The profit-maximizing non-profit

Abstract

This article explores behaviour that is the opposite of that usually considered in analyses of the private provision of a public good. The charity (or NGO), rather than aiming to maximize provision of the public good financed by contributions, maximizes profits. The model describes an equilibrium with many people contributing, and where the provision of the public good may be less than the amount donated by any one person, the other contributions being appropriated by the NGO. An NGO constrained to spend a fixed fraction of all contributions on the public good can have an incentive to produce inefficiently. Last, its behaviour will generate incomplete crowding out of governmental grants.

1. Introduction

Models of the private provision of a public good commonly assume that voluntary contributions sum to the aggregate amount of the public good provided. This model has interesting features: income redistribution amongst contributors affects neither consumption of the private good nor aggregate provision of the public good, and only the rich contribute. The standard model also implies that individuals can fully offset governmental contributions of the public good by contributing less ( Warr, 1982 , 1983 ; Bernheim, 1986 ; Bergstrom et al. , 1986 ). The result concerning perfect crowding out has strong policy implications regarding the desirability of government financing a non-profit that provides a public good.

The full crowding-out result, however, is not supported by empirical observations. A study of 300 British charities found little evidence that public donations crowd out private donations ( Posnett and Sandler, 1989 ); other studies in the USA find that crowding out is only partial ( Steinberg, 1989 ), with an additional governmental $1 spent on charity crowding out only 28 cents ( Abrams and Schmitz, 1978 ).

Such evidence suggests that donations may enter directly into a person’s utility function (see, e.g., Andreoni, 1989 ). Crowding out will also be reduced if provision of the public good involves discontinuities, and also if tax subsidies for contributions are discontinuous (see Glazer and Konrad, 1993 ).

Moreover, studies of private contributions usually assume that the recipient organization spends all the money on either fund-raising, fixed costs necessary to provide the public good, or the public good. Ignored is the possibility that the leader of the organization steals the money or uses it for purposes disliked by the contributors.

Consider examples of abuse. American University (a non-profit) dismissed its president, Ben Ladner, for his profligate spending. He had used university money on a French chef, weekend trips abroad, and extravagant parties for friends and family. The university spent $200,000 in renovations and improvements on the president’s home; landscape designers created a waterfall and pond behind the patio at a cost of about $30,000. On a two-day trip to London, Ladner and his wife billed the university $2,352 for hotel, and $2,513 for other expenses, including a car and driver. The university paid a personal chef $88,000 annually, on top of annual compensation of over $800,000. ¹ William Aramony, who was president of the United Way of America for 20 years, was jailed in 1995 for defrauding the organization of more than $1 million. Amongst other abuses, he had used United Way funds to pay for extramarital affairs and for gambling in Las Vegas. The United Way paid more than $90,000 for his limousine. ²

The head of the British Ethnic Minority Fund charity charged it £40,000 to pay for his personal chauffeur, had the charity spend almost £100,000 on rent for premises he owned, placed a relative and a long-term acquaintance on the charity payroll when they were private personal assistants working mainly for him, and charged the charity almost £25,000 for private medical insurance for three members of his family, on top of a generous salary. ³

Contributions are also misused when they are spent for purposes contributors did not intend. In 1961, Princeton University accepted a $35 million gift to benefit the university’s Woodrow Wilson School of Public and International Affairs, with the endowment eventually growing to over $900 million. Descendants of the contributor claimed that the money was to be used only to educate men and women for government careers in international affairs, that the school dishonored its vision, and that only 5% of the Wilson School’s alumni work for the federal government in international relations. ⁴ Following the September 11, 2001 terrorist attacks, the Red Cross raised more than $564 million for the Liberty Fund to aid victim’s families, but distributed only $154 million to that purpose. At a congressional hearing, New York Attorney General Eliot Spitzer testified, ‘I see the Red Cross, which has raised hundreds of millions of dollars that was intended by the donating public to be used for the victims of September 11—I see those funds being sequestered into long-term plans for an organization.’ ⁵

