## 1. Defining Public Goods and Distinguishing Between Different Kinds of Public Goods


### 1.1 Non-Rivalry and Non-Excludability



Even though Nobel laureate Paul Samuelson is usually credited with
having introduced the theory of public goods to modern economics
(e.g., in Sandmo 1989), the origins of the idea go back to John Stuart
Mill, Ugo Mazzola (an Italian writer on public finance), and the
Swedish economist Knut Wicksell (Blaug 1985: 218-9 and
596-7]). Samuelson defined what he called a "collective
consumption good" as:



> 
> 
> [a good] which all enjoy in common in the sense that each
> individual's consumption of such a good leads to no subtractions
> from any other individual's consumption of that good....
> (Samuelson 1954: 387)
> 
> 
> 



In the contemporary debate, this feature or characteristic of goods is
usually referred to as "non-rivalry". A good is rivalrous
if and only if an individual's consumption of it diminishes
others' ability to consume it. Bob's consumption of a
grain of rice makes it impossible for Sally to consume the same grain
of rice. By contrast, Sally's enjoyment of Bruckner's
Symphony No. 9 in no way diminishes Bob's ability to do the
same. Rice is thus rivalrous while music is
 not.[1]




A few years after Samuelson, Richard Musgrave introduced an
alternative criterion, that of (non-) excludability (Musgrave 1959).
As the name suggests, a good is excludable if and only if it is
possible to prevent individuals from consuming it, to "draw a
fence around it" as it were. Land is thus a good that is
considered excludable, while streetlight is not excludable: if Bob
pays for a streetlight to be installed, he cannot stop his neighbour
Sally from benefitting from it.



In contemporary economics, goods are usually defined as public goods
if and only if they are *both* non-rivalrous and non-excludable
(e.g., Varian 1992: 414). Rivalrous and excludable goods are called
private goods. National defence is a paradigmatic example of a public
good. Not only does Sally's consumption of national defence not
reduce Bob's consumption; she could not prevent him from
consumption if she tried. Food, clothes and flats are paradigmatic
examples of private goods.



There are also goods that are rivalrous and non-excludable and goods
that are non-rival and excludable. The former are sometimes called
"common pool resources" (e.g., V. Ostrom & E. Ostrom
1977, E. Ostrom et al. 1994; E. Ostrom 2003). An example is fish
stocks. The latter are sometimes called "club goods"
(e.g., Mankiw 2012: 219; see also Buchanan 1965). Examples include
watching a movie in a cinema and the services provided by social and
religious associations.



Table 1 provides an overview of the different types of goods that have
been distinguished so far.





|  |  |  |
| --- | --- | --- |
| *Characteristic* | **Rivalrous** | **Non-rivalrous** |
| *Excludable* | Private goods (homesteads, bathroom cleaner) | Club goods (Sports clubs, movie theatres) |
| *Non-excludable* | Common resource goods (fish stocks) | Public goods: local (fire protection), national (national defence),
global (climate mitigation measures), partial (parades) |


Table 1: Different kinds of economic goods



### 1.2 Porous Boundaries



The boundaries between these different types of goods are neither
sharp nor fixed. For example, whether or not Bob's enjoyment of
a movie in a theatre is affected by Sally's watching the movie
in the same theatre at the same time depends on Bob's values or
tastes as well as details of the context. Sally might sit in front of
Bob and partially block his view. Or she might be one of those people
who sits right next to you even though fifty other seats are
available. Or Bob might be bothered by anyone sitting in the same
theatre at the same time, or enjoy watching the movie together with
others. Thus, even supposing that Sally doesn't alter
Bob's viewing of the movie as such, her presence can have a
positive or negative effect on Bob's enjoyment of it. Thus,
whether or not a good is rivalrous in consumption depends on many
contextual details and not just the nature of the good alone.



The same good can be excludable at one time, but non-excludable at
another, or excludable in one society, but non-excludable in another.
For example, radio broadcasts used to be a public good because it was
not (easily) possible to prevent individuals from tuning in, but this
is no longer the case in the digital age. But technology is only part
of the story. A particular plot of land--a prime example of a
private good--can be protected by building a fence around it. But
there is no fence that cannot be overcome. In reality, a fence is more
like a signal indicating that the owner prefers to keep others out, or
it makes it more costly for them to do so. What matters for the
characterisation of land as a private good is that the landowner has
the *right* to stop potential trespassers and that this right
will be enforced by the legal system. Of course, which sets of rights
are attached to property depends on the norms prevailing in a society.
Property rights are never absolute (property in a chain saw gives me
the right to use it to cut my own trees but not to cut my
neighbour's trees, much less to use it to hurt anyone), and
always the result of past negotiations.



To give a silly example, not everyone enjoys the sight of
(particularly, white) socks in sandals. In our society, the sight of
socks in sandals is something individuals have to endure because it is
considered to be within the rights of the owners of white socks that
they can wear them in public, in sandals or in other types of shoes.
It is easy, however, to imagine societies that define the rights of
sock-owners differently and value the tastes of those who are bothered
by the blight of socks in sandals more highly. Indeed, even in modern
liberal societies social norms regulate what is decent to wear in
public. Since a good's degree of excludability depends in part
on property rights, and what property rights entail may differ between
societies and, within societies, may change over time, a good's
excludability may differ between societies and change over time. 



