In this paper we investigate a general equilibrium mathematical model of an economy that contains a type of private sector money alongside legal tender.  The private sector money, trade dollars, is only accepted by members of the organisation known as Bartercard.  Firms weigh the benefit of increased sales against the disadvantage of earning a less useful currency to decide whether to join.  We find that at all stable membership equilibria, the presence of Bartercard has no real effect on the economy.  If further constraints are added to induce an interior equilibrium, this is inefficient.