Tatonnement

A Walrasian auction, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand.

Walras suggests that equilibrium will be achieved through a process of (French for "trial and error"), a form of hill climbing.

The Walrasian auctioneer is the presumed auctioneer that matches supply and demand in a market of perfect competition. The auctioneer provides for the features of perfect competition: perfect information and no transaction costs. The process is called tâtonnement, or groping, relating to finding the market clearing price for all commodities and giving rise to general equilibrium.

In a Walrasian auction, the market clearing price is determined by setting the total demand across all agents equal to the total amount of the good. The tatonnement process is a model for investigating stability of equilibria. Prices are announced (perhaps by an "auctioneer"), and agents state how much of each good they would like to offer (supply) or purchase (demand). No transactions and no production take place at disequilibrium prices. Instead, prices are lowered for goods with above-equilibrium prices and excess supply. Prices are raised for goods with excess demand. The question for the mathematician is under what conditions such a process will terminate in an equilibrium in which demand equals supply for goods with positive prices and demand does not exceed supply for goods with a price of zero. Walras was not able to provide a definitive answer to this question.

The device is an attempt to avoid one of deepest conceptual problems of perfect competition, which may, essentially, be defined by the stipulation that no agent can affect prices. But if no one can affect prices no one can change them, so prices cannot change. However, involving as it does an artificial solution, the device is less than entirely satisfactory.

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