Another, related aspect is that the cost of enforcing property rights
differs between cases, partly for technological, partly for legal and
political reasons. That automobiles are private goods depends on the
relatively cheap availability of suitable locks and also on the fact
that the government enforces property rights in automobiles. If the
price of locks were higher, or the government made it illegal to
secure one's car using a lock, or the government stopped
prosecuting theft, automobiles would be "non-excludable"
(Demsetz 1964).



A corollary of the non-excludability characteristic is that there are
limitations to consumers' consumption decisions regarding the
public good, if it is produced. Individuals might have different
preferences for the level of security provided by national defence,
but once national defence is in place, they will consume the level
that has been produced, not more or less of it. One cannot "opt
out" of the consumption of a public good. Similarly, while
everyone might like clean air, individuals will differ in their degree
of tolerance of pollution. But once "clean air" has been
produced, consumers must consume it independently of their
preferences.



It has been suggested that the "public" nature of a public
good may be an *effect* of its provision by the public rather
than its cause (Cowen 1992: 6 credits unpublished work from 1987 by
Boudewijn Bouckaert). If a good is provided by government, private actors
have no reason to develop technologies that allow the exclusion of
non-paying individuals. Accordingly, public investment in the good
thereby makes a good that could be private a public good. Even if this
idea is mistaken, it illustrates the fact that the boundary between
private and public goods is not fixed because what is technologically
possible depends in part on investment in research and
development.



The physical characteristics of a good, then, together with the
context of its consumption, values, tastes, legal, moral and social
norms as well as technological possibilities determine the proper
categorisation of a good as a private, common pool, club, or public
good.


### 1.3 Different Kinds of Public Goods



Distinctions can also be drawn *among* public goods. Most
public goods do not affect all inhabitants of a large community
equally. Fire protection services in Lower Manhattan are not consumed
by those living in the Bronx, much less by Californians. Public parks
benefit those who live in the neighbourhood, playgrounds only those
who live in the neighbourhood and have children of a certain age (and
indeed they might constitute a public bad for others). Charles Tiebout
has developed a theory of *local* government, after which the
term "local public good" was coined (Tiebout 1956,
Stiglitz 1982). Other public goods may benefit all of humanity, such
as climate change mitigation. We can therefore distinguish
*local*, *national*, and *global* public goods
(on the latter, see Kaul et al. 2003).



A *partial* public good is one from whose consumption some
individuals can be excluded but not others. Mancur Olson gives the
example of a parade that is a public good for those living in tall
buildings overlooking the parade route but a private good to those who
need to buy a ticket for a seat in the stands along the way (Olson
1971: 14). A *full* public good, by contrast, is one from whose
consumption all individuals can be excluded.


### 1.4 Examples of Public Goods



The following are examples of goods that are typically regarded as
public goods:


* *Security*. National defence has already been mentioned as
an example. More generally, the ability to live safely and peacefully
in a neighbourhood, city, region, or country (for instance, through
police and armed forces) is considered a public good because it is
difficult to exclude any inhabitant of the protected area from
benefitting from the protection and one inhabitant's enjoyment
of protection does not generally diminish other inhabitants'
equal enjoyment.
* *Education and science*. The public goods character of
education and science is somewhat more subtle. It is easily possible
to exclude individuals from being schooled, and so "having an
MIT engineering degree" is a private good. However, the more
educated the general population is, the more individuals benefit from
this general education--independently of how much they invest (or
the public invests) in their own education--in a manner that is
non-excludable and non-rivalrous. A better educated population makes
it easier for businesses to thrive, and everybody profits from a
thriving economy, not only those who are well-educated. It is
difficult to exclude individuals from a thriving economy and a given
individual's benefit is not diminished by anybody else's
benefit. Scientific ideas are also considered to be public goods
(Boldrin & Levine 2008). Once an idea (such as a scientific
theory) has been created it is difficult to exclude individuals from
benefitting (unless the idea is protected by a patent, see below), and
individuals' benefit is non-rivalrous. It is important to
distinguish between the idea and its physical manifestation. The idea
of a steam engine is a public good, whereas particular steam engines
are both excludable and rivalrous.
* *Infrastructure*. Though infrastructure is often referred
to as a public good (e.g., OECD 2016), whether the classification is
correct depends on the details of the specific kind of infrastructure
and technology. Paradigmatic examples of infrastructure are often not
public goods. Roads and motorways are excludable, as the existence of
toll roads attests. If the toll for a private road is sufficiently
low, it can be rivalrous as well due to congestion. The same can be
said about the internet. A traditional lighthouse is more likely to
have public-goods character, though depending on the physical nature
of the signal it sends, it may well be excludable (Varian 1992: 415).
The reason many commentators classify infrastructure as a public good
is that it tends to lead to positive externalities. The (close)
relationship between public goods and externalities is explained
below.
* *Environment*. Clean air is a paradigmatic good, at least
outside. Without massive infringements of an individual's rights it is
virtually impossible to exclude him or her from benefitting from clean
air. And outside of narrowly enclosed spaces, clean air is non-rival.
Similarly with the absence of littering. If I decide not to litter, I
cannot easily prevent you from enjoying the clean space, and your
enjoyment of it does not reduce anyone else's.
* *Public health*. Individuals benefit from a healthy
population in a variety of ways. For example, the fewer individuals
are infected with a contagious disease, the less likely it is that any
given (currently healthy) infects him- or herself. These benefits
obtain in a non-excludable and non-rivalrous manner. A healthier
population is also more likely to be productive, making public health
analogous to education.


