Is Competition Among Charities Bad?

Transcription

1 Is Competition Among Chrities Bd? Inkyung Ch nd Willim Neilson Tes A&M University, College Sttion, TX 7783 December Abstrct This pper studies tht the eect o incresed competition mong chrities or dontions, nd shows tht it results in decresed provision o the public good. For chrities to receive dontions, they must py trvel cost nd premium tht rises rom the etr time, eort, or incentives chrity must provide to grner contribution rom donor who is solicited by other chrities. Incresed competition rises this premium, nd cuses ded weight loss, so tht the totl mount o chritble services provided lls ter new chrity enters into the mrket. JEL clssiiction: L3 Keywords: undrising, chrities, competition, crowding out Neilson wishes to thnk the Privte Enterprise Reserch Center nd the Progrm in the Economics o Public Policy or inncil support.

2 I. Introduction This pper nlyzes the eects o incresed competition mong chrities or dontions, nd the ded weight loss which results. As motivtion or our interest in this topic, consider the ollowing recent hedline. The AIDS Wlk In Wshington, D.C., usully ttrcts close to 5, people nd rises up to $ million or AIDS services in the city. This yer, just 5, people showed up or the wlk nd only rised bout $,. Ater the September ttcks, mny new chrities begn providing public services, nd this hs led them to compete with eisting chrities or dontions. The concern o this pper is on the eects this dditionl competition hs on undrising, nd wht will be the impct on the totl provision o public good. The pper closest to ours is Rose-Ackermn (98). In her model, chrities solicit dontions by sending brochure, which hs ied cost. Competition reduces the epected number nd size o the positive responses to the brochures, nd thereore on the mount o unds rised by given chrity. She shows tht competition or dontions cn cuse ecessive undrising in the sense tht, with unlimited entry, the cost o the mrginl dontion ectly equls the mount o tht dontion. Our pper tkes dierent pproch. Wheres in Rose-Ackermn s work the cost o soliciting dontion rom single individul is ied nd the yield is vrible, in our model the yield is ied but the cost o rising the unds is vrible. This pproch relects the ct tht when more chrities ttempt to rise unds rom the sme pool o donors, the chrities must work hrder to get given individul s dontion. We employ sptil model with ied pool o donors, ech o whom hs the sme indivisible mount to contribute. To grner contribution, the undriser must visit the potentil donor, resulting in trvel cost. I nother chrity is soliciting unds rom the sme donor, the undriser must py premium to the donor to grner the contribution. This premium could tke the orm o physicl good, like coee mug or T-shirt, but is best thought o s the undriser spending more time nd eort with the donor. The donor mkes the contribution to the chrity tht pys the higher Plzzolo, Rose, bcnews.com, October 9,, Feeling the Pinch-Nonproits Reeling Since Sept..

3 premium or the dontion. Both trvel costs nd the undrising premi pid to donors come out o the unds rised by the chrity. Competition in this setting hs two eects. First, it reduces trvel costs becuse ny entering chrity will be locted closer to some donors thn incumbent chrities were. Second, competition increses undrising costs by incresing the premium. Since unds rised lso py the trvel nd undrising costs, it is possible tht incresed competition results in reduced net mount o unds. Our results show tht the undrising costs rise by more thn the trvel costs ll, so tht incresed competition ctully reduces the net mount o unds vilble or chritble works. This result cn be thought o s crowding out eect. Severl uthors hve studied the crowding out eect on dontions ollowing government grnts. Wrr (98) presents model in which i the government gives grnt to individuls in n eort to redistribute income, it is neutrlized by chnge in contributions to chritble goods. Roberts (98) lso shows dollr-or-dollr crowding out eect in his model. Bergstrom, Blume, nd Vrin (98) show tht in Nsh equilibrium, smll redistribution o welth will not chnge the equilibrium lloction o chritble goods under certin conditions. All o these uthors present neutrlity theorems. Kingm (989) inds incomplete crowding out or contributions to public rdio sttions. Andreoni (998) shows tht when giving is bsed on impure ltruism, the crowding out eect is incomplete. Strub () provides lterntive estimtes o the crowding out eect or noncommericil rdio sttions nd his results show tht there is zero crowding out. In our model, we study dierent crowding out eect, tht is, with no chnge in government grnts, we nlyze the eect o n increse in the number o chrities on unds rised by eisting chrities. The theoreticl results show tht there eists supercrowding out eect. New chrities stel dontions rom eisting ones, so tht the totl mount o unds rised stys the sme. However, incresed competition pushes up the cost o rising unds, resulting in decrese in the totl mount o unds vilble or chritble services cross chrities. In Section II we describe the model. Section III shows the min result, nd section IV provides the conclusion. This pper is the irst to nlyze competition in the undrising mrket, so we recognize t the outset tht dditionl work is needed.

