In a Walrasian world, prices vary so as to balance supply and demand for each good. Arrow and Debreu proved that under some conditions there exists a set of prices which make the agents' plans compatible. In such a framework, there is really no logical need to require that a particular good plays a special role in trade. We shall prove that such a need arises if we try to set up a concept of equilibrium when the prices are not necessarily Walrasian, and for which there is only one " market " for each good, that is one equation that says that there is equality between resources and uses for each good. The existence of a non-Walrasian equilibrium requires that there be a good, called money, which has to appear in each transaction or which simply has to be the measuring rod of the profitability of each transaction. We assume a pure exchange economy. There are m consumers (i= 1, ..., m). There are r goods (h = 1, ..., r). Let R'+ be the consumption set of consumer i (H.1). wi his positive initial allocation (H.2). Ui his strictly concave, continuously differentiable, and monotone utility function3 (H.3). We assume that the price vectorp (strictly positive) is given. We prescribe the following condition on an allocation:

We discover that letting agents pairwise sequentially exchange at "wrong" prices has a robust effect on prices at convergence. If the initial relative price for a good is cheaper than the equilibrium walrasian price due to initial endowments, the initial excess demand effect pushes resource allocation. This paper characterizes the out-of-equilibrium dynamics of a symmetric, pure exchange economy with two goods and N agents with uniformly distributed preferences and identical endowments. Relaxing the auctioneer assumption, but maintaining a global price rule, sequentially random pairwise trading at out-of-equilibrium prices is allowed. Initial mispricing implies rationing, determining excess demand (supply) fading away only at convergence, when the price of the initially cheaper (more expensive) good becomes more expensive (cheaper) than the walrasian one. The system converges when the sequential price reaches the walrasian price evaluated at current updated endowments. A perfectly symmetric setting, by initial mispricing and consequent rationed trading, creates asymmetric resource allocations even at convergence, where welfare is less than a standardized 1% lower than the auctioneer Pareto one. This model sketches a possible basis for price over-reaction microfoundation and captures endogenous "wealth divide" among the population, induced by whether agent trading is dominated by good preferences or just by speculation around their prices.

This paper proposes a price adjustment process that converges globally for a set of pure exchange economies, in which each agent has a Constant Elasticity of Substitution (CES) utility function. In this process, the auctioneer approximates demand schedules by assuming that each trader has a Cobb-Douglas utility function. The process generates prices that cannot be represented by linear combinations of previous prices, and hence precludes cycles. In the so-called unstable Scarf economies, prices spiral towards the Walrasian equilibrium in the same direction as found by Scarf. Simulation in large scale Scarf economies suggests that the speed of convergence may be polynomial in the size of the economy.

This paper analyzes, via intensive use of simulation techniques, the effects of the introduction of direct exchange relationships through bilateral trades in a simple general equilibrium pure exchange economy. Agents are heterogeneous in their endowments and repeatedly match in random pairs bargaining on how to split the advantages of a trade; possibly they can agree to exchange at the known market clearing prices. Simulations of this evolutionary process show that while walrasian outcomes emerge in the interaction among people with similar outside opportunities, people of different groups converge to accept an equilibrium in which agents with the best outside opportunity extract the greater part of the surplus out of an exchange. On other hand the acceptance of market mediation (i.e. walrasian outcomes) is more probable when either the parties try to exploit too much from the opponent or when there is anonymity in the trading process. The results show evidence that the acceptance of decentralized, personalized contracting (apart from efficiency considerations) increases the probability of amplifying the asymmetries in the initial distribution beyond what is produced by the pure market mechanism.

It is known that the outcome function realizing Walrasian equilibrium correspondence can easily be constructed provided an auctioneer is permitted. Schmeidler and Hurwicz have shown that, even if an auctioneer is not permitted, there are some mechanisms implementing Walras correspondence. Their formulations were restricted, however, to the cases of pure exchange economy. In this note, we construct mechanisms which implement Walras correspondence in a private ownership economy which is not particularly restricted to the pure exchange economy. In these mechanisms prices are set by firms or consumers and no auctioneer is required.

of economics through the concept of general equilibrium. For Walras, exchanges only take place after a Walrasian tâtonnement (French for "trial and error") Marie-Esprit-Léon Walras (French: [valʁas]; 16 December 1834 – 5 January 1910) was a French mathematical economist and Georgist. He formulated the marginal theory of value (independently of William Stanley Jevons and Carl Menger) and pioneered the development of general equilibrium theory. Walras is best known for his book Éléments d'économie politique pure, a work that has contributed greatly to Marie-Esprit-Léon Walras (French: [valʁas]; 16 December 1834 – 5 January 1910) was a French mathematical economist and Georgist. He formulated the marginal theory of value (independently of William Stanley Jevons and Carl Menger) and pioneered the development of general equilibrium theory. Walras is best known for his book Éléments d'économie politique pure, a work that has contributed greatly to the mathematization of economics through the concept of general equilibrium. For Walras, exchanges only take place after a Walrasian tâtonnement (French for "trial and error"), guided by the auctioneer, has made it possible to reach market equilibrium. It was the general equilibrium obtained from a single hypothesis, rarity, that led Joseph Schumpeter to consider him "the greatest of all economists". The notion of general equilibrium was very quickly adopted by major economists such as Vilfredo Pareto, Knut Wicksell and Gustav Cassel. John Hicks and Paul Samuelson used the Walrasian contribution in the elaboration of the neoclassical synthesis. For their part, Kenneth Arrow and Gérard Debreu, from the perspective of a logician and a mathematician, determined the conditions necessary for equilibrium. t…

commodity in the economy, given certain assumptions. It can be used to prove the existence of general equilibrium (or Walrasian equilibrium) of an economy. Arrow-Debreu This glossary of economics is a list of definitions containing terms and concepts used in economics, its sub-disciplines, and related fields. Arrow–Debreu model Also called the Arrow–Debreu–McKenzie model or ADM…