### 1.5 An Alternative Definition



Angela Kallhoff has offered an alternative, albeit similar, definition
of a public good (Kallhoff 2011: Ch. 2). According to her, a public
good is one that satisfies the "basic availability
condition" and the "open access condition". Basic
availability is her analogue of non-rivalry. A good satisfies this
condition whenever each person benefitting from it has access to the
same amount and the same types of benefits. To state the condition in
these terms makes explicit that there may exist a level of consumption
at which sameness of amount and types of benefit are no longer
guaranteed. A single ship's enjoying the benefits of a
lighthouse does not affect another ship's doing the same but
once the sea is congested this may no longer be the case. A lighthouse
is a public good because there *exists* a level at which each
person has access to the same amount and the same types of benefits.
Open access is Kallhoff's analogue of non-excludability. It
states that 



> 
> 
> entrance barriers that regulate access to a good are not combined with
> criteria which define a list of potential beneficiaries and exclude
> others. (Kallhoff 2011: 43) 
> 
> 
> 



Clubs produce services for a specific group of beneficiaries, the club
members. In order to profit from a lighthouse, an individual needs a
boat and a desire to travel to the coast where the lighthouse is
located but there is no pre-specified collective that constitutes the
intended beneficiaries of this good.


## 2. Public Goods and Externalities



Externalities are effects of economic transactions on individuals that
are not party to the transaction. The paradigm example is pollution: a
company produces some good the production process for which is
"dirty" in that it affects individuals independently of
whether or not they are customers of the company. If such effects are
undesired, as in the case of pollution, they are called
*negative* externalities; if they are desired,
*positive* externalities. A paradigmatic example of a positive
externality is the pollination created by a honey producer's
bees. Individuals benefit from pollination whether or not they buy
honey.



Public goods create positive externalities. Suppose a group of
individuals get together and pay some company to produce (analog)
radio broadcasts. Individuals who are not party to the transaction can
now benefit from the good. Similarly, if a group of citizens get
together to clean up a public park, individuals will benefit whether
or not they were part of the group of citizen cleaners.



The existence of a public good implies the existence of (positive)
externalities, but the reverse is not true. The beekeeper's bees
may pollinate the trees in the neighbouring orchard, thereby
increasing its production, but that does not mean that it is
impossible to exclude others from this or other benefits or that these
benefits are non-rivalrous.

 
## 3. The Economics of Public Goods and the Public-Goods Problem


### 3.1 The Public-Goods Problem



The provision of public goods is often associated with market failure
due to the externalities created by the public good. Suppose that in a
two-by-two toy economy Bob and Sally decide how much to invest in a
discrete public good *G* such as a radio station. Both have an
initial endowment of a private good (which functions as money in this
economy). The public good will be produced \((G = 1)\) if the sum of
contributions \(g\_{\textrm{Bob}}\) plus \(g\_{\textrm{Sally}}\) is
higher than the production cost *c*. Thus (Varian 1992: 415):



\[
G = \begin{cases}
1 & \textrm{if } g\_{\textrm{Bob}} + g\_{\textrm{Sally}} [?] c\\
0 & \textrm{if } g\_{\textrm{Bob}} + g\_{\textrm{Sally}} < c. \\
\end{cases}
\]


How much they will contribute will depend on their reservation prices
\(r\_{\textrm{Bob}}\) and \(r\_{\textrm{Sally}},\) i.e., on the maximum
amount of the private good each agent is willing to give up for the
public good. It is then easy to show that the production of the public
good will be a Pareto-improvement if and only if (Varian 1992:
 416)[2]:


 

\[
r\_{\textrm{Bob}} + r\_{\textrm{Sally}} > c,
\]


that is, if the *sum* of reservation utilities exceeds the cost
of providing the public good. This is analogous to the efficiency
condition for a private good, which is efficiently provided whenever
an individual's willingness to pay exceeds the cost of producing
it. In case of a public good, since consumption is non-rivalrous, it
is enough when the sum total of all reservation prices exceeds the
production cost.



In the simple two-by-two case, let us assume that \(r\_{\textrm{Bob}} =
r\_{\textrm{Sally}} = 100\) and that \(c = 150,\) so that the
efficiency condition is satisfied. If either Bob or Sally buy the
public good, but not both, they would have to be charged the full
cost, leading to an outcome of \(-50.\) The not-buying individual will
free-ride on the other's contribution and get 100. If both
contribute, each receives a benefit \(100 - 150/2 = 25.\) If neither
contributes, the good will not be produced and both end up with zero.
The payoffs are displayed in the matrix in Table 2.





Table 2: A Public Goods Game|  |  | **Sally** |
|  |  | *Contribute* | *Don't Contribute* |
| **Bob** | *Contribute* | (25; 25) | ([?]50; 100) |
| *Don't Contribute* | (100; [?]50)  | (0; 0) |




This payoff structure is identical to a Prisoner's Dilemma and
illustrates the free-rider problem. Bob prefers the public good to be
produced but since he benefits from it whether or not he contributes,
his most preferred alternative is that in which Sally pays for its
production and he free rides on her contribution. Sally faces
identical payoffs. Therefore, both will choose not to contribute,
meaning that the public good will not be produced, even though the
alternative outcome in which both contribute would be Pareto superior.
A Pareto-superior outcome is one that makes at least one individual
better off while making no-one worse off. (Contribute; Contribute) is
Pareto-superior to (Don't contribute; Don't contribute).
(Don't contribute; Don't contribute) is the equilibrium
strategy (in the sense that no player has a reason to deviate from
playing it, given the other player's move) but at the same time
there is an outcome both would prefer if it could be reached, namely,
(Contribute; Contribute).



