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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 suggested that equilibrium would always be achieved through a process of tâtonnement (French for "trial and error"), a form of hill climbing. [1]
Envy-free pricing - a relaxation of Walrasian equilibrium in which some items may remain unallocated. Fisher market - a simplified market model, with a single seller and many buyers, in which a CE can be computed efficiently. Allocative efficiency; Economic equilibrium; General equilibrium theory; Walrasian auction
The Walrasian auction 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's law is a consequence of finite budgets. If a consumer spends more on good A then they must spend and therefore demand less of good B, reducing B's price. The sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium.
Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost.
Theorem — Let be a positive integer. If : {: =,, >} is a set-valued function with closed graph that satisfies Walras's law, then there exists an economy with households indexed by , with no producers ("pure exchange economy"), and household endowments {} such that each household satisfies all assumptions in the "Assumptions" section except the "strict convexity" assumption, and is the excess ...
In fact, we can use revenue equivalence to prove that many types of auctions are revenue equivalent. For example, the first price auction, second price auction, and the all-pay auction are all revenue equivalent when the bidders are symmetric (that is, their valuations are independent and identically distributed).
[1]: 164 A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for , …, does not depend on wealth and is thus not subject to a wealth effect; [1]: 165–166 The absence of a wealth effect simplifies analysis [1]: 222 and makes quasilinear utility functions a common choice for modelling.