Third Degree Price Discrimination in Linear‐Demand Markets: Effects on Number of Markets Served and Social Welfare
Third Degree Price Discrimination in Linear‐Demand Markets: Effects on Number of Markets Served and Social Welfare
复制标题
线性需求市场中的三级价格歧视：对服务市场数量和社会福利的影响
DOI：
10.1002/j.2325-8012.2008.tb00919.x
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发表时间：
2008
影响因子：
1.9
通讯作者：
Debashis Pal
中科院分区：
文献类型：
--
作者：
V. Kaftal;Debashis Pal
[作者单位]维克托卡夫塔尔，数学科学系，839 C旧化学楼，辛辛那提大学，辛辛那提，OH 45221，美国;维克托.卡夫塔尔@uc.eduDebashis，经济系，1204克罗斯利塔，辛辛那提大学，辛辛那提，OH 45221，debashis. uc.edu;通讯作者[鸣谢]我们感谢Rick Harbaugh，Laura Razzolini，大卫Sappington和两位匿名评论者。Debashis也感谢塔夫脱研究中心的财政支持。引言垄断性三度价格歧视是否会降低社会福利？半个多世纪以来，这个问题一直困扰着经济学家和政策制定者。罗宾逊（Robinson，1933）的开创性工作表明，如果一个垄断者在两个具有线性需求的不同且独立的市场上销售，那么福利福尔斯会随着三级价格歧视而下降。几乎半个世纪后，Schmalensee（1981）重新检验了罗宾逊的结果，并证明了对于任何数量的线性需求市场，三级价格歧视都会降低福利。Schmalensee（1981）还更普遍地认为，价格歧视只有在增加总产出的情况下才能增加福利。随后，Varian（1985）和Schwartz（1990）使用巧妙的对偶方法，将相关需求和非线性边际成本的结果进行了推广。[1]因此，众所周知，对于线性市场需求和恒定的边际成本，垄断性三度价格歧视确实会降低福利。然而，必须指出的是，三度价格歧视的福利减少效应是在一个关键假设下得出的。假设垄断者被迫在所有市场上收取相同的价格（统一定价），垄断者将在每个市场上出售正数量的产品。在最近的一篇文章中，科万（2007）考虑了各种形式的非线性需求，并提出了价格歧视减少福利的必要和充分条件。然而，科万（2007）也假设所有市场都是在统一定价下提供服务的。然而，当这一假设不成立时，垄断性第三度价格歧视的福利效应变得更加复杂，可以观察到，当所有市场都不是在统一定价下服务时，价格歧视可能会增加福利，因为价格歧视可能会服务于在统一定价下无法服务的市场。因此，相对于统一定价，价格歧视对福利有两种抵消作用。在那些最初在统一定价下提供服务的市场中，总福利下降;而在那些没有统一定价的市场中，福利上升。因此，在价格歧视下，“新市场”带来的额外福利可能会抵消最初在统一定价下提供服务的市场的福利损失，这一点在Schmalensee（1981）的开创性工作中得到了强烈强调。在处方药的背景下，最近瓦里安（2000）也表达了同样的观点。在两个市场的背景下，Battalio和Ekelund（1972）首先分析了价格歧视开辟“新市场”的可能性（图表）。Layson（1994）也考虑了两个市场，但包括非线性需求，并根据内生特征（如弹性）提出了“新市场开放”的条件。在专利政策的背景下，豪斯曼和麦基-梅森（1988年）明确纳入了通过价格歧视“打开新市场”。通过两个市场，他们表明，专利保持器的价格歧视在许多情况下是社会所希望的，因为它允许专利保持器“打开新的市场。“空间经济学中有一个相关的文献，始于Greenhut和Ohta（1972）和Holahan（1975），涉及空间价格歧视和线性需求的市场开放。…
[Author Affiliation]Victor Kaftal, Department of Mathematical Sciences, 839 C Old Chemistry Building, University of Cincinnati, Cincinnati, OH 45221, USA; victor.kaftal@uc.eduDebashis Pal, Department of Economics, 1204 Crosley Tower, University of Cincinnati, Cincinnati, OH 45221, debashis.pal@uc.edu; corresponding author[Acknowledgment]We are grateful to Rick Harbaugh, Laura Razzolini, David Sappington, and two anonymous reviewers. Debashis Pal is also grateful to Taft Research Center for financial support.1. IntroductionDoes monopolistic third degree price discrimination reduce social welfare? The question has continued to intrigue economists and policy makers for more than half a century. The seminal work of Robinson (1933) shows that if a monopolist with a constant marginal cost sells in two distinct and independent markets having linear demands, then welfare falls with third degree price discrimination. Almost half a century later, Schmalensee (1981) reexamines Robinson's result and demonstrates that for any number of markets with linear demands, third degree price discrimination lowers welfare. Schmalensee (1981) also establishes, more generally, that price discrimination increases welfare only if it increases aggregate output. Subsequently, using ingenious duality approaches, Varian (1985) and Schwartz (1990) generalize the results for correlated demands and nonlinear marginal costs.1It is, therefore, well known that for linear market demands and constant marginal costs, monopolistic third degree price discrimination indeed lowers welfare. It is important to note, however, that the welfare reducing effect of third degree price discrimination is derived under a crucial assumption. It is assumed that if the monopolist is forced to charge the same price in all markets (uniform pricing), the monopolist would sell a positive quantity in each market. In a recent article, Cowan (2007) considers various forms of nonlinear demands and presents the necessary and sufficient and/or sufficient conditions for price discrimination to reduce welfare. Cowan (2007), however, also assumes that all markets are served under uniform pricing. Yet, when this assumption does not hold, the welfare effects of monopolistic third degree price discrimination turn out to be significantly more intricate.Observe that when all markets are not served under uniform pricing, price discrimination may increase welfare because price discrimination may serve markets that would not be served under uniform pricing. Thus, relative to uniform pricing, price discrimination has two countervailing effects on welfare. Aggregate welfare goes down in those markets that are originally served under uniform pricing; whereas, welfare goes up in those markets that are not served under uniform pricing. Therefore, the additional welfare from the "new markets" under price discrimination may offset any loss of welfare in the markets that are originally served under uniform pricing.The point is strongly emphasized in Schmalensee's (1981) seminal work. In the context of prescription drugs, an identical sentiment is recently echoed in Varian (2000). In the context of two markets, the possibility of price discrimination opening up "new markets" is first analyzed (graphically) by Battalio and Ekelund (1972). Layson (1994) also considers two markets but includes nonlinear demands and presents conditions for "opening of new markets" based on endogenous features, such as elasticities. In the context of patent policy, "opening of new markets" by price discrimination is explicitly incorporated by Hausman and MacKie-Mason (1988). Using two markets, they show that price discrimination by a patent holder is socially desirable in many cases because it allows the patent holder to "open new markets."There is a related literature in spatial economics, beginning with Greenhut and Ohta (1972) and Holahan (1975), that deals with spatial price discrimination and market opening with linear demand. …