Optimal Taxation Paper 7, Part IIb Dr Hamish Low

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Optimal TaxationPaper 7, Part IIbDr Hamish Low
Lecture 3
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Summary

• Minimise deadweight loss by minimising marginal
  tax rates (S.E.).
• Maximise revenue by increasing average tax rate
  (I.E.)
• Trade-off between individuals an increase in Cs
  marginal tax means an increase in Bs average tax

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Outline Optimal Income Tax

• Shape of tax schedule
• Incentive compatibility
• Choosing marginal tax rates
• Criticisms

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The Optimal Tax Problem

• Choose tax schedule
• to raise revenue required for government
  spending
• to redistribute to those lower down
• to minimise distortions to the economy
• Observe income, not ability

Combining equity and efficiency considerations
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Information for Optimal Tax
Individual Behaviour
Elasticities of substitution
Preferences over leisure and consumption
Social Welfare Function
? coefficient of inequality aversion
Distribution of Abilities
Pre-tax wages reflect ability
Restrictions on Functional Form
E.g. linear
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Linear Tax Schedules
Work h hours for wage w and earn income y w h
Tax schedule 1
Tax schedule 2
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Tax Schedules (cont)
Map from gross income to consumption
No Intervention
c
1
0.8
0.6
0.4
0.2
y
0.2
0.4
0.6
0.8
1
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Revenue Neutrality
c
1
0.8
0.6
0.4
0.2
y
0.2
0.4
0.6
0.8
1
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Marginal and Average Tax
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Income tax schedules
No Intervention
c
B
y
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Changing marginal tax, keeping average tax
unchanged
General Tax Schedule
Tax Paid
c
Benefit Received
y
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Individual Behaviour
c
Common Preferences between consumption and labour
h
H
Take,
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So, utility of person i can be written,
and we can find the slope of the indifference
curve between c and y.
Higher ability means higher wage
Assume Pre-tax wage reflects ability i.e.
For a given c and y, indifference curves are
flatter if greater ability
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Common Preferences between consumption and
labour, with different abilities.
Different Preferences between consumption and
gross income
c
Slope of indifference curve is Flatter for
higher ability
j
Increasingly Preferable
i
ywh
Wage structure implies consumption increases with
ability if no taxation
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Single-Crossing Property
c
j
i
ywh
Indifference curves of individual i will cross
the indifference curves of individual j once
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Self-Selection
i
j
c
Incentive Compatibility
y
Tax Schedule It must be in the individuals
interests to choose the income-consumption pair
that the government intends. intended y and c
must increase with ability. If not better to
pretend to be low ability.
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Imagine (intended) c fell with ability
i
j
j
c
y
person j would prefer to be like person i.
ß is not incentive compatible
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Summary

• Considering equity and efficiency simultaneously
• Interdependencies between individuals affect
  optimal tax schedule
• Can show tax as mapping from gross income to
  consumption
• Preferences of individuals same between
  consumption and leisure, but differ for
  consumption vs gross income because of ability
• Single crossing and incentive compatibility