The Laffer Curve
Tax revenue as a function of the tax rate, and why the relationship isn't monotonic.
Built and reviewed by Stephen Omukoko Okoth
Mathematical Economist · ex-Morgan Stanley FI · Equilar
Theory
What the model says, and why
At a 0% tax rate, revenue is zero — nothing’s being collected. At a 100% tax rate, revenue is also zero — no one would work or trade. Somewhere in between is a rate that maximizes revenue. That’s the Laffer curve, sketched on a napkin in 1974 by economist Arthur Laffer for Dick Cheney and Don Rumsfeld and subsequently used to argue for tax cuts under Reagan.
The intuition is uncontroversial. The shape and the location of the peak are heavily contested. A simple parametric form:
B₀ is the tax base at zero rates; e is the elasticity of the base with respect to (1 − t). Higher elasticity means the base shrinks faster as rates rise — so the revenue peak occurs at a lower rate.
Solving dR/dt = 0:
With e = 1 (a common reference value), t* = 50%. With e = 0.25 (low elasticity), t* = 80% — the system can tax heavily without much avoidance. With e = 4 (high elasticity), t* = 20% — even modest rates cause significant base erosion.
Why this matters. The actual revenue-maximizing rate depends on what behaviors the tax changes — labor supply, evasion, capital flight, formality. Empirical estimates of the income-tax revenue-maximizing rate cluster around 60-70% for high earners in the US (Diamond & Saez 2011), which is higher than where many countries actually operate.
Where it’s misused. Politically the Laffer curve is often invoked to argue that tax cuts “pay for themselves.” They almost never do, except in narrow cases where the existing rate is genuinely above the peak. For most everyday rate changes, base shrinkage doesn’t fully offset the rate cut.
Interactive playground
Move the parameters, watch the equilibrium move
Parameters
Base & elasticity
Result
Peak at t* = 50.0%
Revenue-maximizing rate (t*)
50.0%
Maximum revenue (R*)
25.00
In the classroom
How to teach it well
The point isn’t the peak. The point is that at some rate, the curve does turn. That’s the deep idea: tax revenue is bounded, and trying to extract more by raising rates can backfire. Whether any given economy is to the left or right of the peak is an empirical question — slider-driven theory can’t answer it.
Calibrate students’ expectations. Empirical estimates of the income-tax peak hover around 60-70% for high earners in advanced economies. For VAT and corporate taxes, peaks are different and generally lower because of avoidance/evasion margins. The takeaway: most countries operate well to the left of the peak, so a rate increase usually does raise revenue, even if not as much as static analysis suggests.
Common political abuse. The Laffer argument was used to justify the 1981 Reagan tax cuts and many since. The empirical result: revenue did not rise; deficits widened. Worth showing students because the curve is often weaponized in policy debates without acknowledging that real economies are usually nowhere near the peak.
African application. Where the formal tax base is narrow and informality is high, base elasticity tends to be high — meaning the peak is at a relatively low rate. This is partly why African countries can struggle to raise tax-to-GDP much above 15-20%, even with rate increases. Connect to public finance and the African Macro 101 module on fiscal sustainability.