Social Choice
Session 9
Carmen Pasca and John Hey
Public Goods
• Today we discuss problems with the private provision of
public goods.
• In economics, a public good is a good that is nonrival
and non-excludable.
• Non-rivalry means that consumption of the good by one
individual does not reduce availability of the good for
consumption by others.
• Non-excludability that no one can be effectively excluded
from using the good.
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In the real world, there may be no such thing as an absolutely non-rivalled
and non-excludable good; but economists think that some goods
approximate the concept closely enough for the analysis to be economically
useful. We will give some examples later.
Plan for today
• Public and semi-public goods create particular problems for
an individualistic society.
• Because of the goods’ non-rivalry and non-excludability,
individuals have an incentive to free-ride … leading to nonprovision.
• Everyone is worse off than if they were forced to contribute.
• This result is an obvious argument for state provision…
• …though there may be other ways around the free-rider
problem.
• We discuss these before concluding that here we have some
kind of argument for existence and functioning of the State.
But first…..
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What exactly do we mean by public goods…
…and what do we think of as the State and its role.
Should it be minimalist (laissez-faire) or interventionist?
To provide Defence? Education?/Knowledge? Fundamental
Research? Health? Laws? Police? Unemployment benefit?
State Insurance of various kinds?
Which of these are public goods?
Do they have private as well as public elements?
Which are provided by the State? What if the State is corrupt?
Are they for provision or for redistribution?
Is the State involved for economic, social or political reasons?
Today we talk solely about public goods and their provision.
Public Goods – the Problem
• A Public Good is one that in non-excludable (people can not
be excluded from consuming it) and non-rival (one person’s
consumption does not diminish what others can consume).
• Pure examples are rare but close ones exist: lighthouse,
national defence, flood control, knowledge, TV, radio.
• There is a natural (monetary) incentive to free-ride – that is,
consume it and let others pay for it.
• And there is a price – if everyone individually benefits by freeriding, everyone collectively suffers.
• This seems to be an argument for state provision/existence.
• But first we explore other ways to ensure provision.
An economic issue?
• Free-riding is usually only considered to be an economic
"problem" (as distinct from a social problem concerned with
fairness) when it leads to the non-production or underproduction of a public good, and thus to Pareto inefficiency,
or when it leads to the excessive use of a common property
resource.
• We start with a general description of the ‘public goods game’
and show why it leads (without public intervention) to the
‘free-rider problem’.
• We consider the simplest version – which shows the problem
in its starkest form.
Public Goods – the statement of the problem
• There are N members in society and each has an income m
that can either be contributed to the ‘public good’ or
consumed privately. Let xn denote the amount contributed to
the public good by individual n and hence (m-xn) that privately
consumed by individual n.
• Total contributions to the public good are multiplied by some
number k (>1) and distributed equally to all.
• Suppose individual n’s utility is simply the sum of his or her
private consumption and his or her share of the public good.
• Then Un = (m-xn) + k(x1 + x2 + x3 +… + xN)/N
• What is n’s optimal contribution xn? (Assume k/N<1).
The Nash Equilibrium
• A little bit of maths shows us that, given everyone else’s
contributions, the best thing for individual n to do is to put
xn = 0, that is, to contribute nothing. This is the Nash
Equilibrium. (This assumes that k/N < 1 and k>1.)
• Also we can show that what is collectively best is for
everyone contributing everything – that is xn = m.
• Note: if everyone contributes nothing then everyone gets
utility m, whereas if everyone contributes everything then
everyone gets utility km – which is much better.
• But note the incentive problem – in the table on the next
slide.
An example – from the individual point of view
• The following table shows n’s utility in four cases. We
take m=100 and N=10. Also k = 3.
n’s
contribution
n’s
utility/happiness if
all others
contribute 100
n’s
utility/happiness if
all others
contribute 0
100
300
30
0
370
100
• n has a very strong incentive to contribute nothing – that is to
completely free-ride. But if everyone does this then everyone gets
just 100! This is the ‘free-rider’ problem.
An example – society’s point of view
• The following table follows up the previous example. It
supposes that all 10 people in society contribute the
same. We take m=100 and k = 3.
everyone’s contribution
everyone’s utility/happiness
100
300
0
100
• Everyone in society is better off if everyone contributes
everything – despite the private incentives.
