Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States

We construct a tractable neoclassical growth model that generates Pareto's law of income distribution and Zipf's law of the firm size distribution from idiosyncratic, firm-level productivity shocks. Executives and entrepreneurs invest in risk-free assets, as well as their own firms' risky stocks, through which their wealth and income depend on firm-level shocks. By using the model, we evaluate how changes in tax rates can account for the evolution of top incomes in the United States. The model matches the decline in the Pareto exponent of the income distribution and the trend of the top 1 percent income share in recent decades. (JEL D31, H24, L11)

Income and Wealth Distributions from Stochastic Strategy Minority Game

We propose a version of the Minority Game where the agents at each time make investments either in terms of money or stock from their possessions. The amount of investments at each time step, and not the number of people opting for a choice, determines the ‘minority’. The invested money is returned to the stock investors and the invested stock is returned to the money investors in proportion of their respective investments at each time. In this way, agents in the less investment side faces higher demand, and hence are in ‘minority’, receiving higher pay-off for their investments. This dynamics lead the ‘market’ to a self-organized state. We measure the distributions of income of the agents at every step and also the accumulated wealth, both of which have a stationary distribution. The distribution functions follow Pareto’s law when the agents invest random fractions of their wealth. This reflects the role of heterogeneity in economic interactions.

Fokker–Planck description of wealth dynamics and the origin of Pareto's law

The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B. M. Boghosian, Phys. Rev. E89, 042804 (2014)], it was shown that this results in a Fokker–Planck equation governing the distribution of wealth. With the addition of a mechanism for wealth redistribution, it was further shown that this model results in stationary wealth distributions that are very similar in form to Pareto's well-known law. In this paper, a much simpler derivation of that Fokker–Planck equation is presented.