considered. It is clear that a 0% tax rate raises no revenue, but the Laffer curve hypothesis is that a 100% tax rate will also generate no revenue because at such a rate there is no longer any incentive for a rational taxpayer to earn any income, thus the revenue raised will be 100% of nothing. If both a 0% rate and 100% rate of taxation generate no revenue, it follows from the extreme value theorem that there must exist at least one rate in between where tax revenue would be a maximum. The Laffer curve is typically represented as a graph that starts at 0% tax, zero revenue, rises to a maximum rate of revenue raised at an intermediate rate of taxation, and then falls again to zero revenue at a 100% tax rate. One potential result of the Laffer curve is that increasing tax rates beyond a certain point will become counterproductive for raising further tax revenue. A hypothetical Laffer curve for any given economy can only be estimated and such estimates are sometimes controversial. The New Palgrave Dictionary of Economics reports that estimates of revenue-maximizing tax rates have varied widely, with a mid-range of around 70%. Optimal Most governments take revenue that exceeds that which can be provided by non-distortionary taxes or through taxes that give a double dividend. Optimal taxation theory is the branch of economics that considers how taxes can be structured to give the least deadweight costs, or to give the best outcomes in terms of social welfare. The Ramsey problem deals with minimizing deadweight costs. Because deadweight costs are related to the elasticity of supply and demand for a good, it follows that putting the highest tax rates on the goods for which there are most inelastic supply and demand will result in the least overall deadweight costs. Some economists sought to integrate optimal tax theory with the social welfare function, which is the economic expression of the idea that equality is valuable to a greater or lesser extent. If individuals experience diminishing returns from income, then the optimum distribution of income for society involves a progressive income tax. Mirrlees optimal income tax is a detailed theoretical model of the optimum progressive income tax along these lines. Over the last years the validity of the theory of optimal taxation was discussed by many political economists. Rates Taxes are most often levied as a