Laffer Curve

The Laffer curve is a graph showing how government tax revenue changes as a tax rate rises from 0% to 100%. At a 0% rate the government collects nothing; at 100% people have no reason to earn, report or keep taxable income, so revenue also falls towards nothing. Between the two extremes revenue first rises and then falls, which means there is a revenue-maximizing rate. Above that point, a cut in the rate would in theory raise revenue rather than lower it.

The curve is named after American economist Arthur Laffer and became a symbol of supply-side economics in the late 1970s and 1980s. The shape itself is widely accepted by economists. The dispute is about where actual tax systems sit on it, and therefore whether particular tax cuts pay for themselves. It is linked to the marginal tax rate, tax incidence and tax competition.

Think of a toll on a busy bridge. A small toll brings in money and hardly changes traffic. A much higher toll brings in more per car, but some drivers start taking the long way round. Set the toll absurdly high and almost nobody crosses, so the toll booth collects very little.

The Laffer curve applies that logic to taxes. Raising a tax rate brings in more money only as long as people do not cut back too much on the taxed activity, whether by working less, moving, or finding legal or illegal ways to shrink the income they report. Where the turning point lies is an empirical question, not something the drawing can answer.

The underlying idea is old. The 14th-century scholar Ibn Khaldun observed that low tax rates could yield large revenues, and John Maynard Keynes, founder of Keynesian economics, made a similar point in the 1930s. The modern version is usually traced to a 1974 meeting at a Washington, D.C., restaurant, where Laffer is said to have sketched the curve on a napkin for White House official Dick Cheney, with journalist Jude Wanniski present; accounts differ on the exact date and on whether Donald Rumsfeld was there. Wanniski popularized the term "Laffer curve" in 1978. The idea influenced the Economic Recovery Tax Act of 1981 under President Ronald Reagan, which cut the top federal income tax rate from 70% to 50%, followed by a cut to 28% under the Tax Reform Act of 1986.

Revenue equals the tax rate multiplied by the tax base, and the base shrinks as the rate rises:

Here $R$ is revenue, $t$ is the tax rate and $B(t)$ is the taxable base, which depends on the rate. For the top income tax bracket, economists Peter Diamond and Emmanuel Saez (2011) derived a widely cited formula for the rate that maximizes revenue from top earners:

• $t^{*}$ is the revenue-maximizing top marginal tax rate, including all taxes on that income.
• $a$ is the shape parameter of the Pareto distribution of top incomes, which measures how thick the top tail is.
• $e$ is the elasticity of taxable income, how much reported income falls when the share kept after tax falls.

With $a = 1.5$ and $e = 0.25$, the rate is 1 ÷ (1 + 0.375) ≈ 0.73, or about 73%. With a much higher elasticity of 1, it falls to 1 ÷ 2.5 = 40%. The answer therefore depends heavily on the elasticity, which is hard to measure and differs between countries and types of income.

Most empirical work finds that broad income tax rates in the United States and most rich countries are below the revenue-maximizing level, so general rate cuts lose revenue, though some of the loss may be offset by higher growth. In a 2012 survey of leading economists by the University of Chicago's IGM Forum, none agreed that a cut in US federal income tax rates would raise total revenue within five years. Official scorekeepers such as the Congressional Budget Office estimated that the 2017 Tax Cuts and Jobs Act would add to deficits even after counting growth effects. The 2012 income tax cuts in Kansas, which were followed by revenue shortfalls and partly reversed in 2017, are often cited by critics.

Supporters point to cases where rates were very high. Revenue responses to cuts in capital gains taxes can be large in the short run because investors time their sales. Very high rates, such as the UK's former 98% top rate on investment income in the 1970s, plausibly sat on the declining side. Advocates also argue that lower rates reduce avoidance and evasion, strengthen incentives to supply labor and invest, and boost productivity, and that revenue estimates understate these effects.

Critics argue the curve has been used to promise that tax cuts are "free" when evidence suggests they usually raise national debt unless offset by cuts in government spending, a point central to debates over austerity and the government budget. The curve is also not a fixed shape: it shifts with enforcement, the breadth of the base, international mobility and the time horizon. Maximizing revenue is not the same as maximizing welfare; many economists argue the best rate is below the peak because of efficiency costs, while others argue for the peak rate at the top for inequality reasons, in line with a progressive tax system. Finally, revenue effects depend on how the cut is financed and on monetary policy, which the simple curve ignores.

• American Economic Association: Diamond and Saez, "The Case for a Progressive Tax" (2011)