NONPROFIT ORGANIZATIONS AS MULTISIDED PLATFORMS

非营利组织作为多角色平台

JENNIFER KUAN California State University Monterey Bay JENNIFER KUAN 加利福尼亚州立大学蒙特雷湾分校

JEREMY THORNTON Samford University 杰里米·桑顿 萨姆福德大学

Nonprofit organizations provide various important social goods and services. Consequently, management and strategy scholars are increasingly interested in the nonprofit sector. Existing theories of nonprofit organizations posit multiple profit-deviating objective functions to explain below-cost pricing but these theories raise problems for management and strategy. Importantly, the literature provides scant guidance on how nonprofit managers should select objectives. We propose that nonprofits can be modeled as profit-maximizers serving a two-sided market, also known as a multisided platform (MSP). We present a formal model to demonstrate how MSPs, so influential in the technology sector, can also explain nonprofit behavior. In our model of donative nonprofits, donors comprise one side of the market and recipients of services comprise the other side. This article addresses a long-standing theoretical question about what nonprofits optimize. Our approach also gives rivals the analytical tools to compete against nonprofits. The theory we propose can be used to explain nonprofit types and the differences between nonprofits and for-profits, addressing some of the important limitations of existing nonprofit theory. 非营利组织提供各种重要的社会公益和服务。因此，管理学和战略学学者对非营利部门的兴趣日益浓厚。现有的非营利组织理论提出了多种偏离利润的目标函数来解释低于成本定价的现象，但这些理论给管理和战略研究带来了问题。重要的是，现有文献对非营利组织管理者应如何选择目标提供的指导极少。我们提出，可以将非营利组织建模为服务于双边市场的利润最大化者，也就是所谓的多边平台（MSP）。我们构建了一个正式模型，以展示在科技行业极具影响力的多边平台（MSP）如何也能解释非营利组织的行为。在我们关于捐赠型非营利组织的模型中，捐赠者构成市场的一方，服务接收者构成另一方。本文探讨了一个长期存在的理论问题：非营利组织优化的目标是什么。我们的方法也为竞争对手提供了与非营利组织竞争的分析工具。我们提出的理论可用于解释非营利组织的类型以及非营利组织与营利组织之间的差异，解决了现有非营利组织理论的一些重要局限性。

Nonprofit organizations provide an array of social goods and services in the U.S. economy, including arts, human services, education, and healthcare. Consequently, the nonprofit sector is a growing area of interest for management and strategy scholars (Kaul & Luo, 2018; Lu0 & Kaul, 2019; Mahoney, McGahan, & Pitelis, 2009). As a category of firms, nonprofits comprise a complex mix of legal types, objectives, and strategies. Accordingly, formal theories of nonprofit organizations have proposed a heterogeneous set of firm objectives, such as net-revenue maximization (Lakdawalla & Philipson, 2006; Steinberg, 2003), output maximization (Malani, Philipson, & David, 2003; Steinberg, 1986), and budget maximization (Brooks, 2005; Brooks & Ondrich, 2007), each of which tries to explain pricing below cost, which commonly occurs among nonprofits. 非营利组织在美国经济中提供一系列社会商品和服务，包括艺术、人文服务、教育和医疗保健。因此，非营利部门是管理和战略学者日益关注的领域（Kaul & Luo, 2018; Lu0 & Kaul, 2019; Mahoney, McGahan, & Pitelis, 2009）。作为一类企业，非营利组织包含法律类型、目标和战略的复杂组合。因此，关于非营利组织的正式理论提出了一系列异质的企业目标，例如净收入最大化（Lakdawalla & Philipson, 2006; Steinberg, 2003）、产出最大化（Malani, Philipson, & David, 2003; Steinberg, 1986）和预算最大化（Brooks, 2005; Brooks & Ondrich, 2007），每一种目标都试图解释非营利组织中常见的低于成本定价现象。

Existing theories of nonprofit behavior treat the objective function as a choice variable, unlike with for-profits, where managers uniformly maximize profit.1 At least three problems arise from this approach. First, the literature has provided scant guidance on how these objective functions are chosen or endure. Oster (1995) maintained that anticipating the strategies of competitors in the nonprofit sector is important and requires an understanding of their objectives. Second, the existing menu of objective functions does not predict commonly observed nonprofit behaviors. Nonprofits may charge negative prices or run long-term deficits. Existing theories of nonprofit behavior do not predict negative prices and are largely silent on how nonprofits might finance deficits. Finally, theories of nonprofit behavior impose altruistic preferences to generate their outcomes. 现有的非营利组织行为理论将目标函数视为一个选择变量，这与营利组织不同，在营利组织中，管理者统一追求利润最大化。1 这种方法至少会引发三个问题。首先，现有文献很少指导如何选择或维持这些目标函数。Oster（1995）认为，预测非营利部门竞争对手的策略很重要，这需要了解它们的目标。其次，现有的目标函数“菜单”无法预测非营利组织常见的行为。非营利组织可能会收取负价格或长期出现赤字。现有的非营利组织行为理论无法预测负价格，并且对非营利组织如何为赤字融资几乎没有提及。最后，非营利组织行为理论通过强加利他偏好来产生其研究结论。

We propose that the theory of multisided platforms (MSPs), a more general term for two-sided markets, can explain nonprofit behavior in a more coherent, parsimonious, and complete way. The platform literature has historically focused on technology-related industries. However, in its most basic form, an MSP is simply a firm that serves two or more distinct sets of consumers, or “sides” of a market. Crucially, value on one side of the market is contingent upon the demand from another side. Newspapers are a canonical example, serving both subscribers and advertisers, with an advertisement becoming more valuable to advertisers as subscribers become more numerous. We demonstrate that a nonprofit, modeled as a profit-maximizing platform, can generate low, zero, or even negative prices without altruistic preferences by the nonprofit. 我们认为，多边平台（MSPs）理论——这是对双边市场的更通用表述——能够以更连贯、更简洁且更完整的方式解释非营利组织的行为。平台文献历史上主要聚焦于与技术相关的行业。然而，从最基本的形式来看，多边平台只是一种服务于两个或更多不同消费者群体（即市场的“方面”）的企业。关键在于，市场某一侧的价值取决于另一侧的需求。报纸是一个典型例子，它同时服务于订阅者和广告商，随着订阅者数量增加，广告对广告商的价值也会提升。我们证明，若将非营利组织建模为追求利润最大化的平台，即便该组织不存在利他偏好，也能制定低价格、零价格甚至负价格。

We begin by focusing on nonprofits that serve “clients” with goods or services while another set of customers (“donors”) finances client consumption. For example, a homeless shelter serves homeless clients by providing beds and meals, but shelters are typically funded by donors who do not consume shelter services and may never interact with shelter clients. The homeless shelter, termed donativeentrepreneurial by Hansmann (1980), thus serves two interrelated sets of customers, or two sides of a market. 我们首先关注那些向“客户”提供商品或服务的非营利组织，而另一类客户（“捐赠者”）为客户的消费提供资金支持。例如，一家流浪者收容所通过提供床位和食物来服务无家可归的客户，但收容所通常由不使用收容所服务、可能从未与收容所客户互动的捐赠者资助。汉斯曼（1980）将这种流浪者收容所称为“捐赠型创业”，因此它服务于两个相互关联的客户群，即市场的两个方面。

The nonprofit literature has historically examined these two sides of the market separately (List, 2011; Vesterlund, 2006). Literature on the client side has typically examined such outcomes as consumption, efficacy, legitimacy, and efficiency (Chang & Tuckman, 1996; Gayle, Harrison, & Thornton, 2017; Lakdawalla & Philipson, 1998; Tuckman, 1998). On the donor side, the literature has examined motivations for giving, such as experiencing a “warm glow” (Andreoni, 1990), boosting one’s reputation (Ye, Teng, Yu, & Wang, 2015), or assuaging guilt (Andreoni, Rao, & Trachtman, 2017). Nonprofit scholars have also studied the pricing decisions of nonprofits, which are often subsidized to increase client-side consumption, as well as competition from private donors (Karlan & List, 2007; Oster, Gray, & Weinberg, 2003; Thornton, 2006), government agencies (Ashley & Van Slyke, 2012), or private foundations (Faulk, McGinnis Johnson, & Lecy, 2017). 非营利组织相关文献历史上曾分别研究市场的这两个方面（List, 2011；Vesterlund, 2006）。关于客户方的文献通常研究消费、效力、合法性和效率等结果（Chang & Tuckman, 1996；Gayle, Harrison, & Thornton, 2017；Lakdawalla & Philipson, 1998；Tuckman, 1998）。在捐赠方，相关文献研究了捐赠动机，例如获得“温暖的感觉”（Andreoni, 1990）、提升个人声誉（Ye, Teng, Yu, & Wang, 2015）或减轻内疚感（Andreoni, Rao, & Trachtman, 2017）。非营利组织学者还研究了非营利组织的定价决策，这些决策往往会得到补贴以增加客户方的消费，以及来自私人捐赠者（Karlan & List, 2007；Oster, Gray, & Weinberg, 2003；Thornton, 2006）、政府机构（Ashley & Van Slyke, 2012）或私人基金会（Faulk, McGinnis Johnson, & Lecy, 2017）的竞争。

We treat client and donor markets jointly using a simple MSP model because treating clients and donors separately misses key interactions. We present a formal model of a stylized donative-entrepreneurial nonprofit in which the nonprofit maximizes profit while serving both clients and donors. Our model replicates an important pricing result common to other models of two-sided markets (i.e., one side of the platform will be priced lower than it would have been priced by a single-sided firm). The nonprofit model thus harmonizes nonprofit pricing behavior, especially below-cost prices, with traditional models of profit-maximizing firms.2 我们采用简单的MSP模型联合处理客户和捐赠者市场，因为单独处理客户和捐赠者会忽略关键互动。我们提出了一个程式化的捐赠-创业型非营利组织的正式模型，其中该非营利组织在服务客户和捐赠者的同时实现利润最大化。我们的模型复制了双边市场其他模型中常见的一个重要定价结果（即平台的一侧定价会低于单边企业的定价）。因此，该非营利组织模型将非营利组织的定价行为（尤其是低于成本的定价）与利润最大化企业的传统模型相协调。

The MSP model of nonprofits has implications for both theory and practice. First, by demonstrating the applicability of MSP theory to the nonprofit sector, we open an extensive MSP toolkit to nonprofit managers. MSP theory can facilitate nonprofit management decisions related to pricing, number of sides to serve, types of services to offer, or governance practices (Hagiu, 2014). Second, while this article focuses on donative-entrepreneurial nonprofits, future work can extend to other types of nonprofits and explain them as the outcomes of strategic decisions. Finally, our model contributes to existing MSP models (Belleflamme & Peitz, 2010; Rochet & Tirole, 2003) by expanding the settings to which these models can be applied to include nonprofits. 非营利组织的MSP模型对理论和实践都有影响。首先，通过展示MSP理论在非营利部门的适用性，我们为非营利组织管理者打开了一个广泛的MSP工具包。MSP理论可以促进与定价、服务对象数量、服务类型或治理实践相关的非营利管理决策（Hagiu，2014）。其次，虽然本文侧重于捐赠型创业非营利组织，但未来的研究可以扩展到其他类型的非营利组织，并将它们解释为战略决策的结果。最后，我们的模型通过将这些模型的应用场景扩展到包括非营利组织，为现有的MSP模型（Belleflamme & Peitz，2010；Rochet & Tirole，2003）做出了贡献。

LITERATURE ON NONPROFIT OBJECTIVES

非营利组织目标相关文献

Economic theories of firm behavior predict strategies that are profit-maximizing. A body of nonprofit literature has arisen to explain nonprofits as deviating from profit-maximizing output and pricing, which are commonly below their long-run cost of production. However, the nonprofit literature has not coalesced around a common objective of the nonprofit firm, instead proposing a variety of objectives. We summarize this literature and identify gaps that a model of nonprofit MSP can address. To establish a context for our model, we first discuss a taxonomy of nonprofit organizations based on Hansmann’s (1980) classification. 企业行为的经济理论预测了追求利润最大化的策略。非营利组织领域的文献应运而生，用以解释非营利组织偏离利润最大化的产出和定价行为，这类组织的产出和定价通常低于其长期生产成本。然而，非营利组织文献并未围绕非营利企业的共同目标形成共识，而是提出了多种目标。我们将总结这一文献，并指出非营利性医疗服务提供者（MSP）模型能够填补的研究空白。为了为我们的模型建立背景，我们首先基于汉思曼（Hansmann, 1980）的分类法讨论非营利组织的分类。

Nonprofit Taxonomy: A Focus on Donative-Entrepreneurial Nonprofits

非营利组织分类：关注捐赠型创业非营利组织

Hansmann (1980) used variation in revenue and governance to create a widely used two-by-two taxonomy of nonprofits.³ Nonprofit revenues may originate from donations, which are characteristic for human service organizations and disaster relief. Alternatively, revenues may be generated from fees for goods and services, which is common among healthcare organizations, universities, and clubs. While nonprofits may have both donations and commercial revenues, Hansmann (1980) described donative nonprofits as organizations that receive revenues primarily from charitable donors. Hansmann（1980）利用收入和治理的差异创建了一个广泛使用的非营利组织两维分类法³。非营利组织的收入可能来自捐赠，这是人类服务组织和救灾组织的典型特征。或者，收入也可能来自商品和服务的费用，这在医疗机构、大学和俱乐部中较为常见。虽然非营利组织可能同时拥有捐赠收入和商业收入，但Hansmann（1980）将捐赠型非营利组织描述为主要从慈善捐赠者那里获得收入的组织。

Nonprofits also vary by governance. Some nonprofits are controlled by their members while others operate under professional managers and hierarchical control. Hansmann (1980) developed a taxonomy in which “mutuals” describes clubs, civic organizations, and cooperatives that operate by mutual control. Alternatively, many human service organizations are governed by a board of directors that are distinct (though sometimes drawn from) the organization’s members. Hansmann (1980) labeled these “entrepreneurial” nonprofits (and they would be referred to as “managerial” by Jensen & Meckling [1976]). The boundary between mutual and entrepreneurial organizations can be blurry. For example, churches may be governed as large member organizations, or may have professional managers and governing boards. Table 1 reproduces the taxonomy, with exemplars listed for each category. 非营利组织的治理结构也各不相同。有些非营利组织由其成员控制，而另一些则由专业管理人员和层级控制体系运营。汉森（Hansmann）于1980年提出了一种分类法，其中“互助型组织（mutuals）”指的是通过相互控制运作的俱乐部、公民组织和合作社。另外，许多服务类组织的治理由理事会负责，这些理事会成员与组织成员虽有区别（尽管有时这些成员也来自组织内部）。汉森（1980）将这类组织称为“创业型”非营利组织（而简森和梅克林（Jensen & Meckling）[1976]则将其称为“管理型”）。互助型组织与创业型组织之间的界限可能较为模糊。例如，教堂可能作为大型成员组织进行治理，也可能设有专业管理人员和管理理事会。表1重现了这一分类法，并列出了每个类别的示例。

This article focuses on donative-entrepreneurial nonprofits. It is these organizations that are commonly considered “charities” and are subject to inquiry about their objectives (McKeever, 2018). However, we also expand our analysis in the discussion section to demonstrate how MSP theory can extend to other cells of the taxonomy and may help explain how nonprofits differ across quadrants. 本文聚焦于捐赠型创业非营利组织。这类组织通常被视为“慈善机构”，其目标会受到质疑（McKeever，2018）。然而，我们在讨论部分也会拓展分析，以展示MSP理论如何延伸至分类法的其他单元格，并可能有助于解释不同象限中的非营利组织存在何种差异。

Extensive Margin: Should Nonprofits Charge a Positive Price?

