Working Paper

Public and Private Money: Inflation Dynamics and Optimal Policy

Abstract: The total money supply of a modern economy is a combination of publicly and privately issued monies. This paper develops a theory of inflation dynamics and optimal policy for a system in which public fiat money and collateral-backed private liabilities jointly circulate. Private money finances investment projects, and its supply depends on the issuer’s net worth and collateral constraints. The resulting feedback mechanism can generate persistent oscillations and stable banking cycles without aggregate shocks. For some public money growth rates, a dual-money steady state coexists with a boundary regime in which private money displaces fiat money. Policy affects liquidity and investment. When the collateral constraint is slack, the Friedman rule attains the first best; when it binds, a public money growth rate above the Friedman rule can be optimal. The Ramsey problem considers the transitional dynamics in the net worth of banks.

JEL Classification: E42; E51; E52; E31; C62;

https://doi.org/10.21799/frbp.wp.2026.50

Bibliographic Information

Provider: Federal Reserve Bank of Philadelphia

Part of Series: Working Papers

Publication Date: 2026-11-02

Number: 26-50