A distributional dispersion condition on C2 monotone preferences, defined by unit normals to indifference surfaces, yields a C0 mean demand function when one integrates over such suitably diffuse consumers with convex preferences, regardless of the distribution of their initial endowments. For non-convex preferences, the dispersion condition implies that at any price vector, individual demands are finite sets for almost every agent. A stronger dispersion condition, involving both utility functions and unit normals, yields C0 mean demand functions with monotone non-convex preferences.
Bibliographical noteFunding Information:
The first draft of this paper was written during the author’s visit to the Sonderforschungsbereich 21 at the University of Bonn. Financial support from the Deutsche Forschungsgemeinschaft and N.S.F. grant SOC79-07228 is gratefully acknowledged. The author has benefitted from seeing unpublished work by Egbert Dierker, Hildegard Dierker and Walter Trockel, and from discussions with each of them, Werner Hildenbrand, Andreu Mas-Cole11 and Akira Yamazaki. Walter Trockel and an anonymous referee gave helpful suggestions for the preparation of the final version. When told about the dispersion condition in this paper, Dieter Sondermann remarked that it reminded him of a conjecture that Bob Aumann made in the early 1970s. Of course, the author retains responsibility for errors and omissions. Revisions were worked out while visiting the Group for the Applications of Mathematics and Statistics to Economics at the University of California, Berkeley in February and March of 1981.