The Economics of the Public Sector

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The Economics of the Public Sector

• Public Choice

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• Differences individuals have different
  preferences about the allocation of resources in
  society.
• What is the optimal amount of public goods we
  should have?
• How should the distribution of income look like?
• How much of an efficiency loss are we willing to
  tolerate for an increase in inequality?

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• Therefore, it becomes important to design
  adequate mechanisms to aggregate heterogeneous
  preferences.
• However, of greater practical relevance, is the
  issue of how governments actually make decisions.
  In order to understand the rationale behind
  government decisions we need to understand the
  political process that originated them.
• This is an area at the border between political
  science and economics, often called political
  economy.

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• When it comes to private goods the market is a
  simple and effective way for individuals to
  express their preferences if they like a good at
  a given price they buy it, if they do not like it
  they do not buy it.
• Firms then have a clear way to decide what to
  produce produce whatever I can sell for a value
  larger than its cost, i.e., produce whatever
  goods the consumers value more than what it costs
  to produce them.

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• When it comes to public goods and decisions
  about public resources there is not really a
  simple and clear way for individuals to express
  their preferences. We could specify a variety of
  rules, each with different characteristics.
• One simple one that is discussed a lot is
  Majority Voting.

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• Majority Voting
• Majority Rule Among two alternatives, the one
  that receives the majority of votes wins.
• The majority rule can be applied to decide
  between any two given issues.

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• The Median Voter
• Suppose there is an economy with three
  individuals (A, B and C) who have to decide what
  level of public good to provide. Providing the
  public good is costly and therefore the larger
  the quantity of public good provided, the higher
  the level of taxes, and as a consequence, the
  lower the amount of (net) income available for
  private consumption.
• Each individual has different preferences.

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• We can represent the preferences of each
  individual over the level of public good in the
  following way

Utility
B
C
A
Ga
Gb
Gc
Public Good
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• Consider now how individuals would vote.
• i) Ga vs. Gb Gb wins (B and C vote for it)
• ii) Gc vs. Gb Gb wins (A and B vote for it)
• Gb wins agains any alternative.

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• More generally, suppose we have N (odd number)
  individuals in the economy with preferences
  similar to the ones above.
• Suppose that for (N-1)/2 individuals the
  preferred level of expenditure is below Gb. Let
  these be the Low Types. For (N-1)/2 individuals
  the preferred level of expenditure is above Gb.
  Let these be the High Types. There is one
  individual, B, whose preferred level of
  expenditure is Gb. This individual is called the
  median voter.

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• Notice that, under majority voting, Gb beats any
  alternative below Gb since the High Types prefer
  Gb to any level of expenditure below Gb. Gb gets
  the majority of votes in such an election.
• Similarly, Gb beats any alternative above Gb
  since the Low types prefer Gb to any of level of
  expenditure above Gb. Again, Gb wins.
• Since Gb beats any alternative above or below,
  Gb is the chosen level expenditure. Under
  majority voting the alternative prefered by the
  median voter prevails (need single peaked
  preferences).

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• There are several problems with majority voting.
  We will mention a few of them
• - It may lead to inefficient outcomes
• - One person has one vote no room for
  intensity of preferences
• - The final solution may depend on how issues
  are scheduled for voting.
• - There may be no equilibrium. Instead we may
  have infinity cycles. Single peaked preferences
  are restrictive.
• - Arrows Impossibility Theorem

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• Is Majority Voting Equilibrium Efficient?
• Suppose we have an economy deciding on the level
  of public good to provide. The majority voting
  equilibrium does not have to be the efficient
  solution. It corresponds to the preferences of
  the median voter, which equates his private
  marginal utility of the public good with its
  marginal cost (through taxes). In general this
  does not correspond to the optimality conditions
  for provision of public goods we saw before.

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• Voting Paradox
• Condorcets Paradox
• Suppose there are three voters (1, 2 and 3)
  voting over three alternatives (A, B and C).
• Voter 1 prefers A to B and B to C.
• Voter 2 prefers C to A and A to B.
• Voter 3 prefers B to C and C to A.

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• Suppose we start by deciding A vs. B, and then
  decide between the winner and C.
• In the first round A wins since 1 and 2 vote for
  A. In the second round C wins since 2 and 3 vote
  for C.
• Therefore, C is preferred to A, and A is
  preferred to B.
• Does this mean that C is preferred to B? No, if
  I have a decision between C and B, B wins.

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• This is known and Condorcets Paradox.
• Majority voting may generate non-transitivity
  which gives rise to ciclicality A is preferred
  to B, C is preferred to A B is preferred to C

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• The final outcome depends on the sequence by
  which alternatives are voted. If individuals
  realize this they may choose to vote
  strategically.
• Ex Voter 1 know that if he votes for A in the
  first stage then A will win and in the second
  stage C will win. However, C is the least
  preferred alternative for Voter 1. If in the
  first stage he instead votes for B then B wins
  both in the second and third stage. Therefore, he
  may vote strategically for B in the first stage.

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• Arrows Impossibility Theorem
• It is not possible to design a social choice
  rule with the following properties
• - non-dictatorial
• - transitivity
• - independence of irrelevant alternatives
• - Pareto if every one prefers A to B then the
  choice rule should prefer A to B.

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• Models of Political Equilibrium
• - Voting Models Ex Hotelling
• Suppose there are two parties deciding where to
  position themselves in the political spectrum.
  Both parties will decide to locate near the
  median voter. Voters will basically have no
  choice even though there are two parties.

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• - Why do people vote?
• The probability that each individual vote will
  decide any election is zero
• Utility of voting? Civic duty?
• - Interest Group Models
• In these models the political equilibrium is
  decided through lobbying rather than through
  voting.