

Demand

Quantity

5000

$2.00

$1.50

Tax

Supply with tax

(2) The economic incidence and the legal incidence are entirely

different. The entire burden of the tax is shifted from suppliers to consumers through higher prices. The entire economic incidence rests on consumers. Each consumer's real income is reduced in proportion to her/his pre-tax expenditure on gasoline.

c. Intermediate case (negatively-sloped demand curve) See

PowerPoint Slides Figure 8-5.

(1) Supply decreases (the supply curve shifts up by the amount of the tax). Price increases.

(2) The higher price provides an incentive for consumers to

reduce their purchases of gasoline. Therefore, equilibrium price rises by $0.40 (from $1.50 to $1.90), which is less than the full amount of the tax. Equilibrium quantity decreases to 4900.

(3) Consumers bear part of the tax burden in higher gasoline

prices (from $1.50 to $1.90 per gallon). Suppliers also bear part of the tax burden in lower revenues per gallon (from $1.50 to $1.40 per gallon).

(4) The amount of the tax that can be shifted to consumers

depends on the elasticity of demand. If demand is relatively more elastic (closer to horizontal), suppliers bear more of the


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tax. If demand is more inelastic (closer to vertical), consumers bear more of the tax.

C. Incidence, elasticity, and substitutability

1. Elasticity reflects the possibility of substitution. The greater the possibility of substitution, the greater is the elasticity.

a. If consumers have good substitutes for the taxed good, demand will

be relatively elastic. Consumers can then avoid the tax by substituting other non-taxed or lower-taxed goods for it.

b. Similarly, if suppliers have good substitute uses for their resources,

supply will be relatively elastic. Suppliers can avoid the tax by producing less of the taxed good and shifting their resources to other uses.

2. In summary, consumers bear a smaller share of the tax when demand is more

elastic and supply is more inelastic. Suppliers bear a smaller share of the tax when supply is more elastic and demand is more inelastic.

III. Excess burden

A. Income effect and substitution effect

1. A tax increases the price of the taxed good or activity relative to the prices of untaxed or lower-taxed goods and activities. The increase in the relative price affects the taxpayer in two ways.


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a. Income effect: The tax reduces the taxpayer's purchasing power or real income. It takes resources away from the taxpayer and transfers them to the government. This is often referred to as the direct burden of the tax.

b. Substitution (or price) effect: The tax creates an incentive for the

taxpayer to substitute less-preferred but untaxed or lower-taxed goods for the more-preferred taxed good. The loss in consumer utility from this substitution is the excess burden (or welfare cost) of the tax.

2. Any tax that imposes an excess burden is economically inefficient. The

inefficiency of the tax is a result of the substitution effect. All current taxes impose an excess burden so all current taxes are inefficient.

B. Example

1. Suppose without the tax the equilibrium price is $1.50 per gallon and the equilibrium quantity is 5000 gallons. Then, a tax of $6.00 per gallon is imposed. Supply decreases (the supply curve shifts up by the amount of the tax). The equilibrium price rises to $7.50 per gallon. Equilibrium quantity decreases to zero.

Price

Supply without tax

Demand

Quantity

5000

$7.50

$1.50

Supply with tax

2. Because consumers simply stop purchasing gasoline when the tax is $6.00

per gallon, the tax raises no revenue. Because taxpayers pay no tax, there is no loss of purchasing power or real income. The income effect is zero, so the tax imposes no direct burden.

3. Even though consumers pay no tax and lose no real income, they are still

worse off with the tax than without the tax. They substitute other less-preferred but lower-taxed goods for gasoline, but the other goods do not provide as much utility or satisfaction as the gasoline. Because they are no longer consuming gasoline, they lose the consumer surplus they would obtain from gasoline consumption without the tax. The loss in consumer surplus is


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the excess burden of the tax. It is a burden in excess of, or over and above, the loss in purchasing power or real income from paying the tax.

C. Definition: The excess burden of a tax is the loss of social (consumer and producer)

surplus (measured in dollars) in excess of the tax revenue collected by the government. See PowerPoint Slides Figure 8-6.

1. The loss in taxpayers’ utility or satisfaction is greater than the amount of the

tax. First, taxpayers lose purchasing power (and therefore utility or satisfaction or real income) equal to the amount of the tax. This is the direct burden of the tax. But taxpayers also lose additional utility or satisfaction or real income in excess of the tax because of the substitution effect. This is the excess burden of the tax.

2. The excess burden reflects an inefficient allocation of resources. Resources

are shifted from production of the more valuable taxed good to less valuable untaxed or lower taxed goods.

3. The concept of welfare cost provides a dollar measure of this inefficiency or

excess burden. 4. Example

a. Without a tax, the equilibrium price is $1.50 per gallon and the equilibrium quantity is 5000 gallons. The tax is $0.50 per gallon.

b. The tax increases cost so supply decreases (the supply curve shifts up

by the amount of the tax). Equilibrium price rises to $1.80. Equilibrium quantity decreases to 4000 gallons. The social surplus is reduced by the sum of the blue area and the purple area.

Price

Supply without taxDemand

Quantity

5000

$1.80

$1.50Tax

Supply with tax

$1.30

4000

c. The blue area is equal to the tax revenue. It is the direct burden of the tax. Taxpayers (consumers and suppliers) lose purchasing power or


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real income equal to the direct burden. However, when the tax revenues are spent by the government, those who benefit from the expenditure are better off by this amount. Therefore, this part of the taxpayers’ loss is just offset by a gain to the beneficiaries of the government expenditure. There is no net loss to society from the direct burden of the tax.

d. The purple area is a loss in consumer and producer surplus in excess

of the tax revenue. It is a loss to consumers and suppliers that is not offset by a gain to anyone else. Therefore, it is a net loss of real income (or utility or satisfaction) to society. This is the excess burden of the tax.

D. Efficient taxes

1. If the same revenue could be collected without creating incentives for consumers and producers to substitute less-preferred for more-preferred goods, the excess burden of a tax could be eliminated. To avoid creating substitution incentives, the same tax must be imposed on every good, service, or activity.

2. Taxpayers would be better off, but the tax revenue (the direct burden) would

be the same so the beneficiaries of the government expenditure would be unaffected. Therefore, taxes that impose an excess burden are inefficient because there exists an alternative tax (one without an excess burden) that makes taxpayers better off without making anyone worse off.

3. A tax with no substitution effects is called a lump-sum tax. With a lump-sum

tax, an individual’s tax liability is independent of any economic decisions or choices or behavior. A lump-sum tax is the only truly efficient tax.

4. Problem: There are no lump-sum taxes. A hypothetical lump-sum tax is often

used as a benchmark against which to measure the welfare cost or excess burden of actual taxes, but no existing taxes are lump-sum taxes. In fact, lump-sum taxes are usually considered to be inequitable even though they are efficient.

IV. Principles of excess burden analysis

A. Excess burden and the elasticity of demand

1. General proposition: For a fixed elasticity of supply, excess burden is larger the more elastic is demand. See PowerPoint Slides Figure 8-7.

2. Example

a. The excise tax on gasoline increases suppliers’ costs so supply decreases (the supply curve shifts up by the amount of the tax). With perfectly elastic supply, the entire economic incidence of the tax is shifted forward to consumers. Equilibrium price increases by the full amount of the tax.


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b. Elastic demand: Suppose demand is relatively elastic. When price

increases, equilibrium quantity decreases from 5000 gallons to 2000 gallons. The substitution effect is large, creating a large excess burden shown by the blue triangle.

c. Inelastic demand: Suppose demand is relatively inelastic. Now, when

price increases, equilibrium quantity only decreases from 5000 gallons to 4000 gallons. The substitution effect is smaller and the excess burden, shown by the purple triangle, is also smaller.

B. Excess burden and the elasticity of supply

1. General proposition: For a fixed elasticity of demand, the excess burden is larger the more elastic is supply. See PowerPoint Slides Figure 8-8.

2. Example

a. With perfectly elastic demand, consumers are unwilling to pay a higher price for gasoline. Equilibrium price is unchanged by the tax. Instead, the net price received by sellers decreases to $1.00 per gallon so that sellers bear the entire economic incidence of the tax.


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b. Elastic supply: Suppose supply is relatively elastic. When price

increases, equilibrium quantity decreases from 5000 gallons to 2000 gallons. The substitution effect is large, creating a large excess burden shown by the blue triangle.

c. Inelastic supply: Suppose supply is relatively inelastic. When price

increases, equilibrium quantity decreases from 5000 gallons to 4000 gallons. The substitution effect is smaller and the excess burden, shown by the purple triangle, is also smaller.

