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On steady-state money distributions and monetary policy: Smoothness in a matching model

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  • Bertolai, Jefferson D.P.
  • Machado, Nathan T.

Abstract

We study smoothness properties of non-degenerate, steady-state money distributions in a matching model with indivisible money and bounded individual holdings. In particular, we demonstrate that money creation – via the monetary policy studied in Deviatov and Wallace (2001) – drives steady-state money distributions in a continuous (and differentiable) fashion.

Suggested Citation

  • Bertolai, Jefferson D.P. & Machado, Nathan T., 2026. "On steady-state money distributions and monetary policy: Smoothness in a matching model," Journal of Mathematical Economics, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:mateco:v:122:y:2026:i:c:s0304406825001090
    DOI: 10.1016/j.jmateco.2025.103192
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    References listed on IDEAS

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    1. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
    2. Deviatov Alexei, 2006. "Money Creation in a Random Matching Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(3), pages 1-20, December.
    3. Shi Shougong, 1995. "Money and Prices: A Model of Search and Bargaining," Journal of Economic Theory, Elsevier, vol. 67(2), pages 467-496, December.
    4. Miguel Molico, 2006. "The Distribution Of Money And Prices In Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 701-722, August.
    5. Ricardo de O. Cavalcanti & Andres Erosa & Ted Temzelides, 1999. "Private Money and Reserve Management in a Random-Matching Model," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 929-945, October.
    6. Ricardo de O. Cavalcanti & Neil Wallace, 1999. "Inside and outside money as alternative media of exchange," Proceedings, Federal Reserve Bank of Cleveland, pages 443-468.
    7. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    8. Deviatov Alexei & Wallace Neil, 2001. "Another Example in which Lump-sum Money Creation is Beneficial," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-22, February.
    9. Trejos, Alberto & Wright, Randall, 1995. "Search, Bargaining, Money, and Prices," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 118-141, February.
    10. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    11. Alexei Deviatov & Neil Wallace, 2014. "Optimal inflation in a model of inside money," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 287-293, April.
    12. Kiyotaki, Nobuhiro & Wright, Randall, 1991. "A contribution to the pure theory of money," Journal of Economic Theory, Elsevier, vol. 53(2), pages 215-235, April.
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