Strictly monotonic preferences

Abstract

Monotonicity assumptions of preferences are natural and useful. A strictly monotonic preference is such that an increase in even only one commodity consumption is always strictly preferred. However, when we consider a continuum of commodities, it is not easy to find examples of strictly monotonic preferences. We survey some previous results in order to show that purely strictly monotonic preferences always exist but, if the commodity space is rich enough, they cannot be continuous in any linear topology defined on the consumption set and they cannot be represented by a utility function.