Adv. Math. Econ. 15, 123–127 (2011)

An existence result and a characterization of the least concave utility of homothetic preferences

Yuhki Hosoya ^{1}

Graduate School of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan (e-mail: stairlimit@moon.cims.jp)

Received: July 24, 2010 Revised: October 22, 2010 JEL classification: D11 Mathematical Subject Classification (2010): 91B16, 91B08 Abstract. This note shows that a utility function of a homothetic preference relation satisfying u(0) = 0 is a least concave utility function if and only if it is homogeneous of degree one. Key words: least concave utility, homothetic preference, homogeneity of degree one

1We are grateful to Toru Maruyama and an anonymous referee for helpful comments and suggestions.