A Leviathan central bank: Modeling seigniorage in a money search model

This paper studies the nature of optimal monetary policy under a utility-maximizing monetary authority in a micro-founded model of money based on Lagos and Wright (2005). Such a monetary authority represents a monopoly private money supplier or situations where fiscal policy drives monetary policy and hence the name Leviathan. Under no commitment, I characterize an equilibrium with reputation concerns. The centralized market interaction is modeled as an infinitely repeated game between the Leviathan monetary authority (a large player) and the economic agents (small players), where the size of the players refers to the ability to influence aggregate outcomes. This large–small player dynamics pins down the equilibrium set of payoffs. Under the assumption that agents do not refuse to use money purely for coordination reasons, the one shot game has a unique Nash equilibrium with maximum inflation tax. The set of equilibria is considerably enlarged in the infinite repetition of the game and equilibria with a lower inflation tax can also be supported by providing appropriate incentives to the money supplier.