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The Laffer Curve

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The Laffer Curve
The Laffer curve, named after the economist Arthur Laffer, is a curve that demonstrates the trade-off between tax-rates and tax-revenues (Wanniski 1978). It is used to illustrate the concept of taxable income elasticity, the idea that a government can maximise the revenue by setting the tax rates at an optimum point. This curve can be traced back as far as 1844 to a French economist Jules Dupit who in 1844 found similar effects as Laffer did (Laffer 2004). Dupit also saw tax revenues rising from zero with a small increase in the rate, reaching a maximum PMTQ at rate pM, then falling with further rate increase and eventually returning to zero when the rate becomes prohibitive (Humphrey 1992: 9). In fact in 1844, Dupuit wrote:
If a tax is gradually increased from zero upto the point where it becomes prohibitive, its yield is at first nil, then increases by small stages until it reaches a maximum, after which it gradually declines until it becomes zero again. Figure 1 Dupuit’s Tax Theorems (Humphrey 1992: 8)

Adam Smith in his book, Wealth of Nations (Smith 1776: 414), outlined that high taxes, sometimes by diminishing the consumption of the taxed commodities, and sometimes by encouraging smuggling, frequently afford a smaller revenue than what might be drawn from more moderate taxes.
The Laffer curve assumes the existence of two points where state tax revenues amount for zero. At these two points, the Aggregate Average Tax (AAT) amounts either for 0% (t=0) or 100% (t=1). At a certain point in between these two points on the curve is t*, where the AAT (tmax) lies, tax revenue reaches its maximum point T (Papava 2002: 66-70). At t=0 the reason why the state does not earn any revenue is clear as the tax rate amounts for zero. At t=1, corresponding to a rate of 100%, all production ceases because people will not work in the money economy if all fruits of their labours are confiscated by the government (Wanniski 1978: 3).

The Laffer curve, however, does

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