We study a random matching model of money in which a subset of people, called bankers, have known histories and the rest, called nonbankers, have unknown histories. Earlier, we showed that if there are no outside assets, then an optimal arrangement has bankers issuing objects, banknotes, that are used in trades involving nonbankers. Here, the same model is used to compare such exclusive use of inside money to the exclusive use of outside money. We show that the set of implementable outcomes using outside money is a strict subset of the set using inside money.
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