  The question about fair income inequality has been an important open question
in economics and in political philosophy for over two centuries with only
qualitative answers such as the ones suggested by Rawls, Nozick, and Dworkin.
We provided a quantitative answer recently, for an ideal free-market society,
by developing a game-theoretic framework that proved that the ideal inequality
is a lognormal distribution of income at equilibrium. In this paper, we develop
another approach, using the Nash Bargaining Solution (NBS) framework, which
also leads to the same conclusion. Even though the conclusion is the same, the
new approach, however, reveals the true nature of NBS, which has been of
considerable interest for several decades. Economists have wondered about the
economic meaning or purpose of the NBS. While some have alluded to its fairness
property, we show more conclusively that it is all about fairness. Since the
essence of entropy is also fairness, we see an interesting connection between
the Nash product and entropy for a large population of rational economic
agents.
