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
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: