The existing literature that primarily bases the evaluation of income distribution on the theory of social welfare function tends to place emphasison the equalization of distribution. Considering different income distributions as different social states, theories in welfare economics, such as thetheory of fairness, may provide other criteria for evaluating distributions.This paper proposes to define fair income distribution in terms of fairnessin the resulting commodity distribution, assuming the individual or household comsumption bundle is chosen optimally. Therefore, the theorem thatproves unequal value endowments can induce fair commodity distributionat the equilibrium suggests the fair income distribution could be unequal,which makes it possible to take departure from the existing literaturesince unequal distribution could be favored by fairness criterion. Baumol'sstudy (1982), the only empirical application of fairness theory until now,provides the heoretical reference for this paper in applying the theory todemonstrate that preference difference can cause the result of fair andunequal income distribution.