广泛的边际：非营利组织是否应该收取正价格？

A trait commonly associated with the nonprofit sector is a zero price for charitable output (e.g., public concerts, food pantries, health clinics, or crisis centers). This tradition has stimulated a body of academic literature examining whether nonprofits should ever charge positive prices for their services (Oster, 1995). One scholarly tradition views commercial activity, or charging prices, as conflicting with charitable objectives, i.e. an “ugly necessity” (Oster, Gray, & Weinberg, 2003: 30). In many situations, such as after a natural disaster, it might seem inappropriate or illegitimate to charge a positive price for goods and services. That is, market allocation is viewed as inferior or unethical relative to alternative political processes for allocation (Eikenberry, 2009; Eikenberry & Kluver, 2004). A variation of this critique argues that commercial orientation reduces services to lowincome constituencies and leads to mission drift away from an organization’s charitable purpose (Chetkovich & Frumkin, 2003; Moeller & Valentinov, 2012). In the arts, for example, commercial interests might come to dominate the creative direction set by artists (Castaner, 2013). 非营利部门常被关联的一个特征是慈善产出（例如，公共音乐会、食品储藏室、健康诊所或危机中心）的零价格。这一传统催生了大量学术文献，探讨非营利组织是否应该对其服务收取正价格（Oster, 1995）。有一种学术传统认为，商业活动或定价与慈善目标相冲突，即所谓的“丑陋的必要之举”（Oster, Gray, & Weinberg, 2003: 30）。在许多情况下，例如自然灾害后，对商品和服务收取正价格似乎不合时宜或不合情理。也就是说，市场分配相对于替代的政治分配过程被视为劣质或不道德（Eikenberry, 2009; Eikenberry & Kluver, 2004）。这一批评的一种变体认为，商业导向会减少对低收入群体的服务，并导致使命偏离组织的慈善宗旨（Chetkovich & Frumkin, 2003; Moeller & Valentinov, 2012）。例如，在艺术领域，商业利益可能会主导艺术家设定的创作方向（Castaner, 2013）。

TABLE 1 Hansmann’s (1980) Taxonomy of Nonprofit Organizations
表1 汉思曼（1980）非营利组织分类法

A competing stream of literature advocates for positive prices in the nonprofit sector. Brown and Slivinski (2006) and Jean, Robinson, and Foreman (2011) maintain that prices may ration goods and services by helping them identify constituents who value them most. This type of rationing has been documented in blood banks (Jacobs & Wilder, 1984) and homeless shelters (Associated Press, 2003). Prices can also mitigate congestion and smooth demand intertemporally by shifting consumption away from times of peak demand to times of lower demand, thus improving the client experience. Arts organizations employ this tactic by discounting underattended shows and increasing prices for shows that will sell out. Museums may offer discounted admission on weekdays or other low-utilization times. Ostensibly counterintuitive, positive prices may increase total consumption if the nonprofit can charge some people more to cross-subsidize targeted clients (James, 1983). Finally, positive prices may increase the perceived value of the service to the client by signaling its relative scarcity and value (Gorn, Tse, & Weinberg, 1991; Yoken & Berman, 1984). Arguments for or against prices can be cast in normative terms, ascribing particular virtue to nonmarket allocation mechanisms (Yu & Chen, 2018). However, nonprofit managers are faced with strategic choices that require positive theories of nonprofit behavior to make decisions. 另一股文学研究流派主张非营利部门应采用正价格策略。Brown和Slivinski（2006）以及Jean、Robinson和Foreman（2011）认为，价格可以通过帮助识别最珍视商品和服务的群体来实现资源配给。这种配给机制已在血库（Jacobs & Wilder, 1984）和流浪者收容所（Associated Press, 2003）中得到证实。价格还能缓解高峰期的拥挤问题，并通过将消费从需求高峰时期转移到低峰时期来平滑跨期需求，从而提升客户体验。艺术组织采用这种策略，例如对上座率低的演出打折，对即将售罄的演出提高票价。博物馆可能在工作日或其他低利用率时段推出折扣门票。乍一看似乎有悖直觉，但如果非营利组织能通过向部分人群收取更高费用来交叉补贴目标客户，正价格反而可能增加总消费量（James, 1983）。最后，正价格通过传递商品或服务的相对稀缺性和价值信号，可能提高客户对服务的感知价值（Gorn, Tse, & Weinberg, 1991；Yoken & Berman, 1984）。支持或反对价格的论点可从规范角度阐述，即赋予非市场分配机制特定的优势（Yu & Chen, 2018）。然而，非营利组织管理者面临战略决策，需要基于非营利行为的积极理论来制定决策。

Intensive Margin: How Much Should Nonprofits Charge? A Menu of Objective Functions

密集边际：非营利组织应收取多少费用？目标函数菜单

A problem for nonprofit managers (and researchers) is that classic profit-maximization models of firm behavior do not predict pricing outcomes commonly observed in the nonprofit sector. To accommodate this, the nonprofit literature has proposed a menu of objective functions to explain below-cost or zero pricing (Young, Jung, & Aranson, 2010). Unlike in the literature on for-profit firms, the nonprofit literature has not coalesced around a single objective function (Pauly, 1987). Instead, a set of objectives has been explored that typically assumes a preference for output (altruism) by the nonprofit manager. While varied, nonprofit theories are some variant of: (a) net-revenue maximization (analogous to profit maximization), (b) budget maximization, or (c) output maximization. Importantly, the literature has treated the objective function as a choice variable by the firm. Museums will set prices and output differently than hospitals, while orchestras differ from universities, because of their chosen objective. Steinberg and Weisbrod (2005) summarize the variation in objectives along a continuum, with pure netrevenue maximization at one extreme and altruistic output-maximization at the other. We summarize the intuition of these objectives below. For each case, formal derivations and numerical examples are available in Appendix A. 非营利组织管理者（及研究人员）面临的一个问题是，经典的企业行为利润最大化模型无法预测非营利部门中常见的定价结果。为解决这一问题，非营利组织文献提出了一系列目标函数来解释低于成本或零定价现象（Young, Jung, & Aranson, 2010）。与营利性企业文献不同，非营利组织文献尚未围绕单一目标函数达成共识（Pauly, 1987）。相反，已有研究探索了一系列目标，这些目标通常假设非营利管理者对产出存在偏好（利他主义）。尽管各不相同，非营利理论大致可分为三类：（a）净收入最大化（类似于利润最大化）、（b）预算最大化，或（c）产出最大化。重要的是，文献将目标函数视为企业的选择变量。博物馆和医院的定价与产出策略不同，交响乐团与大学也存在差异，这源于它们各自选择的目标。Steinberg和Weisbrod（2005）将目标差异总结为一个连续体，一端是纯粹的净收入最大化，另一端是利他主义的产出最大化。我们在下文总结这些目标的核心逻辑。每种情况下的正式推导和数值示例见附录A。

Net-revenue maximization. At one extreme, nonprofits maximize net revenue and are “for-profits in disguise” (Weisbrod, 1988). This is possible because the nondistribution constraint imposed by most nonprofits’ charters do not prohibit profits, but rather the distribution of profits to residual claimants (Hopkins, 2011). Profits may be reinvested toward the organization’s charitable purpose or potentially distributed as perquisites (Castaneda, Garen, & Thornton, 2008). A body of empirical evidence from several nonprofit sectors has suggested that education and arts organizations may act as netrevenue maximizers (Lakdawalla & Philipson, 2006; 净收入最大化。在一个极端情况下，非营利组织会最大化净收入，并且是“伪装的营利性组织”（Weisbrod，1988）。这是可能的，因为大多数非营利组织章程中规定的非分配约束并不禁止利润，而是禁止将利润分配给剩余索取者（Hopkins，2011）。利润可以再投资以实现组织的慈善目标，或者可能作为额外福利分配（Castaneda，Garen，& Thornton，2008）。来自多个非营利部门的大量实证证据表明，教育和艺术组织可能会充当净收入最大化者（Lakdawalla & Philipson，2006；

Steinberg, 2003). Net-revenue-maximizers charge the highest prices to their clients, relative to nonprofits with other objective functions (Vitaliano, 2003), and only enter markets when profitable opportunities arise (Glaeser & Shleifer, 2001). Steinberg, 2003）。以净收入最大化为目标的企业会向客户收取最高价格，这与具有其他目标函数的非营利组织形成对比（Vitaliano, 2003），并且只有在出现有利可图的机会时才会进入市场（Glaeser & Shleifer, 2001）。

Output maximization. At the opposite extreme, some nonprofits set prices as low as possible to maximize consumption by clients. Steinberg (1986) maintains that nonprofits deviate from profit maximization, and the magnitude of this deviation depends on the degree of altruism (or preference for output) embedded in the firm’s objective function. Examples may include advocacy or human-service nonprofits, which commonly charge nothing in order to maximize consumption of their charitable output.4 Universities often also offer zero, or negative, prices to candidates with high academic achievement or from preferred demographic groups (Steinberg & Weisbrod, 2005). This approach is somewhat ad hoc, with discounting dependent upon both the intensity of the organization’s preferences and the ability of the nonprofit to finance the subsidy.5 Output maximization. At the opposite extreme, some nonprofits set prices as low as possible to maximize consumption by clients. Steinberg (1986) maintains that nonprofits deviate from profit maximization, and the magnitude of this deviation depends on the degree of altruism (or preference for output) embedded in the firm’s objective function. Examples may include advocacy or human-service nonprofits, which commonly charge nothing in order to maximize consumption of their charitable output.4 Universities often also offer zero, or negative, prices to candidates with high academic achievement or from preferred demographic groups (Steinberg & Weisbrod, 2005). This approach is somewhat ad hoc, with discounting dependent upon both the intensity of the organization’s preferences and the ability of the nonprofit to finance the subsidy.5

One common method to address an open-ended commitment to output maximization is to impose a break-even or zero-profit constraint (Lakdawalla & Philipson, 1998; Malani et al., 2003; Steinberg, 1986). In this circumstance, the firm will set prices to maximize the consumption of its charitable output but must be able to fully finance production (or break even) over some relevant time horizon. Young, Jung, 解决对输出最大化的开放式承诺的一种常见方法是施加收支平衡或零利润约束（Lakdawalla & Philipson，1998；Malani等人，2003；Steinberg，1986）。在这种情况下，企业会设定价格以最大化其慈善性产出的消费量，但必须能够在某个相关的时间范围内完全为生产提供资金（或实现收支平衡）。Young、Jung，

5 It is interesting to note that while zero prices are common in the nonprofit sector, negative (nominal) prices are relatively rare. There is nothing in the theoretical models that makes zero pricing special, or limits negative prices, so this outcome is curious. We suspect that there are specific (and nonlinear) transaction costs that emerge once prices drop below zero. While it may be relatively costless to charge a client nothing, paying them to consume could require a much more complex transaction. We offer further analysis and extensions on this topic in the discussion section. 5 值得注意的是，虽然零价格在非营利部门很常见，但负（名义）价格相对罕见。理论模型中并没有什么内容使零定价具有特殊性，也没有限制负价格，因此这种结果令人好奇。我们推测，一旦价格降至零以下，就会出现特定的（且非线性的）交易成本。虽然向客户收取零费用可能相对无成本，但支付费用让他们消费可能需要更复杂的交易。我们在讨论部分提供了关于这一主题的进一步分析和扩展。

and Aranson (2010) cited assisted-living facilities and childcare programs as operating under this type of zero-profit model. Some nonprofits may be able to cross-subsidize output from other sources. Museums or hospitals are further examples where the main charitable output (exhibits or indigent care) can be subsidized by gift shops or elective procedures (Frey & Meier, 2006; Hirth, 1999). Put another way, an output maximizer provides as much output as it can until it exhausts its resources to finance the deficits. And Aranson (2010) cited assisted-living facilities and childcare programs as operating under this type of zero-profit model. Some nonprofits may be able to cross-subsidize output from other sources. Museums or hospitals are further examples where the main charitable output (exhibits or indigent care) can be subsidized by gift shops or elective procedures (Frey & Meier, 2006; Hirth, 1999). Put another way, an output maximizer provides as much output as it can until it exhausts its resources to finance the deficits.

Budget or revenue maximization. A middle ground between profit-maximizing and output-maximizing firms is revenue-maximizing (or budget-maximizing) firms. Increased budgets can increase organizational influence or consumption of perquisites such as better facilities, staff, or technology (Brooks, 2005; Brooks & Ondrich, 2007; Hansmann, 1981). To do this, budget-maximizing firms lower their prices to where the incremental (marginal) revenue of selling one more unit of output equals zero. Thus, the firm maximizes total revenues by lowering the price below what a profit-maximizing firm would set (to increase sales) but not as much as an outputmaximizing firm. Budget maximizers are most likely when managerial authority for production is separated from those overseeing costs. Examples include academic departments and government agencies. Steinberg (1986) maintained that healthcare nonprofits appear to behave like budget maximizers. 预算或收入最大化。在追求利润最大化和产量最大化的企业之间存在一种折中情况，即收入最大化（或预算最大化）的企业。增加的预算可以增强组织影响力，或增加对额外福利（如更好的设施、员工或技术）的消耗（Brooks, 2005；Brooks & Ondrich, 2007；Hansmann, 1981）。为实现这一点，预算最大化的企业会将价格降低到销售一单位额外产品的边际收入等于零的水平。因此，该企业通过将价格设定在低于利润最大化企业的价格（以增加销量）但又不像产量最大化企业那样低，来实现总收入的最大化。当生产的管理权限与成本监督权限分离时，最有可能出现预算最大化的情况。例如学术部门和政府机构。Steinberg（1986）认为，医疗非营利组织似乎表现得像预算最大化者。

Figure 1 offers an illustrative example of the relative differences in price, output, and profit across the three models discussed. Analytic and numerical examples for each of these outcomes are provided in Appendix A. 图1提供了一个说明性示例，展示了三种讨论的模型在价格、产出和利润方面的相对差异。每个结果的分析和数值示例见附录A。

The nonprofit literature has left several gaps in both theory and practice. For scholars, the existing menu of objective functions is inferred from empirical observation (Steinberg, 1986). There is little theoretical guidance regarding how managers choose an objective function, whether the objective function may change over time, or how to anticipate the actions of rival organizations. How might a nonprofit budget 非营利组织的文献在理论和实践中都留下了几个空白。对于学者而言，现有的目标函数“菜单”是从经验观察中推断出来的（Steinberg，1986）。关于管理者如何选择目标函数、目标函数是否会随时间变化，以及如何预测竞争对手组织的行动，几乎没有理论指导。非营利组织的预算可能会如何

FIGURE 1 Demand and Objective Function: Output and Pricing for Nonprofit Objective Functions 图1 需求与目标函数：非营利组织目标函数的产出与定价

Note: This illustration uses a simple linear demand function, $D ( p _ { x } ) = A - p _ { x }$ and unit cost, $c _ { x } = 1$ , to illustrate how optimal pricing and out put depends upon the maximand. 注：此图使用简单的线性需求函数 \( D(p_x) = A - p_x \) 和单位成本 \( c_x = 1 \)，以说明最优定价和产出如何取决于目标函数。

maximizer compete with an output maximizer? How will an output maximizer respond to significant shifts in demand? These questions raise issues for both nonprofit managers and for-profit managers that operate in mixed (for-profit and nonprofit) industries, such as healthcare and education. 最大化者会与输出最大化者竞争吗？输出最大化者将如何应对需求的重大变化？这些问题给在混合（营利和非营利）行业（如医疗保健和教育）运营的非营利组织管理者和营利组织管理者都带来了挑战。