Given this structure of benefits as well as rationality and
self-interest of the members of a group, we can expect that free
markets will undersupply public goods. As individuals have strong
incentives to free ride and the incentive structure is exactly the
same for everyone, everyone tries to free ride and the public good
will not be produced in consequence. Let us call the apparent
inability of the market to provide public goods in a sufficient
quantity the problem the "public-goods problem".


### 3.2 Responses to the Public-Goods Problem



Many economists regard the public-goods problem as a justification for
advocating coercive government action (e.g., Sidgwick 1901; Pigou 1920
[1932]; Samuelson 1954). The argument actually goes back to the
origins of economics. In Book 5 of the *Wealth of Nations*,
Adam Smith listed three functions of government. "The third and
last duty of the sovereign or commonwealth," Smith says,



> 
> 
> is that of erecting or maintaining those public institutions and those
> public works, which, although they may be in the highest degree
> advantageous to a great society, are, however, of such a nature, that
> the profit could not repay the expense to any individual or small
> number of individuals, and which it therefore cannot be expected that
> any individual or small number of individuals should erect or
> maintain. (1776: Bk 5, ch. 1)
> 
> 
> 



Similarly, in the nineteenth century John Stuart Mill wrote that:



> 
> 
> ... it is a proper office of government to build and maintain
> lighthouses, establish buoys, etc. for the security of navigation: for
> since it is impossible that the ships at sea which are benefited by a
> lighthouse, should be made to pay a toll on the occasion of its use,
> no one would build lighthouses from motives of personal interest,
> unless indemnified and rewarded from a compulsory levy made by the
> state. (1848 [1963: 968])
> 
> 
> 



However, it is not easy for the government to estimate the demand for
a given public good and calculate the appropriate level of taxes. If
preferences were observable, the government could charge each citizen
according to their marginal benefit (thereby levying so-called
"Lindahl taxes"), and an efficient equilibrium (the
"Lindahl equilibrium") would result (Varian 1992: 426;
Roberts 1974). But preferences can't be observed. If they
can't, people have an incentive systematically to understate
their reservation prices in the hope that others won't do the
same so they can free-ride on others' tax contributions. If
everyone does that, the public good doesn't get funded
publicly.



Leif Johansen has argued that the free-riding argument is less
compelling than it appears (Johansen 1977). On the one hand, there is
little evidence that people systematically misstate their preferences
in elections. On the other hand, public goods are produced at rates
that are much higher than would be suggested by the free-rider theory,
which assumes that utility is strictly increasing in private
consumption. The empirical evidence on these questions will be
reviewed in
 Section 5
 of this entry.



There are mechanisms that encourage individuals to reveal their true
valuations of the public good. One is the so-called Groves-Clarke
mechanism (after Groves 1973 and Clarke 1971). Here each individual
submits a bid, which may be positive or negative, and which may or may
not reflect the individual's true value of the public good
(i.e., the reservation price minus the cost). The public good is
provided if and only if the sum of bids is at least zero. Apart from
the public good, each individual receives a "side payment"
calculated as the sum of all other individuals' bids (which may
also be negative, i.e., a tax).



No individual has an incentive to misrepresent his or her true values
under the Groves-Clarke mechanism. Suppose we change the valuations in
the above example so that the public good is now worth [?]24 to
Bob (by adjusting his reservation price to 51). It should still be
produced as the sum of valuations remains positive (alternatively, the
sum of Bob's and Sally's reservation prices remains above
the cost of producing the public good). Bob does not have an incentive
to misrepresent his valuation (by bidding below [?]24) because
with the transfer of 25 he receives he is still better off than if the
public good was not produced. The same is true of Sally. She'll
have to pay a tax of 24 but is still better off than if the public
good was not produced. If we lower Bob's reservation price
further to below [?]25, he would be worse off despite the transfer
and thus accurately bid the true, low value. Sally, even though she
would prefer the public good to be produced in the absence of
transfers would also be worse off after paying the tax and therefore
has no incentive to overstate her valuation.



The problem with the Groves-Clarke mechanism is that it is very
expensive--large payments are needed in order to induce
individuals to bid their correct value. There are alternative
mechanisms that avoid positive payments but at the expense of
generating social waste (Varian 1992: 428).


## 4. The Private Provision of Public Goods


### 4.1 Coupling



Mancur Olson was among the first economists who studied the private
provision of public goods in great detail (Olson 1971). He argued that
the existence of a common purpose or common interests is
characteristic of *organisations*. But if these interests are
served, that means that a public good has been created. Therefore:



> 
> 
> It is of the essence of an organization that it provides an
> inseparable, generalized benefit. It follows that the provision of
> public or collective goods is the fundamental function of
> organizations generally. (Olson 1971: 15)
> 
> 
> 



But that doesn't mean that organisations cannot also produce
private goods:



> 
> 
> There is no suggestion here that states or other organizations provide
> only public or collective goods. Governments often provide
> noncollective goods like electric power, for example, and they usually
> sell such goods on the market much as private firms would do.
> Moreover, as later parts of this study will argue, large organizations
> that are not able to make membership compulsory *must also*
> provide some noncollective goods in order to give potential members an
> incentive to join. (Olson 1971: 16; emphasis in original)
> 
> 
> 



The coupling of private and public goods is one important mechanism
through which private enterprises can be enabled to provide public
goods. In the eighteenth century, lighthouses were public good because
their "consumption" was non-rivalrous (barring congestion)
and non-excludable (using the technology available then). Port spaces
are private goods, however. British lighthouses were often financed by
imposing light dues on ship owners at the ports (Coase 1974). The dues
were calculated by the net ton per voyage for all ships arriving at,
or departing from, ports in Britain. A public good that is coupled
with a private good as a mechanism for its financing is called an
"impure" public good (Cornes & Sandler 1984).



