Foundationspublic finance
The Laffer Curve: Tax Rates and Revenue
Overview
Draw tax rates on one axis, revenue on the other: at 0% and 100%, revenue is zero — so revenue peaks somewhere between. That's the Laffer curve (1974, famously sketched on a napkin). It's a genuine insight wrapped in political mythology. This lesson explains the logic, what determines the peak, the empirical estimates, how politicians abuse it, and the honest way to use it.
Learning objectives
- State the Laffer curve logic
- Explain what determines the revenue-maximizing rate
- Summarize empirical estimates of the peak
- Distinguish the curve from 'tax cuts pay for themselves'
- Apply Laffer reasoning honestly
The logic
At a 0% tax rate, revenue is zero (nothing collected). At 100%, revenue is also ~zero (no one works or reports income if everything is taxed). Between them, revenue rises then falls — the curve is an inverted U, so some rate maximizes revenue. The economics: higher rates raise revenue per dollar of base but shrink the base (less work, more avoidance, emigration, slower growth). The revenue-maximizing rate balances these. Note what the curve doesn't say: that we're past the peak (an empirical question), or that maximizing revenue is desirable (it isn't — the optimal rate is below the peak, trading revenue for welfare).
Revenue is zero at both 0% and 100% rates — so a maximum exists in between. Everything else (where the peak is, whether we're past it) is empirical, not logical.
What determines the peak
The peak depends on the elasticity of taxable income: how much the base shrinks as rates rise. High elasticity (easy avoidance, mobile earners, many loopholes) → low peak. Low elasticity (broad base, few deductions, immobile workers) → high peak. The simple formula: revenue-maximizing rate ≈ 1/(1 + a·e), where a measures income-distribution thinness at the top and e the elasticity. With typical estimates (e ≈ 0.2–0.5), top-rate peaks land around 60–80%. Broaden the base (close loopholes) and the peak rises — base design matters more than the rate. The peak isn't a constant of nature; it's a function of the tax system's plumbing.
τ* = 1/(1 + a·e): with Pareto parameter a ≈ 1.5–2 and elasticity e ≈ 0.25, the revenue-maximizing top rate is ~65–75%. Change the elasticity, change the peak.
The evidence
Where are we relative to the peak? For top US income-tax rates: most estimates place the revenue-maximizing rate well above current levels (~60–75% vs. 37% federal) — the US is on the left side, where hikes raise revenue. Historical cuts: the 1981 Reagan cuts lost revenue (Treasury estimates); the 2017 TCJA cut corporate revenue substantially. Cases of cuts raising revenue exist (some corporate cuts in small open economies attracting mobile profit — Ireland) but they're special cases, not general laws. The serious literature's consensus: major economies are below the peak for income taxes; claims otherwise need extraordinary evidence.
Small open economies can raise corporate revenue by cutting rates (attracting mobile profits). Large economies can't import a tax base this way — the Laffer peak is country- and tax-specific.
The political misuse
'Tax cuts pay for themselves' is the Laffer curve's bastard child. The curve says cuts raise revenue only past the peak — but politicians invoke it at any rate, treating a conditional possibility as a universal law. Dynamic scoring debates, 'self-financing tax cuts,' and the 2017 TCJA's growth claims all leaned on Laffer logic without Laffer evidence. The honest use: the curve disciplines both sides — it reminds progressives that rates can't rise forever (avoidance is real), and reminds conservatives that we're usually below the peak (cuts cost revenue). A concept both sides misuse is a concept worth understanding precisely.
The Laffer curve cuts both ways: it caps how high rates can usefully go AND shows most current rates are below the peak. Anyone citing it one-sidedly is misusing it.
Using it honestly
The right questions: What's the elasticity of this specific base? (Payroll: low. Capital gains realizations: high — timing is elastic.) How broad is the base? (Broader base → higher peak.) Are we above or below? (Estimate, don't assume.) And crucially: should we maximize revenue? No — the welfare-maximizing rate is below the peak (the last revenue dollar costs more in distortion than it's worth). Optimal-tax theory, not Laffer-maximization, sets policy. The curve is a constraint on dreams, not a policy program — it tells you what you can't do, not what you should.
Key points
- The Laffer curve: revenue is zero at 0% and 100% rates, peaking somewhere between — inverted U.
- The peak depends on the elasticity of taxable income: τ* ≈ 1/(1 + a·e), typically 60–80% for top rates.
- Evidence: the US is below the peak — major tax cuts (1981, 2017) lost revenue; self-financing cuts are special cases.
- 'Tax cuts pay for themselves' misuses the curve — it applies only past the peak, which requires evidence, not assertion.
- Honest use: the curve constrains both sides; optimal (not maximal) revenue is the policy goal.
Common misconceptions
✓ Truth: It proves revenue peaks somewhere — cuts raise revenue only if rates exceed the peak. For major economies' income taxes, evidence puts current rates below it.
✓ Truth: Every tax has its own curve: payroll (inelastic base, high peak), capital gains (elastic timing, lower peak), corporate (mobile base, country-specific). No universal number exists.
✓ Truth: The curve is mainstream public finance — Saez, Piketty, and Stantcheva all use it. It's the political misuse, not the concept, that's ideological.
Practice questions
Q1. The Laffer curve's core logical claim is:
- Tax cuts always raise revenue
- Tax revenue is zero at both 0% and 100% rates, so a revenue-maximizing rate exists between them
- Taxes should be zero
- Revenue rises forever with rates
The inverted-U follows from the two zeros. Where the peak is — and whether current rates exceed it — is empirical, not given by the logic.
Q2. The revenue-maximizing tax rate is higher when:
- Avoidance is easy
- The tax base is broad and inelastic — few loopholes, immobile earners (low elasticity of taxable income)
- The economy is small
- Rates are already high
τ* = 1/(1 + a·e): lower elasticity e means a higher peak. Base-broadening (closing loopholes) raises the peak — plumbing matters more than the rate dial.
Q3. The honest policy implication of the Laffer curve is:
- Always cut taxes
- Always raise taxes
- It constrains both sides: rates can't rise forever (avoidance is real), but most current rates are below the peak — and the welfare optimum is below the peak anyway
- Ignore elasticities
The curve disciplines progressives (diminishing returns to rate hikes) and conservatives (cuts usually cost revenue). Optimal-tax theory, not revenue maximization, should set rates.
Click a question to reveal the answer and explanation.
Frequently asked questions
Did Arthur Laffer really sketch it on a napkin?
Legend says yes — at a 1974 dinner with Rumsfeld and Cheney. The idea predates him (Ibn Khaldun, 14th century; Dupuit, 1844), but Laffer made it politically famous.
What is the elasticity of taxable income?
How much reported income shrinks as rates rise — via real effort, avoidance, timing, and evasion. The master parameter: it determines the Laffer peak and optimal top rates. Estimates center ~0.2–0.5 for top earners.
Why is the capital-gains Laffer peak lower?
Realizations are highly timing-elastic — investors defer sales when rates rise. The base shrinks fast, so the revenue-maximizing rate is lower than for labor income.
What's the difference between the Laffer peak and the optimal rate?
The peak maximizes revenue; the optimum maximizes welfare — trading revenue against the distortions and burdens of taxation. The optimal rate is always below the peak.