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The question about fair income inequality has been an important open questionin economics and in political philosophy for over two centuries with onlyqualitative 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 inequalityis a lognormal distribution of income at equilibrium. In this paper, we developanother approach, using the Nash Bargaining Solution (NBS) framework, whichalso leads to the same conclusion. Even though the conclusion is the same, thenew approach, however, reveals the true nature of NBS, which has been ofconsiderable interest for several decades. Economists have wondered about theeconomic meaning or purpose of the NBS. While some have alluded to its fairnessproperty, we show more conclusively that it is all about fairness. Since theessence of entropy is also fairness, we see an interesting connection betweenthe Nash product and entropy for a large population of rational economicagents.

How much income inequality is fair? Nash bargaining solution and its connection to entropy