Mathematics in Economic Inequality Jong Ho Chong Economic Inequality Large Contrast in the Distribution of Personal Income within a Social Group The gap itself is not a problem the problem is that it is widening 21% increase of Income Growth from the Low 20% 28% increase of Income Growth from the Median Income Households 62% increase of Income Growth from the High 20% Pareto’s Law 80-20 Rule Business, Software, Economics 20% of Italians owned the 80% of the lands MATH behind Pareto’s Law Nx = Ax-α Nx = Number of Population that gets an higher or same income than x X = A certain income chosen A = A certain value of a country that is measured statistically α = Pareto’s degree of inequality The measurement of inequality The measurement measured by the formula MATH behind Pareto’s Law log Nx = log A – αlog x With the logarithmic axis with log Nx being the Y-axis and log x being the X-axis…. Jnj α becomes the angle of curve as it is the gradient of log x MATH behind Pareto’s Law Coming Back to the formula log Nx = log A – αlog x Take derivative for x Aαx-(α+1) Multiply x both sides Aαx –α Take integral for the formula above Divide by N0 = M0 MATH behind Pareto’s Law To relate to the M0, Ratio will be calculated Nx : N0 Summing up the Rest 1 = (1-y) Mx : Mo Y = sum of the rest of the income Disproving the MATH Mathematical Error Different Aspects on Inequality Mathematical Error Angle of the CURVE?? The Degree of Inequality was classified to be an angle…. Different Inequalities α should get smaller for equality Nope! α should get higher for equality Vilfredo Pareto Corrado Gini & Max O. Lorenz Different Inequalities Vilfredo Pareto Corrado Gini & Max O. Lorenz Focused on Population Focused on Income There should be less difference of population between the rich and poor to be equal. There should be less difference of income between the rich and poor to be equal. So… α should get smaller So… α should get higher