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
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