Sonnenschein–Mantel–Debreu theorem
Economic theorem / From Wikipedia, the free encyclopedia
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The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel [es], and Hugo F. Sonnenschein in the 1970s.[1][2][3][4] It states that the excess demand curve for an exchange economy populated with utility-maximizing rational agents can take the shape of any function that is continuous, has homogeneity degree zero, and is in accordance with Walras's law.[5] This implies that the excess demand function does not take a well-behaved form even if each agent has a well-behaved utility function. Market processes will not necessarily reach a unique and stable equilibrium point.[6]
More recently, Jordi Andreu, Pierre-André Chiappori, and Ivar Ekeland extended this result to market demand curves, both for individual commodities and for the aggregate demand of an economy as a whole.[7][8][9][10][note 1] This means that demand curves may take on highly irregular shapes, even if all individual agents in the market are perfectly rational. In contrast with usual assumptions, the quantity demanded of a commodity may not decrease when the price increases. Frank Hahn regarded the theorem as a dangerous critique of mainstream neoclassical economics.[11]