Evidence also shows that some non-profits (also called here non-governmental organizations, or NGOs) spend much on overhead or on fund-raising expenses, rather than providing public goods. Telemarketers registered in New York reported raising more than $249 million in contributions in 2012, but only 38% of donors’ contributions in response to solicitations actually went to charities. ⁶ A 2013 investigation by the Tampa Bay Times ranked nearly 6,000 US charities based on money paid to solicitors over a decade. The top 50 paid $970.6 million whilst allocating less than 4% of collected donations in direct cash aid to their intended causes. ⁷ Administrative expenses can also be high. For example, in 2007, West Virginia’s Charleston Area Medical Center Foundation raised $26 million, purportedly to support the local hospital, but spent 49% of that on administrative expenses. ⁸

Nor does revelation that a charity poorly spent its contributions necessarily reduce contributions. In December 2008 the charity Hadassah announced that it had invested some $90 million in a fraudulent pool run by Bernard Madoff. But contributions and grants increased from $20 million in 2008 to $26 million in 2009. Other charities have also survived scandals. An example is the Association for the Prevention of Addiction, which rebranded itself as Addaction shortly after the head of one of its teams was exposed as a drug dealer in 1997. More than a decade of expansion followed with Addaction managing more than 120 services in 80 locations in Britain, and an annual income of over £41 million. ⁹

Why then do people contribute, knowing that much of the money contributed will be wasted? The following analysis considers the behaviour of contributors and heads of organizations providing a public good financed by private contributions, when all realize that the head wants to maximize the equivalent of profits—the difference between aggregate contributions received and spending on the public good the contributors value.

2. Literature

The literature on the private provision of a public good is vast, with no need to review its essentials here. Of more interest are studies of the behaviour of a non-profit. The standard model assumes that the output of the public good equals the sum of contributions by individuals, not considering how the non-profit works. Andreoni (1998) models a charity with fixed costs, showing how a lead gift can co-ordinate a move away from a Nash equilibrium with no donations to an equilibrium with aggregate contributions sufficiently high to more than cover the fixed costs. Other works, such as Andreoni and Payne (2003) , model the fund-raising activity of charities, allowing the heads to view fund-raising as costly or unpleasant, but allowing the non-profit to use contributions only for fund-raising and provision of the public good.

Another form of fixed costs arises when the public good is discrete. An equilibrium with efficient provision of the good can then exist: the discreteness creates a threshold for contributions, below which the project is infeasible. This principle is established in theory ( Palfrey and Rosenthal, 1984 ; Bagnoli and Lipman, 1989 ) and confirmed in both laboratory and natural experiments ( Albert, 1972 ; Bagnoli and McKee, 1991 ). Each participant prefers the project to no project, even if each would also prefer a smaller project funded only by everyone else’s contribution. If the good is discrete, an equilibrium with full (efficient) funding exists where each beneficiary is decisive, so that free-riding results in no spending, rather than in smaller spending. This idea of making each contributor decisive is used by Tabarrok (1998) in discussing assurance contracts: a discrete public good will be provided if and only if each person contributes the amount the fund-raiser specifies. (Groupon and Kickstarter work on this principle.) Andreoni (1989) considers an organization that would provide a public good only if the capital campaign reaches some minimum threshold of contributions; his focus, however, is on seed grants rather than on profit-maximizing policies.

Consideration of a non-profit with preferences different from those of contributors (including budget maximization and quality maximization) is found in Hansmann (1981) . But he does not look at profit-maximizing behaviour of the NGO in attracting contributions. A related problem studied in the literature is the profit-maximizing provision of an excludable good by a monopolist (see Burns and Walsh, 1981 ; Brennan et al. , 1983 ). In contrast to the assumptions in these two papers that anyone refusing to pay the price charged can be refused access to consumption, I suppose that the only threat the provider can make concerns the level of the public good it will provide. Nevertheless, one insight of the model that follows is to show how the provider of a non-excludable public good can make the contribution of each person pivotal, and thus make the problem equivalent, in some ways, to that of a monopolist selling an excludable public good. ¹⁰ My analysis shows that the assumption of excludability is unnecessary, and so may also contribute to literature on the behaviour of a profit-maximizing firm. But the central point of my basic model is not to determine output or the equilibrium contribution. Rather, I describe a mechanism that allows a charity to exploit donors, when the charity produces a non-excludable public good.

