Ordients : Optimization and Comparative Statics without Utility Functions

This paper introduces the concept of ordient for binary relations (prefer-ences), a relative of the concept of gradient for functions (utilities). The mainmotivation for this study is to replace the binary relation at the center stageof economic analysis, rather than its representation (whenever it exists). Ordi-ents have a natural economic interpretation as marginal rates of substitution.Some examples of ordientable binary relations include the lexicographic order,binary relations resulting from the sequential applications of multiple rationalesor binary relations with differentiable representations. We characterize the con-strained maxima of binary relations through ordients and provide an implicitfunction theorem and an envelope theorem