University of Athens Department of Economics Course: Public Finance Instructor: Vassilis T' Rapanos

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University of Athens Department of Economics
Course Public Finance Instructor Vassilis T.
Rapanos Academic year 2004-2005
Outline of chapter 6 Public Goods and Publicly
Provided Private Goods
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Public goods

• Focus questions
• What distinguishes public goods from private
  goods? What is a pure public good?
• Why will private markets undersupply pure public
  goods? What is the free rider problem?
• Why the government provides goods that are not
  pure public goods?
• What determines the efficient supply of pure
  public goods?

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Public goods

• Rivalry
• Rival if a good is used by one person, it
  cannot be used by another
• Non-rival one persons consumption does not
  detract from or prevent another persons
  consumption (example national defence)
• Excludability
• If exclusion is impossible, the use of the
  price system is impossible consumers have no
  incentive to pay

4
Public goods

• Rivalry Excludable
• Private goods Yes Yes
• Public goods No No
• Pure public goods No Impossible

5
Public goods

• It should be clear that rivalry implies that
  marginal cost is greater than zero, i.e. (MC) gt
  0. If, however, there is non-rivalry then
  marginal cost is zero, i.e. MC 0. On the other
  hand, the degree of excludability depends on the
  costs of exclusion. For non-excludable goods the
  costs of exclusion are extremely high (e.g.
  lighthouse, defence). There are, however, many
  goods which could be excludable but the cost of
  exclusion is high, (semi-excludable goods), e.g.
  TV, roads.

6
Public goods

• .

Congested highways
Pure Private goods
MC
Impure Public goods
Rivalry ?
Pure Public goods Natioal defence, lihgthouse
Fire Protection
Easiness of exclusion ?
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Public goods

• The presence of public goods implies that the
  market does not lead to a Pareto efficient
  outcome for the following reason. Suppose that a
  public good brings benefits to users, i.e MBgt0.
  If there is non-rivalry then MC0. If exclusion
  is not possible then no one pays, and therefore
  no production takes place. Since MBgtMC0, and no
  production it means that there is inefficiency.
  But even if exclusion is possible, since MC0 and
  MBgt0. it means that we have under-consumption of
  this good, which is again inefficient.

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Public goods

• Take, for example, the case of a bridge, with
  exclusion (toll), and MC 0 (non-rivalry).

P (toll)
DDcomp
A
PA
B
C
0
Q
QM
QA
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Public goods

• With P 0, demand will be at Qm, which is
  efficient, but there are no revenues for the
  bridge. If PA gt 0 then quantity demanded will be
  at QA . This may cover the cost, but creates
  inefficiency (under-consumption), with an welfare
  loss equal to C. So, if there is no user fee i.e.
  there is no exclusion there will be no revenues
  and the bridge may not be built. As a result
  there will be undersupply and an efficiency loss
  equal to A C. With a user fee (exclusion) there
  will be underdemand with an efficiency loss C.
  Therefore the result is to build the bridge using
  user fee

10
Public goods

• So
• First best solution Build the bridge finance
  it by using lump-sum taxes.
• Second best solution Build the bridge and
  finance it by using user fee

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Public goods

• Non-excludability
• There are certain goods, the pure public goods,
  which are not excludable, e.g. defence,
  lighthouse. If the financing of these goods is
  done on a basis of voluntary contributions, then
  we shall have the free rider problem, which
  means that nobody wants to contribute.
• The game could be a follows
• If others pay, I dont pay.
• If others dont pay, I dont pay.
• So, nobody pays
• However, in several occasions people are not as
  selfish, and there may be some who are not free
  riding

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Public goods

• Sum up
• Non-rivalry implies undersupply
  (under-consumption if exclusion possible).
• Non-excludability implies undersupply.
• Private provision of public good inefficient!

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Efficiency conditions for public goods.

• As we noticed earlier, the market equilibrium in
  the case of public goods is not efficient. In the
  case of a private good we know that efficiency
  implies that
• MRT MRS
• With MRT equal for all producers and MRS equal
  for all consumers.

