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

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.