People may contribute to a charity that provides little of a public good for reasons other than those discussed here. One is the ‘warm glow’ feeling arising from the (perhaps mistaken) belief of having done good. ¹¹ People may also contribute if they care not about the public good provided but about the high status they enjoy from the publicity of having made large contributions (see Glazer and Konrad, 1996 ; Harbaugh, 1998 ; Munoz-Garcia, 2011 ).

Much work examines how a profit-maximizing firm can extract consumer surplus, as by price discriminating or by using a two-part tariff. But surprisingly little work explores how an organization financed by voluntary contributions can maximize profits and extract consumer surplus. This article does.

3. Assumptions

3.1 Head of the NGO

The NGO has a monopoly on the provision of the public good under consideration. Its head, or leader, L, aims to maximize revenue minus spending on the public good, subject to the condition that individuals have an incentive to donate to the NGO. To use the term introduced by Hansmann (1981) , I consider donative non-profits.

The difference between contributions the NGO receives and its spending on the public good can be for L’s personal use. But the same analysis applies if L spends some of the contributions on a public good that contributors value little: contributors to a university may want to improve undergraduate education, whereas the university president wants to attract star researchers who teach little. The head of the NGO aims to maximize net revenue.

The NGO can commit to a schedule, specifying how much it will spend on the public good for any given set of contributions. It is convenient to think of the amount of the public good provided as equal to the amount spent on its provision, or that the marginal cost of producing the public good is 1. But the analysis that follows also applies to increasing marginal cost of production—any amount spent on the public good determines the amount of the public good produced, so a contributor can view spending on the public good as determining provision of the public good and his marginal valuation of spending on the public good.

The provider’s threat to provide the good only if everyone contributes can be interpreted in a more plausible way: it will provide some of the public good only after covering its fixed costs (which can be the CEO’s salary!).

3.2 Contributors

The number of potential contributors is N. All contributors have the same preferences. A person’s utility increases with the aggregate provision of the public good, and increases with his consumption of other, private goods. Given a fixed income, consumption of the private goods is larger the smaller the contribution to the NGO. For simplicity, let utility be separable between consumption of the public good and the other goods. The corresponding utility function is $v(G)+u(x)$ , where G is provision of the public good (with $v′>0$ and $v″<0$ ), and x is consumption of the private good (with $u′>0$ , and $u″<0$ ). The separability simplifies the exposition by allowing me to speak of an individual’s marginal benefit from the public good, MV ( G ) (which is a positive but declining function of total provision), and of the marginal cost of his contribution, MC ( d ) (which is a positive and increasing function of his contribution, d ).

3.3 Commitment

The NGO’s ability to attract contributions depends critically on its ability to commit. I assume unlimited commitment, subject to donations made voluntarily. The head of the NGO cannot, for example, commit to killing anyone who gives him less than $1 million. Contributors cannot commit and cannot co-ordinate amongst themselves; that is, the behaviour of contributors is described by a Nash equilibrium. A commitment to use only contributions exceeding some critical level for provision of the public good can be interpreted as the NGO having fixed costs of that amount, where the fixed costs may consist of mortgage payments for the CEO’s condo, salary commitments, rent for fancy offices, and so on.

