Charity as a Tool to Maximize
Donations to a Congestible Club Good
Andrey Zubanov1
Introduction
The paper aims to show economic reasons why some organizations and societies such as social
and political movements or authorities of parks and beaches may profit from financing a public
good. I consider an economy where the entrance to the club is voluntary and the club good is
congestible. I assume that donations to the club fund can be made by club members only, and the
fund is further distributed in some proportion between production of the club and the public
good. The club good is enjoyed solely by club members while the public good is consumed by
each member of the economy. I show that under the assumptions that marginal congestion
increases with the club size, the club should devote a positive share of its funds to the production
of a public good in order to maximize donations to its fund.
Model Description
I consider the economy with one free-entry club as in Buchanan (1965) with voluntary
participation. All agents in the economy have equal endowments but they are heterogeneous
(uniformly distributed) in how they value the club good. There is a natural exclusion mechanism
for the club, which prevents agents from obligation to participate in the club. Each agent decides
for herself whether to participate in the club or not. Club members then can choose a donation
within their endowment to the club fund. The donation is voluntary and club members only can
donate to the club fund.
1
Undergraduate student, National Research University Higher School of Economics, Faculty of Economics,
Moscow, Russia; e-mail: andr1904@gmail.com, andreyzubanov@yahoo.com.
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The fund is distributed in some proportion between the production of the club and the
public good. They both have linear production functions but marginal per capita return from the
club good is greater than that of the public good (otherwise, only the public good will survive). I
consider the club good as congestible, which means that each agent gets less utility from
consuming it the more agents, use it, whereas there is neither congestion nor network effects in
the public good.
Club members enjoy the club good (and suffer from its congestion) and the public good as
well as whatever is left for their private consumption after making a donation. Agents who are
not members of the club consume only their initial endowment and enjoy the public good. The
timeline of the game is as follows. In the first stage, agents decide whether they want to enter the
club or not. In the second stage, the club members decide how much of their initial endowment
they want to donate to the club fund. Then the outcomes are realized.
The congestion of the club good reduces the returns on the club good. So, when the
number of club members (club good users) increases, other things equal, the return from the club
good falls, and club members receive less utility from the club good.
Overall, the agents can be divided into three groups according to their preferred action:
members of the club who donate, members of the club who do not donate, and agents who do not
enter the club.
Results
The proposed mechanism in which the public good is created by the club members helps to
mitigate the free-rider problem and allows to naturally exclude from the club the agents who
create congestion without making donations.
The mechanism works due to the fact that higher share of the club fund devoted to the
production of the public good creates additional incentives for agents to stay out of the group and
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makes some of the free-riders leave the club. The latter reduces congestion of the club good and
increases its marginal per capita return. These increased returns make some club members
choose to donate.
On the one hand, a greater share of funds spent on the public good decreases overall return
for club members (since the public good is less productive than the club good) and this
demotivates them from making donations. On the other hand, the overall return for the club
members increases because of lower levels of congestion. Under the model assumptions, there
exists equilibrium where the positive effect of such new donations outweighs costs of the public
good provision. Moreover, there exists the optimal positive share of the club fund that has to be
devoted to the public good, so that the total amount of donations is maximized.
I also analyze how robust this result is to relaxing the assumption that the degree of
congestion monotonously increases with the number of agents in the club. In the robustness
check, I assume the presence of network effects that create a non-monotonic relationship
between the number of agents and club good quality. In particular, I assume that when there are
few club members, as additional participants are welcomed to the club, the club good users enjoy
this good more. However, when there are too many users, the congestion increases and agents
start to get lower returns on the club good. These effects produce a parabolic relationship
between the number of club members and the degree of congestion. The result for this case is the
same as for the main model, except there is an additional equilibrium with zero donations, which
is typical for network effects.
Conclusion
The paper explains how clubs may benefit from establishing a public good at their own expense,
and this instrument can be used by the club authorities in order to alleviate the free-rider problem
and boost donations. The effects shown in the paper need further empirical testing in order to
find exact scope of cases this theory can be applied to.
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References
1. Buchanan, J. M. (1965). An economic theory of clubs. Economica, 1-14.
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