Revealed preference with optimal transport: money pumps, bounded rationality, and preference recovery

Abstract

This paper explores the connection between two distinct notions of irrationality: the extent to which the consumer fails to maximize his utility function and the extent to which the consumer can be turned into a money pump. We show that the amount of money which can be pumped by an arbitrageur is equal to both (i) the minimum amount of money which the consumer overpays to attain his utility targets (minimum over all utility functions) and (ii) the minimum amount of wasted quasilinear utility (minimum again over all utility functions). Under the assumption that the consumer's true utility function belongs to the aforementioned argmins, we present a method for recovering this true utility function even when choices are non-optimal. Further, we show that this recovered utility function can be interpreted as belonging to a utility maximizing consumer who systematically mis-perceives prices. These results and many more are proved by exploiting a novel connection between revealed preference analysis and optimal transport.