Prices in the utility function and demand monotonicity

Abstract

We analyze utility functions when they depend both on the quantity of the goods consumed by the agent and on the prices of the goods. This approach allows us to model price effects on agents' preferences (e.g. the so-called Veblen effect and the Patinkin formulation). We provide sufficient conditions to observe demand monotonicity and substitution among goods. Power utility functions are investigated: we provide examples of price dependent utility functions that cannot be written as an increasing transformation of a classical utility function dependent only upon quantities.