# A simple proof of the nonconcavifiability of functions with linear not-all-parallel contour sets

*Philip Reny* ()

*Journal of Mathematical Economics*, 2013, vol. 49, issue 6, 506-508

**Abstract:**
Consider a real-valued function that, on a convex subset of a real vector space, is continuous on line segments and has convex contour sets. Inspired by a compelling intuitive argument due to Aumann (1975), we provide a simple proof that no strictly increasing transformation of such a function can be concave unless all contour sets are parallel, i.e., unless for every pair of contour sets, either their affine hulls are disjoint or one of their affine hulls contains the other.

**Keywords:** Concavifiability (search for similar items in EconPapers)

**Date:** 2013

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0304406813000980

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:49:y:2013:i:6:p:506-508

Access Statistics for this article

Journal of Mathematical Economics is currently edited by *Atsushi (A.) Kajii*

More articles in Journal of Mathematical Economics from Elsevier

Bibliographic data for series maintained by Dana Niculescu ().