Laffer Curve

How the Laffer curve works

Tax revenue is rate × base. The base — taxable income, taxable consumption, the taxed activity — depends on behavior, and behavior depends on the rate. Two boundary cases pin down the shape. At a 0% rate, the rate is zero, so revenue is zero regardless of the base. At a 100% rate, take-home falls to zero, so rational workers stop reporting income to the formal economy; the base goes to zero, and revenue is zero again.

Between these endpoints, revenue must rise from zero, reach some maximum, and fall back to zero. The peak — call it t* — is the revenue-maximizing rate. Below t*, raising the rate raises revenue because the base shrinks less than the rate rises. Above t*, raising the rate lowers revenue because the base shrinks faster than the rate rises. Equivalently: below t*, you collect less by cutting rates; above t*, you collect more by cutting rates.

The location of t* depends entirely on the elasticity of the tax base with respect to the rate — the "elasticity of taxable income" (ETI) in modern public finance. Inelastic bases (cigarette demand, immobile property) have peaks far above 70%. Elastic bases (capital gains, top-income earners with avoidance options) have peaks far below 70%. A single Laffer curve summarizes the population's behavioral response.

Why the curve is asymmetric

Textbook diagrams often draw the Laffer curve as a symmetric parabola. Empirical Laffer curves are asymmetric — usually steeper on the high-rate side. The reason is that behavioral responses are themselves nonlinear in the rate. At low tax rates (0-30%), most people barely adjust behavior; the marginal cost of avoidance exceeds the marginal benefit. At moderate rates (30-50%), avoidance investments — accountants, tax-deferred vehicles, business-form changes — start paying off. At high rates (above 60%), aggressive avoidance, retirement, emigration, and informal-sector substitution accelerate. The base falls slowly at first, then fast.

The asymmetry has a deep welfare implication. Two rates can produce the same revenue — say, 25% and 75% — but the social welfare costs are dramatically different. At 25%, deadweight loss is small. At 75%, deadweight loss is large because more people are heavily distorting decisions to avoid tax. Even if the government is indifferent between the two on revenue grounds, society is not.

Laffer-style results across tax types

	Income tax (top bracket)	Corporate tax	Capital-gains tax	Cigarette tax	VAT / sales tax	Property tax
Base elasticity	High (especially top earners)	Very high (profit-shifting)	Very high (realization timing)	Moderate	Low	Very low (land immobile)
Estimated peak rate	50-70%	20-30%	20-35%	~75% effective	Above empirical experience	Above 50%
Foundational reference	Saez 2001; Diamond-Saez 2011	Gravelle 2014	Auerbach-Hassett 2007	Gallet 2003 surveys	Slemrod 1998	Skinner 1996
Real-world peak observed?	Reagan cut took US from 70% to 50%	Most countries 15-30%	Cuts in 1978, 1997 raised receipts (debated)	NYC, Chicago hit smuggling thresholds	Few experiments above 25%	No — typically far below peak
Behavioral mechanism	Labor supply, avoidance, emigration	Profit-shifting to low-tax jurisdictions	Realization deferral	Smuggling, switching, quitting	Informal sector	Limited — land doesn't leave
Policy implication	Top rates below 70% to stay below peak	Lower rates raise more (esp. small countries)	Lower rates trigger realization waves	Optimization for revenue not welfare	Room to raise	Most efficient tax (Henry George)
Estimated current position	US below peak; some Nordics near peak	Most countries below peak	Probably below US peak	Some cities above	Below peak	Below peak

Worked example: behavioral response and the revenue peak

Consider a single tax on labor income. Let the tax base B(t) — total taxable income — depend on the rate t through a constant-elasticity relationship: B(t) = B₀ · (1 − t)^ε. Here ε > 0 is the elasticity of taxable income; doubling the after-tax share raises the base by 2^ε.

Revenue is R(t) = t · B(t) = t · B₀ · (1 − t)^ε. Take the derivative: dR/dt = B₀ · [(1 − t)^ε − ε · t · (1 − t)^(ε−1)]. Set to zero: (1 − t)^ε = ε · t · (1 − t)^(ε−1), simplifying to t* = 1 / (1 + ε). For ε = 0.25 (the modal ETI estimate from Saez-Slemrod-Giertz 2012), the peak rate is 1/1.25 = 80%. For ε = 0.5 (top-earner estimates), peak is 1/1.5 ≈ 67%. For ε = 1 (very elastic base), peak is just 50%.

Now plug in numbers. Suppose B₀ = $10 trillion (US wage base), ε = 0.5. At t = 30%: R = 0.3 · $10T · (0.7)^0.5 = $2.51T. At t = 50%: R = 0.5 · $10T · (0.5)^0.5 = $3.54T. At t = 67%: R = 0.67 · $10T · (0.33)^0.5 = $3.85T (peak). At t = 80%: R = 0.8 · $10T · (0.2)^0.5 = $3.58T. At t = 95%: R = 0.95 · $10T · (0.05)^0.5 = $2.12T. The curve rises from $2.5T at 30% to $3.85T at 67%, then falls back.