C. Excess burden and the tax rate

1. General proposition: The excess burden of a tax increases exponentially as the tax rate increases. See PowerPoint Slides Figure 8-9.

2. Example

a. Assume that supply is perfectly elastic so that the entire economic incidence of the tax is shifted forward to consumers. (This assumption is made only for convenience. The result is valid regardless of the elasticities of demand and supply.)

b. If a tax of $0.50 per gallon (equal to 33.3% of the initial price) is

imposed, equilibrium price rises by the amount of the tax to $2.00 per gallon. Equilibrium quantity decreases from 5000 gallons to 3500 gallons. The welfare cost or excess burden is shown by the blue area.


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c. If, instead, a tax of $1.00 per gallon (equal to 66.7% of the initial

price) is imposed, equilibrium price rises by the amount of the tax to $2.50 per gallon and equilibrium quantity decreases from 5000 gallons to 2000 gallons. The welfare cost or excess burden is shown by the sum of the blue area and the purple area.

d. The higher tax is double the lower tax ($1.00 per gallon versus $0.50

per gallon), but the excess burden of the higher tax is $1500, four times the $375 excess burden of the lower tax. The excess burden increases exponentially, not proportionately, with the tax rate.

V. Average and marginal tax rates

A. Two different tax rate concepts are used in the economic analysis of taxation, the average tax rate (ATR) and the marginal tax rate (MTR).

1. The average tax rate indicates the individual’s total tax liability as a

percentage of an appropriate index or benchmark:

Average tax rate (ATR) = Total tax liability ÷ Benchmark

The benchmark is usually either the tax base or income. a. Tax base as benchmark: Suppose the price of gasoline is $1.50 per

gallon and your annual consumption of gasoline is 600 gallons. Your total annual expenditure on gasoline is $900. If the excise tax on gasoline is $0.50 per gallon (33.3% of the price), your total annual tax liability is $300. This is 33.3% of your expenditure on gasoline (the tax base). Using the tax base as the benchmark, the average tax rate on gasoline is 33.3%.


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b. Income as benchmark: Suppose your annual income is $15,000. Your $300 annual gasoline tax liability is 1% of your income. Using income as the benchmark, the average tax rate on gasoline is 1%.

2. The marginal tax rate indicates the percentage change in your tax liability

when the benchmark changes:

Marginal tax rate (MTR) = Change in total tax liability ÷ Change in benchmark

a. Tax base as benchmark: Suppose next year you use 660 gallons. At

$1.50 per gallon, next year’s gasoline expenditure is $990. Next year’s tax liability is $330. The change in your tax liability is $30; the change in your gasoline expenditure is $90. The marginal tax rate using the tax base as the benchmark is 33.3%.

b. Income as benchmark: Suppose your gasoline expenditure increased

because your income increased to $16,500. Again the change in your tax liability is $30; the change in your income is $1500. The marginal tax rate using income as the benchmark is 2%.

3. The average tax rate is relevant for equity issues while the marginal tax rate

is relevant for efficiency issues.

a. The average tax rate is most useful in analyzing the distribution of the tax burden among individuals or groups of taxpayers. It provides information about the effect of the tax on the distribution of income.

b. The marginal tax rate is most useful in analyzing how individuals’

economic behavior at the margin is affected by the tax. It provides information about the effect of the tax on resource allocation.

B. Progressivity, proportionality, and regressivity

1. Taxes are classified as progressive, proportional, or regressive based on how

the average tax rate changes when the benchmark changes. 2. Definitions

a. Progressivity: A tax is progressive if the average tax rate increases when the benchmark increases.

b. Proportionality: A tax is proportional if the average tax rate remains

constant when the benchmark increases. c. Regressivity: A tax is regressive if the average tax rate decreases

when the benchmark increases.

3. Examples: Suppose income is the benchmark. The table shows three different examples of how tax liability might change as income increases.


