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Public Goods and Government intervention

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Title: Public Goods and Government intervention


1
Lecture 3
  • Public Goods and Government intervention
  • Suggested Readings Connolly Munro, The
    economics of the public sector, chapter 4

2
Market failures
  • Market failures occur when prices do not fully
    reflect either the marginal social benefits or
    costs
  • such failures provide scope for political
    interaction
  • how does this happen?
  • Potential sources of market failure
  • Public Goods

3
Public Goods
  • Introduction
  • In market economies, private suppliers provide
    the majority of goods and services to consumers.
    However, certain goods are publicly provided.
    These include for example defense, education, and
    health. Why does the government instead of the
    market provide these goods? Which
    characteristics differentiate goods that are
    privately provided from goods that are publicly
    provided? How do we define public goods?
  • The terminology might induce the conclusion that
    public goods are good that are publicly provided
    as opposed to private goods. This conclusion is
    simply WRONG! The public or private nature of the
    good is an intrinsic characteristic of goods that
    is not related to the provider of the good
  • Hence, it may well be that the state provides a
    private good or that the market provides a public
    good.

4
Public Goods
  • When is a good public?
  • Definition
  • A pure public good is a good that has two
    characteristics
  • NON-EXCLUDABLE
  • NON-DEPLETABLE (NON-RIVAL, NO-CONGESTION)
  • Non excludability once the good is provided, it
    is not possible to prevent any individual (even
    individuals that eventually have not paid to
    access the good!) from using the good. The reason
    for non-excludability could be for example that
    is technically impossible to check who is using
    the good or that the cost of monitoring the use
    of the good is so high that de facto monitoring
    does not take place
  • Non-depletability (non rivalness) the fact that
    some people are using the good doesnt not
    prevent other people from using the same good. In
    other words, the consumption by one person
    doesnt reduce the quantity available for the
    consumption of other individuals
  • When a good has these two characteristics, i.e.
    is non-excludable and non-depletable, then it is
    a pure public good. On the other hand, if a good
    is excludable and depletable, then the good is a
    private good. Finally, you have some good that
    possess just one of these properties.

5
Public Goods
6
Public Goods
  • Pure public goods
  • street light
  • defense
  • air
  • radio emissions

7
Public Goods
  • What are the implications of non-excludability
    and non-rivalness?
  • Lets compare a pure private good (X) and a pure
    public good (G)
  • Suppose that X1 and G1
  • Suppose there are two consumers Anne and Bill
  • Who consumes X?
  • Who consumes G?

8
Public goods versus Private Goods
  • Since X is excludable and rival, either Anne or
    Bill will consume it (it cannot be consumed by
    both!). Hence, the consumer that values the good
    the most (i.e. the consumer who is willing to pay
    the highest price) will consume X.
  • With the public good this is not the case

9
OPTIMAL PUBLIC GOOD PROVISION
  • To provide optimally G, we need to take into
    account that G is simultaneously consumed by Anne
    and Bill, i.e. we need to take into account that
    each unit of G is going to increase the utility
    of both agents!
  • Social Marginal Benefit as opposed to Private
    Marginal Benefit!

10
Market Failure
  • Can the market provide efficiently public goods?
  • Private provision through voluntary contributions
  • examples charity, private security
  • naively following own demand curves can lead to
    over or under provision

11
Marginal benefit and demand curve for public goods
Marginal Cost
Marginal cost
15
Optimal provision of Public good
10
10
No provision of public good
5
5
Individual marginal benefit
Social marginal benefit
10
7.5
7.5
10
12
Strategic contributions
  • contributors are not naïve they observe and
    react to others behavior so act strategically
  • Suppose that the student union decides to buy a
    new big TV screen (lets say to watch soccer or
    cricket!) and every member of the student union
    declares that he will really enjoy a new big
    screen!. To purchase the TV screen the union
    relies on the voluntary contributions of each
    member of the student union. Once the TV screen
    is bought, each member of the student union has
    access to the TV independently on the fact that
    he has contributed or not to the purchase of the
    TV.

13
Strategic contributions
  • The TV screen is in other words a public good for
    the members of the student union since it is
  • non-excludable (no member can be prevented from
    watching the TV)
  • non-rival (the fact that one member watches the
    TV does not prevent other members from watching
    it)
  • Question assuming that you care about watching
    the next World Cup (or something better!) will
    you contribute to buy the TV screen?

14
Strategic contributions
  • Lets give some numerical values
  • Suppose that the cost of the TV is 100. Suppose
    that if two people contribute they will each pay
    50. On the other hand if just one person
    contributes while the other refuses to pay, then
    she will pay the entire cost of 100. If nobody
    contributes, the TV is not bought. Lets assume
    that the benefit for each individual from
    watching the TV in monetary terms is 75, on the
    other hand if the TV is not bought their payoff
    is just zero.
  • Lets write down the payoffs of the contribution
    game

15
Payoffs
16
The free-rider problem
  • This is an example of prisoner dilemma. The two
    individuals would clearly be better off
    contributing but they end up not contributing!
  • Why do we obtain this result?
  • This result is related to the public nature of
    the good. Because the good is non-excludable and
    non-rival, there is a strategic interdependence
    in the contribution decision of the two players.
  • Loosely speaking, consider what individual 1 is
    thinking when he has to decide whether or not to
    buy the TV
  • if he buys the TV, he cannot prevent individual 2
    from using the TV
  • if individual 2 buys the TV, he can use it for
    free
  • and similarly for individual 2!
  • Hence, although each individuals enjoys having
    the TV, since each would enjoy it much more to
    use it for free, then they end up having no TV!
  • This is known as the free-rider problem