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Efficiency conditions for public goods.
?
PPF
MRTXYMRSXY
Infifference curve
?
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Efficiency conditions for public goods
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Efficiency conditions for public goods

• Suppose that we have two goods, one private good
  X and one public good G. Suppose also that there
  are two individuals, A and B. Does the condition
  for efficiency of the private goods also hold for
  public goods?
• Not really since the same good is consumed
  jointly by both individuals. The efficiency for
  public goods is

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Efficiency conditions for public goodsSome
mathematics

• Suppose a society with two individuals A and B
  with utility functions respectively
• UA UA(XA,G) and UB UB(XB,G)
• where X is the private good and G is the public
  good with
• XAXB X, and GAGBG
• The income of this society is
• Px XA Px XB PG GI
• where Px and PG are the prices of X and G
  respectively

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Efficiency conditions for public goodsSome
mathematics

• Set up the Lagrangean, assuming that the utility
  of individual B remains unchanged

The first order conditions are
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Efficiency conditions for public goodsSome
mathematics

• With some rearrangements we get

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Efficiency conditions for public goodsSome
mathematics
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Demand curves for public goods

• In the case of the demand curves for private
  goods, we ask for given price how much does each
  individual demand?
• The demand curve for a good is the sum of the
  demand curves of all individuals. In other words
  we have a horizontal addition of individual
  demand curves.
• In the case of the demand curves for public goods
  we at given supply of public good how much is
  each individual willing to pay for one extra unit
  public good?
• The collective demand curve for a public good is
  the sum of amounts all individuals are willing to
  pay. So the collective demand curve is the
  vertical addition of individual demand curves

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Efficiency conditions for public goods
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Alternatives for determining public goods
expenditures Lindahl equilibrium

• Collective demand curve shows at any given level
  of the public good, the sum of all individuals
  marginal willingness to pay

Supply
Lindahl equilibrium
Collective demand
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Lindahl equilibrium

• Lindahl equilibrium is at the intersection of
  supply curve and collective demand curve.
• The allocation of public goods in a Lindahl
  equilibrium is Pareto efficient.
• In order to see that let us assume that we
  produce less than the Lindahl equilibrium. Then
  the collective willingness to pay for an extra
  unit is higher than MC, which is inefficient.
  Also if we produce more the collective
  willingness to pay for an extra unit is lower
  than MC which is also inefficient. At the Lindahl
  equilibrium the collective marginal willingness
  to pay is equal to MC.

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Lindahl equilibrium

• The efficient provision of pure public good is at
  the point where
• It should be made clear, however, that the
  Lindahl equilibrium is not market equilibrium,
  and that nothing ensures that the Lindahl
  equilibrium can be reached.
• Efficiency could be ensured if each individual
  could pay his/her marginal willingness to pay,
  which means that all individuals would reveal
  their true preferences.

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Publicly provided private goods

• Publicly provided goods (easy to exclude) for
  which there is a large MC associated with
  supplying additional individuals are referred to
  as Publicly provided private goods. Such goods
  are education, health, nursing homes, etc.
• If we have free provision of these goods, when MC
  gt 0, then there will be overconsumption and
  efficiency losses

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Publicly provided private goods
P
MB D Dc
Welfare loss
MC gt 0
0
Qc Qm
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Publicly provided private goods

• It is clear that the size of the welfare
  (deadweight) loss depends on the shape of demand
  curve. The steeper (price inelastic) the demand
  curve the lower the welfare loss, and the flatter
  (price elastic) the demand curve the large the
  welfare loss.

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Publicly provided private goods

• Some times the supply of certain goods is free of
  charge because of high transaction costs or high
  exclusion costs

P
MB D Dc
Welfare loss from reduced sale
P
Welfare loss from overconsumption
Transaction costs
MC gt 0
MC
0
Qc Qm
Qe
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Publicly provided private goods

• Free public provision of private good is least
  inefficient if
• Transaction costs Welfare loss from reduced sale
  gt Welfare loss from overconsumption Welfare
  loss from distortionary taxation)
• E.g. Insurance, disability benefits, TV

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Rationing

• Given the inefficiencies arising from
  overconsumption when freely provided private
  goods, governments try to find ways to limit
  consumption. Any method restricting consumption
  is called a rationing system

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Uniform provisioning

• By uniform provisioning we offer the same
  quantity to everybody, e.g. uniform level of free
  education. We find the aggregate (average) demand
  average MB, and provide good at MC.
• The result of uniform provisioning is that we
  avoid aggregate overconsumption, but this does
  not satisfy individual needs / demands and as a
  result we have a welfare loss if all individuals
  are not identical
• Possible solution Offer relatively low uniform
  quantity and the possibility to buy extra
  quantities. This creates small welfare loss, for
  example, education, basic pension coverage.

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Uniform provisioning
Averagedemand
P
High demand
Groups 2 loss from underconsumption
Low demand
Groups 2 loss from underconsumption
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Queuing and queuing costs

• E.g. Medical services, libraries,,

DDC
P
Welfare loss from queuing
Welfare loss from overconsumption
Demand after queuing
MCgt 0
Qc Qm
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Queuing and queuing costs

• Welfare loss from queuing might or might not
  be larger than welfare loss from overconsumption
  when there are no provision limit.