Laffer curve and possible differences in the incentive to work for different income groups complicate the task of estimation. The structure of the curve may also be changed by policy decisions. For example, if tax loopholes and tax shelters are made more readily available by legislation, the point at which revenue begins to decrease with increased taxation is likely to become lower. Laffer presented the curve as a pedagogical device to show that in some circumstances, a reduction in tax rates will actually increase government revenue and not need to be offset by decreased government spending or increased borrowing. For a reduction
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