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
From each according to his ability, to each according to his needs in solidum is that 'everyone assumes responsibility for anyone who cannot pay his debt, and he is conversely responsible for everyone else'. James Furner then argues: 'If x = a disadvantage, and y = action to redress that disadvantage, the principle of solidarity is: if any member of a group acquires x, each member has a duty to perform y (if they can assist). All we then need to add, to get to the fundamental principle of developed communism, is to assume that non-satisfaction of a need is a disadvantage. The corresponding principle of solidarity in respect of need says: