Monopolistic Competition and Public Good Provision with By‐Product Firms

• DOI: http://doi.org/10.1111/jems.12036
• Date: 01 December 2013
• Published date: 01 December 2013
• Author: Paul Pecorino

Monopolistic Competition and Public Good Provision

with By-Product Firms∗

PAUL PECORINO

Department of Economics

Finance and Legal Studies, Box 870224

University of Alabama

Tuscaloosa AL 35487

ppecorin@cba.ua.edu

I develop a model in which the voluntary contributions mechanism for the provision of public goods

totally breaks down in a large society. A by-product firm sells a private good and uses its profits

to provide a public good. By-product firms compete with for-profit firms in a monopolistically

competitive industry. If the number of by-product firms is proportional to the size of the society,

then public good provision rises without bound as the society grows large. This stands in strong

contrast to the results under the voluntary contributions mechanism.

1. Introduction

A by-product firm sells a private good and uses the profits to provide a public good. In

this paper,I examine by-product firms in a model where private goods are produced in a

monopolistically competitive market. In this environment, the voluntary contributions

mechanism for the provision of public goods totally fails in a large group. By contrast,

when there are by-product firms whose number increases in proportion to the size of

the society, public good provision rises without bound in group size. This shows that

by-product firms can achieve a significant degree of success in providing a public good

in an environment where the voluntary contributions mechanism fails totally.

One category of by-product firms is industry associations which sell private goods

to members and engage in lobbying activity with the profits. This is discussed in Olson

(1965) as a mechanism by which an interest group can overcome the free-rider problem

inherent in lobbying.1The AARP is an example of such an organization. This group

sells memberships which provide a magazine and group discounts, while using profits

from these memberships to lobby the government on issues such as Medicare and Social

Security. Similarly, the National Rifle Association provides a variety of services to its

members, and uses the resulting profits to lobby the government on issues related to

firearms. A second category of by-product firms includes nonprofit organizations that

sell private goods and use the resulting profits to provide a public good. For example,

groups such as the World Wildlife Fund and the Audubon Society sell calendars and

other items and use the profits to help support their activities which provide environ-

mental amenities.2

∗I would like to thank Matt Van Essen and two anonymous referees for providinghelpful comments on the

paper.

1. Also see the discussion of this issue in Moore (1961). The lobbying activity will constitute a public good

to the members of the interest group, but will not necessarily be a public good to the society at large.

2. It is quite common for groups such as schools and the Girl Scouts to fund raise by selling private goods

(candy,cookies, etc.), even though very close substitutes for these private goods are offered by for-profit firms.

C2013 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume22, Number 4, Winter 2013, 875–893

876 Journal of Economics & Management Strategy

The by-product firms in my model turn over all their profits toward provision

of the public good, and in this sense are “nonprofit entities.” Thus, the model does

not cover related activities by for-profits firms. These firms sometimes link the sale of

private goods to the provision of public goods. For example, Targetgives 5% of its pretax

profits to charitable activities.3Although, the model does not encompass the activities of

for-profit firms, the framework it provides should provide an important basis for future

work addressing this issue.4

2. Background

2.1 Public Goods and Monopolistic Competition

Pecorino (2009) has previously analyzed the voluntary contributions mechanism in a

model in which private goods are produced in a monopolistically competitive market.

(This work does not analyze by-product firms.) In such an economy, the marginal utility

of income may increase with the size of the society.As the society gets larger, the number

of private goods available for consumption endogenously increases, and this is what

may lead to an increase in the marginal utility of income. When the marginal utility

of income increases, the opportunity cost of contributing to the public good increases

and the equilibrium level of contributions falls. Thus, in Pecorino (2009), public good

provision is monotonically decreasing in the size of the society and falls toward 0 in a

large group. In this paper, I consider a generalization of the preferences considered in

Pecorino (2009), but I find that the large group results continue to hold. For a sufficiently

large group, provision of the public good will decrease in the group size and will fall to

zero as group size grows without bound. This is true for all admissible parameter values

for the utility function used in this paper. Thus, the model provides a backdropin which

the voluntary contributions mechanism totally fails in a large group. By contrast, in this

same setting, by-product firms will succeed in providing public goods, even as group

size grows large.

2.2 By-Product Firms

As noted earlier, the concept of a by-product firm dates to Olson (1965). Posnett and

Sandler (1986) consider a by-product firm in a perfectly competitive market. In this

setting, the by-product firm can only replicate the level of contributions achieved un-

der the voluntary contributions mechanism.5When the market for the private good is

monopolistically competitive, Pecorino (2001,2010) has shown that the by-product firm

can provide a higher level of the public good than can be achieved by the voluntary

contributions mechanism. Pecorino (2001) analyzes a single by-product firm in partial

equilibrium. Pecorino (2010) analyzes by-product firms in general equilibrium, and al-

lows the number of these firms to grow in proportion to the size of the society. In that

paper, the public good is an intermediate input into production. When the public good

To the extent that these groups are able to sell these private goods at a premium, this is consistent with the

mechanism which drives the success of by-product firms in this paper.

3. See the corporate site at http://pressroom.target.com/pr/news/community-giving.aspx.

4. There are also organizational hybrids such as (RED), which is a nonprofit that partners with for-profit

firms. Some of the goods sold by these for-profit firms are specially labeled indicating that 50% of the profit

from the sale of the good will be donated to the Global Fund in order to fight AIDS.

5. A similar result is found in Besley and Ghatak (2007: 1650) where firms are Bertrand competitors and

output is homogenous.