4 II. Model Firms re non-proit chrities tht rise unds in order to provide services. Funds rised re used or two purposes. I the irm rises n mount F i, it must epend n mount C i to do so. The remining unds, termed vilble unds nd denoted by φ i = F I - C i, cn be used to provide services. There is production unction, U(φ i ) which governs the trnsormtion o vilble unds into chritble services, nd is ssumed to be strictly incresing. The chrity s objective is to mimize services produced, which, since the production unction is strictly incresing, implies tht it mimizes vilble unds. Firms nd donors re locted on circle o unit circumerence. Donors re distributed continuously nd uniormly round the circle. Ech donor hs ied mount to donte to chrity. Donors will not give to chrity unless representtive o the chrity visits them to sk or the money, though, nd so the chrity must py trvel cost or the dontion. I donor is visited by only one chrity, he gives the entire mount to tht chrity. Suppose tht the chrity is locted t point nd tht the donor is locted t point. Then the chrity must py trvel cost o to solicit the dontion o. Obviously, the chrity will only solicit dontions rom people who re locted suiciently ner the chrity; tht is, chrity locted t point never solicits dontions rom n individul whose loction stisies >, becuse then the trvel cost is more thn the solicited dontion nd the net beneit to the chrity is negtive. Accordingly, chrity i locted t point i hs set o esible donors who re locted t points in the set D i = {: i }. Ech set o esible donors hs length. I two djcent irms re locted rther thn prt, they do not compete with ech other or donors becuse their esible donor sets do not intersect. I, however, the two sets do intersect, the chrities must compete or donors. Chrities cn epend eort in ddition to trvel costs in n ttempt to get dontions. I chrity i epends eort e i on donor, nd chrity j epends eort e j on the sme donor, the donor gives to chrity i i e i > e j, he gives to chrity j i e j > e i. I e i = e j the donor gives to the closer o the 3

5 neither. Now suppose tht donor locted t point is in the esible donor sets o two two chrities, nd i e i = e j nd the donor is equidistnt rom both i nd j, he gives to chrities, locted t nd, but tht chrity is closer thn chrity : <. As stted bove, the donor gives to chrity i e e, nd gives to chrity i e > e. In equilibrium, it must be the cse tht t the level o eort epended by the close irm, chrity, it is unproitble or chrity to secure the dontion. In other words, e = -, so tht i irm is the closest chrity to donor, it eerts n mount o eort equl to the dontion less the distnce o the donor rom the second-closest chrity. The net beneit to chrity rom the donor locted t, then, is - - ( - ) = -, which is the dierence between the distnces between the donor nd the two chrities. It is now possible to describe the equilibrium behvior o donors nd chrities. Suppose tht there re n chrities locted sequentilly t,..., n round the circle, with i between i nd i or i =,...,n, nd n between n nd. The esible donor sets re D,...,D n, respectively. Consider donor locted t point. Then there eists i {,...,n} such tht i i. Donor gives to irm i i i < i nd gives to irm i i i > i. Chrity i receives dontions rom donors in the intervl ( i min{, ( i i )/}, i min{, ( i i )/}),using the conventions tht n = nd - = n. III. Incresed competition Suppose tht n chrities re locted sequentilly round the circle, s bove. Let us restrict ttention to two chrities, nd, locted t <. Assume, or the purposes o this eercise, tht or ny donor in [, ], the two closest chrities re chrities nd ; tht is, or ny [, ], - < n nd < 3. This ssumption implies tht the competition or unds rom donor [, ] is between chrities nd, nd tht the premium is bsed on their reltive distnces. Further ssume tht <, so tht every donor in [, ] is subject to competition or unds. Other cses re possible, nd we sy more bout these lter. This lst ssumption hs no eect on our results, becuse we re interested in totl contributions, nd donors equidistnt rom two chrities represent set o mesure zero.

