The Simple Analytics of Competitive Equilibrium with Multiproduct Firms
构建了一个允许多产品企业存在的自由进入竞争均衡模型，该模型易于操作和扩展，可用于分析多产品企业与单产品企业共存时的均衡形态及价格决定。
The familiar model of free-entry, competitive equilibrium has long played a central role in applied analysis of product markets. Among its stylizations is the restriction that firms produce a single output. For many situations, however, it is necessary to relax this assumption. While models permitting multiproduct firms exist, so far there is no framework that begins to rival the singleproduct analysis in terms of the ease with which it may be manipulated and extended to deal with specific applications. This paper develops such a model.' Specifically, in Section I a two-good model is set out that parallels the classic singleproduct analysis very closely. The sole difference is that alongside the single-product (specialized) technologies, which would usually be permitted, a multiproduct (diversified) technology is available. The model's competitive equilibrium is then characterized, and it is shown that this equilibrium may take one of three forms. Obviously, if diversification offers large cost advantages, no specialized firms can operate in equilibrium, and conversely if there are sizable disadvantages. The only other possibility is that diversified firms and exactly one type of specialized firm operate contiguously. Section II shows that the model is easy to manipulate, extends straightforwardly, and simple as it is, offers some new propositions. This demonstration involves examining the predictions the model offers in both its most general form and several extensions. To illustrate, basic features of equilibrium in the standard single-product environment are that price is determined by the cost of production with all operating firms producing the same level of output. Also, demand variation has no effect on either price or the actions of these firms. In contrast, in any equilibrium *Centre for Decision Sciences and Econometrics, Social Science Centre, University of Western Ontario, London, Ontario, N6A 5C2. Comments from David Donaldson, Ignatius Horstmann, Boyan Jovanovic, Peter Lloyd, Michael Parkin, Charles Plott, Edward Prescott, Sherwin Rosen, Christopher Robinson, Hugo Sonnenschein, and the referees are gratefully acknowledged. 'Research allowing multiproduct firms comes in a variety of forms. Early work by Roy G. D. Allen, 1938; John Hicks, 1939; Paul Samuelson, 1947; as well as more recent efforts by Keith Laitinen, 1980, analyzed in detail the isolated behavior of firms having access to an m-input/n-output production technology. Also, the Arrow-Debreu-McKenzie general-equilibrium model allows each producer a distinct production set, so that firms might choose to produce many goods. More recently, the literature (surveyed by Elizabeth Bailey and Ann Friedlander, 1982) analyzes a setting in which firms produce more than one good. Of all the contestability material, the work of William Baumol et al., 1982, Ch. 9, is the most closely related to the present analysis. Therein firms are permitted to choose a set of goods to produce, and a condition is provided that is necessary and sufficient for the (otherwise exogenously imposed) symmetric outcome to be supported in equilibrium. That this condition is indeed a relevant restriction is shown by means of a two-good numerical example in which the condition fails and the equilibrium is asymmetric. Finally, there is what might be termed the where there is sawdust there may be ' pressed logs' approach, dating back at least to Alfred Marshall, 1920, pp. 321-22, in which joint products are the result of unstructured technological complementarities.