An additional gap in the nonprofit literature pertains to the inability to fully explain a range of observed prices and output. Donative-entrepreneurial nonprofits often price their services below both average and marginal cost, which generates long-run operating losses. For example, many universities experience operational losses year after year, with a plan for losses to be offset by donations. To explain this, the literature has often added an exogenous parameter to balance the profit function (Steinberg & Weisbrod, 2005) or force the nonprofit firm to break even (Schiff & Weisbrod, 1991). However, these models are often silent on the source of these funds or how they are influenced by the decisions of the recipient nonprofit. 非营利组织文献中还有一个额外的空白点，即无法充分解释一系列观察到的价格和产出。捐赠型创业非营利组织常常将其服务价格定在平均成本和边际成本之下，这会产生长期运营亏损。例如，许多大学年复一年地出现运营亏损，计划通过捐赠来抵消这些亏损。为了解释这一现象，文献中常常添加一个外生参数来平衡利润函数（Steinberg & Weisbrod，2005），或者迫使非营利组织实现收支平衡（Schiff & Weisbrod，1991）。然而，这些模型往往没有说明这些资金的来源，也没有说明这些资金如何受到接受捐赠的非营利组织决策的影响。

We submit that platform theory offers a comprehensive method to address these gaps. Platform firms deviate from classic single-sided firms by having consumption by one group of clients funded by a separate, distinct group of customers. Our proposed model of nonprofit platforms offers a parsimonious and integrated model that generates the full range of pricing behaviors. Crucially, our model does not treat the organization’s objective function as a choice variable. Instead, the optimal pricing behavior emerges endogenously from client and donor demand. Second, by incorporating two markets, the model has a built-in mechanism for financing losses on one side of the market. Finally, the interaction between the consumption of charitable good by clients and the magnitude of donations provided by funders is explicitly modeled. 我们认为平台理论为解决这些缺口提供了一种全面的方法。平台型企业与经典的单边企业不同，其特点是一组客户的消费由另一组独立且不同的客户群体提供资金支持。我们提出的非营利平台模型是一个简约且整合的模型，能够产生全系列的定价行为。关键在于，我们的模型不将组织的目标函数视为一个选择变量。相反，最优定价行为是从客户和捐赠者的需求中内生形成的。其次，通过纳入两个市场，该模型内置了一个机制来为市场一侧的损失提供资金支持。最后，客户对慈善产品的消费与资助者提供的捐赠金额之间的相互作用被明确地建模。

OVERVIEW OF MSP THEORY AND APPLICATION TO NONPROFITS

非营利组织的MSP理论概述与应用

In this section we discuss existing models of MSPs and present our own simple model that includes features particular to donative nonprofits. These models demonstrate that a platform may deliberately “underprice” or “subsidize” one side of a market to maximize profit. In the context of nonprofits, pricing (below cost, zero, or negative) can arise from simple profit maximization and does not require altruistic preferences in the nonprofit objective function. 在本节中，我们将讨论现有微公益平台（MSPs）的模型，并提出我们自己的简单模型，该模型包含捐赠型非营利组织特有的特征。这些模型表明，一个平台可能会故意“低价”或“补贴”市场的一方以实现利润最大化。在非营利组织的背景下，定价（低于成本、零或负价格）可能源于简单的利润最大化，而不需要非营利组织目标函数中包含利他偏好。

Originally, MSP theory was motivated by a puzzle. Microsoft’s persistent monopoly in personal computers (PCs) demonstrated that PC customers needed to be able to easily share documents and work with other PC users. Just as a phone or fax machine is only useful if other people have a phone or fax machine, network effects mean that a good or service becomes increasingly valuable as more consumers use it (Farrell & Saloner, 1986; Katz & Shapiro, 1985; Shapiro, & Varian, 1998). There may also be network effects for donors, who gain from their interactions with other donors. These network effects can be considered a consumption externality, where one consumer benefits from consumption by others. A PC user not only gains utility personally from using a PC, but their consumption of the PC also creates value for other consumers. 最初，MSP理论是由一个难题推动的。微软在个人电脑（PC）领域持续的垄断地位表明，PC用户需要能够轻松地共享文档并与其他PC用户协作。就像电话或传真机只有在其他人也拥有电话或传真机时才有用一样，网络效应意味着一种商品或服务随着更多消费者的使用而变得越来越有价值（Farrell & Saloner，1986；Katz & Shapiro，1985；Shapiro & Varian，1998）。捐赠者也可能存在网络效应，他们从与其他捐赠者的互动中获益。这些网络效应可以被视为一种消费外部性，即一个消费者从其他人的消费中获益。PC用户不仅能从个人使用PC中获得效用，他们对PC的消费还会为其他消费者创造价值。

In their models of two-sided markets, Parker and Van Alstyne (2005) and Rochet and Tirole (2003) explicitly combined consumption externalities with the concept of multiproduct firms, where firms produce and sell multiple products to distinct sets of consumers (Rohlfs, 1974). In the PC setting, researchers realized that as more users adopted PCs, more third-party software developers wanted to produce software for those users (Boudreau & Jeppesen, 2015). These software “complements,” in turn, further increased users’ consumption value of the PC. Early models of two-sided markets described PC users and software developers as the relevant sides of the PC market, but it soon became clear that there could be more than two sides (Hagiu, 2014). Hence, a more general term, “multisided platform,” or platform, emerged. In sum, the platform model combines the concepts of consumption externalities with multiproduct firms to create a general set of characteristics that define a multisided market (Evans & Schmalensee, 2005). That is, a platform (a) has two or more distinct sets of customers (or “sides”), (b) provides a distinct good or service to each side, and (c) has at least one side that creates a consumption externality for another side, or a “cross-platform effect.” 在其双边市场模型中，Parker 和 Van Alstyne（2005）以及 Rochet 和 Tirole（2003）明确将消费外部性与多产品企业的概念结合起来，其中企业向不同的消费者群体生产和销售多种产品（Rohlfs，1974）。在个人电脑（PC）环境中，研究人员意识到，随着更多用户采用个人电脑，更多第三方软件开发商希望为这些用户开发软件（Boudreau & Jeppesen，2015）。这些软件“互补品”反过来进一步提高了用户对个人电脑的消费价值。早期的双边市场模型将个人电脑用户和软件开发商描述为个人电脑市场的相关“边”，但很快就发现可能存在超过两个“边”（Hagiu，2014）。因此，一个更通用的术语“多边平台”（或简称“平台”）应运而生。总之，平台模型将消费外部性与多产品企业的概念相结合，形成了一组定义多边市场的通用特征（Evans & Schmalensee，2005）。也就是说，一个平台（a）拥有两个或更多不同的客户群体（或“边”），（b）为每个“边”提供独特的商品或服务，并且（c）至少有一个“边”会对另一个“边”产生消费外部性，即“跨平台效应”。

Models of Transaction Fees and Access Fees in the Literature

文献中的交易费与准入费模型

Formal models of two-sided markets incorporate these essential features. Credit cards are a quintessential platform, serving merchants on one side and merchants’ customers on the other side. Models analyze two revenue models, or ways to charge for the service. First, transaction fees are charged each time the customer uses the credit card. Typically, the credit card platform charges the merchant for every customer transaction. Second, access fees are charged for the right to use the credit card. Credit card platforms have been known to charge such membership fees to both merchants and customers, but typically only charge the merchant. 双边市场的正式模型包含了这些基本特征。信用卡是典型的平台，一方面服务于商家，另一方面服务于商家的客户。模型分析了两种收入模式，即服务收费的方式。首先，每次客户使用信用卡时会收取交易费用。通常，信用卡平台会向商家收取每笔客户交易的费用。其次，为使用信用卡的权利收取接入费。众所周知，信用卡平台会向商家和客户收取此类会员费，但通常只向商家收取。

Rochet and Tirole (2003) constructed a model of a two-product firm in which the demand curves are multiplied by one another. This model deviates from the simple two-product profit function in which total profit, $\pi$ ,is the sum of profits from the production and sale of two distinct and unrelated goods: 罗歇和梯若尔（2003）构建了一个两产品企业的模型，其中需求曲线相互相乘。该模型偏离了简单的两产品利润函数，在简单的两产品利润函数中，总利润$\pi$是生产和销售两种不同且不相关商品的利润之和：

\pi = ( p _ { x } - c _ { x } ) D _ { x } - ( p _ { y } - c _ { y } ) D _ { y } π = (pₓ - cₓ)Dₓ - (pᵧ - cᵧ)Dᵧ

where $p _ { x }$ and $p _ { y }$ are the prices of goods $X$ and $y , c _ { x }$ and $c _ { y }$ are the constant marginal costs of goods $X$ and $\begin{array} { r } { { \cal Y } _ { : } } \end{array}$ ,and $D _ { x }$ and $D _ { y }$ are the demand functions for goods $X$ and y—that is, $D _ { x } ( p _ { x } )$ and $D _ { y } ( p _ { y } )$ . 其中 \( p_x \) 和 \( p_y \) 分别是商品 \( X \) 和 \( Y \) 的价格，\( c_x \) 和 \( c_y \) 分别是商品 \( X \) 和 \( Y \) 的固定边际成本，\( D_x \) 和 \( D_y \) 是商品 \( X \) 和 \( Y \) 的需求函数，即 \( D_x(p_x) \) 和 \( D_y(p_y) \)。

Instead, Rochet and Tirole (2003) constructed demand as follows: 相反，罗歇和梯若尔（2003）构建的需求如下：

\pi = ( p _ { x } + p _ { y } - c _ { x y } ) D _ { x } D _ { y } π = ( pₓ + pᵧ - cₓᵧ ) Dₓ Dᵧ

where $c _ { x y }$ is the cost of providing a platform (which is assumed to be a single cost incurred per transaction). The credit card company earns revenues when a match is made between the merchant and the merchant’s customer (i.e., when a customer charges a purchase to their credit card). In this model, $p _ { x }$ is the transaction fee paid by the consumer, $p _ { y }$ is the transaction fee paid by the merchant, and $D _ { x } ( p _ { x } )$ and $D _ { y } ( p _ { y } )$ are the demand curves for the consumer and the merchant, which are assumed to be independent. The cross-platform effect is derived from the fact that the two demand curves are multiplied. The consumer and merchant only gain when a match is made. With this minimal alteration of a two-product firm, the model generates the basic pricing result of platforms. That one side will be priced lower than by a one-sided, nonplatform firm. where $c_{xy}$ is the cost of providing a platform (which is assumed to be a single cost incurred per transaction). The credit card company earns revenues when a match is made between the merchant and the merchant’s customer (i.e., when a customer charges a purchase to their credit card). In this model, $p_x$ is the transaction fee paid by the consumer, $p_y$ is the transaction fee paid by the merchant, and $D_x(p_x)$ and $D_y(p_y)$ are the demand curves for the consumer and the merchant, which are assumed to be independent. The cross-platform effect is derived from the fact that the two demand curves are multiplied. The consumer and merchant only gain when a match is made. With this minimal alteration of a two-product firm, the model generates the basic pricing result of platforms. That one side will be priced lower than by a one-sided, nonplatform firm.

The first-order conditions generate the following result: 一阶条件产生以下结果：

D _ { x } ^ { ’ } D _ { x } = D _ { y } ^ { ’ } D _ { y } D_{x}’^{D_{x}} = D_{y}’^{D_{y}}

When written in terms of price elasticities, $\eta$ , the model generates: 当用价格弹性 $\eta$ 表示时，该模型会生成：

\eta _ { x } = - { \frac { p _ { x } D _ { x } ^ { ’ } } { D _ { x } } } a n d \eta _ { y } = - { \frac { p _ { y } D _ { y } ^ { ’ } } { D _ { y } } } \eta_{x} = - \frac{p_{x} D_{x}’}{D_{x}} \text{ and } \eta_{y} = - \frac{p_{y} D_{y}’}{D_{y}}

The price structure can be written as the ratio of elasticities. This relationship implies that, for a given demand, the relatively elastic side should be charged a lower price than a single-product firm would charge. 价格结构可以表示为弹性之比。这种关系意味着，对于给定的需求，相对有弹性的一方应该被收取比单一产品企业更低的价格。

{ \frac { p _ { x } } { \eta _ { x } } } = { \frac { p _ { y } } { \eta _ { y } } } $\frac{p_{x}}{\eta_{x}} = \frac{p_{y}}{\eta_{y}}$

Rochet and Tirole (2003) modeled transaction fees when a match is made and both consumers gain utility. For a model of access fees, Belleflamme and Peitz (2010) designed a credit card market that charges a one-time membership fee to merchants. The merchant’s surplus is given by: Rochet和Tirole（2003）在双方消费者均获得效用时对交易费用进行了建模。对于接入费模型，Belleflamme和Peitz（2010）设计了一个对商家收取一次性会员费的信用卡市场。商家的剩余由下式给出：

v _ { x } = n _ { y } \pi - M _ { x } v_{x} = n_{y}π - M_{x}

where $n _ { y }$ is the number of consumers, $\pi$ is the profit per consumer, and $M _ { x }$ is the membership fee charged to merchants. Thus, the number of consumers directly affects the utility of the merchant. Similarly, the consumer’s surplus is given by: 其中\( n_y \)是消费者数量，\(\pi\)是每个消费者的利润，\( M_x \)是向商家收取的会员费。因此，消费者数量直接影响商家的效用。同样，消费者剩余由下式给出：

v _ { y } = n _ { x } u - M _ { y } v_{y} = n_{x}u - M_{y}

where $u$ is the utility of the consumer from the number of merchants, $n _ { x }$ ,and $M _ { y }$ is the membership fee for consumers. The platform’s profit is thus: 其中\( u \)是消费者从商户数量\( n_x \)中获得的效用，\( M_y \)是消费者的会员费。因此，平台的利润为：

\pi = n _ { x } ( M _ { x } - c _ { x } ) + n _ { y } ( M _ { y } - c _ { y } ) π = nₓ(Mₓ - cₓ) + nᵧ(Mᵧ - cᵧ)

where different sides of the market involve separate costs, $c _ { x }$ and $c _ { y }$ . The profit-maximizing membership fee can be written as: where different sides of the market involve separate costs, \( c_{x} \) and \( c_{y} \). The profit-maximizing membership fee can be written as:

M _ { x } = N _ { y } ( { \boldsymbol { V _ { y } } } ) { \boldsymbol { \pi } } - { \boldsymbol { V _ { x } } } M_{x} = N_{y} \left( \boldsymbol{V_{y}} \right) \boldsymbol{\pi} - \boldsymbol{V_{x}}

where the number of consumers, $n _ { y }$ is a function of the consumers’ surplus—that is, $\dot { N _ { y } } ( v _ { y } ) = n _ { y }$ Thus, the membership fee for merchants increases with demand from consumers. Because both sides are modeled symmetrically, the consumer’s membership fee increases as the number of merchants increases. 其中消费者数量 \( n_y \) 是消费者剩余的函数，即 \( \dot{N_y}(v_y) = n_y \)。因此，商家的会员费随消费者需求增加而增加。由于双方的模型是对称的，随着商家数量的增加，消费者的会员费也会增加。