The timeline is as follows

1. L commits to a schedule relating contributions to provision of the public good.

2. Contributors simultaneously make their contributions.

3. L implements his commitment to spending on the public good.

4. Payoffs are realized.

4. Exploiting contributors

Consider an exogenously fixed number, N , of identical contributors, and let L commit as follows. With N contributions each of d _M , L will provide the quantity G of the public good. Otherwise, he will provide nothing. If the contributions are made, then L’s profit is $NdM−G$ . The head of the NGO sets d _M so that the cost to the donor of his contribution equals his benefit from the public good, generating no consumer surplus.

Given this commitment by L, it is an equilibrium for each person to donate d _M . For suppose that each contributor believes that each other person will make such a contribution. Consider any one contributor, say, D. He knows that a contribution of d _M makes provision of the public good be G , but generating no consumer surplus. If D contributes less than d _M , then provision of the public good is 0, again generating no consumer surplus. Because D is indifferent between contributing d _M and contributing 0, and the same applies to each other contributor, then it is an equilibrium for each to contribute d _M . Of course, if L’s take-it-or-leave-it offer is for a bit below d _M , say $dM−ϵ$ , then a person would strictly prefer contributing that amount over contributing nothing, making the equilibrium discussed more plausible.

Formally, let each contributor have an endowment Y. The goal of L is to $Maximiz edM,GNdM−G$ subject to $v(G)+u(Y−dM)≥v(0)+u(Y)$ . The solution has the constraint binding, with the first-order condition $Nv′(G)=u′(Y−dM)$ . Further intuition into the result is given in Appendix 1.

The solution is depicted in Fig. 1 . Call MV the marginal valuation ( $v′$ ) to D of the public good, and call MC his marginal cost ( $u′$ ) of spending on the public good. The head of the NGO can make any commitment he wishes, saying that he will provide G if and only if each person contributes d _M . In Fig. 1 , if the NGO provides G₁ units of the public good, then a person’s benefit is the area under his marginal valuation curve ( MV ). The maximum L can extract from a donor is a level of d , d₁ , such that the donor’s cost equals his benefit, or the area under the marginal cost curve equals the area under the marginal valuation curve; in the figure that means that area $OG1CF$  = area $Od1BA$ .

Now consider an increase in G from G₁ to G₂ . Following the reasoning just given, the maximum any donor would be willing to give is d₂ , where the area under the marginal valuation curve from 0 to G₂ equals the area under the marginal cost curve from 0 to d₂ . The difference between these payments is L’s marginal revenue from each donor.

From the foregoing analysis, we can determine L’s marginal revenue as a function of G from all donors combined (that is, N times the marginal revenue from each donor). The marginal production cost of an additional unit of the public good is, by assumption, 1. So L will choose that level of G where its marginal revenue equals its marginal cost. ¹²

The outcome for the private provision of a public good differs from the standard efficiency solution in two ways. First, the marginal cost to a person of his contribution is evaluated at d _M , which exhausts his consumer surplus, rather than at G / N. That does not make for inefficiency, but reflects an income effect, with a contributor essentially poorer because of the money taken by L.

Second, total provision is not Nd _M but only G. Thus, less of the public good is provided than the amount consumers, acting jointly, would want. But the solution is Pareto-optimal, with L gaining at the expense of consumers, and with the marginal conditions for efficiency satisfied.

For an algebraic example of L’s policy, let a consumer’s marginal valuation be a – bG , and his marginal cost c. A consumer’s benefit from enjoying G units of the public good is $aG−bG2/2$ . The maximum amount, d _M , a donor would give to have G rather than none of the public good satisfies $aG−bG2/2=(c)(dM)$ , or $dM=G(2a−bG)/(2c)$ , yielding L a profit of $N(G(2a−bG)/(2c))−G$ . Solving the first-order condition yields $G=(aN−c)/(bN)$ , so that profits are $(aN−c)22bcN$ , and $dM=(aN+c)(aN−c)2bcN2$ .

