There are situations where marginal tax rates of 100% or nearly 100% may be justified. Three models will be sketched, using indifference curves. One, which makes unusual assumptions about preferences for labour, can justify income subsidies of low incomes with implicit marginal tax rate of 100%. The second, assuming high substitutability between consumption and work, might justify marginal tax rates approaching 100% on the highest incomes. The last, with competition between skilled workers (such as sportsmen or inventors) for market share, might justify marginal rates of 100% on high incomes of a particular type. The assumptions under which these conclusions follow may not hold in actual economies, but they might sometimes. In any case, extreme results, and the reasons for them, can help us understand how incentives work and their implications for taxation.