Solutions to Three Functional Equations Arising from Different Ways of Measuring UtilityU

Utility of gains losses.can be measured in four distinct ways: riskless vs risky choices and gains losses.alone vs the gain-loss trade-off. Conditions forcing these measures all to be the same lead to functional equations, three of which are Fy1wF X.qF yY.xZsFy1wF XZ.qF yYZ.x Xw x X X X F:xyk, k ª yK, Kw; k, k , K, K )0. i. F XyR.w1yF Y.xqF Y.sFwFy1 F X.w1yF Y.xqF Y..ySx F: w0,1wªw0, 1w. ii. * This research was supported in part by the Natural Sciences and Engineering Research Council of Canada Grant OGP 002972, the National Science Foundation Grant SBR-9540107 to the University of California, Irvine, CA, and the Orsz´agos Tudom´anyos Kutat´asi Alap of Hungary Grant HT-016846. † Address correspondence to J´anos Acz´el, 97 McCarron Crescent, Waterloo, Ontario, N2L 5M9, Canada.