社会收入分布规律的理论探究
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摘要
本文尝试在Arrow-Debreu一般均衡模型的框架内，研究经济处于均衡时社会收入分布的一般性规律。具体而言，长期竞争经济一般会产生大量的竞争均衡，而每一个竞争均衡对应一种可能的社会收入分配方式，并且每一种分配方式都是Pareto有效的。这时，根据社会选择理论中的Arrow不可能定理，社会成员不可能一致选出一个最好的收入分配方式。但是本研究利用统计物理学中的“最大概率原理”方法可以求出一种“以最大概率出现”的“均衡收入分布”，它可以包容尽可能多的收入分配方式。具体研究表明，在异质代理人竞争的情形下，自由经济的“最大概率收入分布”将服从指数函数分布；而在同质代理人竞争的情形下，自由经济的“最大概率收入分布”将服从Bose-Einstein函数型分布。众所周知，Bose-Einstein函数是不稳定的，因此同质竞争市场可能会失稳；事实上，同质竞争是一种非常极端甚至是过度的竞争，这似乎可以解释为什么一些过热的市场可能会导致经济失稳。不过，考虑到同质竞争是一种极端罕见的情形，在现实中一般是可以被忽略的；因此，总的来看，本研究认为：公平、自由的竞争经济在均衡时其社会收入分布会服从指数函数分布。稍后，进一步的研究发现，对于多个经济系统共存的情形，各个经济系统的最大概率收入分布在异质竞争时仍旧服从指数型函数，并且在同质竞争时仍旧服从Bose-Einstein函数型分布，只不过各个经济系统的行业数目必须满足一定的约束条件。
此外，本文也研究了当经济处于非均衡状态下的收入分布规律。具体研究显示：如果经济处于非均衡状态并且其运行机制依赖于非公平竞争的“富者愈富”法则，那么其社会收入分布将服从幂函数分布规律。显然，真实社会一般是不可能处于绝对公平的竞争状态，因此本研究推断：真实社会的收入分布应该由两部分组成，其中一部分服从指数型函数分布，而另一部分服从幂函数分布。这一推断已经被国外的最新实证研究所证实，以1997年的美国社会为例，其总人口中大约有3%的部分服从幂函数分布，大约有97%的部分服从指数函数分布。
在另一方面，经济核定理认为若经济是处于一般均衡状态的，那么这个经济将处于经济核中，并且因而是“经济核意义上”稳定的，这样就不存在任何的小集团会不满意现有的均衡收入分配，从而破坏经济的稳定。考虑到一般均衡下的社会收入分布必定处于稳定的经济核中，因此本研究推断：指数函数型收入分布必定处于经济核中。考虑到指数函数型收入分布的最大基尼系数为0.5，因此本研究建议将0.5作为基尼系数的警戒值，这比国际上的经验值0.4要大。尽管这样，本研究关于基尼系数警戒值的计算却是基于标准的Arrow-Debreu一般均衡模型，而国际上的经验值0.4还没有严格的经济理论作为支撑。因此本研究的一大特色是给出了一个基于标准的主流经济理论框架下的基尼系数警戒值。
总的来说，本文主要有以下3点创新：
1.推导出当竞争社会处于“理想的一般均衡状态下”的收入分布规律，从而为Arrow-Debreu一般均衡模型联系实际经济对象提供了一个新的视角。一般来说，理论经济学界在多数情况下只是对一般均衡的存在性证明感兴趣，很多理论经济学者偏好在不同的条件下来证明一般均衡的存在性，更有心者会比较各个均衡之间的效率，但是如果均衡达到Pareto有效，研究的目的就结束了。而本研究的创新是开拓出一般均衡解背后更深一层的含义。准确的说是，长期一般均衡本质上给出了各种可能的Pareto有效的收入分配。将这些收入分配进行分类后可以进一步求出最有可能出现的收入分布，也即“最大概率收入分布”。
2.将统计物理学中的“最大概率原理”方法运用到新古典经济学的研究中，这对于促进不同学科之间的交叉有一定的意义。在将所有的均衡收入分配方式进行分类后，为了求出最有可能出现的收入分布，需要利用统计物理学中的“最大概率原理”方法。该方法在研究自然界的大量分子所导致的宏观行为时非常的成功。同样，一般均衡理论本质上给出了经济系统中各个代理人的具体微观行为，但是要从这所有可能的微观行为出发得到宏观行为，统计物理学中的“最大概率原理”方法是一种可能的途径。
3.在Arrow-Debreu一般均衡模型的标准分析框架内导出基尼系数的警戒值可能为0.5，这为确定基尼系数的警戒值提供了一个较为新颖的理论观点。由于本研究的目的是求出一般均衡时社会的收入分布规律，按照经济核理论，此时的收入分布可以保障经济社会是处于经济核中，从而是“经济核意义上”稳定的。而从这个收入分布求出其基尼系数的最大值（上限）具有重要的意义和参考价值。因为它可以用于比较一个真实的收入分布是否可能处于稳定的经济核中，而这个最大值正为0.5。
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.
