Third Order Fokker Planck Equation to Model Income Distribution in the US

This paper investigates income dynamics through the lens of econophysics, employing a model designed for a weakly open economy. The model features agents engaging in random interactions involving money exchange, which undergo Brownian motion with noise derived from a first-order Edgeworth expansion. A third-order Fokker-Planck equation is formulated to describe the random money exchange process. By simulating the solution to the Fokker-Planck equation, a three-parameter stationary solution is obtained, expressed in terms of income distribution. Subsequently, this stationary income distribution is compared to various models and validated against US annual household income distribution data across multiple years, demonstrating significant alignment. Furthermore, an equation for the income average is numerically derived based on the three parameters. It is observed that the income average of the US economy exhibits a monotonically increasing trend for the parameters, except for the money agents receive in terms of income per intervention "rc", where it displays a minimum and is bounded from the left. This phenomenon is interpreted as a trapping state detrimental to the country's unbounded economic growth.