Implications
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Public Goods are goods that are freely available to all – and where one
person’s ‘consumption’ of the good does not decrease the ‘consumption’ of
anyone else.
We have stated the ‘free-riding problem’ in its starkest form – and have
shown that, if everyone individually decides what to contribute then no-one
will contribute anything. But it is best for everyone for everyone to contribute
everything.
There are ways around the problem, which we discuss in the rest of this
lecture. These include:
Forced provision and forced payment (what if you do not like it?);
Openness – everyone is told what everyone has contributed;
Punishment and/or rewards;
Threshold;
Tax concessions;
Voting
Groups with identity.
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Let us look at each of these in turn.
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Forced Provision
• First we note that the predictions of the theory have
been shown in experiments not to be very good....
• ...people do contribute (though in decreasing
amounts).
• So what do we do?
• We (The State) can force people to contribute. (Tax?)
• In a very real sense, this is not a ‘solution’.
• Also it may penalise those who do not wish to
consume the good. (Distribution and Poll Tax)
Openness
• We could ‘embarrass’ people into contributing.
• Experiments have shown that telling all subjects
which subjects have contributed, and how much
they have contributed, makes a difference to
contributions.
• This ‘should not’ make a difference but it does.
• What is the real world counterpart?
• Charities that list contributors? Wedding present lists.
• Does the theory need amending? (Shame? Altruism?)
• Do we need a State?
Punishment and Rewards
• One proposal – which appears to work – to encourage
contributions is to add an extra stage to the game...
• ...in which players can punish other players for low
contributions or reward others for high contributions.
• To make sense of this both rewarding and punishing
must be costly.
• But if no-one punishes and/or rewards we are back to
the standard public good game.
• Note however, that someone (The State?) has to
propose and implement the rewards and punishments.
Tax concessions
• In a similar vein, the State could propose tax
concessions on contributions.
• This is actually the case in the UK for
contributions to charity.
• An interesting question: How does this work
in the context of the standard public goods
model?
• One for the nonna?
Thresholds
• So far we have considered public goods whose
provision can be in any positive amount.
• For certain public goods, there may be a lower
bound or a threshold.
• So the good is provided if and only if contributions
cross the threshold. All-or-nothing public goods.
• This transforms the public goods game (with an
inefficient equilibrium) into a coordination game
with a set of Pareto-superior equilibria. May work.
Majority Voting
• If I am voting whether the good is to be provided, I
cannot free-ride and I need not worry that anyone else
can either.
• We can all vote our overall preferences between supply
at the relevant individual cost versus no supply and no
cost of provision, so that democratic choice turns our
problem into a simple coordination problem - if the
majority of us are in agreement that a relevant good
should be collectively provided, then under majority
voting it will be provided.
• Is this a good thing?
Provision through groups
• The above analysis has been based firmly on individual action.
• An alternative approach is one proposed by Mancur Olsen in
his book The Logic of Collective Action: Public Goods and the
Theory of Groups in 1965.
• Olsen propounded a novel and influential theory of the
behaviour of groups with some collective or common interest.
• He argued that the smaller the group the better it will further
its common interests. Indeed, he argued that one of the most
crucial factors in determining whether or not it is possible
that the voluntary, rational pursuit of individual interest will
bring forth group-oriented behaviour is the size of the group.
Olson and groups
• According to Olson, small groups of people are more efficient
and viable than large ones and that ‘action-taking’ groups and
subgroups tend to be smaller than ‘non-action-taking’ groups
and subgroups.
• Olson has argued that economic incentives are not the only
incentives, for instance, people are also motivated by a desire
to win prestige, respect, friendship, and other social and
psychological objectives.
• When there are no economic incentives for an individual to
contribute to the achievement of a group interest, there
might be a social incentive for him or her to make such a
contribution. We have noted this elsewhere.
Size of the group
• The idea of group theory is supposed to follow
logically from the widely accepted premise of
rational self-interested behaviour.
• According to Olsen, social pressure and incentives
operate only in groups of smaller size where
members can have face-to-face contact with one
another.
• Olson has come to the conclusion that the larger the
group, the less it will further its common interest.
Conclusions
• Without some non-economic considerations or some
additions to the issue of contribution to public goods, we
have shown that they will not be provided.
• Groups may somehow collectivise their utilities and coordinate their activities.
• State provision is justified when private provision breaks
down.
• However there are cases (for example, charities) when
private provision works. These seem to be where motives
are non-economic.