Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

• Author: ARTHUR J. CAPLAN
• Date: 01 December 2016
• Published date: 01 December 2016
• DOI: http://doi.org/10.1111/jpet.12214

UNCERTAINTY AND THE VOLUNTARY PROVISION OF A PURE

PUBLIC GOOD IN A TWO-MOMENT DECISION MODEL

ARTHUR J. CAPLAN

Utah State University

Abstract

In this paper, we explore the potential benefits of uncertainty that may

arise in a two-moment model of the voluntary provision of a pure pub-

lic good. We find that an increase in a given contributor i’s risk as -

sociated with the aggregate contribution level of the other contribu-

tors (i.e., an increase in social uncertainty) induces that contributor

to increase his own contribution level if and only if the uncertainty’s

incremental effect on the expected value of his net marginal utility is

negative. Contributor i’s welfare likewise increases when a closely re-

lated condition is met, namely that the uncertainty’s marginal effect

on his expected marginal utility value of the public good exceeds its

countervailing effect on the numeraire. Further, the corresponding ag-

gregate contribution to the public good increases in the presence of

free-riding if and only if the incremental effect of contributor i’s con-

tribution on the aggregate expected value of all other contributors’ net

marginal utilities is small-enough positive. We derive similar conditions

for the case of private uncertainty, where the increase in contributor i’s

risk is associated with his own marginal valuation of the public good. A

simple example illustrates these conceptual results. Numerical analysis

demonstrates that an increase in private uncertainty can have a non-

monotonic impact on contributor i’s welfare.

1. Introduction

In this paper, we investigate the potential benefits of uncertainty that may arise in the

context of the voluntary provision of a pure public good; a context that to date has

received little, albeit increasing attention. Early studies considered uncertainty associ-

ated with a discrete public good’s provision point for both contribution and subscrip-

tion games.1For example, McBride(2006) characterizes conditions for a contribution

1Contributions are not refunded in a contribution game if the project is ultimately not funded, while

in a subscription game they are.

Arthur J. Caplan, Department of Applied Economics, Utah State University, 4835 Old Main Hill, Logan,

UT 84322-4835 (arthur.caplan@usu.edu).

Funding for this study was provided by the Utah Agricultural Experiment Station (UAES), grant

number UTAO-1074.

Received May 2, 2016; Accepted June 15, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (6), 2016, pp. 910–922.

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