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An Axiomatic Analysis of the Effects of Interest Rate on the Inflation and Convergence Speed in Achiving to Equilibrium in a Banach Space


  • Askari, Seyed Ehsan

    () (Ph.D. Student in Economics, University of Payam Noor)

  • Pourkazemi, Mohammad Hossein

    () (Associate Professor of Mathematics, University of Shahid Beheshti)

  • Biabani, Jahangir

    () (Assistant Professor of Economics, Payam Noor University of Tehran)

  • Dallali Isfahani, Rahim

    () (Professor of Economics, University of Isfahan)


This paper provides an axiomatic analysis of the formation of equilibrium in a macro economic structure. For this purpose, primarily it is accorded to mathematical features of the prices space assume that these spaces are normed complete spaces or a “Banach spaces”. Then it is showed that the conventional macroeconomic production function is a contraction mapping, and it is proved that there exists a fixed point for the basic neoclassical macroeconomic model in a Banach space. By using a quantity theory of money framework and introducing interest rates, it is showed the formation of inflation in the macroeconomic environment. In the next step we use real analysis and numerical analysis to explain the convergence speed of macroeconomic production function in the context of barter economy, monetary economy without money interest rate, and monetary economy with money interest rate. In this space, the existing money interest rate would necessarily lead to inflation, and inflation would retard the convergence speed.

Suggested Citation

  • Askari, Seyed Ehsan & Pourkazemi, Mohammad Hossein & Biabani, Jahangir & Dallali Isfahani, Rahim, 2016. "An Axiomatic Analysis of the Effects of Interest Rate on the Inflation and Convergence Speed in Achiving to Equilibrium in a Banach Space," Quarterly Journal of Applied Theories of Economics, Faculty of Economics, Management and Business, University of Tabriz, vol. 3(1), pages 115-138, June.
  • Handle: RePEc:ris:qjatoe:0037

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    Interest rate; Inflation; Banach Space; Convergence speed; Existence of equilibrium;

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers


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