Lotteries and Lindahl prices in public good provision

• Author: Jörg Franke,Wolfgang Leininger
• DOI: http://doi.org/10.1111/jpet.12307
• Published date: 01 December 2018
• Date: 01 December 2018

Received: 25 August 2017 Accepted: 14 February2018

DOI: 10.1111/jpet.12307

ARTICLE

Lotteries and Lindahl prices in public good

provision

Jörg Franke1Wolfgang Leininger2

1Universityof Bath

2Universityof Dortmund

JörgFranke, Department of Economics, Uni-

versityof Bath, 3 East, Bath BA2 7AY,UK

(j.franke@bath.ac.uk).

WolfgangLeininger, Department of Eco-

nomics,University of Dortmund (TU),

Vogelpothsweg87, 44227 Dortmund, Germany

(wolfgang.leininger@udo.edu).

Lotteries are traditionalinstruments for fundraising in general. Mor-

gan has shown that they can also be very effective in the provision

of a public good. However, a fair lottery can only enhance provi-

sion but never result in the efficient amount. Franke and Leininger

show how—by borrowing from optimal contest theory—biased lot-

teries can provide the efficient amount of the public good. This paper

aligns this result with standard public good theory, in particular the

classic notion of Lindahl pricing. It shows that biased lotteries can—

implicitly—implement Lindahl pricing of the public good in noncoop-

erative Nash equilibrium.

1INTRODUCTION

There is a huge literature on the provision of public goods. Morgan (2000), however,was the first to link the old insti-

tution of lotteries directly to the theory of the provision of public goods. He views a lottery,part of whose proceeds go

to the provision of a public good, as a voluntary contribution scheme (and not merely a substitute for confiscatory tax

schemes by the state). And, indeed, many private charities or institutions that lack any taxing power use lotteries to

generate revenuesfor their respective aims.

Lotteries are a worldwide phenomenon (for an extensive study of U.S. state lotteries, see, e.g., Clotfelter & Cook,

1991) and the traditional view of them as inefficient and regressive instruments for raising surrogate tax money is

challenged by Morgan's question, by which they rather may constitute an effective contribution scheme toward the

supply of public goods.

Morgan (2000) showed that the provision of a public good can be enhanced by the use of lotteries or—in Morgan's

terms—fixed-prizeraffles. The reason for this interesting result is that the positive externality of a contribution on oth-

ers in the pure voluntary provision scheme is now counteracted to some extent bythe negative externality on others

of buying additional lottery tickets (which lowers their probability of winning the contest for the fixed prize R). As a

result, contributions toward financing the public good increase in comparison to voluntary contribution. However,any

prize sum of finite value is never sufficient to finance and providethe efficient amount of the public good. In this regard,

Morgan's model can be viewed as a fund-raising model; he is not primarilyinterested in efficient provision of the public

good.

Frankeand Leininger (2014) directly address efficiency within Morgan's model. By using insights from optimal con-

test theory (Franke, Kanzow, Leininger, & Schwartz, 2013), they show that an appropriately biased lottery together

with a finite prize sum can induce the efficient amount of public good provision, if consumers differ sufficiently in the

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840 © 2018 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/jpet Journal of Public Economic Theory. 2018;20:840–848.