A discrete characterization of Slutsky symmetry

Summary A smooth demand function is generated by utility maximization if and only if its Slutsky matrix is symmetric and negative semidefinite. Slutsky symmetry is equivalent to absence of smooth revealed preference cycles, cf. Hurwicz and Richter (Econometrica 1979). To observe such a cycle would require a continuum of data. We characterize Slutsky symmetry by means of discrete antisymmetric revealed preference cycles consisting of either three or four observations.The first author's research was supported in part by NSF grant DMS-9401355, and the second author's by the Deutsche Forschungsgemeinschaft, SFB 303, and by a SUNY Faculty Research award.