Inside-outside money competition
We study how competition from privately supplied currency substitutes affects monetary equilibria. Whenever currency is inefficiently provided, inside money competition plays a disciplinary role by providing an upper bound on equilibrium inflation rates. Furthermore, if "inside monies" can be produced at a sufficiently low cost, outside money is driven out of circulation. Whenever a 'benevolent' government can commit to its fiscal policy, sequential monetary policy is efficient and inside money competition plays no role.
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