The NGO may spend less on the public good than the amount any donor contributes. Continuing with the example in the previous paragraph, G will be less than d _M if $aN−cbN<(aN+c)(aN−c)2bcN2$ , which will be satisfied if $a>c(2N−1)/N$ . Or consider an extreme case. Let MV be very high for a quantity up to $q¯$ , and 0 after that. Then the NGO will provide $q¯$ , and get from each person a contribution greater than $q¯$ , extracting all consumer surplus.

I summarize with:  

The results appear because L’s strategy makes each contributor pivotal; that is, in equilibrium any one person’s contribution determines how much of the public good is provided. The head of the NGO does this by committing to providing G units of the public good if and only if each individual contributes d _M . If in equilibrium any one potential contributor believes that all others contribute d _M , then this potential contributor determines whether provision will be G instead of 0. Furthermore, in satisfying the incentive compatibility constraint of one donor, or making a given donor willing to contribute the amount d _M (which may require providing only little of the public good), the NGO also satisfies the incentive compatibility constraints of all other (identical) donors, each of whom sees himself as pivotal.

One might ask if it is credible that L will spend G on the public good, rather than stealing all the contributions. Such a commitment can be credible if potential donors hold a set of beliefs sustaining this equilibrium. Following the logic of the folk theorem, suppose donors believe that if in any period L provides less than G of the public good, then in all future periods he will steal all contributions, providing none of the public good. Suppose that donors believe that otherwise he will provide G in the next period. Then L will prefer to provide G of the public good in any current period if his discounted profits are greater than his discounted profits when providing none of the public good (which increases current profits by G , and reduces future profits to 0). Algebraically, this condition has $G<(NdM−dM)/r1+r$ , with r the inter-temporal discount rate. That is, given these beliefs by donors, and given that r is not excessively large, L will prefer to provide G of the public good over providing none of it.

5. Extensions

5.1 Random number of potential donors

So far I have considered a deterministic model. The model also applies if the number of potential donors is random, but L knows how many people will contribute—for each realization of the number of contributors, L would set a different threshold. Alternatively, even if L does not directly know the number of contributors, he does know aggregate contributions. Profit maximization could then be achieved by committing to a contingent schedule—for each level of aggregate contributions, L commits to how much he would spend on the public good.

Inability to commit to such a schedule reduces profits. Suppose that L must specify how much of the contributions he will steal before he knows the number of contributors. Suppose, however, that each contributor, at the time he makes a contribution, knows how many people are contributing, or equivalently, the level of aggregate contributions by others. Though I cannot provide an analytical solution, clearly L cannot extract all consumer surplus. For suppose that the number of potential donors is either N₁ or N₂ , with $N2>N1$ . Let L’s profit-maximizing policy when he knows that there are N _i donors have the NGO provide G _i of the public good if and only if total contributions are $Nidi$ . In the presence of uncertainty, L must set G and d independently of the realized number of donors. So if L sets G  =  G₁ and d  =  d₁ , but the number of donors is N₂ , then the NGO will earn revenue of only $N2d1$ instead of $N2d2$ under perfect information. If L sets G  =  G₂ and d  =  d₂ , then if N  =  N₁ , it will receive no contributions. Thus, when L is uncertain about the number of donors, it cannot earn as high profits as when he knows the number of donors.

More generally, let the threshold L sets be K , so that if each of N persons contributes d and $Nd≥K$ , then provision of the public good is Nd – K.¹³ Maximizing expected profits then involves a trade-off: if K is large but the number of potential donors is small, then in equilibrium none will contribute; but if K is small then L spends much of the money raised on the public good, and in the equilibrium for any given N each person contributes little.

For example, let the number of possible donors follow a Poisson distribution with mean 100; let $MV=10−G$ and MC  =  d , with d the amount a donor contributes. The head of the NGO maximizes profits at K  = 598, earning expected profits of 564. The expected profits are a bit below the threshold value, because with positive probability the number of potential donors is sufficiently small that no one donates. But notice that even if everyone contributed $d=52$ (the equilibrium contribution, if any, at the profit-maximizing level of K ), expected aggregate contributions would be only 707. That is, L takes as a profit 80% of total contributions if people always contributed.

