  The excessive compensation packages of CEOs of U.S. corporations in recent
years have brought to the foreground the issue of fairness in economics. The
conventional wisdom is that the free market for labor, which determines the pay
packages, cares only about efficiency and not fairness. We present an
alternative theory that shows that an ideal free market environment also
promotes fairness, as an emergent property resulting from the self-organizing
market dynamics. Even though an individual employee may care only about his or
her salary and no one else's, the collective actions of all the employees,
combined with the profit maximizing actions of all the companies, in a free
market environment under budgetary constraints, lead towards a more fair
allocation of wages, guided by Adam Smith's invisible hand of
self-organization. By exploring deep connections with statistical
thermodynamics, we show that entropy is the appropriate measure of fairness in
a free market environment which is maximized at equilibrium to yield the
lognormal distribution of salaries as the fairest inequality of pay in an
organization under ideal conditions.
