Serving the many or serving the most needy

Authors: Christoph Starke

Publish Date: 2012/11/01

Volume: 13, Issue: 4, Pages: 365-386

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Abstract

Free subsidized or costcovering The decision on how much to charge for a good or service is fundamental in social business planning The higher the fee paid by the recipient the more people in need can be served by the additional revenues However charging a fee simultaneously excludes the very poor from consumption This paper argues that the entrepreneur’s tradeoff between both effects is governed by her level of poverty aversion ie her preference intensity for the service of needy people with different incomes Additionally we account for the possibility of excess demand for the provided good and assume that applicants are rationed by nonpriceallocation mechanisms We therefore contribute to the extensive literature on the pricing and rationing behavior of nonprofit firms Within our theoretical model we find ambiguous reactions of the entrepreneur to a cut in donations Given a sufficiently low level of statusquo donations entrepreneurs with relatively high poverty aversion tend to increase the project volume whereas those with relatively low poverty aversion do the oppositeThis paper benefited greatly from extensive discussions with Matthias G Raith and Steffen Burchhardt Comments by Anne Chwolka university colleagues and conference participants were also extremely helpful I would also like to thank coeditor Amihai Glazer and an anonymous referee for their valuable feedbackYet we assumed that alpha hatalpha and derived the requirement that alpha mathop alpha limits smile Consequently an increase in donations leads to a reduction in the optimal project volume if mathop alpha limits smile hatalpha and alpha in left mathop alpha limits smile hatalpha right However mathop alpha limits smile hatalpha requires a sufficiently low level of donations For Drightarrow barnleft 0 rightcdot c ln barnln underlinen which determines hatalpha and alpha prime is infinitely large such that hatalpha rightarrow 0 and alpha prime rightarrow 1 Since mathop alpha limits smile alpha prime it must hold that mathop alpha limits smile in left 01 right and consequently mathop alpha limits smile hatalpha In other words given that the amount of donations is relatively high all entrepreneurs react by enlarging their project volumes when they experience an increase in donations In contrast for Drightarrow 0 left left ln barnln underlinen right right F=0 rightarrow 0 and hence hatalpha rightarrow infty According to proposition 3 all entrepreneurs with alpha hatalpha choose F0 Consequently left left ln barnln underlinen right right F=F 0 and alpha prime in left 1infty right Since mathop alpha limits smile alpha prime it holds that mathop alpha limits smile hatalpha As a result there exists a specific level of donations Dprime such that mathop alpha limits smile =hatalpha if D=Dprime and mathop alpha limits smile hatalpha if Din left 0Dprime right Hence for all Din left 0Dprime right an increase in donations leads to a reduction in the optimal project volume F+D if alpha in left mathop alpha limits smile hatalpha right square

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