5.2 Proportional theft

The analysis supposed that L can commit to provide none of the public good if aggregate contributions fall below a critical level. That commitment can make each contributor’s behaviour the same as when he is the only contributor, with L exploiting him alone. But such commitment may be difficult, and the existence of an equilibrium with no contributions may hurt L.

So L may be constrained to having his profit consist of a share, t , of total contributions. He may steal this fraction of contributions. Clearly, some value of t  > 0 maximizes L’s profits. Or L may be constrained, perhaps by governmental regulations, perhaps by the effectiveness of auditing by contributors, in the value of t he can impose. Consider then a fixed value of t. The smaller the provision of the public good, the greater the marginal benefit to a donor of an increase in provision of the public good. The NGO may therefore raise more contributions by producing inefficiently (thereby reducing provision of the public good).

Though, by assumption, t is fixed, L may control the production function, determining the amount of the public good provided for each level of spending. Denote the efficiency of production by α , which is positive but less than or equal to 1. A value of 1 denotes full efficiency. A value less than 1 means that spending of q results in only an additional αq of the public good. Note that this inefficient production differs from a tax—L does not get the difference between q and αq , and a smaller α reduces production of the public good for any amount of money spent on it. ¹⁴

For intuition, consider a single donor. As seen in Fig. 2 , if production is efficient, L would set the provision of the public good at G₀ , where the marginal valuation to the contributor equals his marginal cost (with both curves already reflecting the proportional theft made by L). Now let efficiency of production decline, say to $α=1/2$ . A contribution of G₀ provides $G0/2$ of the public good, and the contributor’s marginal valuation is MV _A . If the contributor gives an additional $1, the added output is half of what it would have been under efficient production, so the marginal benefit to the contributor is $MVA/2$ , which can exceed $MV(G0)$ . See Appendix 2 for algebraic analysis.

For a numerical example, let MC  = 1, t  = 1/2, and N  = 2. Let a contributor’s marginal valuation, as a function of output of the public good, G , be 6 for $G≤5$ , and 0 for G  > 5. Then in the equilibrium when α  = 1 each person contributes 10; provision of the public good is $10(1−t)=5$ , and L’s profits are 5. Now let L set α to 1/3. Then in equilibrium aggregate contributions are 30 (spending on the public good is $(30)(1/2)=15$ , and output is $(15)(1/3)=5$ ).

An individual contributes because the marginal benefit of a dollar spent on the public good for $d≤5$ is $(6)(1/3)=2$ , which equals the marginal cost to a contributor of $1/(1/2)=2$ . L’s profit is $(30)(1/2)=15$ , which exceeds the profits of 10 when production is efficient.

I summarize with:  

Furthermore, a governmental grant that increases spending on the public good increases L’s incentive to produce inefficiently. The increased spending on the public good increases its provision, thereby reducing the marginal benefit to the contributor of his contribution. Inefficient production reduces provision, and so increases private contributions.

5.3 Entry

Entry of a new NGO may be difficult because it requires co-ordination—given a fixed cost, no one contributor wants to move from one NGO to another. Furthermore, suppose that the existing NGO is constrained to a profit of a fraction of contributions, and that it does so by setting a fixed cost. Then no one contributor benefits from moving to a different NGO, because at the existing NGO none of a marginal contribution goes towards covering the fixed cost.

Anti-trust action may not suffice. Suppose that one of the two NGOs uses all the contributions it raises to provide the public good. The other spends only the contribution made by the marginal donor to provide the public good, using all the rest of the money raised for purposes donors do not like. Nevertheless, in equilibrium a donor could be indifferent between these two organizations—his marginal benefit from his contribution is the same—it is spent on the public good.

5.4 Governmental tax and grant

A common question in analyses of the private provision of a public good is the effect of a government grant. In the standard model, a governmental grant financed by a tax perfectly crowds out private contributions. That outcome differs with the profit-maximizing non-profit.

