Optimal Taxation Paper 7, Part IIb Dr Hamish Low

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Optimal TaxationPaper 7, Part IIbDr Hamish Low
Lecture 1
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Outline for Today

• Government Objectives
• Fundamental Theorems of Welfare Economics
• Social Welfare Functions
• Deadweight Loss

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Government Objectives

• Protection against each other / outsiders
• Maximise economic efficiency (stability!)
• Provision of fair procedures
• Reduction in inequality of outcome
• or reduction in inequality of opportunity
• Reduction in poverty
• Providing public services and resources
• Re-election

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From the point of view of an individual
Direct benefits government provides goods and
services Indirect benefits government
redistributes resources to other individuals

• Taxation
• What is the most efficient way to pay for direct
  benefits ?
• What is the optimal way to redistribute ?
• Public Expenditure
• What is the optimal level of government
  provision of direct benefits?
• Who should benefit from government spending?

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Government Objectives

• Protection against each other / outsiders
• Maximise economic efficiency (stability)
• Provision of fair procedures
• Reduction in inequality of outcome
• or reduction in inequality of opportunity
• Reduction in poverty
• Providing public services and resources
• Re-election

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Failures

• Market Failure
• Credit crunch
• Keynes and Great Depression
• Coordination failure
• Poverty
• Lack of insurance
• Government Failure
• Limited information
• Limited control over individuals
• Limited control over implementation
• Political Limitations

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Fundamental Theorems

• A competitive equilibrium will be Pareto
  Efficient
• Any point on the Pareto frontier can be achieved
  by a competitive equilibrium with an appropriate
  reallocation of resources
• Assumption that lump sum taxes are feasible

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• If a tax does not change or distort prices it
  will only have an income effect.

• Lump sum taxation must be person specific
  and vary with ability the most able face the
  highest tax.

• Government observes income which is related
  to ability but affected by choice of hours

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Lump Sum Taxes and Incentive Compatibility
2 individuals (1 high ability, 1 low ability).
Government maximises total utility
First-order conditions
Same level of consumption, but high ability
person works more
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Tools of Analysis

• Objectives of tax policy
• Deadweight Loss
• Behavioural Response elasticities

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Inequality and Poverty

• Equivalence scales

Income required for a 2 person family
y
Income required for a 1 person family
x
A couple require 1.67 times the total spending of
an individual to be as well-off
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• Poverty
• Absolute vs relative poverty
• What is it indecent for creditable people to be
  without?
• Discrete nature of poverty lines
• Inequality
• Transfer from person i to person j who is
  better-off should increase inequality
• Size of the change in inequality index contains a
  value judgement should change in index depend on
  level of utility of i and j
• Turn to Social Welfare functions

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Social Welfare Functions
individual utilities are comparable (cardinal vs
ordinal utility)
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(i) Utilitarian

• Maximise the sum of individual utilities
• Assume utility functions dependent only on income
• Utility has diminishing marginal utility of
  income
• Total amount of income is fixed

Complete equality
E
E
0
0
Jessies income
Peters income
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Unhappy Peter
E
E
0
0
Jessies income
Peters income
Assumption of identical utility functions is
crucial for equality conclusion
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Utilitarianism implies utility of Peter is a
perfect substitute for the utility of Jessie
This does not imply that giving 1 to Jessie has
the same benefit as giving 1 to Peter
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(ii) Rawlsian
Maximise the welfare of the worst off person in
society
Rawlsian SW implies utility of Peter is a perfect
complement for the utility of Jessie
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(iii) Intermediate Case
? 0 Utilitarian ? ? 8 Rawls
Rawls, Utilitarian
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Implications
If transferring 1 unit of utility to someone
worse off, how many units of utility are you
willing to give up?
Peter has 1000. Jessie has 100. How many
should Peter pay to give Jessie an extra 1?
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Rawls
Utilitarian
Differences in utility functions or in production
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Summary

• Objectives of individualistic governments
• direct or indirect benefit
• Constraints market and government failure
• leading to failure of fundamental theorems
• Need tax to be individual specific and
  independent of choices to avoid distortion
• Need to weight up utility of different
  individuals
• identical utility functions
• equivalence scales
• poverty vs inequality

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Plan

• Deadweight loss
• Implications for tax policy
• Estimates of elasticities

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Deadweight Loss

• Taxation reduces individual income. This is a
  welfare loss to the individual.
• Deadweight loss arises if raising 1 of revenue
  requires individuals to give up more than 1.