Credit card markets are an example of a setting in which two sides gain from a match. The platform generates profits by facilitating this transaction. Both models therefore apply to a large class of platforms, such as online auction sites and marketplaces, dating apps, and videogame consoles. However, a limitation of these models is that a single good or service is provided to both sides of the platform. Specifically, the product of two demand curves in Rochet and Tirole (2003) generates a new, single demand curve. 信用卡市场就是一个双方都能从匹配中获益的场景的例子。平台通过促成这种交易来获取利润。因此，这两种模型适用于一大类平台，比如在线拍卖网站和市场、约会应用以及电子游戏机。然而，这些模型的一个局限性在于，向平台的双方提供的是单一的商品或服务。具体来说，罗歇和梯若尔（2003）提出的两条需求曲线的乘积会生成一条新的单一需求曲线。

This setup constrains the model from representing platforms in which different sides consume different goods, and where cross-platform effects are asymmetric. This is the case with our newspaper example, where advertisers gain from having more subscribers (a positive cross-platform effect), but subscribers do not gain by consuming advertising (no cross-platform effect). We therefore modify previous models to better describe this type of platform, which includes donative-entrepreneurial nonprofits. In our focal example, homeless clients gain only from consuming shelter (no cross-platform effect) while donors gain from client consumption via such mechanisms as a warm glow (Andreoni, 1990), eternal rewards (Thornton & Helms, 2007), or social status (Dellavigna, List, & Malmendier, 2012). 这种设置限制了模型对不同平台的表征，在这些平台中，不同的参与方消费不同的商品，并且跨平台效应是不对称的。这一点与我们的报纸例子相符：在报纸平台中，广告商因拥有更多订阅者而受益（正的跨平台效应），但订阅者通过消费广告并没有获得收益（无跨平台效应）。因此，我们修改了之前的模型，以更好地描述这类平台，其中包括捐赠型创业非营利组织。在我们的焦点例子中，无家可归的客户仅从消费庇护所中受益（无跨平台效应），而捐赠者则通过诸如温暖感（Andreoni, 1990）、永恒奖励（Thornton & Helms, 2007）或社会地位（Dellavigna, List, & Malmendier, 2012）等机制从客户的消费中获益。

Model of donative-entrepreneurial nonprofits with asymmetric cross-platform effects. To model a platform in which utility gains are not match-based, we combine elements from both of the above models. We model demand as transactional, so buyers and sellers pay for a good or service in their own markets, as in Rochet and Tirole (2003). Yet, at least one demand function incorporates the magnitude of demand from another side, as in Belleflamme and Peitz (2010). To clearly isolate the cross-platform effect, we model a single cross-platform effect to make our results easier to interpret. Among donative nonprofits, it is reasonable to suppose that clients are unaffected by the number of donors, yet donors value a platform more if they can reach more clients. Hence, client demand is a function of price, $D _ { x } ( p _ { x } )$ and donor demand is a function of donor willingness to pay to reach $D _ { x }$ clients, $D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } )$ . The only other assumption we make about donor demand is that it is downward-sloping, and the “donor” side of the market could include private donors, foundations, or government grants. 具有不对称跨平台效应的捐赠型创业非营利组织模型。为了构建一个效用收益不基于匹配的平台模型，我们结合了上述两种模型的元素。我们将需求建模为交易型，因此买卖双方在各自的市场中为商品或服务付费，这与Rochet和Tirole（2003）的研究一致。然而，至少有一个需求函数纳入了来自另一方的需求规模，这与Belleflamme和Peitz（2010）的研究一致。为了清晰地分离跨平台效应，我们仅建模单一的跨平台效应，以使我们的结果更易于解释。在捐赠型非营利组织中，合理的假设是客户不受捐赠者数量的影响，然而，捐赠者如果能接触到更多客户，会更看重该平台。因此，客户需求是价格的函数，$D _ { x } ( p _ { x } )$，而捐赠者需求是捐赠者为接触$D _ { x }$个客户而愿意支付的金额的函数，$D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } )$。我们对捐赠者需求的唯一其他假设是它是向下倾斜的，并且市场的“捐赠者”方面可能包括私人捐赠者、基金会或政府拨款。

We represent profit as coming from the sale of two products to two sources of demand. 我们将利润表示为向两个需求来源销售两种产品所产生的收益。

\pi = ( p _ { x } - c _ { x } ) D _ { x } ( p _ { x } ) + ( p _ { y } - c _ { y } ) D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } ) π = (pₓ - cₓ)Dₓ(pₓ) + (pᵧ - cᵧ)Dᵧ(Dₓ(pₓ), pᵧ)

The $X$ -side (client) of the platform does not experience a cross-platform effect; thus, demand for client services, $D _ { x }$ , is only a function of the price of $X _ { i }$ . $p _ { x }$ By contrast, there is a positive cross-platform effect on the $y .$ -side (donor). In our example, demand on the $y$ side, $D _ { y }$ , decreases in its own price, $p _ { y }$ (i.e. a downward-sloping demand curve). However, donor utility increases with the number of clients on the $X ^ { \prime }$ side, or $D _ { x } ( p _ { x } )$ . For tractability, we assume $D _ { x } ( p _ { x } )$ and $D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } )$ are jointly concave in $p _ { x }$ and $p _ { y }$ To find the profit-maximizing price, we take the derivative of the profit function with respect to $p _ { x }$ and $p _ { y }$ to generate first-order conditions, hence $\begin{array} { r } { { \frac { \delta \pi } { \delta p _ { x } } } } \end{array}$ and b $\begin{array} { r } { \frac { \delta \pi } { \delta p _ { y } } = 0 } \end{array}$ 平台的X端（客户端）不存在跨平台效应；因此，对客户端服务的需求\( D_x \)仅取决于\( X_i \)的价格\( p_x \)。相比之下，Y端（捐赠者）存在正向跨平台效应。在我们的示例中，Y端的需求\( D_y \)随自身价格\( p_y \)的上升而减少（即需求曲线向下倾斜）。然而，捐赠者的效用随X端客户数量（即\( D_x(p_x) \)）的增加而提高。为便于分析，我们假设\( D_x(p_x) \)和\( D_y(D_x(p_x), p_y) \)在\( p_x \)和\( p_y \)上共同凹性。为找到利润最大化价格，我们对利润函数关于\( p_x \)和\( p_y \)求导，得到一阶条件，即：

和

( p _ { x } - c _ { x } ) \ D _ { x } ^ { ’ } + D _ { x } + ( p _ { y } - c _ { y } ) \biggl ( \frac { \delta D _ { y } } { \delta D _ { x } } \biggr ) D _ { x } ^ { ’ } = 0 \( (p_{x} - c_{x}) D_{x}' + D_{x} + (p_{y} - c_{y}) \left( \frac{\delta D_{y}}{\delta D_{x}} \right) D_{x}' = 0 \)

\left( p _ { y } - c _ { y } \right) D _ { y } ^ { ’ } + D _ { y } = 0 \left( p _ { y } - c _ { y } \right) D _ { y } ^ { ’ } + D _ { y } = 0

Result: The MSP charges a lower price to the side that generates a (positive) cross-platform externality. 结果：MSP 会向产生（正）跨平台外部性的一方收取较低的价格。

The cross-platform effect in Equation (11) is identified as $\begin{array} { r l } { ( p _ { y } - c _ { y } ) \left( \frac { \delta D _ { y } } { \delta D _ { x } } \right) D _ { x } ^ { ’ } } \end{array}$ Noe that the cross-platform effects result in $\begin{array} { r } { ( p _ { y } - c _ { y } ) \left( \frac { \delta D _ { y } } { \delta D _ { x } } \right) > 0 } \end{array}$ . Downwardsloping demand requires that $D _ { x } { < } 0$ Therefore, the total cross-platform effect term is negative, implying that $p _ { x }$ is less than what it would be without the cross-platform effect. Consequently, our nonprofit pricing model reproduces a result consistent with previous for-profit platform model formulations. Offering a discount to clients increases consumption of the client goods and services and, when both sides are included, may increase total profit by drawing in more donors. In our stylized nonprofit, a lower price, $p _ { x }$ , allows more clients to consume the nonprofit’s services, $D _ { x }$ , and client consumption in turn increases donor consumption, $D _ { y }$ , through the cross-platform effect. Appendix A shows this using a numerical example. 方程（11）中的跨平台效应被识别为 $\begin{array} { r l } { ( p _ { y } - c _ { y } ) \left( \frac { \delta D _ { y } } { \delta D _ { x } } \right) D _ { x } ^ { ’ } } \end{array}$。需要注意的是，跨平台效应导致 $\begin{array} { r } { ( p _ { y } - c _ { y } ) \left( \frac { \delta D _ { y } } { \delta D _ { x } } \right) > 0 } \end{array}$。向下倾斜的需求要求 $D _ { x } { < } 0$。因此，总跨平台效应项为负，这意味着 $p _ { x }$ 低于没有跨平台效应时的价格。因此，我们的非营利定价模型重现了与之前的营利性平台模型公式一致的结果。为客户提供折扣会增加客户商品和服务的消费，并且当双方都被纳入时，可能会通过吸引更多捐赠者来增加总利润。在我们的简化非营利模型中，较低的价格 $p _ { x }$ 允许更多客户消费非营利组织的服务 $D _ { x }$，而客户消费反过来通过跨平台效应增加捐赠者消费 $D _ { y }$。附录 A 通过一个数值示例展示了这一点。

This setup can offer nonprofit managers explicit guidance on pricing by rewriting the first-order conditions. Equations 13 and 14 rearrange the first-order conditions to describe the nonprofit’s optimal price as a function of the cross-platform effect. This setup can offer nonprofit managers explicit guidance on pricing by rewriting the first-order conditions. Equations 13 and 14 rearrange the first-order conditions to describe the nonprofit’s optimal price as a function of the cross-platform effect.

( p _ { x } - c _ { x } ) = \mathrm { ~ - ~ } \frac { D _ { x } } { D _ { x } ^ { ’ } } - ( p _ { y } - c _ { y } ) \bigg ( \frac { \delta D _ { y } } { \delta D _ { x } } \bigg ) $(p_{x} - c_{x}) = -\frac{D_{x}}{D_{x}’} - (p_{y} - c_{y}) \bigg( \frac{\delta D_{y}}{\delta D_{x}} \bigg)$

( p _ { y } - c _ { y } ) = \mathrm { ~ - ~ } \frac { D _ { y } } { D _ { y } ^ { ’ } } \((p_y - c_y) = -\frac{D_y}{D_y'}\)

Result: The optimal prices given by the MSP model are different from the optimal price for a single-sided firm, and price depends upon the magnitude of the cross-platform externality. Equations (13) and (14) demonstrate that, in an MSP, prices are determined by both client demand $\textstyle { \bigl ( } { \frac { D _ { x } } { n ^ { \prime } } } { \bigr ) }$ $\overline { { _ D _ { x } ^ { - } } }$ and the cross-platform externality $\begin{array} { r } { ( ( p _ { y } - c _ { y } ) ( \frac { \delta D _ { y } } { \delta D _ { x } } ) ) > \mathbf { 0 } } \end{array}$ from donors (Parker & Van Alstyne, 2005; Rochet & Tirole, 2003). The larger the cross-platform externality, the lower the price to clients. Not only does this demonstrate that the profit-maximizing (or net-revenue-maximizing) price will be lower than in a one-sided firm but, given a sufficiently large cross-platform effect, the optimal price could be below marginal cost, or negative. MSP模型给出的最优价格与单边企业的最优价格不同，价格取决于跨平台外部性的大小。公式(13)和(14)表明，在MSP中，价格由客户需求 $\textstyle { \bigl ( } { \frac { D _ { x } } { n ^ { \prime } } } { \bigr ) }$ $\overline { { _ D _ { x } ^ { - } } }$ 和来自捐赠者的跨平台外部性 $\begin{array} { r } { ( ( p _ { y } - c _ { y } ) ( \frac { \delta D _ { y } } { \delta D _ { x } } ) ) > \mathbf { 0 } } \end{array}$ 共同决定（Parker & Van Alstyne, 2005; Rochet & Tirole, 2003）。跨平台外部性越大，对客户的价格越低。这不仅表明利润最大化（或净收入最大化）价格会低于单边企业，而且在跨平台效应足够大的情况下，最优价格可能低于边际成本，甚至为负。

Thus, the MSP model offers an alternative explanation to those given in the existing nonprofit literature. It is not necessary to assume altruistic preferences of the nonprofit to generate low, zero, or negative prices. In the context of platform markets, a profitmaximizing nonprofit will be indistinguishable from an altruistic or output-maximizing nonprofit.6 The full range of optimal pricing emerges endogenously from market conditions rather than a choice variable by the researcher, manager, or firm. The issue of negative prices is one that has not often been discussed in existing nonprofit management theory, even though circumstances in which nonprofits pay clients to consume are common. Examples of (real) negative prices are prevalent in religious institutions, universities, and advocacy nonprofits, where clients are often given in-kind goods or services in return for participation or attendance. Negative prices have been demonstrated in for-profit platform markets (Evans & Schmalensee, 2005); an MSP model of nonprofits allows those same results to be extended to the nonprofit sector. 因此，MSP模型为现有非营利组织文献中给出的解释提供了另一种选择。无需假设非营利组织具有利他偏好来解释其低价格、零价格或负价格的情况。在平台市场的背景下，追求利润最大化的非营利组织与具有利他倾向或追求产出最大化的非营利组织难以区分。6 最优定价的全部范围是由市场条件内生决定的，而非由研究人员、管理者或企业作为选择变量设定。负价格问题在现有的非营利组织管理理论中并不常被讨论，尽管非营利组织向客户支付费用以使其消费的情况十分常见。（真实的）负价格案例在宗教机构、大学和倡导型非营利组织中普遍存在，这些组织通常会向客户提供实物商品或服务作为参与或出席的回报。负价格在营利性平台市场中已有证明（Evans & Schmalensee, 2005）；而MSP模型中的非营利组织则允许将这些结果扩展到非营利部门。

ILLUSTRATIVE EXAMPLES OF THE MSP MODEL

MSP模型的说明性示例

In this section, we use a few examples to illustrate how our pricing equations (Equations 13 and 14) can be used by nonprofit managers. 在本节中，我们使用几个例子来说明非营利组织管理者如何运用我们的定价公式（公式13和14）。

For-Profit Examples

盈利性示例

In practice, nonprofit platforms are more complex than the models presented above. Nonprofits often combine transaction fees, access fees, and multiple sides. For example, airports serve both airlines and retailers (Flores-Fillol, Iozzi, & Valletti, 2018). Airlines are charged landing fees and retailers are charged rental fees. Trade-offs involve two crossplatform externalities because retailers enjoy higher revenues when more planes (and passengers) land at the airport, while airlines attract more customers to airports that offer more food choices and shopping. 实际上，非营利平台比上述模型更为复杂。非营利组织常常结合交易费、接入费以及多方参与模式。例如，机场同时服务于航空公司和零售商（Flores-Fillol, Iozzi, & Valletti, 2018）。航空公司需缴纳着陆费，零售商则需支付租金。这种权衡涉及两种跨平台外部性：一方面，当更多飞机（和乘客）降落在机场时，零售商的收入会更高；另一方面，航空公司会被吸引到提供更多餐饮选择和购物设施的机场，以吸引更多顾客。

