سازمانهای غیرانتفاعی با اهداف توزیعی: تبعیض قیمت و راه حل های دقیق

We characterize the patterns of pricing and rationing when paternalistic nonprofit organizations (either private or governmental) care about the level and distribution of consumer surplus provided to their clients. Equilibrium depends upon marginal cost, the organization's distributional weights, exogenous income levels, and cream-skimming by competing for-profit firms. In equilibrium, some consumers pay their reservation price or a lower price above marginal cost, some pay less than marginal cost, some obtain the good for free, and some are not permitted to buy the good at any acceptable price. Comparative statics here differs from that for output or profit maximizers, with discontinuous price schedules shifting abruptly when exogenous income changes.

Hospitals provide charity care to a limited group of patients. Day care centers and YMCAs offer sliding-scale fees. Selective universities and colleges offer some students need-based financial aid while refusing to admit other students that would happily pay full tuition. Food stamps are given to some eligible recipients, whereas others pay a price that varies with recipient income. In each of these examples, the price charged to some customers is below the marginal cost of serving them, behavior that is hard to explain in a profit-maximizing context.1 In each, there are restrictions on who is eligible for a below-marginal-cost price, which leads to “rationing” in the sense that some who are willing to pay more than successful purchasers will not obtain the good in question. The issues we study apply to both public and private nonprofit agencies, as the food stamp and day care examples make clear. The issues we study apply to monopolies in either sector but also to organizations that face competition from other nonprofit (public and private) and for-profit firms, as in the day care, education, or hospital industries. In this paper, we take a positive approach to the study of pricing policy by governmental and private nonprofit agencies that provide their consumers with a merit good and have the power to set different prices for different consumers. These organizations care about the consumer surplus realized by their clientele, but may care more about some than others. Organizational welfare is maximized, subject to a budget constraint, by choosing a set of personalized prices. We pay careful attention to corner solutions involving rationing, where the equilibrium personalized price exceeds the reservation price for some consumers. As the exogenous parameters of the model change, organizations may choose to make the good available to different sets of consumers, to switch from giving it away to charging, or to make certain types of consumers ineligible for purchases. We also consider the impact of a single and cost-disadvantaged for-profit competitor on the prices and rationing behavior of public and nonprofit organizations concerned with distribution. We thus provide a framework for the empirical analysis of price discrimination by public and private nonprofit agencies with distributional objectives and develop testable hypotheses (although we do not test them here). Because for-profit firms are forced, by the market for control, to ignore distributional preferences except insofar as they coincide with profit goals, we look at nonprofit organizations—organizations, whether governmental or private, that cannot lawfully distribute their financial surplus to those in control of the organization. Because we wish to focus on the key relationships between generating revenue and serving clients in a “best case,” we make two assumptions. First, we assume that any net revenues obtained by the organization must be used to subsidize consumption by a target clientele (that is, to set prices below marginal cost), rather than to increase managerial perks, increase the organization's endowment, serve other aspects of the organization's mission, or covertly enrich owners. Second, we assume the organization has complete information about customer reservation prices and can price discriminate accordingly. Were we to make contrary assumptions, the tradeoff between serving additional consumers and meeting distributional objectives would become even more severe than detailed below. This power to price discriminate reduces the need to trade revenue-generation against serving favored customer classes—prices can be raised for those with high reservation prices, and the surplus generated from those transactions can be used to lower the price and induce increased consumption by other groups. However, two key tradeoffs remain, particularly for organizations that care the most about those who have the lowest reservation prices (say, because of lower income). First, the organization must decide whether to heavily subsidize a small group of customers or lightly subsidize a larger group of customers. Second, if some of the “needy” (those with reservation prices below marginal cost) will go unserved due to insufficient resources, the organization must decide whether to focus its attention on the low-cost cases (those needing small subsidies because their reservation prices are close to marginal cost) or the most important cases (in terms of the organization's distributional preference). This paper focuses on how to make these tradeoffs in a consistent fashion, and on how the resulting equilibrium will change when competition or non-sales revenue (from donations, capital gains, government grants or allocations to agencies, and the like) change exogenously. The results are, perhaps, surprising in that minor changes in non-sales revenue can cause jumps in prices for some customers and changes in rationing for others. There are distinct literatures on price discrimination by organizations in the for-profit, public, and nonprofit sectors. In the vast literature on price discrimination by profit-maximizing firms (summarized in, for example, Phlips, 1983), the key finding for our purposes is that absent strong complementarities or regulatory commands, for-profit firms would never offer a price below the marginal cost of serving that customer. Existing literature on optimal public prices (e.g., Bös, 1985) focuses on departures from marginal cost pricing to balance distributional goals against allocative efficiency and does not consider rationing. Le Grand's (1975) extension of the Diamond and Mirlees (1971) model comes the closest to the present formulation, but differs from us in three particulars. First, his specification, like most of the literature, does not restrict prices and quantities purchased to be non-negative, which explains why rationing does not emerge. Second, like much of this literature, his emphasis is normative, emphasizing how prices should be set for a prespecified group of consumers. Consumers with high distributional weights but low reservation prices (typically the poor) should, in his model, be offered the chance to purchase the good at low or even negative prices. There is no discussion of comparative statics—of how the pricing patterns, and group of consumers to be served, would change if demand, cost, or strategies taken by alternative providers were to change. Third, like much of the literature, he focuses on recommended behavior for a monopoly provider who can discriminate among consumers. This is ill-suited to an analysis of sliding-scale fees utilized by governmental or private nonprofit organizations that face competition from for-profit providers, such as in hospitals, nursing homes, and day care centers. It is also ill-suited to the analysis of financial aid provided by colleges that may lose students to competitive providers of higher learning (governmental, private nonprofit, or, increasingly, for-profit), or to price discrimination by local governments when citizens can migrate across jurisdictional lines. In contrast, the literature on price discrimination by private nonprofits is sparse (our 1998 paper summarizes this more extensively). Like us, Clotfelter's chapter (1992) and the papers included in his edited volume consider distributional effects, but these papers do not consider the determinants of nonprofit pricing. Several authors have studied aspects of nonprofit pricing (notably Dranove, 1988, Schiff and Weisbrod, 1991, Kingma, 1995, Oster, 1995, Hanchate, 1996, Siddarth et al., 1996 and Bilodeau, 2000), but we are unaware of any previous papers that examine price discrimination more generally, either theoretically or empirically. In the next sections, we detail our model and characterize equilibrium and the organization's response to changes in revenues, costs, and competition. Then we provide a simplified example to illustrate many of our main points. The final section concludes, followed by appendices that provide proofs and a graphical treatment of comparative statics.

