# The Definition and Significance of the Walrasian Auctioneer

## A look at obtaining general equilibrium in Walrasian markets

A Walrasian auctioneer is a hypothetical market-maker who matches suppliers and demanders to get a single price for a good in perfect competition. One imagines such a market-maker when modeling a market as having a single price at which all parties can trade.

## The Work of Léon Waltras

To understand the function and relevance of the Walrasian auctioneer in the study of economics, one must first understand the context in which the Walrasian auctioneer appears: the Walrasian auction. The concept of the Walrasian auction first appeared as the design of French mathematical economist Léon Walras. Walras is famed in the field of economics for his formulation of the marginal theory of value and the development of the general equilibrium theory.

It was in response to a specific problem that eventually leads Walras to the work that would develop into the theory of general equilibrium and the concept of the Walrasian auction or market. Walras set out to solve a problem originally presented by the French philosopher and mathematician Antoine Augustin Cournot. The problem was that while it could be established that prices would equate to supply and demand in individual markets, it could not be demonstrated that such an equilibrium existed in all markets at the same time (a state otherwise known as general equilibrium).

Through his work, Walras eventually developed a system of simultaneous equations which ultimately presented the concept of the Walrasian auction.

## Walrasian Auctions and Auctioneers

As introduced by Léon Walas, a Walrasian auction is a kind of simultaneous auction in which each economic agent or actor calculates the demand for a good at every conceivable price then presents this information to the auctioneer. With this information, the Walrasian auctioneer sets the price of the good to ensure that the supply is equivalent to the total demand across all of the agents. This perfectly matched supply and demand are known as equilibrium, or general equilibrium when the state exists overall and across all markets, not just the market for the good in question.

As such, the Walrasian auctioneer is the person conducting the Walrasian auction who effectively matches that supply and demand based upon the bids provided by the economic agents. Such an auctioneer renders the process of finding trading opportunities perfect and cost-free which result in perfect competition in the market. In contrast, outside of a Walrasian action, there might exist a "search problem" in which there is a stochastic cost of finding a partner to trade with and additional transactions costs when one does meet such a partner. ​

One of the key principles of the Walrasian auction is that its auctioneer operates within the context of perfect and complete information. The existence of both perfect information and no transaction costs ultimately gives rise to Walras' concept of tâtonnement or the process of identifying the market clearing price for all goods to secure general equilibrium.

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