Platform pricing is also observed in the classic setting of newspapers. German news magazines discount subscription prices in order to charge advertisers more (Kaiser & Wright, 2006). Seamans and Zhu (2014) reported a similar finding but in the opposite direction: Newspapers raised prices when classified ads declined due to competition from Craigslist. Sports trading-card conventions also provide evidence of a different style of cross-platform discounting. Customers are given a price discount when there are multiple sports-card conventions in town because customers are unlikely to attend more than one convention and they generate the cross-platform externality (dealers gain the more customers there are). Dealers, by contrast, are charged more because they are willing to pay more and attend multiple competing conventions, or “multihome,” in order to reach customers (Jin & Rysman, 2015). 平台定价也在报纸的经典场景中有所体现。德国新闻杂志会降低订阅价格，以便向广告商收取更高的费用（Kaiser & Wright, 2006）。Seamans和Zhu（2014）报告了一个类似的发现，但方向相反：由于Craigslist的竞争导致分类广告减少，报纸提高了价格。体育交易卡展会也提供了不同类型跨平台折扣的证据。当城里有多个体育交易卡展会时，客户会获得价格折扣，因为客户不太可能参加多个展会，并且他们会产生跨平台外部性（参展商的客户越多，收益越高）。相比之下，参展商需要支付更高的费用，因为他们愿意支付更多费用并参加多个相互竞争的展会（即“多归属”），以接触客户（Jin & Rysman, 2015）。

Nonprofit Example: Goodwill Charges a Zero Price to Donors of Used Goods

非营利组织示例： goodwill 对捐赠二手物品的捐赠者收取零费用

（注：此处“Goodwill”为知名非营利组织“ goodwill 工业”的专有名词，保留英文）

Goodwill Industries, and similar thrift-store charities, provide a valuable community service by collecting used clothing, shoes, and furniture and then selling them to buyers who value low prices. Goodwill optimizes pricing by considering the demand curve for both donors of used items and for consumers of used goods. In this example, donors of used items are likely unaffected by the number of buyers in the stores. Their alternative to donations is to simply throw the items away, making their demand for disposal services relatively inelastic. Consequently, Goodwill will pick up clothing, shoes, and other goods for free, despite the significant cost of pick-up and the expense of disposing of unsellable items. If Goodwill charged a positive price, many donors would turn to landfills, lowering the variety of goods available to customers. Meanwhile, the consumers of used items benefit from the greater number of donors and the resulting greater variety and quality of goods available. Goodwill therefore finances its activities by charging positive prices to the buyers of used items but not to donors. These sales of used goods account for more than half of Goodwill’s total revenues. Goodwill Industries以及类似的 thrift-store 慈善机构通过收集二手服装、鞋子和家具并转售给重视低价的买家，提供了宝贵的社区服务。Goodwill 通过考虑二手物品捐赠者和二手商品消费者的需求曲线来优化定价。在这个例子中，二手物品捐赠者可能不受商店中买家数量的影响。他们捐赠物品的替代方案是直接丢弃这些物品，这使得他们对处理服务的需求相对缺乏弹性。因此，尽管取货成本高昂且处理无法售出的物品费用不菲，Goodwill 仍会免费上门收取服装、鞋子和其他物品。如果 Goodwill 收取正价格，许多捐赠者会转而选择垃圾填埋场，从而降低可供顾客选择的商品种类。同时，二手物品的消费者受益于更多的捐赠者以及由此带来的更多样化和更高质量的商品。因此，Goodwill 通过向二手物品买家收取正价格而非向捐赠者收费来资助其活动。这些二手商品的销售占 Goodwill 总收入的一半以上。

Nonprofit Example: San Francisco Chamber Orchestra

非营利组织示例：旧金山室内管弦乐团

Managers of nonprofit San Francisco Chamber Orchestra viewed their business model as a typical donative nonprofit (Hansmann, 1981). A ticketbuying audience is the primary market, with donations a secondary supplement to balance the books. Therefore, when the orchestra began finding it difficult to generate sufficient revenue to cover costs, managers considered raising ticket prices. 非营利组织旧金山室内管弦乐团的管理者将其商业模式视为典型的捐赠型非营利组织（Hansmann，1981）。购票观众是主要市场，捐赠是补充收入以平衡收支的次要来源。因此，当乐团发现难以产生足够收入来覆盖成本时，管理者考虑提高票价。

However, managers then analyzed their business as a platform, where donors were a second side. They determined that concertgoers would be highly sensitive to price increases—that is, very elastic demand. They also learned that donors were interested in providing access to orchestra performances and were willing to contribute more for higher attendance. That is, the goal of donors was to increase consumption of live performances. Given the cross-platform externality, managers instead lowered ticket prices to zero, making all concerts free. They also lowered the nonpecuniary price of their concerts by making them more familyfriendly in terms of content and concert times. Because of the large cross-platform externality, total revenues increased, even though revenues from tickets (now zero) declined. 然而，管理者随后将其业务分析为一个平台，其中捐赠者是第二方。他们确定音乐会观众对价格上涨高度敏感——即需求极具弹性。他们还了解到，捐赠者希望获得管弦乐队演出的入场机会，并且愿意为更高的上座率贡献更多。也就是说，捐赠者的目标是增加现场演出的消费量。考虑到跨平台外部性，管理者反而将票价降至零，使所有音乐会免费。他们还通过在内容和演出时间方面更具家庭友好性，降低了音乐会的非货币价格。由于巨大的跨平台外部性，总收入增加了，尽管门票收入（现在为零）下降了。

DISCUSSION AND CONCLUSION

讨论与结论

MSP theory has long been associated with information technology firms, including economically important digital platforms. Our goal is to show that MSP theory can also be applied to nonprofit organizations. This has implications for nonprofit managers, giving them access to analytical tools and language that help to interpret their activities and behaviors in a bewildering nonprofit sector. We also inform a management literature that takes a growing interest in nonprofits and their many interactions with for-profits and public agencies. Our application of MSP theory to the nonprofit setting also contributes to the platform literature, drawing attention to zero prices, a practice that is especially common among nonprofits. MSP理论长期以来与信息技术公司（包括具有经济重要性的数字平台）相关联。我们的目标是证明MSP理论也可应用于非营利组织。这对非营利组织管理者具有重要意义，使他们能够获得分析工具和语言，以解读其在复杂的非营利部门中的活动和行为。我们还为日益关注非营利组织及其与营利性组织和公共机构众多互动的管理文献提供了信息。我们将MSP理论应用于非营利组织环境，也为平台文献做出了贡献，引起了人们对零价格这一在非营利组织中尤为常见的做法的关注。

Nonprofit Managers Can Apply an Extensive Platform Literature

非营利组织管理者可申请广泛平台文献

Applying a profit-maximizing model to nonprofits offers some coherence to a long-standing dispute about what nonprofits are optimizing. Currently, the objective function is treated as a choice variable and nonprofit scholars have created a menu of possible objectives based on heterogeneous behaviors in nonprofit markets. For managers, a practical consequence of this ambiguity in objective function is that it degrades their ability to forecast, or anticipate the actions of their competitors. Moreover, the various objective functions have become intertwined with normative assumptions about altruistic motives of nonprofits. This has created a perceived conflict about engaging in commercial, revenue-generating activity (Battilana & Lee, 2014; James, 1983; Szymanska & Jegers, 2016). As we demonstrate, the platform model gives nonprofit managers a single coherent model of profit maximization for pricing and output decisions where the optimal behavior is endogenous to demand. Thus, platform theory explains nonprofit behavior, such as pricing and output, not as a normative choice but as the profit-maximizing outcome of demand curves. 将利润最大化模型应用于非营利组织，为长期存在的关于非营利组织优化目标的争议提供了一定的连贯性。目前，目标函数被视为一个选择变量，非营利组织学者基于非营利市场中的异质行为，构建了一系列可能的目标函数。对管理者而言，目标函数的这种模糊性会实际削弱他们的预测能力，或使其难以预判竞争对手的行动。此外，各种目标函数与对非营利组织利他动机的规范性假设交织在一起，这导致了关于参与商业性、创收活动的认知冲突（Battilana & Lee, 2014; James, 1983; Szymanska & Jegers, 2016）。正如我们所展示的，平台模型为非营利组织管理者提供了一个单一连贯的利润最大化模型，用于定价和产出决策，其中最优行为由需求内生决定。因此，平台理论将非营利组织的行为（如定价和产出）解释为需求曲线的利润最大化结果，而非规范性选择。

The platform literature has also provided a rich set of possibilities for strategizing. Evans and Schmalensee (2005) and Hagiu (2014) broke these possibilities down into four categories of decisions: pricing; which sides of a market to serve; what services to offer; and oveae," o o should haveacess o te plat form and what they should be allowed to do. In addition, factors like same-side network effects, which are common in platforms, also appear in nonprofit settings. For example, donors gain utility and status by being associated with other donors. These effects can be formally included as extensions to our baseline model. Governance is also important in how nonprofits reach, vet, and serve clients, which solves an information problem for donors (Kuan & Lee, 2021; Luo & Kaul, 2019). 该平台文献还为战略制定提供了丰富的可能性。Evans 和 Schmalensee（2005）以及 Hagiu（2014）将这些可能性分为四类决策：定价；服务市场的哪一方；提供哪些服务；以及谁应该能够使用该平台以及他们被允许做什么。此外，平台中常见的同边网络效应等因素在非营利组织环境中也存在。例如，捐赠者通过与其他捐赠者建立联系获得效用和地位。这些效应可以作为对我们基准模型的扩展正式纳入。治理在非营利组织如何接触、审查和服务客户方面也很重要，这为捐赠者解决了信息问题（Kuan & Lee，2021；Luo & Kaul，2019）。

Implications for the Management Literature

对管理学文献的启示

This article contributes to the management and strategy literature, which is increasingly interested in the relationship between nonprofits, for-profits, and public agencies. For example, Mahoney, McGahan, and Pitelis (2009) considered the wideranging ways in which private firms, including nonprofits, can and should engage in public goals. More recently, Kaul and Luo (2018) and Luo and Kaul (2019) have theorized about the advantages of different organizational forms, including for-profit, nonprofit, and public agencies. By applying MSP theory to nonprofits, we may help to enable more such analyses. 本文为管理与战略领域的文献研究提供了贡献，该领域正日益关注非营利组织、营利组织和公共机构之间的关系。例如，Mahoney、McGahan和Pitelis（2009）探讨了包括非营利组织在内的私营企业能够且应当参与公共目标的广泛方式。最近，Kaul和Luo（2018）以及Luo和Kaul（2019）对不同组织形式（包括营利、非营利和公共机构）的优势进行了理论化分析。通过将MSP理论应用于非营利组织，我们或许能助力开展更多此类分析。

Future research could further analyze nonprofit business models using MSP theory. Among the selfacknowledged weaknesses of the Hansmann (1980) taxonomy is the extensive gray area between cells. For example, on the donative-commercial dimension, most nonprofits receive revenues from both donations and commercial activity. Our approach models these sources of revenue as two sides of a platform, rather than an expression of more or less altruism. Using platform theory, the composition of donations versus commercial revenues depends on relative price elasticities of the demand curves of donor and client markets. 未来的研究可以利用MSP理论进一步分析非营利组织的商业模式。Hansmann（1980）分类法的公认缺陷之一是类别之间存在大量灰色地带。例如，在捐赠-商业维度上，大多数非营利组织既从捐赠中获取收入，也通过商业活动创收。我们的方法将这些收入来源建模为一个平台的两个方面，而非体现更多或更少的利他主义。利用平台理论，捐赠收入与商业收入的构成取决于捐赠者和客户市场需求曲线的相对价格弹性。

This distinction is important because demand curves and cross-platform effects can change over time. For example, when the Internet shifted demand for news and information, news organizations had to change their revenue models, often with significant experimentation. Some news providers chose to engage donors and thus lowered (or kept) the price to clients at zero, while others experimented with escalating paywalls of various porousness (Powers & Yaros, 2013; Usher & Layser, 2010). Adding donors as a side is a strategic choice and explains how firms can move from for-profit to nonprofit. 这种区别很重要，因为需求曲线和跨平台效应会随时间变化。例如，当互联网改变了人们对新闻和信息的需求时，新闻机构不得不改变其收入模式，这通常需要大量的尝试。一些新闻提供商选择吸引捐赠者，因此将对客户的价格降低（或保持）为零，而另一些则尝试设置各种渗透性的付费墙（Powers & Yaros, 2013; Usher & Layser, 2010）。将捐赠者作为补充是一种战略选择，这也解释了企业如何从盈利模式转向非营利模式。

The other dimension of Hansmann’s (1980) taxonomy, the entrepreneurial-mutual dimension, can also be reframed using platform theory. According to Hansmann (1980), in “entrepreneurial” firms, managers exercise control over the firm, while in mutual firms, members have primary decision-making authority. However, here, too, there is a substantial gray area between manager and member control. Perhaps a more relevant question is ownership. Platform theory applies a make-or-buy analysis to determine whether a firm is a one-sided (nonplatform) firm or a two-sided platform. Hagiu (2014) gives the example of a hair salon, which could operate as a platform by renting out chairs to independent hairdressers on one side and charging clients on the other. This hair salon platform earns revenues from two sets of clients. Alternatively, the salon could hire the hairdressers as employees, making it a one-sided firm. A third approach is for the hairdressers to be equal partners who collectively hire a manager to handle operations, which would be a mutual. All three types of hair salons hire a professional manager; the more important question is whether hairdressers are customers on one side of a platform, employees, or coowners (members). Hansmann（1980）分类法的另一个维度——创业型-互助型维度——也可以用平台理论来重新解读。根据Hansmann（1980）的观点，在“创业型”企业中，管理者对企业行使控制权，而在互助型企业中，成员拥有主要决策权。然而，在这里，管理者控制权与成员控制权之间同样存在大量灰色地带。或许更相关的问题是所有权。平台理论运用“自制或外购”分析来判断企业是单边（非平台）企业还是双边平台。Hagiu（2014）以美发沙龙为例：它可以作为平台运营，一方面向独立美发师出租工位，另一方面向客户收费。这种美发沙龙平台从两类客户那里获取收入。或者，沙龙可以雇佣美发师作为员工，使其成为单边企业。第三种方式是美发师作为平等合伙人，集体雇佣一名经理处理运营事务，这就是互助型企业。这三种类型的美发沙龙都雇佣了专业经理；更重要的问题是，美发师是平台一侧的客户、员工，还是共同所有者（成员）。

This type of professionally managed mutual is how Kuan (2001) describes arts nonprofits. In her model, a small group of high-paying consumers collectively create, own, and operate a performing arts firm. If these customers were the only people to consume, the firm would resemble a private, membersonly club, a mutual-commercial nonprofit in Hansmann’s (1980) taxonomy. Allowing nonmembers to consume performances, even at a low price, generates revenues for club member-owners, but the much higher price that member-owners pay gets interpreted as a charitable donation, classifying the firm as donative-entrepreneurial. By this logic, churches also fall into this category, in which parishioners are exhorted to tithe (make voluntarily contributions to their church) but vary in their willingness to pay for church services. Typically, a relatively small group (or club) of adherents both consume and finance ecclesiastical services for a less dedicated audience. Some churches hold special fee-paying concerts or speaking events, similar to how performing arts firms offer free outdoor concerts in the summer (Thornton & King, 2017).7 The Hansmann (1980) taxonomy does not fully explain these shifts from one quadrant of the taxonomy to another, but these business strategic decisions can be analyzed through a platform lens. 这种由专业人士管理的互助组织，正是Kuan（2001）对艺术非营利组织的描述。在她的模型中，一小群高消费能力的消费者共同创建、拥有并运营一家表演艺术公司。如果这些客户是唯一的消费者，该公司就会类似于私人会员俱乐部，即Hansmann（1980）分类法中的“互助商业型非营利组织”。允许非会员以低价消费演出，会为会员所有者带来收入，但会员所有者支付的更高价格会被解读为慈善捐赠，从而将该公司归类为“捐赠创业型”。按照这一逻辑，教会也属于这一类别：教区居民被劝勉奉献（自愿向教会捐款），但他们为教会服务付费的意愿各不相同。通常，相对较小的信徒群体（或俱乐部）既消费也资助教会服务，服务对象是投入度较低的受众。一些教会会举办付费的特别音乐会或演讲活动，这与表演艺术公司在夏季举办免费户外音乐会的做法类似（Thornton & King, 2017）。7 Hansmann（1980）的分类法无法完全解释从分类法的一个象限到另一个象限的这些转变，但这些商业战略决策可以通过平台视角进行分析。

