Theoretical Research Of Law Of Society’s Income Distribution

This paper attempts to investigate the universe rule of social income distributionwithin the framework of Arrow-Debreu’s general equilibrium theory. Specifically, along-run competitive economy will generate a large number of competitive equilibria,each of which corresponds to a possible income allocation. And each income allocationis Pareto efficient. Then according to Arrow’s Impossibility Theorem, social memberscould not choose the best income allocation from a point of view which is individuallyconsistent and social consistent. However, by using the method of “statisticalequilibrium” in statistical physics, we can find an income distribution which willcontain the most income allocations. Our studies show that the income distribution ofperfectly competitive economy obeys Bose-Einstein distribution, and that the incomedistribution of purely monopolistic-competitive economy obeys the rule of exponentialfunction. As is well known, the Bose-Einstein distribution is unstable, so is the perfectlycompetitive economy. In fact, perfectly competitive economy is an extreme andexcessive competition; thus, the instability of Bose-Einstein distribution seems toexplain why some overheated economy might induce economic crises. However, theperfect competition is an unduly extreme case, so we may almost ignore it in the realworld. In general, our studies imply that for a fairly competitive economy, the socialincome distribution will obey the rule of exponential function. Later, we extend thetheoretical framework of the independent economy so as to include the case of multipleeconomies. Then we find that the income distributions of perfectly competitiveeconomies will obey a special Bose-Einstein distribution which is subject to a constraintabout industries.Moreover, we also investigate that the rule of income distribution ofnon-equilibrium economy. Our study shows that if the non-equilibrium economy relieson rule of “The rich get richer”, the social income distribution will obey the rule ofpower function. Since the real society could not in general be absolutely fair, our studiesimply that the real income distribution should consist of two distinct parts: one partobeys the rule of exponential function, and the other obeys the rule of power function.Indeed, such a conclusion has been supported by the recent empirical investigations; forexample, in1997, the American society’s about3%of the population obey the rule ofpower function, and97%obey the rule of exponential function. On the other hand, the theorem of economic core tells us that if an economy is atgeneral equilibria, then it is in the economic core so that there will no be any smallgroup who disagree with the current income allocation. As a result, the society will bestable. Because of this, we can identify the maximal value of the Gini coefficient of theexponential distribution with the alertness line level, since the exponential distributionis a result of general equilibria. According to our calculation, the alertness line levelshould be0.5rather than0.4which is regarded as the international alertness line level asa conjecture.The innovations of this paper are exhibited by the following three points:1. The theoretical research of Arrow-Debreu’s general equilibrium model will beextended. Up to now, many economists only pay attention to the existence of generalequilibrium under different assumptions. Our study will extend the framework ofgeneral equilibrium so that the equilibrium income distribution can be obtained.2. The methods of statistical physics will be applied into economics. When acompetitive economy arrives at long-run equilibria, there will be many equilibriumincome allocations. Then we can use the method of statistical physics to obtain theequilibrium income distribution which will obtain the most equilibrium incomeallocations.3. Our research may have significant meanings in guiding practice. We haveobtained the equilibrium income distribution. If we note that the equilibrium incomedistribution will be in the core of the competitive economy, then we understand that thesociety will be stable when the equilibrium income distribution arises. As such, themaximum value of the Gini coefficient of the equilibrium income distribution can beregarded as the alertness line level.