Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
Tax Inefficiencies and Their
Implications for Optimal Taxation
Chapter 20
20.1 Taxation and Economic
Efficiency
20.2 Optimal Commodity Taxation
20.3 Optimal Income Taxes
20.4 Tax-benefit Linkages and the
Financing of Social Insurance
Programs
20.5 Conclusion
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Graphical Approach
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20 . 1
Taxation and Economic Efficiency
Elasticities Determine Tax Inefficiency
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Elasticities Determine Tax Inefficiency
The inefficiency of any tax is determined by the extent to which
consumers and producers change their behavior to avoid the tax;
deadweight loss is caused by individuals and firms making inefficient
consumption and production choices in order to avoid taxation.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
 APPLICATION
Tax Avoidance in Practice
1. The British boat designer Uffa Fox lived in a home he constructed from a floating
bridge. When the Inland Revenue (Britain’s tax collectors) attempted to collect
property tax on the home, Fox began sailing it up and down the river. By the time
he was done, Fox had collected so many different addresses that the Inland
Revenue gave up their attempts.
2. An Englishman visiting Cyprus in the early 1980s asked a tour guide why so
many of the houses seemed to have steel reinforcement bars jutting out from their
top floors. The guide informed him that Cyprus had a building tax that applied
only to finished structures. Owners of those houses could thus claim that they
were still in the process of finishing the roof.
3. The Thai government levies a tax on signs in front of businesses. The tax is levied
only on external signs and the rate depends on whether the sign is completely in
Thai (low), in Thai and English (medium), or completely in English (very high).
A walk around Bangkok thus reveals many businesses hanging English signs with
a small amount of Thai writing in the upper-right-hand corner. Some businesses
manage to avoid the tax entirely by printing the message on curtains that are hung
in the front window, rendering the sign “internal” and thus tax-exempt.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Determinants of Deadweight Loss
The formula for DWL is
marginal deadweight loss
The increase in deadweight loss
per unit increase in the tax.
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Determinants of Deadweight Loss
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Deadweight Loss and the Design of Efficient Tax Systems
A Tax System’s Efficiency Is Affected by a Market’s
Preexisting Distortions
preexisting distortions Market failures, such
as externalities or imperfect competition, that
are in place before any government
intervention.
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Deadweight Loss and the Design of Efficient Tax Systems
A Tax System’s Efficiency Is Affected by a Market’s
Preexisting Distortions
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 1
Taxation and Economic Efficiency
Deadweight Loss and the Design of Efficient Tax Systems
Governments Should “Smooth” Tax Rates Over Time
Just as individual utility is maximized by full consumption
smoothing, government efficiency in taxation over time is
maximized by tax smoothing, by having a relatively constant
tax rate over time rather than high taxes in some periods and
low taxes in others.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
 APPLICATION
The Deadweight Loss of Taxing Wireless Communications
Hausman (2000) estimated the deadweight loss from a particularly dynamic sector of
our economy: wireless communications services.
• In 1999, the state and federal tax burden on wireless communication in the typical
state was 14.5%, although the rate was 25% in high-tax states.
• Hausman estimated that for every dollar the government raised in taxes, social
welfare was reduced by 53¢.
This figure is high for three reasons:
• Demand for wireless communications is fairly price sensitive.
• There is already a large preexisting distortion in this market.
• The taxes are fairly high, and the marginal deadweight loss rises with the tax rate.
Hausman estimated that the marginal deadweight loss caused by an additional tax on
wireless services ranged from 72¢ to 90¢ per dollar raised.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 2
Optimal Commodity Taxation
Ramsey Taxation: The Theory of Optimal
Commodity Taxation
optimal commodity taxation Choosing the tax
rates across goods to minimize deadweight loss
for a given government revenue requirement.
Ramsey Rule To minimize the deadweight loss of a tax system
while raising a fixed amount of revenue, taxes should be set
across commodities so that the ratio of the marginal deadweight
loss to marginal revenue raised is equal across commodities.
value of additional government revenues The value
of having another dollar in the government’s hands
relative to its next best use in the private sector.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 2
Optimal Commodity Taxation
Inverse Elasticity Rule
If we assume that the supply side of commodity markets is perfectly competitive
(elasticity of supply is infinite), then the Ramsey result implies that:
This formulation of Ramsey’s rule shows that two factors must be balanced
when setting optimal commodity taxes:
 The elasticity rule: When elasticity of demand for a good is high, it should
be taxed at a low rate; when elasticity is low, the tax rate should be high.
 The broad base rule: It is better to tax a wide variety of goods at a moderate
rate than to tax very few goods at a high rate. Because the marginal
deadweight loss from a tax rises with the tax rate, the government should
spread taxes across a large number of commodities and not tax any one
commodity at a very high rate.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 2
Optimal Commodity Taxation
Equity Implications of the Ramsey Model
Imagine that the government had only two goods it could tax, cereal and caviar.
