Income Inequality Simulator
Boltzmann-Pareto exchange model — random wealth transfers between agents naturally produce extreme inequality
Gini: —
Top 1%: —
Top 10%: —
Median: —
Steps: 0
Boltzmann-Pareto exchange model — random wealth transfers between agents naturally produce extreme inequality
In the Boltzmann wealth model, N agents each start with equal wealth. At every step two random agents are chosen: agent A gives agent B a fraction of their smaller wealth. This simple rule — identical to collisions in statistical physics — spontaneously produces a Pareto (power-law) tail: a few agents accumulate most of the wealth while the majority has little.
The Gini coefficient (0 = perfect equality, 1 = one person owns everything) measures inequality. At 0% tax the Gini converges to ~0.5 with free exchange and can reach >0.8 with larger fractions. Adding a flat tax + universal redistribution reduces Gini by continuously transferring wealth from rich to all agents equally.
The left canvas shows agents as dots coloured by percentile (red = poorest, green = richest). The right panel shows the rank-wealth curve on a log scale — a straight line indicates a Pareto distribution (the real-world pattern for most countries).