Each glowing bar is one household, sorted left→right by pre-tax income (a stylised Pareto-shaped distribution). The green segment is after-tax income; the red cap on top is the tax bite. Under flat tax every household pays the same rate. Under progressive tax, the effective rate rises with income according to the progressivity slider — a bracket-like schedule rather than one flat percentage.
The glowing ribbon at the back is the Laffer curve: it plots aggregate revenue against the tax rate, assuming taxable income shrinks as the rate rises because higher rates discourage work and reporting (the labor-supply response). The marker on the ribbon tracks your current rate; the curve peaks at t* = 1 / (1 + elasticity) — pushing the rate past that point *reduces* revenue even though each remaining dollar is taxed harder.
Y(t) = Y₀ · (1 − t)^e taxable income shrinks with rate t, elasticity e
Rev(t) = t · Y(t) tax revenue
t* = 1 / (1 + e) revenue-maximizing rate
DWL(t) ≈ ½ · e · t² · Y₀ Harberger triangle (deadweight loss)
- Tax rate — the flat rate, or the base rate that the progressive schedule scales around.
- Progressivity — 0 makes progressive behave like flat; higher values steepen how much faster the rate climbs for high earners.
- Labor-supply elasticity — how strongly people cut reported/taxable income as the rate rises. Higher elasticity pulls the Laffer peak toward a lower rate and inflates the deadweight-loss triangle shown floating beside the ribbon.
Real-world relevance: this is the standard optimal-taxation trade-off — a higher rate raises more per taxed dollar but shrinks the taxed base, and the two effects can offset each other entirely once you cross the Laffer peak.