# Laffer curve

## Definition

The Laffer curve is a curve used in the theory of taxes that plots tax revenue collected as a function of the tax rate.

The term is associated with a general idea, namely, that when a tax rate increases, incentive effects usually lead to the quantity being taxed to decrease, and hence, the net effect on the tax revenue generated (which is the product of the tax rate and the quantity taxed) is theoretically ambiguous.

If there is no effect of increases in the tax rate on the quantity being taxed, the Laffer curve would be a straight line through the origin. The term "Laffer curve" thus puts emphasis on the idea that there is (at least potentially) an effect of the tax rate on the quantity being taxed, and that the curve need not in general be a straight line.

The simplest prototype of a Laffer curve is a single-peaked curve, where the tax revenue generated is initially an increasing function of the tax rate, then reaches a peak, and beyond the peak, is a decreasing function of the tax rate. The tax rate that maximizes government revenue is termed the 'revenue-maximizing tax rate. Although theoretically curves with multiple peaks and troughs are possible, we can choose suitable concavity/convexity assumptions to make sure that the curve is single-peaked.

Although the Laffer curve concept has been historically applied to the income tax, the concept can also be applied, more easily, to other taxes, specifically the sales tax.

## Short run versus long run

A distinction can be made between short-run and long-run Laffer curves, and the corresponding short-run and long-run revenue-maximizing tax rates. There are two important effects:

1. In the long run, there is more scope for people to adjust away from the production or consumption activities that are subject to high taxation, or even to leave the high-tax jurisdiction. This reason generally supports the idea that the long run revenue-maximizing tax rate is lower than the short run revenue-maximizing tax rate.
2. Also, revenue in the long run also depends on the overall condition of the economy, which in turn is influenced by tax rates. As noted, taxation generally discourages beneficial activities like work, saving, and investment. A higher tax rate, by discouraging such activities, may slow down economic growth slightly. In the long run, small differences in economic growth add up to considerable differences in economy size, and hence considerable differences in the potential for tax revenue.

For both these reasons, long-run revenue-maximizing tax rates are likely to be lower than the short-run revenu-maximizing tax rates.

## Revenue-maximizing versus optimal tax rate

The peak of the Laffer curve represents the revenue-maximizing tax rate for the government. However, this may be very different from the socially optimal tax rate, which is likely to be lower.

Generally speaking, the optimal tax rate should not be more than the revenue-maximizing tax rate, but it may well be less. There are two kinds of exceptions: exceptions where the goal of taxation is not revenue but discouraging specific activities, and exceptions when some democratically elected politicians are playing to popular dislike of specific groups (the rich, ethnic minorities, foreigners, etc.) by taxing them punitively. In practice, rationally self-interested politicians are likely to endorse high taxes on unpopular groups in rhetoric but not implement them in practice, and/or offer loopholes.

## Policy implications

### Static versus dynamic scoring

When government policymakers are making predictions about tax revenues in future years, and comparing different tax rate policies in terms of the tax revenues they will generate, they need to have a model that will make reasonably accurate predictions.

The simplest type of model, known as static scoring, assumes a linear relationship between tax rates and tax revenues, i.e., it assumes that the Laffer curve is a straight line through the origin. This model does not take into account the possibility that the quantity being taxed will shrink as a response to a higher tax rate.

If Laffer curve effects are weak, then static scoring provides a reasonable approximation in estimating tax revenue. If, however, Laffer curve effects are strong, then static scoring needs to be replaced by dynamic scoring, which makes an explicit attempt to take account of the response effects. The general problem with dynamic scoring is that it is difficult to determine the extent to which the quantity being taxed will respond to tax rate changes, so it is inherently uncertain. However, using some guesstimates here may be more reliable than static scoring if Laffer curve effects are strong and approximately predictable.