Economic Arbitrage and the Econophysics of Income Inequality

Yakovenko and his co-authors have established that the bottom 97– 99% of individual incomes (labor incomes) follow a near-exponential distribution while the top incomes (property incomes) follow a power law. Initial explanations of these patterns relied on various monetary analogues to the physics principle of energy conservation. Subsequent approaches turned to the stochastic dynamics of economic processes, including those of labor and property income modeled as a drift-diffusion processes. Our paper is in the latter tradition, but our specifications of drift-diffusions are derived from the fundamental economic principle of turbulent arbitrage modeled as a mean-reverting process. This approach is well developed in the domain of interest rate arbitrage as in the case of CIR models. Our contribution is to demonstrate that arbitrage can also explain the observed distributions of wages, rates of return on assets, and property income. In the energy conservation approach, stationary distributions are derived from the assumption of entropy maximization. In both stochastic dynamics approaches, the dynamic paths give rise to stationary distributions that turn out to be entropy maximizing.