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

Abstract

Zhu (2003) shows existence of full-support monetary steady States with strictly concave value functions in a random matching model with individual money holdings in {0, 1, 2, ..., B} for a general B. He also shows that corresponding to each such steady state is an l-replica steady state for each 1 is an element of N: money is traded in bundles of 1 units, the support is {0, l, 2l, ..., lB}, and the value function is a step-function with jumps at points of the support. We show that such l-replicas are unstable if the underlying full-support steady state is a pure strategy steady state and if the support of the initial distribution is not {0, l, 2l, ..., lB}. 2014 Elsevier B.V. All rights reserved.