Extensions for Platform Theory

平台理论的扩展

（注：根据结构规则，仅翻译人类可读内容，此处标题“Extensions for Platform Theory”为英文，需译为中文“平台理论的扩展”。若为纯符号或无需翻译内容则保留原符号，此处符合翻译要求。）

The application of MSP theory to the nonprofit setting can also generate novel insights for platform theory. The common practice among nonprofits of pricing goods and services at zero suggests a need for an extended model to explore zero pricing further. The current model allows for zero pricing as a single point that satisfies the first-order conditions; however, zero prices are far more common in practice than a unique point solution would suggest. A better model might include fixed costs of receiving or distributing resources, which introduce discontinuities that make zero pricing a corner solution. Note that zero or negative prices extend beyond nonprofits. For example, cash back or airline points schemes for credit cards are negative prices that are supported by a payment infrastructure, while search engines and social networks price at zero rather than incur the cost of negative prices. However, nonprofits face additional issues that could be modeled, such as legitimacy—for example, charging for disaster relief would be unsavory. Public goals could also be modeled; some public transit systems have gone to zero pricing to increase ridership, speed up passenger boarding, and save on collection costs. Free college tuition and universal basic income are also schemes that avoid administrative costs. A better understanding of discontinuities in cost structure could help explain the popularity of zero pricing. 将MSP理论应用于非营利组织场景，也能为平台理论带来新的见解。非营利组织通常将商品和服务定价为零，这表明需要一个扩展模型来进一步探索零定价现象。当前模型将零定价视为满足一阶条件的单点解；然而，在实际中，零价格远比单一解所暗示的更为普遍。更好的模型可能会纳入资源接收或分配的固定成本，这些成本会引入不连续性，从而使零定价成为一种边界解。需要注意的是，零价格或负价格并不仅限于非营利组织。例如，信用卡的现金返还或航空里程计划是负价格，它们由支付基础设施支持；而搜索引擎和社交网络则采用零价格，而非承担负价格的成本。不过，非营利组织还面临其他可建模的问题，如合法性——例如，收取救灾费用会令人反感。公共目标也可被建模；一些公共交通系统采用零定价以增加乘客量、加快乘客登机速度并节省收款成本。免费大学学费和全民基本收入也是避免行政成本的方案。对成本结构不连续性的更好理解，有助于解释零定价的流行。

REFERENCES

参考文献

Andreoni, J. 1990. Impure altruism and donations to public goods: A theory of warm-glow giving? Economic Journal, 100: 464477. Andreoni, J. 1990. 不纯利他主义与公共物品捐赠：温暖光芒捐赠理论？《经济杂志》，100：464-477。

Andreoni, J., Rao, J., & Trachtman, H. 2017. Avoiding the ask: A field experiment on altruism, empathy, and charitable giving. Journal of Political Economy, 125: 625653.
Andreoni, J., Rao, J., & Trachtman, H. 2017. 避免请求：关于利他主义、同理心和慈善捐赠的实地实验。《政治经济学杂志》，125: 625653。

Ashley, S. R., & Van Slyke, D. M. 2012. The influence of administrative cost ratios on state government grant allocations to nonprofits. Public Administration Review, 72: 4756.
阿什利，S. R.，& 范斯莱克，D. M. 2012. 行政成本比率对州政府向非营利组织拨款的影响。《公共行政评论》，72: 4756.

Associated Press. 2003. Salvation Army shelter charges families to stay. New York Times. Retrieved from https://www.nytimes.com/2003/09/29/us/salvationarmy-shelter-charges-families-to-stay.html
美联社。2003年。救世军收容所向家庭收取住宿费用。《纽约时报》。取自https://www.nytimes.com/2003/09/29/us/salvationarmy-shelter-charges-families-to-stay.html

Battilana, J., & Lee, M. 2014. Advancing research on hybrid organizing—Insights from the study of social enterprises. Academy of Management Annals, 8: 397441.
Battilana, J., & Lee, M. 2014. 推进混合组织研究——来自社会企业研究的见解。《管理学会年鉴》，8：397-441。

Baumol, W., & Bowen, W. 1965. On the performing arts: The anatomy of their economic problems. American Economic Review, 55: 495502.
鲍莫尔，W.，& 鲍恩，W. 1965. 论表演艺术：其经济问题的剖析。《美国经济评论》，55：495-502。

Belleflamme, P., & Peitz, M. 2010. Industrial organization: Markets and strategies (1st ed.). Cambridge, U.K.: Cambridge University Press.
Belleflamme, P., & Peitz, M. 2010. 产业组织：市场与策略（第1版）. 英国剑桥：剑桥大学出版社.

Boudreau, K., & Jeppesen, L. 2015. Unpaid crowd complementors: The platform network effect mirage. Strategic Management Journal, 36: 17611777.
Boudreau, K.，& Jeppesen, L. 2015. 无偿的众包补充者：平台网络效应的幻影。《战略管理杂志》，36：1761-1777。

Brooks, A. 2005. What do nonprofit organizations seek? (And why should policymakers care?). Journal of Policy Analysis and Management, 24: 543558.
布鲁克斯，A. 2005. 非营利组织追求什么？（以及政策制定者为何应关注？）《政策分析与管理杂志》，24：543-558.

Brooks, A., & Ondrich, J. 2007. Quality, service level, or empire: Which is the objective of the nonprofit arts firm? Journal of Cultural Economics, 31: 129142.
布鲁克斯，A.，& 翁德里奇，J. 2007. 质量、服务水平还是帝国：非营利艺术机构的目标是什么？《文化经济学杂志》，31：129-142。

Brown, E., & Slivinski, A. 2006. Nonprofit organizations and the market. In W. W. Powell & R. Steinberg (Eds.), The nonprofit sector: A research handbook: 140 158. New Haven, CT: Yale University Press.
布朗，E.，& 斯利文斯基，A. 2006. 非营利组织与市场。载于 W. W. 鲍威尔 & R. 斯坦伯格（编），《非营利部门：研究手册》：140-158。纽黑文，CT：耶鲁大学出版社。

Castaneda, M., Garen, J., & Thornton, J. 2008. Competition, contractibility, and the market for donors to nonprofits. Journal of Law Economics and Organization, 24: 215246.
卡斯塔涅达（Castaneda, M.）、加伦（Garen, J.）和桑顿（Thornton, J.）。2008年。竞争、契约性与非营利组织捐赠者市场。《法律、经济与组织杂志》，24卷：215-246。

Castaner, X. 2013. Management challenges of cultural heritage organizations. In I. Rizzo & A. Mignosa (Eds.), Handbook on the economics of cultural heritage: 209230. Northampton, MA: Edward Elgar Publishing.
Castaner, X. 2013. 文化遗产组织的管理挑战。载于 I. Rizzo 与 A. Mignosa（编），《文化遗产经济学手册》：209230。马萨诸塞州北安普顿：爱德华·埃尔加出版社。

Chang, C., & Tuckman, H. 1996. The goods produced by nonprofit organizations. Public Finance Review, 24: 2543.
Chang, C., & Tuckman, H. 1996. 非营利组织生产的商品。《公共财政评论》，24: 2543。

Chaves, M. 2002. Financing American religion. New Directions for Philanthropic Fundraising, 35: 4154.
Chaves, M. 2002. 美国宗教的资金筹措。《慈善筹款新方向》，35：4154。

Chetkovich, C., & Frumkin, P. 2003. Balancing margin and mission: Nonprofit competition in charitable versus fee-based programs. Administration $\pmb { \delta }$ Society, 35: 564596.
切特科维奇，C.，& 弗鲁姆金，P. 2003. 平衡边际与使命：非营利组织在慈善项目与收费项目中的竞争。《行政与社会》，35: 564-596.

Dellavigna, S., List, J., & Malmendier, U. 2012. Testing for alruism and socl pressure in charitable iving. Quarterly Journal of Economics, 127: 156.
Dellavigna, S., List, J., & Malmendier, U. 2012. Testing for altruism and social pressure in charitable giving. Quarterly Journal of Economics, 127: 156.

Eikenberry, A. 2009. Refusing the market. Nonprofit and Voluntary Sector Quarterly, 38: 582596.
Eikenberry, A. 2009. 拒绝市场。《非营利组织与志愿部门季刊》，38: 582596。

Eikenberry, A., & Kluver, J. 2004. The marketization of the nonprofit sector: Civil society at risk? Public Administration Review, 64: 132140.
Eikenberry, A., & Kluver, J. 2004. 非营利部门的市场化：公民社会面临风险？《公共行政评论》，64：132-140。

Evans, D., & Schmalensee, R. 2005. The industrial organization of markets with two-sided platforms. Working Paper No. w11603, NBER.
埃文斯，D.，& 施马伦塞，R. 2005. 双边平台市场的产业组织。工作论文第 w11603 号，美国国家经济研究局（NBER）。

Farrell, J., & Saloner, G. 1986. Installed base and compatibility: Innovation, product preannouncements, and predation. American Economic Review, 76: 940955.
法雷尔，J.，& 萨洛纳，G. 1986. 已安装基数与兼容性：创新、产品预发布和掠夺。《美国经济评论》，76：940-955。

Faulk, L., McGinnis Johnson, J., & Lecy, J. 2017. Competitive advantage in nonprofit grant markets: Implications of network embeddedness and status. International Public Management Journal, 20: 261293.
Faulk, L., McGinnis Johnson, J., & Lecy, J. 2017. 非营利组织赠款市场中的竞争优势：网络嵌入性和地位的影响。《国际公共管理杂志》，20：261293。

Flores-Fillol, R., Iozzi, A., & Valletti, T. 2018. Platform pricing and consumer foresight: The case of airports. Journal of Economics & Management Strategy, 27: 705725.
Flores-Fillol, R., Iozzi, A., & Valletti, T. 2018. 平台定价与消费者远见：以机场为例。《经济与管理策略杂志》，27：705725。

Frey, B., & Meier, S. 2006. The economics of museums. In V. Ginsberg & D. Throsby (Eds.), Handbook of the economics of art and culture, vol. 1: 10171047 . New York, NY: Elsevier.
弗雷，B.，& 迈耶，S. 2006. 博物馆的经济学。载于 V. 金斯伯格 & D. 特罗斯比（编），《艺术与文化经济学手册》，第 1 卷：10171047 。纽约，纽约州：爱思唯尔。

Gayle, P., Harrison, T., & Thornton, J. 2017. Entry, donor market size, and competitive conduct among nonprofit firms. International Journal of Industrial Organization, 50: 294318.
盖尔（Gayle, P.）、哈里森（Harrison, T.）和桑顿（Thornton, J.）。2017年。非营利组织的准入、捐赠者市场规模与竞争行为。《国际产业组织杂志》，50：294318。

Glaeser, E. 2002. The governance of not-for-profit firms. Working Paper No. 8921, NRER.
Glaeser, E. 2002. 非营利组织的治理。工作论文第 8921 号，NRER。

Glaeser, E., & Shleifer, A. 2001. Not-for-profit entrepreneurs. Journal of Public Economics, 81: 99115.
Glaeser, E., & Shleifer, A. 2001. 非营利企业家。《公共经济学杂志》，81: 99115。

Gorn, G., Tse, D., & Weinberg, C. 1991. The impact of free and exaggerated prices on perceived quality of services. Marketing Letters, 2: 99110.
Gorn, G., Tse, D., & Weinberg, C. 1991. 免费和夸大价格对服务感知质量的影响。《营销信件》，2：99110。

Hagiu, A. 2014. Strategic decisions for multisided platforms. MIT Sloan Management Review, 55: 7180.
Hagiu, A. 2014. 多边平台的战略决策。《麻省理工学院斯隆管理评论》，55: 7180。

Hansmann, H. 1980. The role of nonprofit enterprise. Yale Law Journal, 89: 835901.
Hansmann, H. 1980. The role of nonprofit enterprise. Yale Law Journal, 89: 835901.

Hansmann, H. 1981. Nonprofit enterprise in the performing arts. Bell Journal of Economics, 12: 341361.
Hansmann, H. 1981. 非营利性表演艺术企业。《贝尔经济学杂志》，12: 341361。

Hirth, R. 1999. Consumer information and competition between nonprofit and for-profit nursing homes. Journal of Health Economics, 18: 219240.
Hirth, R. 1999. 消费者信息与非营利性和营利性养老院之间的竞争。《卫生经济学杂志》，18：219-240。

Hopkins, B. 2011. The law of tax-exempt organizations (5th ed.). Hoboken, NJ: John Wiley & Sons.
霍普金斯，B. 2011. 免税组织法（第5版）。新泽西州霍博肯：约翰·威利父子出版公司。

Horwitz, J., & Nichols, A. 2009. Hospital ownership and medical services: Market mix, spillover effects, and nonprofit objectives. Journal of Health Economics, 28: 924937.
霍维茨（Horwitz, J.）和尼科尔斯（Nichols, A.），2009年。医院所有权与医疗服务：市场组合、溢出效应与非营利组织目标。《卫生经济学杂志》，28：924-937。

Jacobs, P., & Wilder, R. 1984. Pricing behavior of nonprofit agencies: The case of blood products. Journal of Health Economics, 3: 4961.
雅各布斯（P.）和怀尔德（R.），1984年。非营利机构的定价行为：血液制品案例。《卫生经济学杂志》，3：4961。

James, E. 1983. How nonprofits grow: A model. Journal of Policy Analysis and Management, 2: 350365.
詹姆斯，E. 1983. 非营利组织如何发展：一种模型。《政策分析与管理杂志》，2：350-365。

Jean, B., Robinson, H., & Foreman, T. 2011. How to price strategically. Nonprofit World, 29: 2425.
让·B.、罗宾逊·H.和福尔曼·T. 2011年。如何进行战略定价。《非营利世界》，29卷：2425页。

Jensen, M., & Meckling, W. 1976. Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics, 3: 305-360.
詹森，M.，& 梅克林，W. 1976. 企业理论：管理行为、代理成本与所有权结构。《金融经济学杂志》，3：305-360。

Jin, G., & Rysman, M. 2015. Platform pricing at sports card conventions. Journal of Industrial Economics, 63: 704735.
金，G.，& 赖斯曼，M. 2015. 体育卡片展会的平台定价。《产业经济学杂志》，63: 704735.

Kaiser, U., & Wright, J. 2006. Price structure in two-sided markets: Evidence from the magazine industry. International Journal of Industrial Organization, 24: 128.
凯泽（Kaiser, U.）和赖特（Wright, J.）。2006年。双边市场中的价格结构：来自杂志行业的证据。《国际产业组织杂志》，24：128。

Karlan, D., & List, J. 2007. Does price matter in charitable giving? Evidence from a large-scale natural field experiment. American Economic Review, 97: 17741793.
Karlan, D., & List, J. 2007. 价格在慈善捐赠中重要吗？来自大规模自然实地实验的证据。《美国经济评论》，97：1774-1793。

Katz, M., & Shapiro, C. 1985. Network externalities, competition, and compatibility. American Economic Review, 75: 424440.
Katz, M., & Shapiro, C. 1985. 网络外部性、竞争与兼容性。《美国经济评论》，75: 424-440.

