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How Much Inequality Is Fair?Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society$
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Venkat Venkatasubramanian

Print publication date: 2017

Print ISBN-13: 9780231180726

Published to Columbia Scholarship Online: January 2019

DOI: 10.7312/columbia/9780231180726.001.0001

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Fairness in Income Distribution

Fairness in Income Distribution

(p.79) Chapter Five Fairness in Income Distribution
How Much Inequality Is Fair?

Venkat Venkatasubramanian

Columbia University Press

In this chapter, we develop the complete mathematical formalism for π‎-class societies at equilibrium. We prove that the fairest income inequality is lognormal, attained at equilibrium, in an ideal free market society. We also prove that it is unique, stable, social optimal, and moral. We prove that for a 2-class society, the equilibrium distributions are two non-overlapping lognormals, which can be easily mistaken for a lognormal-Pareto pair in practice.

Keywords:   Statistical teleodynamics, multiplicity, lognormal distribution, desert, replicator dynamics, stability, social optimality

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