While competition between ﬁrms producing substitutes is well understood, less is known about rivalry between complementors. We study the interaction between ﬁrms in markets with one-way essential complements. One good is essential to the use of the other but not vice versa, as arises with an operating system and applications. Our interest is in the division of surplus between the two goods and the related incentive for ﬁrms to create complements to an essential good.
Formally, we study a two-good model where consumers value A alone, but can only enjoy B if they also purchase A. When one ﬁrm sells A and another sells B, the ﬁrm that sells B earns a majority of the value it creates. However, if the A ﬁrm were to buy the B ﬁrm, it would optimally charge zero for B, provided marginal costs are zero and the average value of B is small relative to A. Hence, absent strong antitrust or intellectual property protections, the A ﬁrm can leverage its monopoly into B costlessly by producing a competing version of B and giving it away. For example, Microsoft provided Internet Explorer as a free substitute for Netscape; in our model, this maximizes Microsoft’s joint monopoly proﬁts. Furthermore, Microsoft has no incentive to raise prices, even if all browser competition exits. This may seem surprising since it runs counter to the traditional gains from price discrimination and versioning. We also show that a essential monopolist has no incentive to degrade rival complementary products, which suggests that a monopoly internet service provider will oﬀer net neutrality.
There are other means for the essential A monopolist to capture surplus from B. We consider the incentive to add a surcharge (or subsidy) to the price of B, or to act as a Stackelberg leader. We ﬁnd a small gain from pricing ﬁrst, but much greater proﬁts from adding a surcharge to the price of B. The potential for A to capture B’s surplus highlights the challenges facing a ﬁrm whose product depends on an essential good.
A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voter’s most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates diﬀer in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voter’s most preferred outcome is unbeatable according to a 64%-majority rule. The weaker conditions supporting this result represent a signiﬁcant generalization of Caplin and Nalebuﬀ (1988).
The proof of our mean voter result uses a mathematical aggregation theorem due to Prekopa (1971, 1973) and Borell (1975). This theorem has broad applications in economics. An application to the distribution of income is described at the end of this paper; results on imperfect competition are presented in the companion paper [CFDP 937].
We present a new approach to the theory of imperfect competition and apply it to study price competition among diﬀerentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of ﬁrms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a uniﬁed framework.
To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules.