Study On Statistical Dynamics Of Income Distribution

Income distribution is the main reason for changes in social stability.Study on income distribution is a long-term focus of economics and sociology.It can provide theoretical references for the formulation of policies and the distribution of wages and benefits.By using the stochastic dynamic equation and master equation to describe the complex process of income distribution,we can try to quantitatively understand the potential universality and dynamic mechanism of income distribution.The main contents are as follows:Regarding individual as particle with random behavior characteristics,a stochastic dynamic equation of income distribution is established.The Langevin equation expressing the random diffusion of particles in an unstable potential field is used to describe the income changes of individuals in an unstable group or social system.The equation is transformed into Fokker Planck equation and solved by Fourier integral transform.The theoretical results describe that the dependence of income distribution on time�the distribution curve from exponential distribution to uniform Gaussian.These results revealed that the certainty and randomness of the market economy jointly determine the combination structure of weak spike and peaks in income distribution.It indicates decision-making-mindlessly in the face of shocks,and polarization in short-term income distribution.But in the long run,this decision-making-mindlessly must to be replaced by the time fair competition system,and a stable Gaussian distribution will be re-established.In addition,adjusting the intensity factor of the instability external field,it is found that the peak of the income distribution curve shows two situations:decreased firstly and then increased.This result demonstrates indicating that the instability of the market economy has a significant impact on income distribution.How to face up to the risk of economic behavior is an important proposition.The transition of income state is randomness.Therefore,the master equation,the idea of statistical physics,is to describe the state transition process.The transition probability equation describes the dynamic process of income distribution caused by the change of labor cost.It investigates the transfer of income distribution caused by the labor cost of heterogeneous workers.By using the Taylor series expansion of the differential operator,it is transformed into the Fokker-Planck equation of continuous labor cost transformation.The laws of the fluctuation are obtained by the time-dependent solution.The theoretical results show that the difficulty coefficient of labor cost transformation induced to the nonlinear amplification of the uncertainty and random fluctuation of income distribution.The steady distribution structure of income distribution is determined by the change rate factor of increasing/decreasing labor cost.When the increasing conversion rate factor is higher than the decreasing one,the average return decreases with the increase of the decreased one.On the contrary,the return deviates from the tail of the exponential distribution,which provides a useful reference for the macrocontrol of the labor market.