6 Now suppose tht new chrity enters t between nd. This new chrity competes or unds with its two closest competitors. Figure shows how the chrities llocte the donors in the new equilibrium. The segment in contention is [, ]. Chrity keeps donors in the intervl,, chrity keeps donors in,, nd chrity receives dontions rom donors in,. Since donors in this lst intervl re served by closer chrity thn beore, trvel costs or these dontions ll. However, since the second-closest chrity is closer or ll donors in the intervl [, ], undrising premi rise or ll donors. More detil on the chnge in undrising costs is provided by Figure. The top, solid curve represents the undrising premi ter the new chrity enters t. These costs pek t the midpoints between the chrities. The dshed curve tht is second rom the top represents the undrising premi beore the new chrity enters. Since there is less competition beore entry, the premi re lower. The re between these two lines is the dditionl undrising cost due to the incresing premi. The dshed curve t the bottom o the igure represents trvel costs beore entry. These costs re zero t the loctions o the eisting chrities nd pek t the point midwy between them. Finlly, the bottom, solid curve represents the trvel costs ter entry. The re between the two bottom curves represents the svings in trvel costs cused by entry. Note tht ll o the line segments in the igure hve slopes o mgnitude one, either positive or negtive. As is pprent rom Figure, in region d, between nd ( )/, entry leds to n increse in undrising costs. Donors in this region do not chnge who they donte to, so there is no chnge in trvel cost, but they require lrger premium to ttrct their dontions. In region d, between ( )/ nd, there is n increse in the required premium but decrese in trvel cost. However, the re A shown in the igure ectly osets the re A, nd so there is net increse in undrising costs in this region. In region d 3, between nd ( )/, there is gin n increse in premium costs but decrese in trvel costs. The region B is ectly oset by the region B, though, leving net reduction in costs or this region. In region d, between ( )/ nd ( )/, the increse in the premi (re C) nd the decrese in trvel costs (re C ), ectly oset ech other, nd entry hs no net eect on undrising 5

7 costs or this region. Finlly, in region d 5, between ( )/ nd, the donors do not chnge who they donte to, so the only chnge is n increse in the premi required to obtin these dontions. As the igure shows, entry leds to two (shded) regions where undrising costs increse nd one where the costs decrese. As our min result shows, the cost increses outweigh the cost reductions, so tht entry leds to net increse in undrising costs. Since every donor on the intervl [, ] ws lredy contributing beore entry, entry does not increse the totl mount contributed, but increses the mount spent on undrising, nd thereore the mount o unds vilble or chritble services decreses s result o entry. Figure 6

8 Figure Proposition Suppose tht i i < nd i i < min{ i i, i i- }. I new chrity enters t point ( i, i ), the net unds rised rom donors in [ i, i ] decreses. Proo. For nottionl ese, let i =, nd ssume without loss o generlity tht < ( )/. Divide [, ] into ive segments, s shown in Figure, with the segments denoted d,...,d 5. The corresponding totl costs re provided in Tble. 7

9 8 Tble Are Totl cost Beore entrnt enters into mrket Ater entrnt enters into mrket d [ ] d () [ ] d () d [ ] d () [ ] d () d 3 [ ] d (3) [ ] d (3) d [ ] d () [ ] d () d 5 [ ] d (5) [ ] d (5) Integrting nd cnceling yields = ) 3 )( ( ) (, where denotes the totl undrising cost ter entry minus the totl undrising cost beore entry. The irst term is obviously positive, nd the term is positive by the ssumption tht < ( )/. Finlly, note tht, )] ( ) [( ] 3 [ > = since < <. Consequently, >. There is no increse in the totl (gross) mount o unds rised, so net unds vilble rom donors in [, ] decreses by. Our result shows tht when there re lredy enough chrities so tht ll donors re lredy solicited by t lest two chrities (the mrket is sturted), the ddition o new chrities increses the costs o undrising or eisting chrities by more thn enough to oset the svings in trvel costs, nd thereore entry reduces the mount o unds vilble or chritble works. I the mrket is not yet sturted, so tht there re some donors who re not yet solicited or re only solicited by one chrity, this result my not hold. Still, though, i entry eventully leds to sturtion, urther entry leds to decrese in chritble services.

