A Mathematical Analysis for the Effects of Monetary Interest Rate on the Personal Income Distribution in a Macroeconomic Structure

This article provides a mathematical analysis of the formation of the long-run personal distribution income based on factor distribution in a macroeconomic structure. For this purpose, primarily with extraction, the relative factor’s share of national income in conventional macroeconomic production function showed that The factor's shares depend only on the parameter (α), not on the amounts of capital or labor or on the state of technology as measured by the parameter A. Then, in order to extraction, the Lorenz curve organized the parameters of population and economic income recipients based on the relative share of wage earners, stock returns and money interest. In the next step, using techniques of numerical analysis (Lagrange form of the interpolation polynomial), Lorenz curve equation derived based on the cardinal functions. Then we explain the integral Gini coefficient in terms of the Lorenz curve. Then we prove in a monetary system interest-based, the Gini coefficient automatically converges to one, in this condition the distribution of income get worse for wage earners and shareholders.  The results of this research are that interest-based monetary system has a negative effect on the personal income distribution.