Shopping centres and some apartment buildings provide other examples
of impure public goods. Shopping malls provide public spaces, streets,
parking space, and security for which consumers pay indirectly by
buying the merchandise offered in the shopping centre. Similarly, some
apartment buildings offer common spaces and infrastructure for which
owners pay through supplements to the apartment prices or rentals.



The shopping centre example illustrates a potential problem for the
private provision of a public good. Suppose that it is prohibitively
expensive to charge individuals for the use of parking spaces
provided. Parking space is then a public good because non-shoppers can
use it free of charge. Suppose further that the owner of land nearby
exploits the situation by building a competing shopping centre that
does not offer parking space. The new shopping centre can price its
competitor out of the market by offering lower prices for the
merchandise it sells because it does not have to pay for parking
space.



However, at least in principle the owner of the first shopping centre
can avoid this by purchasing the surrounding land before free parking
is allowed. After Ronald Coase this mechanism for solving
externalities problems is referred to as "extending the role of
the firm" (see Demsetz 1964). Another example for this mechanism
involves the public good pollination. If a bee keeper and the owner of
an orchard cannot agree on the value of the pollination and nectar,
either is free to buy the other's property and thus internalise
the externality by extending the firm.


### 4.2 Other Mechanisms



An alternative reason for existence of privately provided public goods
is that people do not always act in a fully self-interested manner.
Most economic models assume that people care only about the benefits a
public good provides to them, but people in fact also care about the
outcomes for others. Donations to charity and political campaigns are
obvious examples. One way to model this is to assume that the act of
giving itself provides additional utility distinct from the utility
obtained from the aggregate level of provision of the public good
(Steinberg 1987).



A third reason for the ability of public goods to be provided
privately to be discussed here is the existence of social norms. For
example, as long as individuals meet *repeatedly* to decide
about the creation of a public good, they might realise that lying is
self-destructive, and as the situation is iterated, it is possible
that a norm of truthful revelation of the valuations is developed upon
which a convention of telling the truth would be built (Taylor 1976;
Schotter 1981). That a non-co-operative strategy is not necessarily
optimal in repeated games is a well-known result in game theory (see
entry on
 game theory, section on repeated games and coordination).



Other norms such as "everyone should do their bit" or
fairness and equality norms can also help to increase private
contributions to public goods. People might simply think that it is
morally wrong to free ride (Sugden 1984). Social norms can motivate
people to act altruistically but also help to solve co-ordination
problems by specifying property rights and the terms of contracts
(Young 1998). Clean streets (the absence of littering) can be regarded
as a public good, and let us assume that littering isn't
punishable by law. In a game-theoretic setting, individuals would be
expected to underproduce the public good, i.e., to litter too much. A
norm not to litter can now help to induce people to co-operate and
play the non-Nash equilibrium but Pareto superior strategy. The
punishment of norm-violators through social sanctions will help to
make people follow the norm without the government having to police
norm following.



Most mechanisms discussed in this section can be expected to work
better for local public goods than for national or global public
goods. It is easier to negotiate with neighbours about littering than
with people who live halfway across the globe, and people tend to feel
more altruistic towards others who live nearby and are in other ways
similar (Hamilton 1964).


## 5. Empirical Work on the Public-Goods Problem



There has been an explosion of experimental work relevant to the
public goods problem since the rise of experimental economics in the
second half of the twentieth century. An important strand in this
literature describes results from so-called "public goods
games" (for a survey, see Ledyard 1995).


### 5.1 Public Goods Games



A typical public goods game set-up is as follows. A number *n*
of university students is brought into a room and seated at a table.
They each receive an endowment of, say, EURx. They are then asked
to decide how much of that to spend on a group project, where
contributions can range from EUR0 to the entire endowment. They put
their contributions into an envelope so that other participants cannot
see how much each individual has contributed. The sum total of the
contributions is then doubled by the experimenter and divided equally
among the participants.



A public goods game is an *n*-person Prisoners' Dilemma.
The Pareto optimal outcome is one in which everyone contributes their
entire endowment. With \(n = 10\) participants and an endowment of \(x
= EUR10,\) each participant would wind up with \(EUR20.\) But
each individual has an incentive to contribute less. If everyone
*else* contributed their entire endowment, each individual
could receive up to \(9\*EUR10\*2/10+EUR10 = EUR28\) if they
contributed nothing. This is the same for everyone in the game, and so
the Nash equilibrium strategy is to contribute \(EUR0,\) resulting
in a payoff of \(EUR10\) for each participant.



In experiments, the Nash-equilibrium strategy is typically played by
only some of the players. Others contribute their entire endowment and
yet others a sum in between. Total contributions typically lie between
40% and 60% of the social optimum. Other stylised facts include
(Ledyard 1995: 13):


1. In one-shot trials and in the initial stages of finitely repeated
trials, subjects generally provide contributions halfway between the
Pareto-efficient level and the free riding level,
2. Contributions decline with repetition, and
3. Face to face communication improves the rate of
contribution.



