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

Abstract

We investigate in details a Trejos-Wright random matching model of money with a consumer take-it-or-leave-it o¤er and the individual money holding set f0; 1; 2g. First we show generic existence of three kinds of steady states: (1) pure-strategy full-support steady states, (2) mixed-strategy full-support steady states, and (3) non-full-support steady states, and then we show relations between them. Finally we provide stability analyses. It is shown that (1) and (2) are locally stable, (1) being also determinate. (3) is shown to be unstable. (JEL classi…cation: C62, C78, E40)

The instability of some non-full-support steady states in a random matching model of money

“…Lomeli and Temzelides [5] show in the B = 1 case that the non-monetary steady state is stable and indeterminate. In a companion paper [4], we provide a stability analysis of full-support monetary steady states for the B = 2 case. We show that the full-support steady states in the {0, 1, 2} economy are locally stable, whether they are pure-strategy or mixed-strategy steady states.…”

“…4 Note that in this definition, the 'boundary' situations in which (1) has more than one solution but in which the randomization is degenerate are included in mixed-strategy equilibria. Such situations are non-generic.…”