Sonnenschein-Mantel-Debreu Theorem

[Burkhard C. Schipper]

Previously there has been continuously critics in this new group on utility
maximisation hypothesis in neo-classical economics. Economists often argued
that the utility maximisation hypothesis is a necessity for economics
whereas others pointed out mainly empirical problems. Often it appeared by
the latter group that mainstream economics as whole has substantial
methodological problems and shows no sign theoretical progress. However, I
will show that most substantial critics on utility maximisation hypothesis
comes from mainstream economists themselves.

Neoclassical economists such as Samuelson postulated that demand functions
have certain properties because individuals are utility maximizer. Contrary
Sonnenschein argued in 1970th, and Mantel and Debreu proofed it
independently, that market demand functions do not have other properties
than the following trivial ones:
a) continuos
b) homogenous Z(ap) = Z(p)
c) p * Z(p) = 0 (Walras Identity)
This means that aggregate demand does not posses typical micro-economic
properties on demand functions and that no additional assumptions on
individual demand functions and preferences can lead to a way out of the
dilemma. A foundation of market demand functions on utility maximisation
hypothesis is logically impossible. This is also known under the
Disaggregation Problem. Assumptions on individual preferences and demand do
not add to determination of uniqueness of general equilibrium.

Burkhard C. Schipper

References:

Sonnenschein, H.F. (1973): Do Walras' Identity and Continuity Characterize
the Class of Community Excess Demand Functions?, Journal of Economic Theory
Vol. 6, pp. 345-54

Mantel, R.R. (1974): On the Characterization of Aggregate Excess Demand,
Journal of Economic Theory Vol. 7, pp. 348-53

Debreu, G. (1974): Excess Demand Functions, Journal of Mathematical
Economics Vol. 1, pp. 15-23