Notes on income heterogeneity and number of contributors: Public goods model

• Published date: 01 December 2018
• Author: Tatsuyoshi Miyakoshi,Kenichi Suzuki
• DOI: http://doi.org/10.1111/1468-0106.12272
• Date: 01 December 2018

ORIGINAL MANUSCRIPT

Notes on income heterogeneity and number of

contributors: Public goods model

Tatsuyoshi Miyakoshi

1

| Kenichi Suzuki

2

1

Hosei University, Tokyo, Japan

2

Tohoku University, Sendai, Japan

Correspondence

Tatsuyoshi Miyakoshi, Faculty of Science and

Engineering, Hosei University 3-7-2, Kajino-cho,

Koganei, Tokyo 184-8584, Japan.

Email: miyakoshi@hosei.ac.jp

Funding information

The 2007 Japan Economic Research Foundation;

The 2007 Zengin Foundation; The Ministry of

Education, Culture, Sports, Science and

Technology of Japan, Grant/Award Number:

23530367

Abstract

This paper proves that a large degree of income heteroge-

neity increases the number of free riders under the nonco-

operative Nash equilibrium of voluntary contributions to

public goods with a Cobb–Douglas utility function. We

prove this by investigating an algorithm structure that

identifies free riders. We also support this proof by

showing the numerical simulation results based on this

algorithm.

1|INTRODUCTION

Bergstrom, Blume, and Varian (1986, 1992), who examine the noncooperative Nash equilibrium of

voluntary contributions to public goods, prove the existence and uniqueness of the equilibrium. To

date, the presumed presence of noncontributors (free riders) is stressed in Bergstrom et al. (1986) and

Cornes and Sandler (1996); however, only a few previous studies have analysed the contributions to

public goods, allowing for the existence of noncontributors. Cornes and Sandler (2000) show that

income transfers from noncontributors to contributors can lead to a new Nash equilibrium that

Pareto-dominates the equilibrium associated with the initial income distribution. As such, income

transfer neutrality by Warr (1983) where all individuals are contributors does not hold.

Under what conditions is free-riding behaviour likely? Andreoni (1988) proves that the propor-

tion of free riders increases as the number of players increases, and Buchholz, Cornes, and Peters

(2006a) explicitly provide an estimate for this proportion. In contrast, it has been predicted that free-

riding behaviour is more likely when incomes or preferences are heterogeneous (see Bergstrom et al.,

1986; Olson, 1965). However, this prediction is not proved yet, to our knowledge. It seems to be easy

to show how many contributors exist, by investigating an algorithm structure and identifying the con-

tributors. Andreoni and McGuire (1993) show a numerical algorithm. Cornes and Hartley (2007)

simplify the previous analysis of the free-rider problem in n-dimensional space based on a graphical

analysis, Nevertheless, to our knowledge, there are no studies that investigate the degree of heteroge-

neity of income: whether or not the large degree of heterogeneity increases the number of free riders.

Received: 18 April 2017 Revised: 20 February 2018 Accepted: 24 April 2018

DOI: 10.1111/1468-0106.12272

732 © 2018 John Wiley & Sons Australia, Ltd wileyonlinelibrary.com/journal/paer Pac Econ Rev. 2018;23:732–741.