Kaul, A., & Luo, J. 2018. An economic case for CSR: The comparative efficiency of for-profit firms in meeting consumer demand for social goods. Strategic Management Journal, 39: 16501677.
考尔，A.，& 罗，J. 2018. 企业社会责任的经济案例：营利性企业在满足消费者对社会产品需求方面的比较效率。《战略管理杂志》，39：1650-1677。

Kuan, J. 2001. The phantom profits of the opera: Nonprofit ownership in the arts as a make-buy decision. Journal of Law Economics and Organization, 17: 507520.
Kuan, J. 2001. 歌剧的幻影利润：非营利组织在艺术领域的自制-外购决策。《法律、经济与组织杂志》，17：507-520。

Kuan, J., & Lee, G. 2021. Governance strategy for digital platforms: Differentiation through information privacy. Strategic Management Review. doi: 10.1177/ 01492063211045023
Kuan, J., & Lee, G. 2021. 数字平台的治理策略：通过信息隐私实现差异化。《战略管理评论》。doi: 10.1177/ 01492063211045023

Lakdawalla, D., & Philipson, T. 1998. Nonprofit production and competition. Working Paper No. 6377, NBER.
Lakdawalla, D.，& Philipson, T. 1998. 非营利组织的生产与竞争。NBER工作论文第6377号。

Lakdawalla, D., & Philipson, T. 2006. The nonprofit sector and industry performance. Journal of Public Economics, 90: 16811698.
Lakdawalla, D., & Philipson, T. 2006. 非营利部门与行业表现。《公共经济学杂志》，90：1681-1698。

Lindsay, D., & Wuthnow, R. 2010. Financing faith: Religion and strategic philanthropy. Journal for the Scientific Study of Religion, 49: 87111.
Lindsay, D., & Wuthnow, R. 2010. Financing faith: Religion and strategic philanthropy. Journal for the Scientific Study of Religion, 49: 87111.

List, J. 2011. The market for charitable giving. Journal of Economic Perspectives, 25: 157180.
List, J. 2011. The market for charitable giving. Journal of Economic Perspectives, 25: 157180.

Luo, J., & Kaul, A. 2019. Private action in public interest: The comparative governance of social issues. Strategic Management Journal, 40: 476502.
罗, J., & 考尔, A. 2019. 公共利益中的私人行动：社会问题的比较治理。《战略管理杂志》, 40: 476502.

Mahoney, J., McGahan, A., & Pitelis, C. 2009. The interdependence of private and public interests. Organization Science, 20: 10341052.
Mahoney, J., McGahan, A., & Pitelis, C. 2009. The interdependence of private and public interests. Organization Science, 20: 10341052.

Malani, A., Philipson, T., & David, G. 2003. Theories of firm behavior in the nonprofit sector. In E. Glaeser (Ed.), The governance of not-for-profit organizations: 181215. Chicago, L: University of Chicago Press.
马拉尼（Malani, A.）、菲利普森（Philipson, T.）和大卫（David, G.）。2003年。非营利部门的企业行为理论。载于E. 格莱泽（E. Glaeser）编，《非营利组织的治理：181215》。芝加哥，L：芝加哥大学出版社。

McKeever, B. 2018. The nonprofit sector in brief. Washington, D.C: The Urban Institute.
McKeever, B. 2018. 非营利部门概况。华盛顿特区：城市研究所。

Moeller, L., & Valentinov, V. 2012. The commercialization of the nonprofit sector: A general systems theory perspective. Systemic Practice and Action Research, 25: 365370.
莫勒尔（Moeller, L.）和瓦连季诺夫（Valentinov, V.），2012年。非营利部门的商业化：一般系统理论视角。《系统实践与行动研究》，25: 365-370。

Newhouse, J. 1970. Toward a theory of nonprofit institutions: An economic model of a hospital. American Economic Review, 60: 6474.
纽豪斯，J. 1970. 非营利机构理论初探：医院的一种经济模型。《美国经济评论》，60：6474。

Oster, S., Gray, C., & Weinberg, C. 2003. Pricing in the nonprofit sector. In D. Young (Ed.), Effective economic decision-making for nonprofit organization: 2746. New York, NY: Foundation Center.
Oster, S., Gray, C., & Weinberg, C. 2003. 非营利部门的定价。载于 D. Young（编），《非营利组织的有效经济决策：2746》。纽约，纽约州：基金会中心。

Oster, S. M. 1995. Strategic management for nonprofit organizations: Theory and cases. Oxford, U.K.: Oxford University Press.
Oster, S. M. 1995. 非营利组织的战略管理：理论与案例。英国牛津：牛津大学出版社。

Parker, G., & Van Alstyne, M. 2005. Two-sided network effects: A theory of information product design. Management Science, 51: 14941504.
Parker, G.，& Van Alstyne, M. 2005. Two-sided network effects: A theory of information product design. Management Science, 51: 14941504.

Pauly, M. 1987. Nonprofit firms in financial markets. American Economic Review, 77: 257262.
保利，M. 1987. 金融市场中的非营利性企业。《美国经济评论》，77: 257-262。

Powers, E., & Yaros, R. 2013. Cultivating support for nonprofit news organizations: Commitment, trust and donating audiences. Journal of Communication Management (London), 17: 157170.
Powers, E., & Yaros, R. 2013. 培育对非营利性新闻机构的支持：承诺、信任与捐赠受众。《传播管理杂志》（伦敦），17：157-170。

Rochet, J., & Tirole, J. 2003. Platform competition in twosided markets. Journal of the European Economic Association, 1: 9901029.
Rochet, J. 和 Tirole, J. 2003. 双边市场中的平台竞争。《欧洲经济协会杂志》，1: 9901029。

Rohlfs, J. 1974. A theory of interdependent demand for a communications service. Bell Journal of Economics and Management Science, 5: 1637.
Rohlfs, J. 1974. 一种通信服务相互依赖需求的理论。《贝尔经济学与管理科学杂志》，5：1637。

Schiff, J., & Weisbrod, B. 1991. Competition between forprofit and nonprofit organizations in commercial markets. Annals of Public and Cooperative Economics, 62: 619640.
Schiff, J., & Weisbrod, B. 1991. 营利性与非营利性组织在商业市场中的竞争。《公共与合作经济学年鉴》，62: 619-640。

Seamans, R., & Zhu, F. 2014. Responses to entry in multisided markets: The impact of craigslist on local newspapers. Management Science, 60: 476493.
Seamans, R., & Zhu, F. 2014. 多边市场中的进入响应：Craigslist 对地方报纸的影响。《管理科学》，60：476493。

Shapiro, C., & Varian, H. 1998. Information rules: A strategic guide to the network economy. Boston, MA: Harvard Business Review Press.
夏皮罗（Shapiro, C.）和瓦里安（Varian, H.）. 1998. 信息规则：网络经济的战略指南. 马萨诸塞州波士顿：哈佛商业评论出版社.

Steinberg, R. 1986. The revealed objective functions of nonprofit firms. RAND Journal of Economics, 17: 508526.
Steinberg, R. 1986. The revealed objective functions of nonprofit firms. RAND Journal of Economics, 17: 508526.

Steinberg, R. 2003. The study of nonprofit enterprise: Theories and approaches. In H. K. Anheier & A. Ben-Ner (Eds.), The study of nonprofit enterprise: Theories and approaches: 227-309. New Haven, CT: Springer.
斯坦伯格，R. 2003. 非营利组织研究：理论与方法。载于H. K. 安海尔与A. 本-纳（编），《非营利组织研究：理论与方法》，227-309页。康涅狄格州纽黑文：施普林格出版社。

Steinberg, R., & Weisbrod, B. 2005. Nonprofits with distributional objectives: Price discrimination and corner solutions. Journal of Public Economics, 89: 22052230.
Steinberg, R., & Weisbrod, B. 2005. 具有分配目标的非营利组织：价格歧视与角点解。《公共经济学杂志》，89：22052230。

Szymanska, A., & Jegers, M. 2016. Modelling social enterprises. Annals of Public and Cooperative Economics, 87: 501527.
Szymanska, A., & Jegers, M. 2016. 社会企业建模。《公共与合作经济年刊》，87: 501527。

Thornton, J. 2006. Nonprofit fund-raising in competitive donor markets. Nonprofit and Voluntary Sector Quarterly, 35: 204224.
桑顿，J. 2006. 竞争性捐赠市场中的非营利组织筹款。《非营利组织与志愿部门季刊》，35: 204224。

Thornton, J., & Helms, S. 2007. Afterlife incentives in charitable giving. Applied Economics, 45: 27792791.
桑顿，J.，& 赫尔姆斯，S. 2007. 慈善捐赠中的来世激励。《应用经济学》，45: 2779-2791.

Thornton, J., & King, D. 2017. Financing social enterprise in the very long run. ACRN Oxford Journal of Finance and Risk Perspectives, 6: 2970.
桑顿，J.，& 金，D. 2017. 长期融资社会企业。《ACRN 牛津金融与风险展望期刊》，6：2970。

Tuckman, H. 1998. Competition, commercialization, and the evolution of nonprofit organizational structures. Journal of Policy Analysis and Management, 17: 175194.
塔克曼，H. 1998. 竞争、商业化与非营利组织结构的演变。《政策分析与管理杂志》，17: 175-194.

Usher, N., & Layser, M. 2010. The quest to save journalism: A legal analysis of new models for newspapers from nonprofit tax-exempt organizations to L3Cs. Utah Law Review: 13151371.
厄舍，N.，& 莱瑟，M. 2010. 拯救新闻业的探索：从非营利免税组织到L3C的报纸新模型法律分析。犹他法律评论：13151371。

Vesterlund, L. 2006. Why do people give? In W. Powell & R. Steinberg (Eds.), The nonprofit sector: A research handbook: 568587. New Haven, CT: Yale University Press.
Vesterlund, L. 2006. 人们为什么会给予？载于 W. Powell 和 R. Steinberg（编）《非营利部门：一本研究手册》，第 568-587 页。纽黑文，康涅狄格州：耶鲁大学出版社。

Vitaliano, D. 2003. Do not-for-profit firms maximize profit? Quarterly Review of Economics and Finance, 43: 7587.
维塔利亚诺，D. 2003. 非营利性企业是否追求利润最大化？《经济学与金融季刊》，43: 758-787.

Weisbrod, B. 1988. The nonprofit economy. Cambridge, MA: Harvard University Press.
Weisbrod, B. 1988. 非营利经济. 马萨诸塞州剑桥市: 哈佛大学出版社.

Ye, N., Teng, L., Yu, Y., & Wang, Y. 2015. What’s in it for me?: The effect of donation outcomes on donation behavior. Journal of Business Research, 68: 480486.
叶, N., 滕, L., 于, Y., & 王, Y. 2015. 对我有什么好处？：捐赠结果对捐赠行为的影响。《商业研究杂志》, 68: 480-486.

Yoken, C., & Berman, J. 1984. Does paying a fee for psychotherapy alter the effectiveness of treatment? Journal of Consulting and Clinical Psychology, 52: 254260.
Yoken, C., & Berman, J. 1984. 付费接受心理治疗是否会改变治疗效果？《咨询与临床心理学杂志》，52: 254-260.

Young, D., Jung, T., & Aranson, R. 2010. Mission-market tensions and nonprofit pricing. American Review of Public Administration, 40: 153169. 杨（Young）、D.、郑（Jung）、T.、& 阿兰森（Aranson）、R. 2010. 使命-市场张力与非营利组织定价。《美国公共行政评论》，40: 153169。

Yu, J., & Chen, K. 2018. Does nonprofit marketization facilitate or inhibit the development of civil society? A comparative study of china and the USA. Voluntas, 29: 925937. Yu, J., & Chen, K. 2018. 非营利组织市场化是促进还是抑制公民社会的发展？——以中国和美国为例的比较研究。Voluntas, 29: 925937.

APPENDIX A

附录 A

NUMERICAL EXAMPLE OF PRICING ANALYSIS FOR AN MSP

托管服务提供商定价分析的数值示例

This appendix offers a numerical example of a platform with two sides. Our goal is to illustrate key findings of the model for those who prefer a more concrete version to the general model discussed in the main article. While the model is a representation of a generic platform, we interpret it as a nonprofit, with donors on one side and clients on the other. Figure 1 in the main text represents the client demand curve for charitable goods and services, $D _ { x }$ , such as rehabilitation beds, university credits, or symphony tickets. Donors have a separate demand curve that has been described as a warm-glow, recognition, and other benefits from donation, $D _ { y }$ . Consistent with the model outlined in the article, donors value the quantity of charitable output consumed by clients, $D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } )$ . This is represented by a shift in the demand curve for donations, $D _ { y }$ , as a function of client consumption, $D _ { x }$ . 本附录提供了一个双边平台的数值示例。我们的目标是为那些更倾向于具体版本而非正文中讨论的一般模型的读者，说明该模型的关键结论。虽然该模型是对一个通用平台的描述，但我们将其解读为一个非营利组织，一方是捐赠者，另一方是客户。正文中的图1代表了客户对慈善商品和服务（如康复床位、大学学分或交响乐门票）的需求曲线\( D_x \)。捐赠者有一条单独的需求曲线，其被描述为来自捐赠的温暖感、认可感及其他收益，记为\( D_y \)。与文章中概述的模型一致，捐赠者重视客户消费的慈善产出数量，即\( D_y(D_x(p_x), p_y) \)。这表现为捐赠需求曲线\( D_y \)随客户消费\( D_x \)的变化而发生的移动。

The article calls out three pricing-related results 这篇文章指出了三个与定价相关的结果

(1) An MSP prices its products differently than a firm that serves only a one-sided market.
(1) MSP对其产品的定价方式与仅服务于单边市场的企业不同。

(2) A profit-maximizing MSP will discount the price of the good with a higher positive crossplatform externality.
(2) 追求利润最大化的微服务提供商（MSP）会对具有更高正跨平台外部性的商品进行价格折扣。

(3) The nonprofit will charge a relatively low price to the side of the market with the relatively elastic demand. (3) 该非营利组织将对需求相对富有弹性的市场一侧收取较低的价格。

The Set-Up: Demand Curves

设定：需求曲线

A nonprofit MSP meets the following three conditions: 一家非营利性MSP需满足以下三个条件：

(1) An MSP has two or more distinct sets of customers, or “sides”.
(1) 多边服务平台（MSP）拥有两个或更多不同的客户群体，即“双边”或“多边”。

(2) An MSP provides a distinct good or service to each side.
(2) 管理服务提供商（MSP）为每一方提供独特的商品或服务。

(3) An MSP has at least one side that creates a consumption externality for another side, or a cross-platform externality. (3) 一个多边服务提供商（MSP）至少有一方会对另一方产生消费外部性，或者跨平台外部性。

FIGURE A1 Demand Shift Due to Cross-Platform Externality

图A1 跨平台外部性导致的需求变化

Our numerical example involves two distinct sets of customers, or “sides,” each with its own demand curve. For simplicity, we assume that only one side, the donor side, $D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } )$ , gains utility from increases in the number of customers on the other, client, side, $D ( p _ { x } )$ . In more general examples, both sides could generate a cross-platform externality. An MSP will maximize profit with respect to both demand curves simultaneously. Our simple example is linear and downward-sloping. At a high price, few people want to buy, while at a low price, many people want to consume the charitable output (see Figure 1). 我们的数值示例涉及两组不同的客户，即“双方”，每组都有自己的需求曲线。为简化起见，我们假设只有一方，即捐赠方，\( D_y(D_x(p_x), p_y) \)，从另一方（客户方）\( D(p_x) \) 客户数量的增加中获得效用。在更一般的示例中，双方都可能产生跨平台外部性。MSP 将同时针对两条需求曲线最大化利润。我们的简单示例是线性且向下倾斜的。在高价时，很少有人愿意购买，而在低价时，很多人愿意消费慈善产品（见图1）。

Demand equations. The main parameters for the demand curve are the y-intercept, $A$ , which is the highest price anyone would be willing to pay, and the slope, $B$ In general, demand, $D$ , is the quantity of output, $X$ , that clients are willing to purchase at price $\left( p _ { x } \right)$ . 需求方程。需求曲线的主要参数是y轴截距\( A \)（即任何人愿意支付的最高价格）和斜率\( B \)。一般来说，需求量\( D \)是客户在价格\( (p_x) \)下愿意购买的产出数量\( X \)。

D _ { x } ( p _ { x } ) = A _ { x } - B _ { x } p _ { x } D_{x}(p_{x}) = A_{x} - B_{x}p_{x}

Numerical example. To fix ideas, we choose convenient numerical values for these parameters: $( A _ { x } , B _ { x } ) = ( 1 0 , 1 )$ . Thus, the demand equation becomes: 数值示例。为便于理解，我们选取这些参数的合适数值：$(A_x, B_x) = (10, 1)$。因此，需求方程变为：

D ( p _ { x } ) = 1 0 - p _ { x } D ( p _ { x } ) = 1 0 - p _ { x }

What Would a One-Sided For-Profit Firm Do?

