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We develop a dual currency search model where agents can hold currency portfolios to buy goods, and analyze an agent's choice to spend safe dollars or risky home currency for internal trade. We focus on two equilibria: a currency competition equilibrium, in which the 'good' currency (dollars) is spent first and the 'bad' (risky home) currency is kept for later purchases, and a Gresham's Law equilibrium in which agents do the reverse. We prove that for the Gresham's Law equilibrium to prevail, trading frictions and the home currency risk must be small. Otherwise, extensive currency substitution occurs and the currency competition equilibrium prevails. Interestingly, because transaction velocity is endogenous, we demonstrate that as the home currency risk rises, currency substitution causes a decline in the transaction velocity of the bad currency while increasing it for the good currency.


money, currency substitution

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