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Public and Private Money: Inflation Dynamics and Optimal Policy

Author

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  • Daniel R. Sanches

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.

Suggested Citation

  • Daniel R. Sanches, 2026. "Public and Private Money: Inflation Dynamics and Optimal Policy," Working Papers 26-50, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:104010
    DOI: 10.21799/frbp.wp.2026.50
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    JEL classification:

    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Systems; Standards; Regimes; Government and the Monetary System
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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