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Income Progressive

Proportional

Regressive

Tax ATR MTR Tax ATR MTR Tax ATR MTR $0 $0 ----- ----- $0 ----- ----- $0 ----- -----

$1,000 $50 5.0% 5.0% $100 10.0% 10.0% $150 15.0% 15.0% $2,000 $150 7.5% 10.0% $200 10.0% 10.0% $250 12.5% 10.0% $3,000 $300 10.0% 15.0% $300 10.0% 10.0% $300 10.0% 5.0%

a. Total tax liability increases when income increases under each tax

system, but

• with the progressive tax, the average tax rate also increases.

• with the proportional tax, the average tax rate remains constant.

• with the regressive tax, the average tax rate decreases.

b. Even with a regressive tax, higher income individuals may pay more

tax. The classification of the tax as progressive, proportional, or regressive is determined by the behavior of the average tax rate, not the behavior of total tax liability.

4. If a tax is progressive, the marginal tax rate is greater than the average tax

rate (MTR>ATR). If a tax is proportional, the marginal tax rate is equal to the average tax rate (MTR=ATR). If a tax is regressive, the marginal tax rate is less than the average tax rate (MTR<ATR). This is an application of the usual rule concerning the relationship between averages and marginals.

5. A tax can be proportional using the tax base as the benchmark but

progressive or regressive using income as the benchmark. Or a tax can be regressive or progressive using the tax base as the benchmark, but proportional using income as the benchmark.

VI. Applied incidence analysis

A. Firms purchase the services of resource inputs (labor services, land services, and capital services) from the owners of these resource inputs. The owners receive income from the sale of their labor, land, and capital services. Firms use the services of the resource inputs to produce goods and services that are demanded by consumers and for which the consumers make expenditures.


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B. Taxes, prices, and incidence analysis

1. The economic effects of taxes are transmitted through price changes. A tax may change the prices of goods and services and also the prices paid to the resource inputs that produce them.

2. Individuals, both consumers and suppliers, respond to these price changes.

Individual responses to these price changes determine both the incidence of a tax and its welfare cost.

3. The same individual may be both a consumer and a resource supplier. This is

a very important point to understanding incidence analysis. Any individual’s share of the tax depends both on how much of her/his income is spent on goods whose prices have changed and how much of her/his income is received from supplying resources whose prices have changed.

C. Applying the theory

1. The first step is to determine how much of a tax is borne by consumers and how much is borne by suppliers, and further, how much of the supplier tax is borne by particular factors of production (labor, capital, land). In other words, we first determine the effect of the tax on the functional distribution of income.

Landowners

Workers

Capitalists

Supply Resources

Receive Income

Land

Labor

Capital

ResourceInputs

Firms

Demand Resources

Supply Goods andServices

Goodsand

ServicesConsumers

Demand Goodsand Services

ConsumptionExpenditures

Output


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2. We generally want to know, however, how the tax affects individuals at different income levels. That is, we want to know the effect of the tax on the personal distribution of income. This requires that we determine the average amount of income spent at each income level on those goods whose prices have changed as a result of the tax and that we determine the average amount of income received by individuals at each income level from those factors whose prices have changed because of the tax.

3. Example: Suppose we determine that a gasoline tax equal to 10% of the pre-

tax price increases the price by 4%.

a. If price rises by 4% when a 10% tax is imposed, forty percent of the tax is borne by consumers of gasoline in proportion to their expenditure on gasoline and 60% is borne by suppliers in proportion to the income they derive from the production and sale of gasoline.

b. While we may be interested in how the tax affects the functional

distribution of income (how much rests on consumers and how much on labor, capital, and land), we are usually equally or more interested in how the tax affects the personal distribution of income. Assume we wish to know how the tax affects individuals with annual incomes between $30,000 and $40,000.

c. Suppose individuals at this income level account for 5% of total

expenditures on gasoline. Then, as consumers they bear 2% (5% of 40%) of the total gasoline tax burden. Suppose that 10% of all income earned from the production and sale of gasoline accrues to individuals at this income level. As suppliers they bear 6% of the total gasoline tax burden. Therefore, individuals with incomes between $30,000 and $40,000 bear 8% of the total gasoline tax in their capacities as both consumers and suppliers.

d. We can then determine the average effective tax rate for individuals

with incomes between $30,000 and $40,000 by dividing their average tax burden by their average income. If this average tax rate decreases as we move up the income distribution, the gasoline tax is regressive.

lecture notes8

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