Econometrica: May 1978, Volume 46, Issue 3

Non-Convexifiable Pareto Sets

https://doi.org/0012-9682(197805)46:3<571:NPS>2.0.CO;2-W
p. 571-575

Rolf Mantel, Yakar Kannai

The existence of comprehensive sets in R^3 which cannot be transformed onto convex sets by means of ordinal transformations (i.e., continuous, strictly increasing transformations of the coordinate axes) is established. Such sets can be realized as the disposable hulls of pure exchange economies with convex preference orderings.

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