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
To each according to his contribution concept also formed the basic definition of socialism for its pre-Marxist proponents, including Ricardian socialists, classical economists, and individualist anarchists. "To each according to his contribution" was a concept espoused by many members of the socialist and labor movement. Examples of this can be found from Ferdinand Lassalle's and Eugen Dühring's statements to Leon Trotsky's writings. However, it was Vladimir Lenin, inspired by Marx's writing on the subject in his "Critique of the Gotha Programme", who claimed the principle to be a fundamental element of socialism within Marxist theory. Libertarian socialist thinkers, such as American anarchist Benjamin Tucker, defined socialism