17
The free-rider problem
  • The essence of the free-rider problem is that the
    contribution by one player is an exact substitute
    for the contribution of the other player.
    Therefore, each player tries to exploit the
    contribution from the other in order to obtain
    the good for free. As each player is reasoning in
    the same way, the result is that none of the
    players will voluntary contribute!
  • In this example, where the quantity of the good
    is discrete (either the good is provided or it is
    not provided), if we rely on voluntary provision
    the good is not provided. In general, if we
    consider a continuos case, then the outcome will
    be that a sub-optimal quantity of public good is
    provided. It can also be shown that the
    free-riding problem becomes more severe as the
    number of players increases

18
The free-rider problem
  • To overcome the free rider problem, co-operation
    or co-ordination of society is required.
  • Obstacle one enforcement is needed to implement
    this behavior
  • repeated interaction with tit-for-tat punishments
  • government activity or centralized decision
    making such as compulsory taxation or regulation

19
Welfare
  • We have learned that when a good is public,
    because of strategic interdependence, the
    quantity of the public good provided by voluntary
    contributions is not Pareto-efficient.
  • This is equivalent to say that if we rely on the
    market to provide the good, then the outcome is
    not efficient.
  • This is an example of market failure
  • Is there a way to solve the market failure?

20
Government Intervention
  • The government considers the utility of all the
    individuals in the society jointly, chooses the
    level of public goods that maximises the social
    surplus and introduces a tax to finance the
    public good.
  • Therefore, if the government knows the
    preferences of each individual, he can provide
    efficiently the public good
  • This is not particularly difficult if all
    individuals have the same preferences (for
    example, if you all enjoy in the same way
    watching the TV at the student union)

21
Government Intervention
  • However, individuals typically are heterogeneous
    in their preferences for goods
  • How should the government choose the quantity of
    public good if individuals have different tastes?
  • Suppose that g is the public good and c(g) is the
    cost of providing the public good. Lets denote
    U1(g) the benefit for individual 1 from using g
    and U2(g) the benefit for of individual 2.

22
The Samueson Rule
  • The social surplus is the sum of the utilities of
    the two individuals, minus the cost of provision
    of the good. The government has to decide the
    optimal level of g, that is the level of g that
    maximises the social surplus
  • Social surplus U1(g)U2(g)-C(g)
  • the optimal g is reached when the marginal
    benefit is equal to the marginal cost. Note that,
    since we are not considering one individuals, but
    several, then the optimal g is reached when the
    sum of the marginal benefit of the individuals is
    equal to the marginal cost (Samuelson rule)
  • U1(g)U2(g)C(g)
  • Samuelson rule the optimal quantity of g is such
    that the sum of the marginal evaluation of the
    goods for the two individuals is equal to the
    marginal cost of the good.

23
Samuelson Rule and Pareto frontier
  • The social surplus maximising outcomes can be
    represented graphically using the Pareto-frontier
    (remember the frontier of UPS from last lecture).
  • We can represent all the levels of net utilities
    that can be achieved choosing different levels of
    g.
  • Every point on the frontier satisfies the
    Samuelson rule. Therefore, the Samuelson rule
    does not determine a precise outcome (doesnt
    pick a specific point on the frontier).

24
Utility possibility frontier (UPF)
UB

A
45

B

M
UA
25
Mechanism of collective decision making
  • How is a point on the frontier actually chosen?
  • To choose a precise point we need to specify some
    type of collective choice rule
  • Ex1 the government has some welfare function
    (i.e. a function that gives a precise weight to
    each individual in the society) and he chooses a
    point according to this welfare function. Then
    depending on the weight he gives to each
    individual, he can choose a different point
  • Ex2 there is some political mechanism, like
    majority voting to decide

26
Local public goods and the Tiebout Mechanism
  • Individuals vote with their feet
  • If there are as many communities as there are
    types, then efficiency will result
  • Argument is related to club solutions to public
    goods
  • This mechanism relaxes assumption somewhat on
    excludability

27
Aggregation of preferences
  • If there are not as many communities as types,
    individuals with different preferences have to
    find a way to undertake decisions affecting the
    entire group
  • Group preferences and group choice

28
Questions (prepare and answer all questions
before next week seminar)
  • Which one of the following goods is a pure public
    good?
  • Health care
  • Roads
  • Education
  • Radio emission
  • Wireless
  • Suppose that Anne and Bill have agreed to buy a
    new dishwasher for their house. Bill values the
    dishwasher more than Anne and he would be willing
    to pay up to 300 pounds for a new dishwasher,
    while Anne is willing to spend up to 150. They
    finally agree to buy a dishwasher whose cost is
    250. If both of them contribute, they will share
    equally equally the cost of 250. If one of them
    refuses to contribute, the other will pay the
    entire cost. If none of them contributes they
    will not buy the dishwasher. Will Anne
    contribute? Does your answer change if we assume
    that Anne and Bill both are willing to pay up to
    160 for the dishwasher? Explain whether the Nash
    equilibrium in both cases is Pareto-efficient and
    discuss whether a compulsory contribution scheme
    would be welfare improving.
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