10 IV. Conclusion We hve demonstrted tht incresed competition mong nonproit irms cn led to less provision o the public good, resulting in socil ineiciency. Speciiclly, we deined n dditionl cost resulting rom competition between nonproit irms. This cost comes in the orm o git, such s T-shirt, book or mug, given to donors, or in the orm o incresed time nd eort spent by the undrising st. Using loction model, we clculted the totl cost (trvel cost nd the etr cost which comes rom competition) beore new irm enters into the mrket, nd ter it enters. Our min result shows tht when there re suiciently mny chrities lredy in the mrket, totl cost increses ter the entrnt enters into the mrket, so tht the provision o public goods decreses when there is ied mount o totl unds. Mny uthors hve studied the crowding out eect when government gives subsidy to chrities or t brek to donors. Little reserch hs studied the crowding out eect cused by competition between chrities. In prctice, nonproit irms epend lrge mounts o time nd eort rising unds, nd even epend lrge mounts o time nd eort on speciic individuls. I there were no competition, irms would not need to mke these ependitures, nd thereore these ependitures cn be considered ded weight loss. Also, becuse this cost depends on the loction o the second closest irm, it is independent o the irm s own loction. Economists re interested in the objective unction o nonproit irms, whether it is net revenue mimiztion or totl revenue mimiztion. A ew empiricl studies show tht some industries mimize net revenue; the other industries mimize totl revenue. Khnn, Posnett nd Sndler (995) nlyzed undrising eects on dontions. They ound tht the helth nd overses sectors mimize net revenue, nd the socil welre sector does not, using pnel dt or the U.K. Okten nd Weisbrod () demonstrted tht undrising hs both positive nd negtive eect on dontions. The positive eect is similr to n dvertising eect with or proit irms. The negtive eect on dontions emntes rom the incresed price o giving. 3 They ound tht chrities do not mimize net beneit rom undrising, using IRS dt, becuse they either under- 3 By Okten nd Weisbrod (), PRICE equls /(-F-A), F is the shre o undrising ependitures in dontions nd A is the shre o dministrtive ependitures in the dontion. By employing sme method, Steinberg (986) deined the price o giving s c t /-w t-, where c t is mrginl cost nd w t- is the undrising shre in the previous period. 9

11 or over- undrise. In our pper, competition mong chrities leds to ecessive undrising epenses.

12 Reerences Andreoni, Jmes, Towrd Theory o Chritble Fund-Rising, The Journl o Politicl Economy, Vol. 6 (998), Bergstrom, Theodore, Lwrence Blume nd Hl Vrin, On the Privte Provision o Public Goods, Journl o Public Economics, Vol. 9 (986), 5-9. Khnn Jyoti, Posnett, John nd Sndler, Todd, Chrity Dontions in the U.K: New Evidence Bsed on Pnel Dt, Journl o Public Economics, Vol. 56 (995), Kingm, Bruce Robert, An Accurte Mesurement o the Crowd-out Eect, Income Eect, nd Price Eect or Chritble Contributions, Journl o Politicl Economy, Vol. 97 (989), Oken, Cgl nd Weisbrod A. Burton, Determinnts O Dontions In Privte Nonproit Mrkets, Journl o Public Economics 75 (), Roberts, Russell D., A Positive Model o Privte Chrity nd Public Trnsers, Journl o Politicl Economy 9 (98), Rose-Ackermn, Susn, Chritble Giving nd Ecessive Fundrising, Qurterly Journl o Economics, Vol. 97 (98), 93-. Steinberg, Richrd, Should Donors Cre bout Fundrising? in Rose-Ackermn, Susn(Ed.), The Economics o Nonproit Institutions : Studies in Structure nd Policy, New York: Oord University Press.(986). Strub, John D. Fundrising nd Government Crowd-out o Privte Contributions to Public Rdio: An Empiricl Study, Working Pper, Univ. o Wisconsin (). Wrr, Peter G, Preto Optiml Redistribution nd privte Chrity, Journl o Public Economic, Vol. 9. (98),3-38.