The first two points have been described as "overcontribution
and decay" (Guala 2005): people tend to contribute more than we
would expect from a purely strategic point of view, but these
overcontributions decline when the game is played repeatedly (though
never to zero). Thus, people free ride less than advocates of
government funding of public goods often suggest, but private
provision is still at suboptimal levels.



There are a number of explanations for these phenomena. An obvious one
is experience and learning: as players become more experienced with
the set up, they come to understand that they can profit from
non-co-operation (especially when others are slower to learn that
lesson). Another one is that players' behaviour is motivated by
different considerations. Jon Elster describes six different types of
co-operative behaviour:



> 
> 
> Cooperation needs some individuals who are not motivated merely by the
> costs and benefits to them. Two categories of such individuals are
> what we shall call *full utilitarians* and *selfless
> utilitarians*. The first will cooperate if and only if their
> contribution increases the average benefit. [...] The second
> category will cooperate if and only if their contribution increases
> the average benefit, *not counting the costs to them*...
> 
> 
> 
> 
> If the selfless utilitarians are too few, or if the predicament I
> described deters them from acting, *unconditional cooperators*
> are needed... These actors take a number of shapes--they may
> be Kantians, saints, heroes, fanatics, or they may be slightly mad.
> What they have in common is that they act neither as a function of the
> expected consequences of their action, nor as a function of the number
> of other cooperators.
> 
> 
> 
> A further category of actors would never act as first movers, however.
> These are the individuals whose motivation is triggered by the
> observation of others' cooperating or by the knowledge that
> cooperators can observe them... A first subset of this group are
> motivated by the quasi-moral norm of fairness: it is not fair for us
> to remain on the sidelines while others are taking risks for our
> common cause. [...] A second subset are motivated by social
> norms. If noncooperators can be identified and subjected to social
> ostracism, as is usually the case at the workplace, for example,
> cooperators may shame them into joining.
> 
> 
> 
> A final category are those who join the movement for its
> "process benefits"--because it is fun or otherwise
> personally appealing. (Elster 2007: 397-9; emphasis in
> original)
> 
> 
> 



The presence of a certain proportion of conditional co-operators would
explain why contributions start relatively high but go down over time.
Empirical investigations confirm this explanation as well as the
presence of "mixed motives" (Villeval 2012). In a classic
paper, James Andreoni has argued that patterns observed in the data
about charitable giving from U.S. national surveys are inconsistent
with a model of pure altruism so that other motivations must be
included to account for these data (Andreoni 1988).



A large number of factors appears to affect the size of the
contributions. Apart from repetition (one-shot vs repeated games and
number of rounds), experience and learning, and communication, the
marginal payoff of contributions, the size of the group, provision
points (in some experiments the public good is provided only if
contributions reach a certain threshold), the heterogeneity of payoffs
and endowments, and moral suasion (i.e., the priming of experimental
subjects by experimenters) are among the factors that make a
difference (Ledyard 1995: 36). Some results are quite surprising. For
example, contributions increase with increasing thresholds at which
the public good is provided while the probability that the threshold
will be reached goes down (Isaac, Walker, & Thomas 1984). However,
with heterogeneous endowments, there are no significant differences of
contributions at different levels (Rapoport & Suleiman 1993).
Similarly, contrary to economists' expectations, group size can
have a *positive* effect on contributions while it dilutes the
effect of marginal returns (Isaac, Walker, & Williams 1994). That
causal factors affect experimental results in unsystematic and quite
unexpected ways appears to be a fairly general feature of experimental
economics (Reiss 2008: Ch. 5).


### 5.2 Other Kinds of Evidence: Field Studies, Observational Studies, Case Studies



Other kinds of empirical evidence that is relevant to the public goods
problem include field experiments, observational studies, and case
studies. They all have in common that they provide evidence that
individuals make *some* voluntary contributions to public
goods. What they investigate are the factors that affect the sizes of
the contributions and the mechanisms used to encourage people to
contribute.



*Field studies* have been used to examine the relationship
between an individual's contributions to a public good and
others' contributions. Depending on what one thinks
individuals' primary motivations are, one would expect an
individual's and others' contributions to be substitutes
or complements. If an individual is primarily motivated by altruism,
he or she will care about the consumption of others and therefore
contribute less when others or the government already contribute
enough. In this case we would expect the two kinds of contributions to
be substitutes. If, by contrast, an individual is primarily motivated
my social norms such as fairness and reciprocity, he or she will
contribute when others do their bit. In that case, we would expect the
two kinds of contributions to be complements. Whether they are on
average substitutes or complements is an issue that is difficult to
determine in laboratory experiments due to the relatively small sample
sizes and because the mix of motivations may differ between experiment
and field.



A field experiment involving an on-air fundraising campaign for a
public radio station found support for the complementarity hypothesis
(Shang & Croson 2009). Specifically, if social information is
provided about a high contribution of another donor, pledges increase
and the likelihood that a donor contributes again next year goes up.
The same has been found in a study of voluntary contributions to an
information good (a newsletter) on the Internet (Borck et al. 2006).
There have also been field studies of alternative provision
mechanisms, comparing a voluntary contribution mechanism for a pure
public environmental good to a green tariff mechanism, which can be
interpreted as an impure public good (Kotchen & Moore 2007).



