are perfectly rational. Significance In the 1982 book Handbook of Mathematical Economics, Hugo Sonnenschein explained some of the implications of his theorem for general equilibrium theory: In other words, it cannot be assumed that the demand curve for a single market, let alone an entire economy, must be smoothly downward-sloping simply because the demand curves of individual consumers are downward-sloping. This is an instance of the more general aggregation problem, which deals with the theoretical difficulty of modeling the behavior of large groups of individuals in the same way that an individual is modeled. Frank Ackerman points out that it is a corollary of Sonnenschein–Mantel–Debreu that a Walrasian auction will not always find a unique and stable equilibrium, even in ideal conditions: Léon Walras' auction model requires that the price of a commodity will always rise in response to excess demand, and that it will always fall in response to an excess supply. But SMD shows that this will not always be the case, because the excess demand function need not be uniformly downward-sloping. The theorem has also raised concerns about the falsifiability of general equilibrium theory, because it seems to imply that almost any observed pattern of market price and quantity data could be interpreted as being the result of individual utility-maximizing behavior. In other words, Sonnenschein–Mantel–Debreu raises questions about the degree to which general equilibrium theory can produce testable predictions about aggregate market variables. For this reason, Andreu Mas-Colell referred to the theorem as the “Anything Goes Theorem” in his graduate-level microeconomics textbook. Some economists have made attempts to address this problem, with Donald Brown and Rosa Matzkin deriving some polynomial restrictions on market variables by modeling the equilibrium state of a market as a topological manifold. However, Abu Turab Rizvi comments that this result does not practically change the situation very much, because Brown and Matzkin's restrictions are formulated on the basis of individual-level observations about budget constraints and incomes, while general equilibrium models purport to explain changes in aggregate market-level data. Robert Solow interprets the theorem as showing that, for modelling macroeconomic growth, the dynamic stochastic general equilibrium is no more microfounded than simpler models such as the Solow–Swan model. As long as a macroeconomic growth model assumes an excess demand function satisfying continuity, homogeneity, and Walras's law, it can be microfounded. The Sonnenschein–Mantel–Debreu results have led some economists, such as Werner Hildenbrand and Alan Kirman,