Excess Demand Functions

It is clear that a demand function derived from an agent’s preference preordering cannot be completely arbitrary . For instance it has to reflect the transitivity of the preference preordering . As our interest is not in individual but in aggregate demand , we are much more interested in characterizing excess demand functions of an economy rather than individual demand functions . One might conjecture that restrictions on individual demand play little or no role after aggregation in a large economy if no particular assumptions are made on the nature of the economy as a whole. If this is so , then the set of equilibria of an economy merely has some general mathematical properties and many finite sets may occur as sets of equilibria . In particular , one would expect that there is no bound for the number of equilibria of an economy . The first attack on this problem was made by Sonnenschein (1972) 1). We are now going to report on the procedure and main results of Sonnenschein (1972) .