Muqaddimah empires to collapse, with the result that lower revenue was collected from high rates." He wrote: Ibn Khaldun introduced the concept now popularly known as the Laffer curve, that increases in tax rates initially increase tax revenues, but eventually the increases in tax rates cause a decrease in tax revenues. This occurs as too high a tax rate discourages producers in the economy. Ibn Khaldun used a dialectic approach to describe the sociological implications of tax choice (which now forms a part of economics theory): This analysis is very similar to the modern economic concept known as the Laffer curve.
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