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 life but life's prime want". Marx explained his belief that, in such a society, each person would be motivated to work for the good of society despite the absence of a social mechanism "compelling" them to work, because work would have become a pleasurable and creative activity. Marx intended the initial part of his slogan, "from each according to his ability" to suggest not merely that each person should work as hard as they can, but that each person should best develop their particular talents. Claiming themselves to be at a "lower stage of communism" (i.e. "socialism", in line with