此外，本文也研究了当经济处于非均衡状态下的收入分布规律。具体研究显示：如果经济处于非均衡状态并且其运行机制依赖于非公平竞争的“富者愈富”法则，那么其社会收入分布将服从幂函数分布规律。显然，真实社会一般是不可能处于绝对公平的竞争状态，因此本研究推断：真实社会的收入分布应该由两部分组成，其中一部分服从指数型函数分布，而另一部分服从幂函数分布。这一推断已经被国外的最新实证研究所证实，以1997年的美国社会为例，其总人口中大约有3%的部分服从幂函数分布，大约有97%的部分服从指数函数分布。
在另一方面，经济核定理认为若经济是处于一般均衡状态的，那么这个经济将处于经济核中，并且因而是“经济核意义上”稳定的，这样就不存在任何的小集团会不满意现有的均衡收入分配，从而破坏经济的稳定。考虑到一般均衡下的社会收入分布必定处于稳定的经济核中，因此本研究推断：指数函数型收入分布必定处于经济核中。考虑到指数函数型收入分布的最大基尼系数为0.5，因此本研究建议将0.5作为基尼系数的警戒值，这比国际上的经验值0.4要大。尽管这样，本研究关于基尼系数警戒值的计算却是基于标准的Arrow-Debreu一般均衡模型，而国际上的经验值0.4还没有严格的经济理论作为支撑。因此本研究的一大特色是给出了一个基于标准的主流经济理论框架下的基尼系数警戒值。
总的来说，本文主要有以下3点创新：
1.推导出当竞争社会处于“理想的一般均衡状态下”的收入分布规律，从而为Arrow-Debreu一般均衡模型联系实际经济对象提供了一个新的视角。一般来说，理论经济学界在多数情况下只是对一般均衡的存在性证明感兴趣，很多理论经济学者偏好在不同的条件下来证明一般均衡的存在性，更有心者会比较各个均衡之间的效率，但是如果均衡达到Pareto有效，研究的目的就结束了。而本研究的创新是开拓出一般均衡解背后更深一层的含义。准确的说是，长期一般均衡本质上给出了各种可能的Pareto有效的收入分配。将这些收入分配进行分类后可以进一步求出最有可能出现的收入分布，也即“最大概率收入分布”。
2.将统计物理学中的“最大概率原理”方法运用到新古典经济学的研究中，这对于促进不同学科之间的交叉有一定的意义。在将所有的均衡收入分配方式进行分类后，为了求出最有可能出现的收入分布，需要利用统计物理学中的“最大概率原理”方法。该方法在研究自然界的大量分子所导致的宏观行为时非常的成功。同样，一般均衡理论本质上给出了经济系统中各个代理人的具体微观行为，但是要从这所有可能的微观行为出发得到宏观行为，统计物理学中的“最大概率原理”方法是一种可能的途径。
3.在Arrow-Debreu一般均衡模型的标准分析框架内导出基尼系数的警戒值可能为0.5，这为确定基尼系数的警戒值提供了一个较为新颖的理论观点。由于本研究的目的是求出一般均衡时社会的收入分布规律，按照经济核理论，此时的收入分布可以保障经济社会是处于经济核中，从而是“经济核意义上”稳定的。而从这个收入分布求出其基尼系数的最大值（上限）具有重要的意义和参考价值。因为它可以用于比较一个真实的收入分布是否可能处于稳定的经济核中，而这个最大值正为0.5。
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.
引文
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