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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

Seyed Ehsan Askari (), Mohammad Hossein Pourkazemi (), Jahangir Biabani () and Rahim Dallali Isfahani ()
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Seyed Ehsan Askari: Ph.D. Student in Economics, University of Payam Noor
Mohammad Hossein Pourkazemi: Associate Professor of Mathematics, University of Shahid Beheshti
Jahangir Biabani: Assistant Professor of Economics, Payam Noor University of Tehran
Rahim Dallali Isfahani: Professor of Economics, University of Isfahan

Quarterly Journal of Applied Theories of Economics, 2016, vol. 3, issue 1, 115-138

Abstract: 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.

Keywords: Interest rate; Inflation; Banach Space; Convergence speed; Existence of equilibrium (search for similar items in EconPapers)
JEL-codes: E31 E43 E51 (search for similar items in EconPapers)
Date: 2016
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