Optimal tax in his article titled "Using Elasticities to Derive Optimal Income Tax Rates" derives a formula for optimal level of income tax using the both compensated and uncompensated elasticities. Saez writes the tradeoff between equity and efficiency is a central consideration of optimal taxation, and implementing a progressive tax allows the government to reallocate their resources where they are needed most. However, this deters those of higher income levels to work at their optimal level. Saez decomposes the marginal effects of a tax change into mechanical, behavioural and welfare effects, as follows: The sum of these effects should be zero at
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