Optimal public money

In most countries, the supply of paper money is controlled by a state institution. This paper provides an explanation for why such an arrangement is typically chosen. I use a deterministic matching model with a continuum of agents where enforcement is limited and where some agents produce public goods. Agents can also, at a cost, produce a distinguishable, intrinsically useless but perfectly durable good: notes. I call a note public if it is printed by an agent who produces public goods. In this framework, I prove that the socially optimal allocation is only implemented by a pattern of trade in which exchanges are effected using public notes.