Lp-Frechet Differentiable Preference and Local Utility Analysis
Abstract This paper introduces the Lp-Frechet differentiable preference functionals, which is an extension of the class of Frechet differentiable preference functionals introduced by M. Machina (Econometrica50 (1982), 277–323). It shows that the type of "local utility analysis" conducted in Machina′s paper is applicable to this broader class of Lp-Frechet differentiable preference functionals. Effort has been made to clarify the relationship between Frechet differentiability and Gâteaux differentiability. Under mild conditions, it is shown that anticipated utility and betweenness functionals are Lp-Frechet differentiable. Journal of Economic Literature Classification Numbers: 022, 026.