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The Sonnenschein–Mantel–Debreu theorem (named after Gérard Debreu, Rolf Ricardo Mantel, and Hugo Freund Sonnenschein) is a result in general equilibrium economics. It states that the excess demand function for an economy is not restricted by the usual rationality restrictions on individual demands in the economy. Thus, microeconomic rationality assumptions have no equivalent macroeconomic implications. The theorem's main implications are that, with many interdependent markets within the economy, there might not exist a unique equilibrium point. ==Statement of the theorem== Informally, the theorem states that the market demand curve doesn't need to be a single downward sloping curve, and "it can have any shape at all-except one that doubles back on itself" (Keen 2011, 52). To obtain a strictly downward slopping demand curve, "the personal Engel curves are parallel straight lines for different individuals at the same prices," which means "an extra unit of purchasing power should be spent in the same way no matter to whom it is given" (Gorman 1953). In another word, there is only one person and one commodity in the market to generate a strictly downward slopping demand curve. Formally, the theorem states that the Walrasian aggregate excess-demand function inherits only certain properties of individual excess-demand functions: *Continuity *Homogeneity of degree zero, *Walras' law, and *boundary condition assuring that, as prices approach zero, demand becomes large. These inherited properties are not sufficient to guarantee that the aggregate excess-demand function obeys the weak axiom of revealed preference. The consequence of this is that the uniqueness of the equilibrium is not guaranteed : the excess-demand function may have more than one root – more than one price vector at which it is zero (the standard definition of equilibrium in this context). But, as Rizvy has explained, the range of implications is not limited to just the absence of uniqueness: "There are problems with establishing general results on uniqueness (Ingrao and Israel 1990,chap. 11; Kehoe 1985, 1991; Mas-Colell 1991), stability (Sonnenschein 1973; Ingrao and Israel 1990, chap. 12; Rizvi 1990, 94–144), comparative statics (Kehoe 1985; Nachbar 2002, 2004), econometric identification (Stoker 1984a, 1984b), microfoundations of macroeconomics (Kirman 1992; Rizvi 1994b), and the foundations of imperfectly competitive general equilibrium (Roberts and Sonnenschein 1977; Grodal 1996). Subfields of economics that relied on well-behaved aggregate excess-demand for much of their theoretical development, such as international economics, were also left in the lurch (Kemp and Shimomura 2002)."〔 Occasionally the Sonnenschein–Mantel–Debreu theorem is referred to as the “Anything Goes Theorem”. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sonnenschein–Mantel–Debreu theorem」の詳細全文を読む スポンサード リンク
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