William Novshek

Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release

This article studies the fulfilled expectations equilibrium for a Cournot duopoly model in which firms acquire information about uncertain linear demand. Several propositions are established concerning the incentives to acquire and release information in this duopoly environment.

Marginal Consumers and Neoclassical Demand Theory

We extend the neoclassical theory of demand so that marginal consumers play a significant role in the determination of the elasticity of aggregate demand. Price-induced demand changes are decomposed into three effects: an aggregate substitution effect, an aggregate income effect, and an aggregate change-of-commodity effect. The final effect measures the rate at which consumers switch consumption to a similar commodity when the price of the commodity which they are currently consuming rises. Theories of consumers who pick one unit of one type of a differentiated commodity as well as the neoclassical theory obtain as special cases.

Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies☆

Abstract We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Nonconvex production sets, decreasing returns in the aggregate, and endogenous determination of the number of active firms are allowed. A Walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition (loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case) holds. The condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the Walrasian equilibrium.

Perfectly competitive markets as the limits of Cournot markets

A perfectly competitive, partial equilibrium market for a single homogeneous good with a (bounded) continuum of infinitesimal firms is considered. Cost functions are essentially unrestricted and are allowed to vary smoothly across firms. A sequence (net) of Cournot markets (each with a finite number of firms) which converge smoothly to the perfectly competitive limit in terms of both the inverse demand functions and the distributioon of firm technologies is introduced and it is shown that all markets sufficiently far along the sequence have a Cournot equilibrium and all the Cournot equilibria converge to the perfectly competitive equilibrium of the limit market.

Small Efficient Scale as a Foundation for Walrasian Equilibrium

Publisher Summary This chapter presents small efficient scale as a foundation for Walrasian equilibrium. The set of aggregate technological possibilities for the economy is obtained by summing the production sets of a very large number of productive units, interpreted as firms. These units are most efficient when their output is small (infinitesimal) relative to the demand, and the classical case of U-shaped average cost is admitted in the analysis. Moreover, because efficient scale is small, firms have only an infinitesimal effect on price when confined to the region in which they make positive profit. This enables one to capture the notion that the demand curve appears flat to a firm, while at the same time demand price may change substantially with substantial changes in aggregate quantity. The mass of firms active in an equilibrium is determined by the conditions of supply and demand. Small changes in aggregate demand will typically change the list of firms which are present in an equilibrium. Because changes in taste cause some firms to leave the market and others to enter, and because there are usually firms on the margin of entry, entry plays an important role in the explanation of value.

Bertrand equilibria with entry: limit results

Abstract We study the limiting behaviour of Bertrand equilibria (where firms must supply the whole of the demand coming to them) for two different cases, first when entry is exogenous, and second when it is free. The limit equilibrium set is characterised for both cases for a large class of cost functions.

Equilibrium in a simple price-location model

Abstract In a spatial model with endpoints we show that when consumers have downward sloping (rather than perfectly inelastic) demand, a price-location equilibrium (with price undercutting barred) exists if the market is sufficiently long relative to the number of firms.

Small efficient scale as a foundation for Walrasian equilibrium

Publisher Summary This chapter presents small efficient scale as a foundation for Walrasian equilibrium. The set of aggregate technological possibilities for the economy is obtained by summing the production sets of a very large number of productive units, interpreted as firms. These units are most efficient when their output is small (infinitesimal) relative to the demand, and the classical case of U-shaped average cost is admitted in the analysis. Moreover, because efficient scale is small, firms have only an infinitesimal effect on price when confined to the region in which they make positive profit. This enables one to capture the notion that the demand curve appears flat to a firm, while at the same time demand price may change substantially with substantial changes in aggregate quantity. The mass of firms active in an equilibrium is determined by the conditions of supply and demand. Small changes in aggregate demand will typically change the list of firms which are present in an equilibrium. Because changes in taste cause some firms to leave the market and others to enter, and because there are usually firms on the margin of entry, entry plays an important role in the explanation of value.

Quantity Adjustment in an Arrow-Debreu-Mckenzie Type Model

Our purpose is to examine long run entry/exit dynamics in a limit economy with infinitesimal firms and in Cournot economies (where firms recognize their influence on price) which are “close” to the limit economy. In the short run certain factors are immobile, and short run equilibrium prices reflect only the relative scarcity of factors that are instantaneously variable. The returns to immobile factors are not necessarily equalized. In the long run all factors are free to vary, and the factors that are immobile in the short run “flow towards that branch of production” in which there are profits to be realized. We formalize this in a long run entry/exit dynamics for a limit economy with infinitesimal firms. We also examine the long run dynamics in Cournot economies, with non-infinitesimal firms, because we view perfect competition as an idealization which should be interpreted as a limit of imperfect competition. With this view, the properties of the dynamics (and the equilibria) of the Cournot economies are the true objects of interest, and the dynamics (and the equilibria) of the limit economy are of interest only insofar as they represent limits of the results for a sequence of Cournot economies which converge to the limit economy. See Novshek and Sonnenschein [1983] for an extensive discussion of this point of view and the basic framework of the analysis. Here we amplify and extend the discussion of dynamics in that paper by explicitly treating decreasing returns to scale in the aggregate and also discussing the dynamics in the Cournot economies.

Capacity Choice and Duopoly Incentives for Information Sharing

We examine a three-stage game in which duopolists face a random-demand intercept. Firms first choose capacities, then decide whether to commit to share the private information they will receive about the intercept. After the private information is observed, firms choose output levels. The costless capacity-limiting case of our model is equivalent to standard models. We show that even small capacity costs may reverse the incentives to share information and lead to equilibria in which information sharing occurs. At some capacity-cost levels, sharing is an equilibrium for conventional reasons (equal expected outputs but higher variance with sharing), while at other cost levels, it is an equilibrium because expected outputs are lower (and, hence, expected prices are higher) with sharing.