单边盈利企业会怎么做？

To demonstrate how an MSP will choose prices and output differently from a firm serving a one-sided market, we first demonstrate what the one-sided firm would do. A net-revenue-maximizing (or for-profit-indisguise) firm will set the price in order to maximize revenues less costs. Thus, the profit function is: 为了展示MSP（可能是指某种市场服务提供商）如何选择价格以及与服务单边市场的企业有何不同的产出，我们首先演示单边市场企业的行为。以净收入最大化为目标（或伪装成盈利目的）的企业会设定价格以最大化收入减去成本。因此，利润函数为：

\pi ( p _ { x } ) = ( p _ { x } - c _ { x } ) D ( p _ { x } ) $\pi ( p _ { x } ) = ( p _ { x } - c _ { x } ) D ( p _ { x } )$

For simplicity, we set the variable cost of producing each unit, $\left( c _ { x } = 1 \right)$ equal to 1 (This is a common simplification, with marginal cost equal to average total cost, but the results are robust to more general specifications.). The firm will optimize by finding the value of $p ^ { * }$ that maximizes $\pi .$ The first-order conditions (FOC) are found by setting $\pi ^ { \prime } ( p ^ { * } ) = 0$ . 为简化起见，我们将生产每单位产品的可变成本（\( c_x = 1 \)）设为1（这是一种常见的简化方式，此时边际成本等于平均总成本，但结果对更一般的规格具有稳健性）。企业将通过找到使\(\pi\)最大化的\( p^* \)值来实现最优化。一阶条件（FOC）通过令\(\pi'(p^*) = 0\)得到。

\begin{array} { c } { { \pi ^ { ’ } ( p _ { x } ) = 1 1 - 2 p _ { x } } } \ { { p _ { x } ^ { * } = 5 . 5 } } \end{array}

Substituting $p ^ { * }$ into the demand equation, $x =$ $1 0 - p _ { x }$ , we find the quantity that maximizes $\pi$ ,or $x ^ { * }$ 将 \( p^* \) 代入需求方程 \( x = 10 - p_x \)，我们得到使 \( \pi \) 最大化的数量，即 \( x^* \)。

x ^ { * } = 4 . 5 x ^ { * } = 4.5

In this numerical example, a for-profit monopolist would set the price to $p _ { x } ^ { * } = 5 . 5$ and output to $x ^ { * } =$ 4.5, resulting in a profit, $\pi = 2 0 . 2 5$ . 在这个数值示例中，一家营利性垄断企业会将价格设定为 \( p_x^* = 5.5 \) 美元，产量设定为 \( x^* = 4.5 \)，从而获得利润 \( \pi = 20.25 \)。

What Would an Output-Maximizing Nonprofit Do?

追求输出最大化的非营利组织会怎么做？

Using the same demand, an output-maximizing nonprofit would optimize output over: 在相同需求下，一家追求产出最大化的非营利组织会优化以下方面的产出：

\pi ( p _ { x } ) = p _ { x } D ( p _ { x } ) - c _ { x } D ( p _ { x } ) - F _ { x } π(pₓ) = pₓD(pₓ) - cₓD(pₓ) - Fₓ

Note that we now include a fixed cost of production, because a common formulation in the nonprofit literature is to constrain the output-maximizing nonprofit such that it must break even (Baumol & Bowen, 1965; Horwitz & Nichols, 2009; Newhouse, 1970). Initially, if fixed costs are zero $( F _ { x } = 0 )$ then the firm would set the maximum output, conditional on breaking even. Again, using parameters $( A , B _ { x } , c _ { x } ) =$ (10, 1, 1), the firm’s break-even output and price are determined by finding $X$ conditional on $\pi = 0$ . 需要注意的是，我们现在纳入了固定生产成本，因为非营利组织文献中的一个常见表述是将追求产出最大化的非营利组织约束为必须实现收支平衡（Baumol & Bowen, 1965; Horwitz & Nichols, 2009; Newhouse, 1970）。最初，如果固定成本为零（\( F_x = 0 \)），企业将设定最大产出，同时满足收支平衡的条件。同样，使用参数（\( A, B_x, c_x \)）=（10, 1, 1），企业的收支平衡产出和价格通过在利润\( \pi = 0 \)的条件下求解\( X \)来确定。

\begin{array} { c } { { \pi ( x ) = ( 1 0 - x ) x - x = 0 } } \ { { x ^ { * } = 9 } } \ { { p _ { x } ^ { * } = 1 } } \end{array}

We find that price is equal to average total cost. This solution corresponds to point (3) on Figure 1. It is worth noting that optimal output will fall (and optimal price will rise) with increases in fixed costs, $F _ { \ast }$ ,if $F > 0$ In some models, an ad hoc exogenous source of funds is included in the profit equation (Glaeser, 2002). In this circumstance, the optimal output-maximizing firm will be able to lower the price until those exogenous resources are exhausted. 我们发现价格等于平均总成本。这个解对应图1中的点（3）。值得注意的是，若固定成本 \( F > 0 \)，最优产量会下降（且最优价格会上升）。在某些模型中，利润方程中会包含一种临时的外生资金来源（Glaeser, 2002）。在这种情况下，以产量最大化为目标的最优企业将能够降低价格，直到这些外生资源耗尽。

What Would a Nonprofit MSP Do?

非营利性 Managed Service Provider（MSP）会做什么？

We construct our MSP such that demand on the donor side is a function of demand on the client side. We represent the cross-platform effect by multiplying the donor intercept, $A _ { y } ,$ by the consumption from the client side, $D ( p _ { x } )$ . This market is sketched out visually in Figure A1. Note that the intercept shifts outward with increases in client consumption, $X$ . 我们构建的MSP（可能是某种市场结构或模型）使得捐赠方的需求是客户方需求的函数。我们通过将捐赠方截距 \( A_y \) 与客户方的消费 \( D(p_x) \) 相乘来表示跨平台效应。该市场的情况在图A1中以图形形式展示。需要注意的是，随着客户消费 \( X \) 的增加，截距会向外移动。

D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } ) = A _ { y } D _ { x } ( p _ { x } ) - B _ { y } p _ { y } D_{y}(D_{x}(p_{x}), p_{y}) = A_{y}D_{x}(p_{x}) - B_{y}p_{y}

A firm serving two markets now maximizes profit over both sets of output. For simplicity, we assume that there are no costs for producing the second good. 一家服务于两个市场的企业现在会在两种产出品上实现利润最大化。为简化分析，我们假设生产第二种产品没有成本。

\pi ( p _ { x } , p _ { y } ) = p _ { x } D ( p _ { x } ) - c _ { x } D ( p _ { x } ) + p _ { y } D _ { y } ( D _ { x } ( p _ { x } ) , p _ { y } ) π ( pₓ, pᵧ ) = pₓ D ( pₓ ) - cₓ D ( pₓ ) + pᵧ Dᵧ ( Dₓ ( pₓ ), pᵧ )

To be concrete, we set parameters for the second side of the market to $( A _ { y } , B _ { y } ) = ( 2 , 2 )$ . All previous parameters remain the same. The joint profit function would then be: 具体来说，我们将市场第二方的参数设置为 $( A _ { y } , B _ { y } ) = ( 2 , 2 )$ 。所有之前的参数保持不变。此时联合利润函数为：

\pi = 1 1 p _ { x } - p _ { x } ^ { 2 } - 1 0 + p _ { y } ( 2 ( 1 0 - p _ { x } ) - 2 p _ { y } ) π = 1 1 p _ { x } - p _ { x } ^ { 2 } - 1 0 + p _ { y } ( 2 ( 1 0 - p _ { x } ) - 2 p _ { y } )

To maximize profit, we find the FOC by taking the partial derivatives, $\begin{array} { r } { { \frac { \delta \pi } { \delta p _ { x } } } } \end{array}$ and $\frac { \delta \pi } { \delta p _ { y } }$ and setting them to 0 to find the values of $p _ { x }$ and $p _ { y }$ that maximize $\pi$ . 为了最大化利润，我们通过计算偏导数 $\begin{array} { r } { { \frac { \delta \pi } { \delta p _ { x } } } } \end{array}$ 和 $\frac { \delta \pi } { \delta p _ { y } }$ 并令它们等于0来找到使 $\pi$ 最大化的 $p _ { x }$ 和 $p _ { y }$ 的值。

\frac { \delta \pi } { \delta p _ { x } } = 1 1 = 2 p _ { y } - 2 p _ { y } = 0 \frac { \delta \pi } { \delta p _ { x } } = 1 1 = 2 p _ { y } - 2 p _ { y } = 0

\frac { \delta \pi } { \delta p _ { y } } = 2 0 - 2 p _ { x } - 4 p _ { y } = 0 \frac { \delta \pi } { \delta p _ { y } } = 20 - 2 p _ { x } - 4 p _ { y } = 0

Combining FOC 1 and FOC 2, we find $p _ { x } ^ { * } = 1$ $p _ { y } ^ { * } = 4 . 5$ , $x ^ { * } = 9$ , $y ^ { * } = 9$ . 将FOC 1和FOC 2结合，我们得到\( p_x^* = 1 \)，\( p_y^* = 4.5 \)，\( x^* = 9 \)，\( y^* = 9 \)。

We can now show the first two pricing-related results: platforms price and produce differently compared to one-sided firms, and this pricing includes discounting. The optimal prices for the platform are $p _ { x } ^ { * } = 1$ for the first side and $p _ { y } ^ { * } = 4 . 5$ for the second side of the market. This compares with $p ^ { * } = 5 . 5$ , the price that the one-sided monopolist would have charged. For the first side, this is a discount of 4.5. Output is also different for the two types of firms. The one-sided firm would have served 4.5 customers, but the two-sided firm would have served nine customers—twice the quantity of the one-sided firm. Joint profits would have expanded for the two-sided firm to $\pi = 4 0 . 5$ . 我们现在可以展示前两个与价格相关的结果：平台的价格和产出与单边企业不同，且这种定价包含折扣。平台在市场第一方的最优价格为 \( p_x^* = 1 \)，第二方的最优价格为 \( p_y^* = 4.5 \)。这与单边垄断企业的定价 \( p^* = 5.5 \) 形成对比。对于第一方，这是一个 4.5 的折扣。两种类型的企业的产出也有所不同。单边企业原本会服务 4.5 个客户，而双边企业会服务 9 个客户——是单边企业数量的两倍。双边企业的联合利润会增加到 \( \pi = 40.5 \)。

Interpretation of Nonprofit Results

非营利组织成果解读

Interestingly, the results of the optimum for output maximization (subject to a zero-profit constraint) are identical to the MSP optimum. The implication of this is significant for nonprofit theory. The output maximization model was put forward to explain lower prices and higher output by many nonprofits that were difficult to explain under net-revenue maximization. However, we demonstrate that an identical set of prices and output can be a result of pure net-revenue maximization over a two-sided (client and donor) market. This finding also weakens the normative claims that some firms can better serve clients because of strong preferences for output. Instead, nonprofit firms may simply be profit maximizing over multiple markets. 有趣的是，以零利润约束为条件的产出最大化最优结果与MSP（边际社会产品）最优结果完全一致。这一结论对非营利组织理论具有重要意义。产出最大化模型最初被提出用于解释许多非营利组织为何能提供更低价格和更高产出，而这一现象在净收入最大化模型下难以得到合理解释。然而，我们证明，在双边（客户和捐赠者）市场中，纯粹的净收入最大化也能产生相同的价格和产出组合。这一发现也削弱了某些企业因对产出有强烈偏好而能更好服务客户的规范性主张。相反，非营利组织可能只是在多个市场中追求利润最大化。

More extreme pricing outcomes are easily generated using the two-sided market approach. In general, decreasing the elasticity on one side results in much higher optimal prices for that side, and lower prices for the other side. For example, reducing the elasticity on the donor side by setting the slope to $B _ { y } = 1 . 1$ results in an optimal price for donors of $p _ { y } = 4 5$ and an optimal price for clients of $p _ { x } = - 3 9 . 5$ Total profits rise to $\pi = 2 2 . 7 5$ With this relatively simple demand structure over a two-sided nonprofit market, we demonstrate that a selfinterested profit-maximizing nonprofit can optimally set prices equivalent to an output-maximizing firm, with prices below 0 if demand is sufficiently inelastic. Thus, altruistic preferences on the part of the firm are not necessary to generate any of these seemingly extreme outcomes. In short, the platform solution, in which donors are a side of a platform, is capable of generating identical outcomes to those derived under the heterogeneous objective functions put forth by the nonprofit literature. 使用双边市场方法更容易产生更极端的定价结果。一般来说，降低某一侧的弹性会导致该侧的最优价格大幅提高，而另一侧的价格则降低。例如，通过将斜率设为 \( B_y = 1.1 \) 来降低捐赠者侧的弹性，会使捐赠者的最优价格为 \( p_y = 45 \)，客户的最优价格为 \( p_x = -39.5 \)，总利润上升至 \( \pi = 22.75 \)。在这种相对简单的双边非营利市场需求结构下，我们证明了一个自利的利润最大化非营利组织能够最优地设定与产出最大化企业等效的价格，当需求足够缺乏弹性时，价格可能低于0。因此，企业的利他偏好对于产生任何这些看似极端的结果并非必要。简而言之，捐赠者作为平台一方的平台解决方案，能够产生与非营利组织文献中提出的异质目标函数下得出的结果相同的结果。

Copyright of Academy of Management Review is the property of Academy of Management and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission. However, users may print, download, or email articles for individual use. 《管理学会评论》的版权归管理学会所有，未经版权所有者明确书面许可，其内容不得复制、发送至多个网站或张贴到电子讨论组。不过，用户可打印、下载或通过电子邮件发送文章供个人使用。