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