• The elasticity of demand for caviar is much higher than that for cereal, so
the inverse elasticity rule would suggest that the government tax cereal
much more highly than caviar.
• This would mean imposing a tax on a good consumed exclusively by
higher-income groups that was much lower than the tax imposed on a good
consumed by all.
This outcome, while efficient, might violate a government’s sense of tax
fairness across income groups (vertical equity).
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
 APPLICATION
Price Reform in Pakistan
Angus Deaton (1997) studied the demands for commodities in several developing
nations. He used variation in prices encountered by consumers of rice, wheat, and
other commodities to estimate their elasticities of demand.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
 APPLICATION
Price Reform in Pakistan
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
optimal income taxation Choosing
the tax rates across income groups to
maximize social welfare subject to a
government revenue requirement.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
A Simple Example
It is helpful to begin with a simple example that makes the following assumptions:
1. Everyone in society has the same utility functions (U1 = U2 = . . .).
2. These utility functions exhibit diminishing MU of income.
3. The total amount of income in society is fixed (so incomes are not determined
by individual choices that might respond to tax rates).
4. Society has a utilitarian social welfare function (V = U1 + U2 + . . .) under which
each individual’s utility is weighted equally in determining social welfare.
Under these assumptions, the optimal income tax system is one that leaves everyone
with the same level of post-tax income.
Any individuals with incomes below this level would receive a transfer from the
government that would increase their incomes to the average amount.
With this system, each additional dollar of earnings either reduces one’s transfer by
$1 (if below the average income level) or raises one’s tax by $1 (if above the average
income level).
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
General Model with Behavioral Effects
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
General Model with Behavioral Effects
The optimal income tax system meets the following condition:
In the case of income taxation, the optimal tax system reflects a different balancing:
 Vertical Equity: Social welfare is maximized when those who have a high level
of consumption, and thus a low marginal utility, are taxed more heavily, and
those who have a low level of consumption, and thus a high marginal utility, are
taxed less heavily.
 Behavioral Responses: As taxes rise on any one group, individuals in that group
may respond by earning less income.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
An Example
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
The Structure of Optimal Income Tax Rates:
A Simulation Exercise
simulation exercises The numerical
simulation of economic agents’ behavior
based on measured economic parameters
in an attempt to determine optimal tax
rates or other outcomes of interest.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 3
Optimal Income Taxes
The Structure of Optimal Income Tax Rates:
A Simulation Exercise
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 4
Tax-benefit Linkages and the Financing of Social
Insurance Programs
tax-benefit linkages Direct ties
between taxes paid and benefits
received.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 4
Tax-benefit Linkages and the Financing of Social
Insurance Programs
The Model
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 4
Tax-benefit Linkages and the Financing of Social
Insurance Programs
Issues Raised by Tax-benefit Linkage Analysis
If There Is No Inefficiency to Providing a Benefit, Why Doesn’t
the Employer Just Do So Without Government Involvement?
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 4
Tax-benefit Linkages and the Financing of Social
Insurance Programs
Issues Raised by Tax-benefit Linkage Analysis
When Are There Tax-benefit Linkages?
The tax-benefit linkage is strongest when taxes paid are linked directly
to a benefit for workers.
What Is the Empirical Evidence on Tax-benefit Linkages?
The existing literature suggests that the cost of social insurance financing is
borne by workers in the form of lower wages and not lower employment.
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
EMPIRICAL EVIDENCE
A GROUP-SPECIFIC EMPLOYER MANDATE
Gruber (1994) examined the impact on wages and labor supply of a group-specific
mandated benefit.
Before the mid-1970s, health insurance plans provided very little coverage for the
costs associated with normal pregnancy and childbirth. This was viewed as
discriminatory by some state governments, leading to the state laws mandating
that pregnancy costs be covered as completely as other medical costs.
These laws significantly increased the insurance costs for women of childbearing
age in those states, thereby raising the costs of employing a specific group of
workers (treatment group). There were two possible control groups: similar
workers in other states that did not pass these laws, or other groups of workers
within the states that did pass these laws.
Gruber’s study compared the changes in wages and labor supply of the treatment
group around the time of the passage of these laws to the changes in both of these
control groups.
The results show that the cost of this new mandate was fully passed on to the
wages of the affected groups, with little effect on their labor supply.
© 2007 Worth Publishers Public Finance and Public Policy, Jonathan Gruber, 2e
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Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation
20 . 5
Conclusion
The fundamental issue in designing tax policy is the equity-efficiency
trade-off.
Understanding tax efficiency really comes down to remembering two
key principles.
• The more elastically supplied or demanded the good, the larger the
deadweight loss from the tax.
• The higher the tax rate, the larger the incremental deadweight loss
of taxation.
Trading off these two considerations is the key to understanding the
efficiency aspects of the tax policies.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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