Notice that t = 30% and t = 95% give roughly the same revenue ($2.5T and $2.1T) — but the social welfare cost at 95% is enormous because deadweight loss scales with the square of the rate distortion. The Saez-Diamond optimal-top-rate formula, t* = 1 / (1 + ε · a), where a is the Pareto coefficient of the income distribution (a ≈ 1.5 for US top incomes), corrects the simple Laffer formula for the distributional weight. For US top earners: ε ≈ 0.5, a ≈ 1.5, giving t* ≈ 1/(1 + 0.75) ≈ 57%.

Why the Laffer curve became politically central

• Supply-side economics. Reagan 1981 took the US top marginal rate from 70% to 50% partly on Laffer-curve logic. Subsequent reductions to 28% (1986), then bounces in the 30s-40s ever since. Roughly half of the Reagan cuts' deficit impact was offset by base expansion.
• Optimal tax theory. Diamond-Mirrlees (1971) and Saez (2001) formalized the Laffer curve in a welfare-maximization framework, deriving the optimal top rate as a function of social welfare weights and ETI.
• Tax competition. Small countries face higher elasticities than large ones (capital can flee easily). Tax competition pushes corporate rates down — Ireland, Switzerland, Singapore have run successful low-rate strategies.
• Behavioral-response measurement. The Laffer curve made elasticity of taxable income a first-class empirical research target. Modern public-finance careers turn on credible ETI estimates.
• Wealth-tax design. Norway, Spain, and (briefly) Switzerland's wealth tax debates explicitly model Laffer-curve-style trade-offs between revenue and capital flight.
• Pigouvian-tax limits. Carbon taxes set to maximize revenue would lie below the Laffer peak; set to minimize emissions, they might lie above. Whether to maximize revenue or activity is a design choice.

Variants and refinements

• Static vs dynamic Laffer. Static analysis holds base constant; dynamic allows base to respond. The Laffer curve is fundamentally dynamic — base responses are the entire point.
• Short-run vs long-run. Short-run elasticities are small (people don't change jobs immediately); long-run elasticities are larger (career choice, location, business formation). The peak rate is lower in the long run.
• Income-tax vs total-burden Laffer. An income tax alone may have a peak at 70%; adding payroll, sales, and property taxes, the total burden's peak is lower because all taxes share the labor base.
• Tax-by-tax Laffer. Different taxes have different peaks. The right policy question is which tax to use, not just what rate, because of differential elasticities.
• Mirrlees optimal tax. James Mirrlees (1971 Nobel) generalized the Laffer apparatus to a continuum of types, deriving optimal nonlinear income-tax schedules. The Mirrlees framework is the modern descendant.
• International tax-competition Laffer. When capital is mobile, each country faces a higher elasticity than a closed economy would. Tax-competition models (Wilson 1986) generate downward pressure on rates.

A brief history

The basic logic — revenue must be zero at both endpoints, so peaks in between — is at least 600 years old. Ibn Khaldun's 1377 Muqaddimah noted that increasing the tax rate eventually decreases the tax base. Jules Dupuit's 1844 essay "On the Measurement of the Utility of Public Works" sketched the inverse-U shape geometrically. Adam Smith and David Ricardo both made similar observations in passing.

Arthur Laffer's 1974 napkin sketch with Donald Rumsfeld and Dick Cheney at the Two Continents restaurant in Washington gave the curve its name. Laffer was not claiming originality; he was using the geometric argument to persuade Ford-administration officials that the 70% top US marginal rate sat above the peak. Robert Mundell made similar arguments in academic papers around the same time.

The 1981 Reagan tax cuts (Economic Recovery Tax Act) lowered the US top rate from 70% to 50%, then the 1986 Tax Reform Act took it to 28%. Empirical evaluations: roughly half the static revenue loss was offset by base expansion, suggesting the US was somewhere between t* and an above-t* region for the highest brackets. Modern academic work (Saez 2001, Diamond-Saez 2011) estimates the revenue-maximizing top rate at 50-70% for the US, depending on which avoidance margins one allows.

Common pitfalls

• Assuming all tax cuts pay for themselves. Only true above t*. Most empirical work puts the US below t* for current rates — meaning cuts reduce revenue.
• Ignoring the elasticity. The peak depends entirely on ETI. Different taxes have different elasticities and different peaks; one Laffer curve doesn't fit all.
• Treating the curve as static. Behavioral responses unfold over time. Short-run revenue effects differ from long-run.
• Conflating revenue maximization with welfare maximization. The Laffer peak maximizes government revenue; the welfare-optimal rate is usually lower because deadweight loss matters even below t*.
• Forgetting the asymmetry. Two rates that produce equal revenue produce very different welfare costs.
• Drawing the curve as symmetric parabola. Real Laffer curves are usually right-skewed — rise slowly, fall sharply.
• Treating it as a supply-side proof. The curve says only that some rate is too high; it doesn't say which side of the peak any particular economy occupies.

When the Laffer perspective matters

• Setting top marginal rates. Modern public-finance work bounds the optimal top rate using ETI estimates and welfare weights.
• Corporate-tax reform. Small open economies face high elasticities; revenue-maximizing rates are well below US-historic levels.
• Capital-gains-rate design. Realization elasticities are extreme; small rate changes shift trillions of dollars of realization timing.
• Wealth-tax debates. Capital is mobile; revenue projections require careful Laffer-curve modeling.
• Cigarette / luxury / vice taxes. Some current rates may exceed peaks; behavior is responsive.
• International tax-competition policy. Country-level Laffer peaks depend on capital mobility; coordination changes the peak.