Public and Private Money: Inflation Dynamics and Optimal Policy

Daniel Sanches

No 26-50, Working Papers from Federal Reserve Bank of Philadelphia

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.

Keywords: Private money; public money; inflation dynamics; collateral constraints; banking cycles; Friedman rule; optimal monetary policy (search for similar items in EconPapers)
JEL-codes: C62 E31 E42 E51 E52 (search for similar items in EconPapers)
Pages: 56
Date: 2026-11-02
New Economics Papers: this item is included in nep-fdg and nep-mon
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DOI: 10.21799/frbp.wp.2026.50

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