Lorenz Curve & Gini Coefficient — Progressive vs Flat Tax Simulator

Population

Population size 300

Income inequality (σ) 0.9

Top 1% wealth multiplier 4×

Tax structure

Rate — poorest 5%

Rate — richest 45%

Rate curve steepness 1.5

Progressive: tax rate rises with income; revenue is paid back to everyone as an equal flat benefit.

Gini coefficient

Pre-tax Gini

–

Post-tax Gini

–

Tax collected

–

Flat benefit / person

–

How it works

The Lorenz curve plots the cumulative share of total income earned by the poorest X% of the population. Perfect equality is the 45° diagonal; a real population's curve always bows below it. The Gini coefficient is twice the area between the diagonal and the curve — 0 is perfect equality, 1 is one person holding everything.

Each agent's tax rate is set by their income rank: rate = rateLow + (rateHigh − rateLow) · rank^steepness. Progressive taxation (low rate for the poor, high rate for the rich) collects revenue and pays it back as an equal flat benefit to everyone — this pulls the post-tax Lorenz curve toward the diagonal and lowers the Gini. Flip the sliders to flat or regressive rates and the same redistribution barely moves the curve, or can even leave inequality unchanged.

Lower income Higher income

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