Stationarity without degeneracy in a model of commodity money

Abstract

We develop a model of macroeconomic heterogeneity inspired by the Kiyotaki-Wright (1989) formulation of commodity money, with the addition of linear utility and idiosyncratic shocks to savings. We consider two environments. In the benchmark case, the consumer in a meeting is chosen randomly. In the auctions case, the individual holding more money can be selected to be the consumer. We show that in both environments socially optimal trading decisions (that are individually acceptable) are stationary and solve a tractable static optimization problem. Savings decisions in the benchmark case are remarkably invariant to mean-preserving changes in the distribution of shocks. This result is overturned in the auctions case.

Independent random matching

“…Moreover, for a wide class of random matching models with a continuum population, it is not possible to capture the relevant attributes of all the agents in a finite type space. This is the case, e.g., for the models described in Cavalcanti and Puzzello (2010), Green and Zhou (2002), Lagos and Wright (2005), Molico (2006), Shi (1997), Zhu (2005), where there are no upper bounds on money holdings or money holdings are perfectly divisible, or those described in Hofbauer et al (2008), Oechssler and Riedel (2002), Sandholm (2001), van Veelen and Spreij (2009), where infinite strategy sets matter.…”