Suppose government taxes each person and uses the revenue to give a lump-sum grant to the NGO. That impoverishes each person, shifting his MC curve. In the new solution each contributor gives d _t . The head of the NGO keeps the government grant, and keeps $(N−1)dt$ . The result here differs from the standard story which has a government grant- cum -tax fully crowding out private donations. In the standard story, the government grant increases provision of the public good, reducing an individual’s benefit from his contribution. In contrast, the profit-maximizing NGO does not use the government grant to provide more of the public good. The only effect on contributions comes from the income effect.

Analytically, consider a government grant or tax, in the amount G₀ . Now let the marginal cost to a donor of his contribution be 2 d. Then the point where MV  =  MC satisfies $a−b(d+G0)=2(d+G0/N)$ , or $d=aN−G0(bN+2)N(b+2)$ . The derivative with respect to G₀ is $−(bN+2)/(N(b+2))$ , whose absolute value is less than 1. That is, crowding out is incomplete.

5.5 Contributions by different types of people

The standard model has only the rich contribute. A profit-maximizing NGO can further increase its profits by having both the poor and the rich contribute. Suppose contributors belong to one of two types—the rich and the poor, or older alumni and younger alumni, and suppose that the NGO can both identify the type of each person and make different offers to different types. Then on the rich, the procedure described above can be used with a threshold. But the NGO can add the condition that the public good is provided only if at least a specified sum is also raised from the poor. Then each rich person is pivotal, and each poor person is pivotal. In practice, this strategy has the spirit of a matching grant, given if only a specified minimum of alumni contribute.

6. Conclusion

This article explored behaviour that is the opposite of that usually considered in analyses of the private provision of a public good. Rather than aiming to maximize provision of the public good financed by contributions, the NGO maximizes profits. Unlike a standard firm, the NGO does not sell a product. Instead, it can commit to a schedule specifying how much of the public good it will provide for any given amount of contributions, so that the organization must consider a person’s incentives to contribute to it.

These strong results can mean that charitable organizations can indeed raise large contributions whilst providing little of the public good. A different interpretation is that the ability of charitable organizations to misuse the funds they raise calls for governmental intervention by policing organizations that misuse the funds.

The analysis showed that in equilibrium the NGO can make large profits from cash contributions, consisting of the aggregate contributions made by all but one of the contributors, and even some of his. Though such extreme behaviour is rare, non-profits often use contributions for purposes other than those contributors prefer, and the profits can then be interpreted as spending on purposes the non-profit prefers. Such behaviour can explain several phenomena that are not as easily explained by a standard model of private contributions to a public good.

• Government provision of a public good does not fully crowd out private contributions.

• For many charities, much of the money raised is not spent on providing the public good. This pattern is observed even after the low spending on the public good becomes known.

• The model suggests that contributions will be larger if the charity sets minimum levels of contributions it will accept. An approximation to that design has suggested contributions, membership categories, and incremental thank-you gifts; such schemes are indeed used by National Public Radio stations in their fund-raising activities (see Barbieri and Malueg, 2014 ). Relatedly, under a range of conditions, a threshold (with a money-back guarantee) significantly increases contributions in laboratory experiments ( Rondeau et al. , 2005 ). Furthermore, charities often use challenge grants, where donations will be matched only if they exceed a threshold amount. For example, the Georgia Center for Nonprofits writes, ‘A challenge grant—funding that’s contingent on meeting a particular goal—is simply one of the best ways to expand and grow your organization’s annual giving program.’ ¹⁵

