Optimal Taxation Paper 7, Part IIb Dr Hamish Low

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Optimal TaxationPaper 7, Part IIbDr Hamish Low
Lecture 2
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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
• Policy Context
• Overall Shape of Tax Schedule

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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 willingness to distort will
depend on desire for redistribution
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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

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Self-Selection
i
j
c
y
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• Suppose tax schedule to y0 already chosen
• SWF attaches no weight to utility of those with
  y gt y0
• Want to induce person i to be at a
• Only person j is left

Marginal Tax rate lt 100
j
c
i
y
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Marginal Tax rate gt 0
c
y

• If tax rate is negative, can move to a situation
  where i is better off and j worse off

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Marginal Tax rate on top earner

• If t lt0, then increase revenue by cutting
  subsidy.
• If t gt0, cut marginal tax and keep average tax
  constant. Raises more revenue.

Revenue from person j
j
c
i
Marginal tax rate is 0
y
Maximise revenue from person j. Maximise distance
between 45 line and tax schedule
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c
Marginal Tax Rates
D
D
m
Leisure, l
H
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Summary so far ...

• Marginal tax rates must lie between 0 and 1
• Marginal tax rate on highest ability (highest
  income) person should be 0

• Unfair!
• Irrelevant!

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Unfair!

• But assumed that person j has no weight in
  social welfare function
• Amount of revenue raised depends on average tax
  rate not marginal tax rate
• although M.T.R.0, average tax rates can
  be high
• Progressive as income increases, proportion of
  income paid as tax increases. i.e. the rich pay
  proportionally more
• how does average tax rate change with
  income.

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Irrelevant!
How robust is 0 result?
Only holds for the person with the very highest
income level and must be able to identify that
person
Does not hold elsewhere because of
interdependence between marginal tax rates for
lower income people and the average tax rates for
people higher up the income scale.
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Individuals B and C
Setting 0 marginal tax rate for person C
increases labour supply and utility of person C.
But, reduces labour supply for B and reduces
revenue.
y
B
B
C
C
l
H
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Policy Context

• UK tax on top earners wage income
• 83 in 1979
• 60 in 1982
• 40 in 1987

• Welfare to work (enter employment, reduce net
  income)
• Addressed by Earned Income Tax Credit (US)
• or Working Tax Credit (UK)

• US 15 rate cut to 10 (Bushs tax rebate)
• UK removal of 10 tax band

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Overall Tax Schedule
Imagine 3 groups of people labelled A, B and C
with low, medium and high incomes
Initial Tax Schedule
Increase marginal tax rate on range yA - yC
(Group B)
c
New Tax Schedule
y
Group A
Group B
Group C
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Take group B (with yC gt y gt yB)
Increased deadweight loss
Both SE and IE. IE (increasing labour supply)
likely to be small SE (reducing labour supply)
likely to dominate
reduction in welfare
fall in labour supply of B
effect on revenue
Elasticity of revenue with respect to the tax rate
Uncompensated Elasticity of hours of work with
respect to the wage rate, ?
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Take group C
Increase average tax rate, no change in marginal
tax rate IE only lose income
increase in labour supply of C
increase in revenue
reduction in welfare
Overall effect on revenue
if revenue from group B falls, then overall
effect on revenue depends on numbers of people in
each group and relative size of uncompensated
elasticities
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Assume revenue increases, then take group A
IE only gain income
decrease in labour supply of A
increase in welfare
Increased transfer to the low income group
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Summary

• General principles
• incentive compatibility restricts the ability to
  increase taxes with income
• tax rates lie between 0 and 1
• Marginal tax rate on top earner is 0
• Consider revenue neutral changes to structure of
  tax policy
• identify different groups affected
• consider labour supply, revenue, deadweight loss
  and welfare implications