ABSTRACT OF PAPER
Title: Price-takers vs. Great Numbers: Revisiting Edgeworth - Walras Convergence on Perfect Competition
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This work is a part of a research project on the evolution of the Perfect Competition concept from the alternative views developed during the so-called “Marginal Revolution” until the consolidation of the price-taker hypothesis. The present papers tries to go beyond the traditional view on the convergence between Walras’s conception of perfect competition based on a price-taker hypothesis and Edgeworth’s process of recontracting. Some recent theoretical developments have underlined the importance of reconsidering the hypothesis of price taking agents . These developments lead us to believe it is interesting to model a perfect competition market based on strategic behaviour. This works intend avoiding the common trend in economic theory where imperfect competition is increasingly taking the place of perfect competition as the general framework. The Economics of Imperfect Competition has reached a great stage of development in terms of complexity without lose in its capacity to raise and answer an important number of issues. This has been manly built upon the abandon of the so-called “walrasian perfect competition framework”. One of the main arguments advanced since the 1970s against the walrasian framework is the absence of an explicit treatment of decentralized exchange and money. Both issues are evidently linked. The failures of the walrasian theory of money are often identified with the presence of a centralized exchange process which would be linked with a centralized price mechanism and the auctioneer. However, it seems generally accepted that the well known Debreu-Scarf theorem (Debreu and Scarf 1963) on the convergence of the core to the set of walrasian equilibria is the final proof of the strong relation between Edgeworth’s and Walras’s views on perfect competition. Following this interpretation, Edgeworth theory of recontracting is a suitable way to make explicit what is only implicit within the walrasian framework: the very conditions under which a perfect competitive allocation emerges endogenously from agents’ descentralized interactions. Edgerwoth approach, still following this interpretation, would show the process of struggle between agents leading to the establishment of a solution which in the walrasian approach is left to the auctioneer fiction. This seems to be a story of two players and two winners. From the Walrasian point of view, the competitive price vector is seen as more than a spurious representation of an efficient allocation. It is the limit case of form of economic competition and it appears to be so a very robust situation. While for Edgeworth the Debreu-Scarf’s result have been seen as the demonstration of his genius conjecture, and a rigorous generalisation of his ideas. However, going deeper in the theoretical and normative constructions of both authors allows us bringing out two different conceptions on perfect competition. Our paper evaluates the traditional interpretation of Walras-Edgeworth convergence on perfect competition. Following modern literature on the Debreu-Scarf theorem, we show that this convergence can be questioned from two main points of view. First, a main challenge for the walrasian approach is revealed by the very theoretical framework within which the notion of core and recontracting has been constructed by Debreu and Scarf. The Walrasian General Equilibrium model is based on hypothesis about individual behaviour and institutional structure of markets avoiding a lot of question becoming unavoidable once the Edgeworthian recontracting process is considered. The Walrsian framework cannot be modified in order to incorporate an important concept of solution from game theory, inspired from Edgeworth, namely the core, because it must be necessary to introduce strategic behaviours. The convergence between Edgeworth and Walras cannot be presented as the definitive proof of an ancient conjecture: perfect competition à la Walras can be obtained as the limit situation of an economy with a great number of agents. The second argument against this convergence is related to a criticism of the traditional view on Edgeworth´s theory of recontracting as it is depicted in the Debreu-Scarf Theorem. In this paper we show, following two recent works from Negishi and Vind, that the Edgeworthian concept of coalition and contract are constructed upon a hypothesis concerning information and networks formation. Following this idea, we can show that the critical element of the convergence to a determinate solution (the competitive solution) is linked with the structures of the market and the flow of information rather than number of agents. Furthermore, information does not need to be perfectly and symmetrically distributed among agents in order to obtain Edworth’s result, as it can be shown from Edgeworth’s own texts. In contrast, Debreu-Scarf theorem must suppose perfect information, as a result of it being pinned to the Walrasian framework. The hypotheses on perfect information and the idea of replica of economies are simply a possible, and not the most interesting, case given as an example by Edgeworth. It is the purpose of this paper to try to restablish the generality of Edgeworth’s theory of perfect competition.
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