Trejos-Wright with a 2-unit bound: Existence and stability of monetary steady states

This paper investigates a Trejos-Wright random matching model of money with a consumer take-it-or-leave-it offer and with individual money holdings in the set {0, 1, 2}. It is shown that three kinds of monetary steady states exist generically: (1) purestrategy full-support steady states, (2) mixed-strategy full-support steady states, and (3) non-full-support steady states. A full-support steady state exists if and only if a non-full-support steady state exists. Stability of these steady states is also studied. Both pure-strategy and mixed-strategy full-support steady states are locally stable. However, non-full-support steady states are unstable. (JEL classification: C62, C78, E40)