The economist Anthony Atkinson has studied the issues of poverty and inequality for over four decades; an index of inequality is named after him. In his most recent work, Atkinson offers a fascinating, encouraging guide to what could be done to reduce monetary inequality. The importance of equal opportunity should not lead us to ignore inequality in outcomes, he explains, not only because the same efforts do not always produce the same results but also because inequality of outcome for one generation can become inequality of opportunity for the next: today's ex-post outcomes shape tomorrow's ex-ante playing field (p. 11). And though income is only one dimension, it is a major source of inequality. The book is divided into three parts: diagnosis; 15 proposals for action that, if implemented, would reduce inequality; and answers to the main objections to taking those actions.While monetary inequality has increased sharply since 1980, there have been non-war periods - primarily the post-WWII decades in Europe and the 2000s decade in Latin America - that have seen falls in inequality. The phenomena at work are clearly and simply explained by means of a diagram detailing the stages through which a household's primary income becomes its disposable income: labour and/or capital income, social transfers, taxation. This in turn enables us to determine at what stage the level of inequality changed in a given country at a given period. While less unequal pay and increases in social transfers and women's labour market participation reduced the extent of overall inequality in post-war Europe, this was not the case in the United States, where the last two factors only worked to compensate for rising pay inequality.Generally speaking, equalizing forces went into reverse in the 1980s in most western countries. Workers and consumers lost power to employers, which, combined with reduced social protection and less progressive taxation, greatly increased inequality. Many of Atkinson's proposals are not new; some, such as the minimum wage, have already been applied. Others are quite radical and so raise the question of feasibility and collateral effects. But they all fit together into a highly consistent whole that forcefully conveys Atkinson's now familiar message: states, and through them citizens (though this is never said explicitly), do have the power to act. Above all, the direction of technological progress is not entirely beyond our control: the state can orient it through investments and stakeholding, and this need not mean increased control over business.Inequality-reducing actions can be taken at three levels: household primary income (labour and/or capital income), taxation policy, and social transfers. These correspond directly to the state's three missions: regulation, redistribution and protection. Atkinson's first set of proposals - minimum wage, a national pay policy, guaranteed public employment, ensuring that technological change and innovation are human-centred - are aimed at reducing pay inequality and containing unemployment. The second set of measures would ensure that every adult receives a minimum inheritance in the form of a capital endowment or state bonds with a guaranteed return.In addition to measures that would work to reduce primary income inequality, Atkinson proposes an ambitious fiscal reform that would make income tax more progressive while widening the fiscal base, easing conditions for low earners, taxing inheritance and gifts during life, and increasing property tax progressiveness.The third raft of proposals is aimed at reforming social protection systems; reductions in this area are one source of recent increases in inequality. …