A simple proof for the existence of Walrasian equilibrium under monotone preferences

When individual preferences are strictly monotone, the continuity of the excess demand functions that is usually assumed to show the existence of a Walrasian equilibrium does not hold for price vectors in which at least one component is equal to zero. In this paper we provide a simple proof of existence for precisely this important case. It is based upon the economic intuition that equilibrium prices will never be equal to zero if preferences are strictly monotone, and it runs surprisingly similar to the one usually adopted for the case of non-monotone preferences.