THREE APPLICATIONS OF RANDOM MATCHING MODELS OF MONEY

Chapter 1: Previous work on the denomination structure of currency treats as exogenous the distribution of transactions and the denominations held by people. Here, by way of a matching model, both are endogenous. In the model, trades in pairwise meetings alternate in time with the opportunity to freely choose aportfolio of denominations and people trade off the benefits of small-denomination money for transacting against the costliness ofcarrying a large quantity of small-denomination money. For a given denomination structure, a monetary steady state is shown to exist.The model implies that too small denominations are abandoned.Chapter 2: There is wide agreement that currency was not available in conveniently small denominations prior to the 19th century.Parameterized versions of a matching model of money are used to provide estimates of the benefit for trade of additionaldivisibility. That benefit is balanced against the cost of providing additional divisibility, the cost as inferred from historical reports, to find the implied optimal degree of divisibility. Although the optima are sensitive to thespecification of the matching model, all display a degree of divisibility that is much lower than what we see in modern economies.Chapter 3: Previous studies that compare a uniform money with separate monies used models in which money is the only asset and in which individuals hold either zero or one unit of money. Here, the comparison is made using a model in which money coexists with a higher-return asset and in which individuals are permitted to hold richer portfolios of assets. The results show that a general conclusion is not possible. A uniform money has a higher expected utility than do separate monies in many examples. However, when the discount on bonds and uncertainty about the nationality of thetrading partner are sufficiently high, then there are examples in which separate monies are better.