Existence of steady states with positive consumption in the kiyotaki-wright model

We prove the general existence of steady states with positive consumption in an N goods and fiat money version of the Kiyotaki-Wright model by admitting mixed strategies. We also show that there always exists a steady state in which everyone accepts a least costly-to-store object. In particular, if fiat money is one such object, then there always exists a monetary steady state. We also establish some other properties of steady states and comment on the relationship between steady states and (incentive) feasible allocations.