The substitutes-vs-complements issue has also been investigated in
*observational studies*. That contributions are perfect
substitutes, i.e., that government contributions or other private
contributions crowd out an individual's contribution completely
is widely rejected. "Complete crowding out" here would
mean that every dollar spent on a public good by the government
reduces private spending by the same amount. Most studies find either
no crowding out, or a merely a small amount. For example, Kingma 1989
and Kingma & McClelland 1995, focusing on public radio, found only
a limited amount of crowding out between 12% and 19% of government
expenditures on public radio (i.e., one dollar spent by government
reduces private contributions by 12-19 cents).



There are a number of historical *case studies* as well. Ronald
Coase's study of the provision of lighthouses in nineteenth
century Britain has already been mentioned. Cowen 1992 contains a
number of further case studies that look closely at contracts between
bee keepers and apple growers (exchanging the public good pollination)
in Washington State, fire protection, leisure and recreation in the
United States, species conservation in the Cayman Islands, and
education in Great Britain before large-scale state subsidies. In each
of these cases, the authors point to private solutions to the public
goods problem. A historical review of publicly financed public goods
is provided in Desai 2003.


## 6. The Ethics of Public Goods: Should the Government Pay for Public Goods?



It is sometimes suggested that the standard justification for
government funding is attractive because it is based on a minimum of
normative assumptions. David Schmidtz, for example, writes that 



> 
> 
> one of the most attractive features of the public goods argument is
> the minimal nature of the normative assumptions it must make in order
> to ground a justification of the state. (Schmidtz 1991: 82) 
> 
> 
> 



Indeed, it seems that all that is required is that a government
intervention is justified if it brings about a state of affairs that
makes everyone better off than under any non-intervention
alternative.


### 6.1 Controversial Assumptions in Welfare Economics



However, to reach the conclusion that the government should provide
public goods, one requires a number of additional assumptions, all of
which are controversial. Standard welfare economics identifies
well-being with preference satisfaction, a view that has received much
criticism (see entry on
 well being;
 Nussbaum 2001; Hausman et al. 2017: Ch. 8; Reiss 2013: Ch. 12). It is
implausible to assume that people always choose what is best for them.
People may have inconsistent or unstable preferences such as the
smoker who flushes his cigarettes down the toilet in an attempt to
quit smoking, just in order to buy a new pack the next day. If people
have inconsistent or unstable preferences, it is unclear which
consistent set to choose for policy. Uninformed preferences also
appear to be a bad basis for policy. If people erroneously believe,
say, that there is no external threat, they might prefer less
investment in national defence than if they were fully informed. It
has been argued that in the political realm, insufficient knowledge is
the norm rather than the exception (Somin 1998, Caplan 2007, Somin
2013). It might be extraordinarily difficult to assess the value of a
public good to an individual, especially if the public good is a
national or global one such as defence, climate change mitigation or
basic research.



It has therefore been argued that rational or laundered or informed
preferences should provide the basis for policy decisions (e.g.,
Thaler & Sunstein 2008, Anomaly 2015). But it is not clear that we
can straightforwardly assess what citizens would prefer if they were
fully rational and informed. There is always the danger that whoever
makes that assessment substitutes his or her preferences for the
citizens' or that his or her preferences influence the judgement
about what the citizens' preferences might be (Rizzo &
Whitman 2008, 2009).



Assessing the value of a public good in terms of preference
satisfaction, actual or rational, involves another problem: the
impossibility of interpersonal comparisons. Suppose there are two
indivisible public goods *A* and *B*, Bob prefers *A*
while Sally prefers *B*, and Bob and Sally's combined
wealth suffices to buy only either *A* or *B*. Under a
preference-satisfaction account of welfare, there arguably is no
normatively defensible way to compare Bob's welfare
when *A* is purchased to Sally's welfare when *B* is
purchased or to compare what Bob would gain by purchasing and what
Sally would gain by purchasing *B*. Dan Hausman has argued that
this problem constitutes a reason to abandon the
preference-satisfaction account of welfare because any moral theory
that assesses situations fully or in part in terms of welfare requires
interpersonal comparisons (Hausman 1995).



Standard welfare economics does not make interpersonal comparisons
because it asks whether policies constitute a Pareto improvement over
the status quo. A policy constitutes a Pareto improvement if and only
if it makes some people better off while making no-one worse off. But
few policies are as unequivocal as this standard demands. Especially
when it comes to the items that are usually discussed under the rubric
of public goods, it is rarely if ever the case that no-one is made
worse off by the provision.



An alternative that has been introduced in the late 1930s is
Hicks-Kaldor improvement (after Hicks 1939 and Kaldor 1939). If there
are winners and losers to a policy, it constitutes a Hicks-Kaldor
improvement whenever losers can be compensated by winners'
gains. But that losers *can* be compensated is little
consolation unless they actually are compensated, and there is no
reason to believe that this always happens (see for instance Rodrik
2017 on the failures to compensate losers from free-trade
arrangements).



Characterising the public goods problem as a simple Prisoners'
Dilemma is therefore a significant idealisation. Frequently, the
production of a public good will benefit some but make others worse
off. Generally speaking, the decision whether to provide a public good
or not involves issues of fairness, equality and justice.



Welfare economists tend to ignore such issues because neither Pareto
improvements nor Kaldor-Hicks improvements (in their usual
interpretations) need information about anything other than
preferences. Indeed, standard welfare economics assumes that
well-being is all that matters to the evaluation of social outcomes.
Most people, however, care also about other values (Sen 1999: Ch. 3;
Hausman et al. 2017: Chs 9-12; Reiss 2013: Ch. 14).



