Econometrica: May, 1978, Volume 46, Issue 3

An Equilibrium Existence Theorem without Convexity Assumptions

https://doi.org/0012-9682(197805)46:3<541:AEETWC>2.0.CO;2-#
p. 541-555

Akira Yamazaki

The main theorem in this paper is one in a long series of theorems which show the existence of equilibrium in economies without convex preferences, without convex consumption sets, or without complete and transitive preorderings. Here, it is proved that a competitive equilibrium exists in a large economy with not necessarily convex consumption sets and where preferences are continuous and transitive. As an additional assumption the continuity of the wealth distribution with respect to the Borel-Lebesque measure is required.