Market Demand Is a Continuous Function of Prices

There is a qualitative difference between individual demand and market demand. This is thoroughly discussed in Mantel (1974) and Shafer and Sonnenschein (1982). While certain structures of individual demand are lost in the process of aggregation others may be gained [cf. Hildenbrand (1982)]. The least that should be expected from aggregation is a continuous market demand function even if individual agents mayhave non-convex preferences and, therefore, set-valued demands. The importance of uniqueness and, therefore since demand correspondences are upper hen-u-continuous continuity of market demand has been sufficiently motivated elsewhere [cf. Allen (1980), Araujo and Mas-Cole11 (1978). Dierker et al. (1980a,b), Hildenbrand (1980) Sondermann ( 1975)]. In the present paper we shall present a natural class of probabilities on the space of preference relations yielding continuous mean demand functions which is dense in the set of all probabilities. The characteristic function of our approach relies on a natural parametrization of preferences by prices which allows via Fubini’s Theorem the consideration of probabilities whose support is the whole space of preferences. The idea of ‘suitable diffusion’ as a necessary condition for