# SFB 303 Discussion Paper No. A - 103

**Author**: Koch, Karl-Josef

**Title**: Revealed Preference Theory and Mean Demand

**Abstract**: It is well known that neither the weak nor the strong axiom of revealed preference are additive . Moreover,
the theory of preference maximization does not imply anything for mean excess demand functions of exchange
economies, as long as the distribution of preferences is unknown and the consumption sets are unbounded.
Taking lower bounds of the consumption sets explicitly into account changes these results. We compute
conditions every mean demand function has to satisfy if the normalized distribution of income does not change
with prices and if all consumers satisfy the weak or the strong axiom of revealed preferences. In the special case
of exchange economies with two commodities only and where consumers satisfy the axiom of revealed
preference these conditions are sufficient for a function to qualify for mean demand of such an economy. Finally
we prove that the class of possible mean demand functions in these models changes with the number of
consumers.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: February 1987

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