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How to measure welfare cost?

• Change in utility
• Consumers own monetary valuations
• Area under Marshallian demand curve
• Area under Hicksian demand curve

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Example Commodity Tax
E.V.
Rev
100 Tax on Good x (Price doubles)
S.E.
D.W. loss E.V. - Rev
I.E.
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Area under a demand curve
Revenue
D.W.Loss
p
Hicksian Demand h(p,u1)
Marshallian Demand x(p,m)
x
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• Deadweight loss arises only from substitution
  effects
• Deadweight loss is measured accurately as the
  area under a compensated demand curve
• Lump sum tax is efficient because no substitution
  effects tax is independent of behaviour
• To estimate efficiency cost, need compensated
  elasticity

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Labour Supply Choices
Increase in wage tax (fall in wage rate)
y

• Effect on labour supply
• Deadweight loss
• Revenue

A
l
H
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Revenue Raised
Individual A
Equivalent Variation
Deadweight Loss
y

• Person A
• Labour supply ambiguous
• Deadweight loss
• Revenue increases

A
A
A
l
H
Substitution Effect
Income Effect
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Individuals B and C
Increase in marginal tax for bottom group
y
B
C

• Effect on labour supply
• Deadweight loss
• Revenue

l
H
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y

• Person B
• Labour supply rises
• No Deadweight loss
• Revenue increases

• Person C
• Labour supply ambiguous
• Deadweight loss
• Revenue increases

B
B
C
C
l
H
Income Effect Only
I.E. and S.E
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Individual D
Reduction in marginal tax rate on additional
earnings
Before tax wage
y

• Effect on labour supply
• Deadweight loss
• Revenue

D
l
H
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Individual D
y
Reduction in marginal tax rate on additional
earnings

• Person D
• Labour supply rises
• Lower deadweight loss
• Revenue increase

Before tax wage
D
D
l
H
SubstitutionEffect Only
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• When effect on labour supply is ambiguous,
  determined by size of wage elasticity.
• Deadweight loss is determined by compensated
  elasticity.
• Difference between marginal tax rates and average
  tax rates

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Marginal Tax Rates
Amount of tax that is paid on an extra unit of
income
Average Tax Rates
Person D reduce marginal tax, average tax
unchanged
Proportion of all income that is paid as tax
Person B increase average tax, marginal tax
unchanged
Answers show
marginal tax rate has a S.E. and labour
supply
average tax rate has an I.E. and labour
supply
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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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Labour Supply Elasticities
Effect of increasing the wage on hours worked
gt lt
2
Uncompensated Wage
Compensated Wage
Income
0.14 (0.075)
0.14 (0.09)
0.00 (0.04)
Female, No children
0.21 (0.13)
0.3 (0.14)
-0.19 (0.10)
Female, child 0-2
-0.06 (0.08)
Female, child 11
0.13 (0.11)
0.16 (0.12)
Standard errors in brackets
Source Blundell et al. (1998) Econometrica
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Implications for Taxation
Ignore interdependencies

• Low marginal tax on women with young children
  (big S.E.), but high average taxes (big I.E.)
• High marginal tax rates on women with no
  children and women with children over 11 small
  welfare loss only
• High average tax rates on women with no children
  and women with children over 11 does not
  increase labour supply, but does raise revenue

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With interdependencies
What are income levels of the different groups?
For example if women with children 0-2 have very
low incomes, may want high marginal tax rates,
despite direct deadweight loss, because of
revenue raising benefits further up the income
scale
Have ignored participation effects
greater revenue means greater lump-sum payment to
people on low incomes