One moral issue that has to be addressed even when the item in
question is unequivocally a public good to everyone affected by its
provision is that of paternalism (see entry on
 paternalism).
 It is by no means obvious that a coercive government intervention,
even one that makes everyone better off is justified. Austrian-School
economist Hans-Herrmann Hoppe expresses scepticism about the
permissibility of such interventions when he writes:



> 
> 
> The norm required to reach the above conclusion is this: Whenever one
> can somehow prove that the production of a particular good or service
> has a positive effect on someone else but would not be produced at all
> or would not be produced in a definite quantity or quality unless
> certain people participated in its financing, then the use of
> aggressive violence against these persons is allowed, either directly
> or indirectly with the help of the state, and these persons may be
> forced to share in the necessary financial burden. (Hoppe 1989:
> 31)
> 
> 
> 



Infringements on rights are not the only worry we might have. Some
public goods might disproportionately benefit those who are already
relatively well-off and therefore exacerbate existing inequalities.
Some aspects of tertiary education, for instance, might well be public
goods but if tertiary education was mainly to the benefit of
relatively well-off individuals, government provision could be
considered unfair. It is therefore not clear whether the government
provision of a public good is morally good, all things considered.


### 6.2 The Market As a Discovery Process



One point that advocates of government provision of public goods often
overlook is the information creation and coordinating function of the
price system (as described by Hayek 1945). In a market, prices
generate information about preferences and scarcities. If a good is
wanted by many individuals, it will become more scarce and its price
will rise. The increase in price does not only provide a reason for
consumers to buy less of it, it also signals to producers to make more
and to potential market entrants that the market is lucrative. In the
long run, supply should therefore increase and the price fall again.
This mechanism does not operate when the government provides the
public good and finances it by taxation. If the government builds,
say, a lighthouse, it will be difficult to determine how much to
invest every year, whether and how to extend or alter the service
provided by the good (e.g., by building a second lighthouse nearby),
and whether to invest in the development of new technologies.


### 6.3 Market Norms and Other Norms



So far, we have looked at public goods mainly as economic goods that
have certain characteristics that give rise to doubts whether they can
be provided privately at efficient levels. The government might be
justified in engaging in the production of a public good because it
corrects a market failure. Such an argument will always be contingent
on private actors' inability to produce the good or enough of
it, which is why mechanisms that encourage private provision have been
examined at some length in
 Section 4
 above.



Some philosophers have offered arguments to the effect that the
government should provide certain goods, independently of whether or
not they could be produced in sufficient quantities by the market.
Michael Waltzer and Elizabeth Anderson have argued that the sphere of
the market should be limited because market norms do not embody
certain important values and market exchange may undermine ideals and
interests legitimately protected by the state (Walzer 1983, Anderson
1993). According to Anderson, market norms have the following five
features: they are impersonal (independent of the relationship and of
the other party's ends), egoistic (the goal is to satisfy
one's personal interests), exclusive (defined as above),
want-regarding (as opposed to responsive to objective needs), and
oriented to "exit" rather than "voice" (rather
than voicing one's complaint one seeks an alternative) (see
Anderson 1993: 143-4).



A good is an *economic* good according to Anderson if its
production, distribution, and enjoyment are properly governed by
market norms (Anderson 1993: 146). This contrasts with a number of
other kinds of goods, such as gift goods. Friendly gift exchange
should be responsive to the personal characteristics of the receiver,
and to the relationship itself, rather than "impersonal".
It should also express an understanding of the relationship and not
merely satisfy the receiver's subjective wants. Giving money is
often regarded as offensive exactly because it ignores these
characteristics of gift goods.



What economists call public goods fall into Anderson's category
of "political goods". They are characterised by three
norms that oppose the respective market norms (Anderson 1993: 159).
First, one's freedom is exercised through voice rather than
exit. Second, goods are distributed according to public principles
rather than subjective wants. Third, the goods are provided on a
non-exclusive basis. About these goods she says:



> 
> 
> Some goods can be secured only through a form of democratic provision
> that is nonexclusive, principle- and need- regarding, and regulated
> primarily through voice. To attempt to provide these goods through
> market mechanisms is to undermine our capacity to value and realize
> ourselves as fraternal democratic citizens. (Anderson 1993: 159)
> 
> 
> 



The examples Anderson discusses in this section of her
book--roads, parks, primary and secondary education--are all
public goods in the economist's sense. Providing them privately
would undermine the "capacity to value and realize ourselves as
fraternal democratic citizens" because exercising freedom by
voice would be replaced by exit (e.g., when parents send their kids to
schools that approximate their values better than others instead of
contributing to curricula through voice), by allowing owners to
dictate terms on the basis of their wants instead of using principles
such as freedom of speech and association (e.g., when owners of malls
suppress speech and political activity they find offensive), and by
the ability of owners to exclude non-payers instead of enabling all to
meet one another on terms of equality (e.g., in the case of
parks).



In a similar vein, Angela Kallhoff argues that some (but not all)
public goods provide additional externalities that are essential for
the functioning of a democracy (Kallhoff 2011, 2014). Some public
goods constitute visible expressions of solidarity and social justice
among citizens ("central goods"), some support
connectivity and serve as representations of shared interests
("connectivity goods"), and some serve as visible
representations of a shared sense of citizenship
("identification goods"). The absence of these goods would
undermine the ability of the citizenry to engage in public
deliberation and develop a sense of self-determination.