DUAL REPRESENTATIONS OF STRONGLY MONOTONIC UTILITY FUNCTIONS

We present theorems that establish dualities, i.e., bijections, be- tween speci¯ed sets of direct utility functions, indirect utility functions and expenditure functions. The substantive properties characterizing the speci¯ed set of direct utility functions are strong monotonicity, upper semicontinuity and quasi-concavity. Our results are strictly in- termediate between two classes of analogous results in the literature. We also provide applications that use all the three classes of duality results.