Existence of monetary steady states in a matching model of money

Existence of a monetary steady state is established for a random matching model with divisible goods, general individual money holdings, and take-it-or-leave-it offers by consumers. For indivisible money, the only assumption is a lower bound on the marginal utility of consumption at zero. For divisible money, there are two additional assumptions: the marginal utility of consumption at zero is bounded above and there is a finite bound on individual money holdings. In each case, the monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is increasing and strictly concave, and the measure over money holdings has full support.