Optimal Taxation Paper 7, Part IIB Dr Toke Aidt

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Optimal TaxationPaper 7, Part IIBDr Toke Aidt
Lecture 1
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Overview of the course

• Welfare economics background
• Taxation and labour supply
• Optimal income taxation
• Taxation as social insurance
• Pensions
• The Lindahl-Wicksell approach to taxation

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Outline for Today

• Different approaches to the study of taxation
• Fundamental Theorems of Welfare Economics
• Lump sum taxes and incentive compatibility
• Social Welfare Functions

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Different approaches to taxation
Lindahl-Wicksell Approach
Optimal Taxation Approach

• Taxation is part of a voluntary exchange between
  state and citizens.
• Taxation is the price of public output.
• Emphasis on institutions that link taxation and
  expenditure and reduce coercion.

• Taxation is coercive taking of resources to
  finance (largely) unspecified public output.
• Emphasis on minimising the efficiency cost of
  taxation and on designing an optimal tax
  structure.
• Efficiency-equity trade-offs resolved through a
  social welfare function.

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Fundamental Welfare Theorems

• A competitive equilibrium will be Pareto
  Efficient
• Any point on the Pareto frontier can be achieved
  by a competitive equilibrium with an appropriate
  redistribution of resources

The role of government is limited to insure that
i) markets are competitive and ii) the right set
of LUMP SUM taxes are employed.
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Edgeworth box for exchange economy
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C
No trade-off between efficiency and equity
B
A
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Optimal lump sum taxes require information on
A

• The contract curve
• Which equilibrium will emerge
• The value of the endowments

B
C
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Optimal Lump Sum Taxes

• A tax is lump sum if the agents on which it is
  levied cannot affect the size of the tax by
  changing their behaviour.
• Optimal lump sum taxes must be levied on economic
  characteristics, such as ability, that are
  private information.
• This is the fundamental fact that hinders the use
  of optimal lump sum taxes.

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The Impossibility of Optimal Lump Sum Taxes
Social welfare is utilitarian
Optimal lump sum tax is
Problem ability (earning capacity) is private
information.
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The Impossibility of Optimal Lump Sum Taxes
Let (T1,T2) be a particular tax schedule.
Incentive compatibility requires that each agent
voluntarily selects to pay the tax intended for
them
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Implications

• Redistribution through optimal lump sum taxes is
  incentive incompatible!
• The practical value of the Second Welfare Theorem
  very limited.
• Second best taxes (income taxes, commodity taxes,
  trade taxes etc.) must be employed
• Inability to achieve the first best allocation.
• Trade-off between efficiency and equity.
• Lump sum taxes are used as a benchmark.
• Non-redistributive lump sum taxes can be used
  (e.g., poll tax).

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The Objective of Tax Policy

• Pareto-efficiency is insufficient as a welfare
  criterion
• Typically there exist many Pareto-efficient
  allocations.
• Pareto criterion does not provide a complete
  ordering of allocations, so some allocations may
  be incomparable.
• Fundamental problem is that the criterion does
  not allow a trade-off between gains and losses.
• Social welfare functions
• Ethical objective of society
• Outcome of an aggregation process

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Axiomatic Approach to Social Welfare Functions

• Individual preferences are aggregated into a
  social preference according to a set of rules
  (axioms).
• The leads to impossibility theorems, such as that
  of Arrow, showing that it is impossible to
  generating social preferences from individual
  preferences.
• The source of the problem is that individual
  utility functions (rankings) do not contain
  information on the strength of preference between
  alternatives for a given individual or between
  individuals.

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Bergson-Samuelson Social Welfare Functions

• Based on some notion of inter-personal
  comparability of utilities.
• The social welfare function embodies some ethical
  objective of society
• Utilitarian principle
• Rawlsian principle

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Social Welfare Functions
individual utilities are comparable and the
function embodies information about how society
is willing to trade off utilities of individuals.
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(i) Utilitarian
Utilitarianism implies utility of agent 1 is a
perfect substitute for the utility of agent 2
This does not imply that giving 1 to agent 2
has the same benefit as giving 1 to agent 1.
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Implications for Redistribution

• Maximise the sum of individual utilities
• Assume identical utility functions.
• 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
Agent 2s income
Agent 1s income
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The role of preference differences
E
E
0
0
Agent 2s income
Agent 1s income
Assumption of identical utility functions is
crucial for equality conclusion
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(ii) Rawlsian
Maximise the welfare of the worst off person in
society
Rawlsian SW implies utility of agent 1 is a
perfect complement for the utility of agent 2
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(iii) Intermediate Case
? 0 Utilitarian ? ? 8 Rawls
Symmetric economy
Rawls, Utilitarian
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Rawls
Utilitarian
Differences in utility functions or in production
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Main Points

• The impossibility of optimal lump sum taxes
• The insufficiency of the Pareto criterion.
• The properties of alternative social welfare
  functions.

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What is next?

• Deadweight loss of taxation
• The tax interaction effect
• Estimates of elasticities