Optimal tax the optimum. Stipulating this condition results in the following formula for the optimal top tax rate, if incomes are Pareto distributed: formula_1 where: Empirical estimation of the parameters of this equation suggests that the revenue-maximising top tax rate is between approximately 50% and 80%, although this estimate neglects long-run behavioural responses, which would imply higher elasticities and a lower optimal tax rate. Saez's analysis can also be generalised to tax rates other than the top rate. In the late 1970s, Arthur Laffer developed the Laffer curve, which demonstrates that there are two effects of changing tax rates: an arithmetic effect—if
Ibn Khaldun scholars is increasingly common. Influential British historian and international affairs specialist Arnold J. Toynbee has called Ibn Khaldun's Muqaddimah "the greatest work of its kind." Ernest Gellner, once a professor of philosophy and logic at the London School of Economics, considered Khaldun's definition of government the best in the history of political theory. More moderate views on the scope of Ibn Khaldun's contributions have emerged. Arthur Laffer, for whom the Laffer curve is named, acknowledged that Ibn Khaldun's ideas, as well as others, precede his own work on that curve. A focus on understanding the nuances of Ibn Khaldun's contributions