This paper investigates the existence and properties of stationary single-price equilibrium in a monetary random matching model where agents can hold an arbitrary amount of divisible money, and where production is costly. For some parameter values of the model, there exists a continuum of single-price equilibria indexed by the aggregate real-money balance. At such an equilibrium, an agent accumulates money only up to a certain point where his marginal value of holding money drops below the cost of production. Different upper bounds on money holdings imply different distributions of money holdings. The coexistence of multiple equilibria with distinct upper bounds but identical aggregate real-money balances suggests the importance of money distribution in determining trade velocity, production and welfare.