Review of Behavioral Economics > Vol 7 > Issue 4

Economic Arbitrage and the Econophysics of Income Inequality

Anwar Shaikh, New School for Social Research, USA, , Juan Esteban Jacobo, Universidad Externado de Colombia, Colombia,,
Suggested Citation
Anwar Shaikh and Juan Esteban Jacobo (2020), "Economic Arbitrage and the Econophysics of Income Inequality", Review of Behavioral Economics: Vol. 7: No. 4, pp 299-315.

Publication Date: 10 Dec 2020
© 2020 A. Shaikh and J. E. Jacobo
Economic theory
JEL Codes: B12C10C18D31D33
Economicsarbitrageeconophysicsincome distributionentropy maximizationFokker–Planck equations


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In this article:
1. Introduction 
2. Maximum Entropy Approaches 
3. A Kinetic Approach to the Dynamics of Income Distribution 
4. An Arbitrage Approach to Income Distribution 
5. Other Economic Approaches to Income Distribution 
6. Summary and Conclusions 


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.