In this paper, we provide a positive characterization of equilibrium by governmental and private nonprofit organizations with distributional objectives and detail the organizations' response to exogenous changes in income, cost, and competition. Whether we are talking about need-based financial aid or sliding-scale fees or income-based dues or selective charity care, price discrimination plays multiple roles. First, it determines how much revenue the organization obtains, i.e., it is a revenue generator. Second, it determines which individuals will consume its services. Third, it determines the distribution of consumer surpluses among those consumers. All these roles enter our model.13 In contrast to the traditional normative approach, our positive approach allows us to derive comparative static predictions about the response of such organizations to exogenous changes in revenue, cost, and competition. These predictions are testable, but the best tests will require panel data, using the price and rationing schedules of individual organizations to infer that organization's objective function parameters, then testing whether temporal variation in behavior is consistent with the model under that parameterization. When nonprofit organizations, both governmental and private, price discriminate, they sometimes provide services at prices below marginal cost, even zero. This means that other clients (who consume the same service or some other “unrelated” service) are charged prices that, although lower than those of a price-discriminating for-profit monopoly, still exceed marginal cost. Revenues from donations, taxes, and other revenue sources reduce the need to rely on high prices for those able to pay, but do not generally eliminate this need. Limited revenues from other sources also force the nonprofit to take a targeted approach whereby some potential clients are rationed–in that they are not subsidized enough, given their willingness-to-pay, to cause them to choose to purchase the service–in order to provide higher-priority clients with more heavily subsidized prices. Much more remains to be done to understand the complexities of nonprofit pricing with distributional objectives. Nonprofit organizations' rationing mechanisms are not limited to price; they use such instruments as waiting lists (Weisbrod, 1998a), inconvenient hours or location, and quality dilution (Kapur and Weisbrod, 2000) to affect the distribution of beneficiaries. Additional empirical evidence on the forms and consequences of price and non-price mechanisms for distributing nonprofit (and governmental) outputs is needed. In addition, the model will need to be elaborated before confronting it with data. Revenue from sales is partly determined by non-sales revenue, contrary to our assumption that we can take the latter as fully exogenous. For example, museums sometimes charge their dues-paying members a lower price for purchases from the museum store. Another example is provided when private foundations and government agencies attach strings to their grants that require the recipient to provide a specified share of services to the poor. Finally, we have omitted an additional dimension of tradeoffs—quality or ideology. When it is costly to produce multiple quality levels, the nonprofit might wish to compromise on the merit aspect of the good it provides in order to generate more revenues and hence serve more of its target audience. Thus, educational curricula or artistic programs may become more mainstream than the provider would like in order to retain more cash cows. The positive integration of efficiency and distributional goals presents a rich vein for scholarly “mining.”