The Sonnenschein-Mantel-Debreu theorem is a result in general equilibrium economics, proved by Gerard Debreu, Rolf Mantel and Hugo Sonnenschein during the 1970s. It shows that the aggregate excess demand curve for an exchange economy of utility-maximizing rational agents can take the shape of any function that is continuous, has homogeneity of degree zero, and satisfies Walras' law, so a well-behaved excess demand curve isn't guaranteed even when every individual agent has a well-behaved utility function. The theorem implies that a market's own price-adjustment process need not settle on a unique and stable equilibrium point, and the economist Frank Hahn treated it as a serious challenge to standard assumptions about aggregate market demand in neoclassical theory.
Facts
StatementThe excess demand curve for an exchange economy of 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. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. SonnenscheinΓÇôMantelΓÇôDebreu theorem
Introduction, sentence 2Quote, Introduction, sentence 2
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.
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