Laffer curve at an intermediate rate of taxation, and then falls again to zero revenue at a 100% tax rate. However, the shape of the curve is uncertain and disputed among economists. Under some assumptions, such as revenue being a continuous function of the rate of taxation, the maximum illustrated by the Laffer curve is a result of Rolle's theorem, which is a standard result in calculus. One implication of the Laffer curve is that reducing or increasing tax rates beyond a certain point is counter-productive for raising further tax revenue. A hypothetical Laffer curve for any given economy can only be
Contract curve the initial allocations. The analysis cannot say which particular point along the contract curve they will end up at — this depends on the two people's bargaining skills. In the case of two goods and two individuals, the contract curve can be found as follows. Here formula_1 refers to the final amount of good 2 allocated to person 1, etc., formula_2 and formula_3 refer to the final levels of utility experienced by person 1 and person 2 respectively, formula_4 refers to the level of utility that person 2 would receive from the initial allocation without trading at all, and formula_5