Existence of a monetary steady state in a matching model: indivisible money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the measure over money holdings has full support.