Stationarity without degeneracy in a model of commodity money

We develop a model of macroeconomic heterogeneity inspired by the Kiyotaki–Wright (J Polit Econ 97:924–954, 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.