Introduction. One of the main tasks of economic theory is to explain the outcomes of a decentralized economy. The best developed model which addresses this problem is the by now standard, Arrow-Debreu, general equilibrium model (further referred to as the standard Walrasian model). Almost nobody has ever claimed that this model gives a realistic description of a decentralized economy, and the founders of this theory have never had any pretension to realism (see Punzo [1988] for a survey, but also Negishi [1962] for an exception). Hence, in this note we will restrict our attention to the, relatively safe, domain of pure theory. In that field, then, frequently something as the following is claimed. Take an economy consisting of a set of autonomous agents with given preferences and endowments. Let these individual agents freely choose their demands, given the prices, then it can be proved that, having made only the appropriate assumptions about the primitives of the economy, there exists an equilibrium in which the choices of all these agents may be realized. Note that this would be a remarkable result, as each individual agent was considering only his own preferences and endowments. In this note we address the question whether such a claim is right.
      An answer to this question is of theoretical importance. Within the social sciences there is a continuous debate about the appropriate basic subject-matter of social theory. To simplify matters in economics terms, there is a spectrum of possibilities ranging from the micro to the macro level (see e.g. Giddens & Turner [1987] for a systematic overview). Now, Walrasian economists claim that they can explain both the behavior of individual agents and the overall outcome of their actions in a decentralized economy, by adopting the methodological point of view of the first of the extremes of the spectrum, that is by starting their analysis at the level of autonomous subjects. An autonomous subject is an agent whose set of possible actions and outcomes is not predetermined by any form of a given structure, a set of rules, a certain context, or anything that transcends the level of the agents. Moreover, a theory which considers the overall outcome of these individual actions is a theory based upon autonomous subjects if and only if this overall outcome is, in one way or another, thought to depend only upon the behavior of these agents. If the Walrasian claim would be right, then that would be an important theoretical achievement.
      But an answer to the question is also of practical importance. For example, a popular idea among both economists and policy makers is that the purely theoretical, mathematical economics, although dealing with unrealistic and abstract models, has at least proved that a decentralized economy is optimal, as far as there are no real world complications in the form of external effects, public goods, increasing returns, etc. Such an idea may lead both researchers (e.g. Hahn [1982]) and policy makers to focus attention exclusively upon the problem of such complications. However, if the Walrasian claim would be unjustified, then statements about the acceptability or optimality of decentralized trade cannot be defended at all by referring to theoretical results concerning Walrasian models.
      We will argue, however, that the claim is not right. In section 2 we describe the Walrasian point of view on how to model a decentralized economy. We expose the structure not only of the standard Walrasian model, but also of fixed price models, imperfectly competitive models and temporary equilibrium models. Although that is not an exhaustive survey of models which exhibit the same structure, it will suffice to indicate the implications and limitations of the Walrasian approach to the modeling of a decentralized economy, and to evaluate the claim in section 3. There we argue that the structure of Walrasian models is such that the Walrasian claim is inconsistent, and that one cannot consider these models as ideal representations of decentralized economies. In section 4, by discussing some other Walrasian views, we anticipate some possible criticisms of Walrasians who will be in disagreement with the analysis of the previous sections. In section 5 we conclude by indicating some possibilities of future developments of economic theory. We argue that a different methodological point of view, paying attention explicitly to the interaction between individual agents in a decentralized economy, is important.