Bergstrom, Blume, and Varian: Voluntary contributions and neutrality

• Date: 01 April 2020
• Author: Emma Moreno‐García,Gareth D. Myles,Marta Faias
• Published date: 01 April 2020
• DOI: http://doi.org/10.1111/jpet.12408

© 2019 The Authors. Journal of Public Economic Theory Published by Wiley Periodicals, Inc.

J Public Econ Theory. 2020;22:285–301. wileyonlinelibrary.com/journal/jpet

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285

Received: 20 October 2019

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Accepted: 22 October 2019

DOI: 10.1111/jpet.12408

ORIGINAL ARTICLE

Bergstrom, Blume, and Varian: Voluntary

contributions and neutrality

Marta Faias

1

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Emma Moreno‐García

2

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Gareth D. Myles

3,4

1

CMA and FCT, Universidade Nova

de Lisboa, Caparica, Portugal

2

Universidad de Salamanca, Salamanca,

Spain

3

School of Economics, University of

Adelaide, Adelaide, Australia

4

Institute for Fiscal Studies, London, UK

Correspondence

Gareth D. Myles, School of Economics,

University of Adelaide, Adelaide, 5005,

Australia.

Email: gareth.myles@adelaide.edu.au

Funding information

Ministerio de Economía y

Competitividad, Grant/Award Number:

ECON2016‐75712‐P; Consejería de

Educación, Junta de Castilla y León,

Grant/Award Number: SA049G19;

Centro de Matemática e Aplicações,

Grant/Award Number: UID/MAT/00297/

2019

Abstract

Bergstrom, Blume, and Varian provided a neutrality

result for the private provision of public goods that

has inspired a considerable literature. The result has

significant implications for income redistribution and

broader policy interventions. Thispaper reviews the basic

result and its applications, and discusses extensions to

general private provision economies.

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INTRODUCTION

A surprising result in the analysis of private contributions to a public good is that the total level

of provision is unaffected by any reallocation of income among consumers that leaves the set of

contributors (those giving some positive amount) unchanged. This neutrality result was first

established by Warr (1983) and extended by Bergstrom, Blume, and Varian (1986), henceforth

BBV. That a transfer of income between consumers induces those receiving income to raise

their contributions to the public good, and that this increase is offset by a reduction in

contributions of those losing income, is unremarkable. What is striking is that the exactly

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

offsetting nature of the change in contributions is not special to particular utility functions but

is a general consequence of the individual rationality conditions for the Nash equilibrium of the

contribution game. Since the publication of BBV, the analysis has been extended to models with

multiple private and public goods with the aim of identifying those redistributions of

endowment, within a variety of situations, that leave the private provision equilibrium

unchanged. Although the focus of this paper is upon the implications of the BBV neutrality

result and its extensions, we should note, before proceeding, that the publication of BBV

inspired a much broader literature on private provision. Some of the theoretical applications of

BBV are noted below, whereas Muñoz‐Herrera and Nikiforakis (2019) provide an extensive

review of experimental investigations.

When a model is constructed to analyze an economic issue, several factors are important: the

concept of equilibrium adopted, the existence and uniqueness of equilibrium, and the comparative

statics of policy interventions. The insightful approach of BBV fully explored all these aspects for the

scenario in which a private good can either be consumed or contributed to public good provision.

To be precise, in contrast to a personalized pricing scheme, BBV analyzed a game‐theoretic model

in which the strategy of each player was their voluntary contribution to the provision of a public

good. For this noncooperative model of public good provision, the proof of existence of a Nash

equilibrium was reinforced by the description of sufficient conditions to obtain uniqueness (see also

Bergstrom, Blume, & Varian, 1992; Fraser, 1992) confirming that there was no way to escape from

the neutrality through appeal to multiple equilibria. In addition, to analyze the extent to which

government provision of a public good impacts on private contributions, BBV also provided a

comprehensive characterization of the comparative statics of redistributive policy.

An earlier literature (Chamberlin, 1974, 1976; McGuire, 1974; Young, 1982) had demonstrated

the inefficiency of the private provision equilibrium and (inconclusively) discussed the consequence

of changing the number of potential contributors upon the degree of efficiency. The publication of

BBV sparked fresh research into private provision due to the generality of their neutrality result and

its obvious implications for redistributive policies. The work of BBV also motivated research into

what have since then become known as “aggregate games”because the neutrality result is a

consequence of the equilibrium level of public good provision being a function of aggregate income.

In fact, the neutrality result can be obtained as a special case of a more general theorem that

characterizes when Nash equilibria are independent of the distribution of agents’characteristics

(see Bergstrom & Varian, 1985). A detailed analysis of public good provision from the aggregate

game perspective is provided in Cornes and Hartley (2005). A more recent line of research,

exemplified by Allouch and King (2019), has extended the BBV model to public good provision

within networks that have local interaction between contributors.

The private provision model has found useful applications in a very wide range of contexts. As

examples, it has formed the basis for understanding noncooperative behavior in the household

(Lundberg & Pollak, 1994) and as the basis of the threat point in bargaining models of the household

(Lundberg & Pollak, 1996). It is also one of the limit points of the semi‐cooperative household model

of d’Aspremont and Dos Santos Ferreira (2019). The contributions of different nations to military

coalitions have been modeled as contributions to a public good (Sandler & Hartley, 2001). The model

has been applied in environmental economics to analyze green markets (Kotchen, 2006) and global

environmental problems (Buchholz & Konrad, 1994; Murdoch & Sandler, 1997). Johnson (2004) used

the model to study open source software and Lévy‐Garboua, Montmarquette, Vaksmann, and Villeval

(2017) to model contributions to a voluntary mutual insurance pool. This is only a small sample of the

very many applications.

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