• Further evidence that setting a threshold can increase contributions is found in the practice of many charitable organizations to publicly announce the fund-raising goal. A typical press release by De Pauw University says, ‘President Brian W. Casey announced tonight that DePauw University has launched a $300 million comprehensive fundraising campaign—The Campaign for DePauw—that will seek new funds to support the University’s academic programs, financial aid efforts, student preparation programs and an array of campus improvements.’ ¹⁶ Similarly, ‘[The] University of Delaware radio station WVUD has announced that its annual Radiothon fundraiser, which will open Friday, April 10, and continue through Sunday, April 19, has a goal of $40,000.’ ¹⁷ And ‘The University of Oregon announced late Friday that it plans to raise $2 billion, double the record for fundraising by an Oregon university. Interim University President Scott Coltrane made the announcement to hundreds of UO partisans gathered under a large tent at Hayward Field on the university’s campus.’ ¹⁸

• The mechanism described herein effectively means that any one donor can see fixed costs as funded by other donors. That is, suppose that 100 donors each contribute $1,000, that overhead costs are $90,000 (say, in salary to the CEO), and provision of the public good is $10,000. That means that on average 90% of each contribution covers overhead costs. The mechanism I describe instead has, in equilibrium, a donor see his contribution as paying little or nothing to the overhead cost. A field experiment (see Gneezy et al. , 2014 ) indeed finds that contributions are greater if a donor believes that overhead costs have been financed by other donors.

• An NGO’s ability to misuse cash contributions can lead contributors to prefer to donate their labour rather than their cash. As seen, an NGO may be able to extract all the consumer surplus from donors. If a donor instead spends his time working on providing the public good (say, by spending time teaching under-privileged children), the NGO cannot so misuse his time. Indeed, voluntary contributions of labour are large. Over one in four residents in the United States formally volunteered between 2001 and 2005. For the year beginning September 2001, 59 million people, or 27% of the US civilian, non-institutional population over 16 years of age, volunteered. Estimated values of volunteer labour in the USA range between 1.9% and 5% of GDP. ¹⁹ That range mostly exceeds the cash contributions, which are around 2% of GDP in the USA. ²⁰

Acknowledgements

I am grateful to seminar participants at KU Leuven, the hospitality of the Max Planck Institute for Tax Law and Public Finance, and particularly Kai Konrad, for stimulating conversations. The comments by the editor and the referees were exceptionally helpful.

References

Appendix 1: profit-maximizing strategy

Call MV the marginal valuation ( $v′$ ) to D of the public good, and call MC his marginal cost ( $u′$ ) of spending on the public good. An increase in G or in the quantity of the public good provided increases the benefit to D by MV ( G ). The value of d _M is determined by the condition that the marginal contributor enjoys zero consumer surplus, or $∫0GMV(x)dx=∫0dMMC(x)dx$ . For any G , this expression determines d _M , determining the function $dM(G)$ .

So an increase in G allows L to collect an additional $MV(G)/MC(dM(G))$ from each contributor, for a total increase of $(N)MV(G)/MC(dM(G))$ . Net revenue is maximized when G satisfies $(N)MV(G)=MC(dM(G))$ . ²¹

Appendix 2: inefficient production

For additional spending of G by the NGO, a contributor must contribute $G/(1−t)$ , leading to a marginal cost function to the contributor of $MCt(G)$ , where for any G , $MCt(G)=MC(G/(1−t))$ . The marginal benefit function to a contributor when spending is G and production is efficient is MV ( G ). The marginal valuation can depend on aggregate contributions by others and on his own contribution, q. But for simplicity here, consider a sole contributor.

Let total spending by the NGO on production of the public good yield output αq of the public good, with $α<1$ . For a given α , a contributor maximizes his utility with a contribution that makes his marginal valuation from provision of the public good equal the marginal cost of his contribution, or his contribution q satisfies $αMV(αq)=MCt(q)$ . In the following write the function $MV(αq)$ as $MVα(q)$ . Taking the total derivative yields the first-order condition for α : $qαMVα′+MVα=0$ . Note that $MVα′<0$ , so this expression can be satisfied. Why? L’s goal is to increase the marginal gain to an individual of increasing his contribution at any given q , which is $dαMVα′+MVα$ . This expression can be negative at α  = 1. That is, L can generate greater profits by producing the public good inefficiently.