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This is the triumph of Capital in the 21st Century: nothing about the book is more impressive than the range and richness of its statistical information. (Piketty excuses the inaccuracy of Kuznets’s theory on the basis of the incomplete data, going back only a few decades, at his disposal.)

One merit of the book is that it both insists on the importance of data and, at least where modern societies are concerned, highlights the uncertainties involved in its collection.

On the one hand, the law is indisputable: if capital grows faster than output, the proportion of wealth to income necessarily rises. Only a dip in the rate of return, broader capital ownership, or the destruction of capital might retard or reverse the process. But what does the formula explain?

The exceptional character of the period between the First World War and the 1973-74 recession becomes the more striking when Piketty emphasises that his second law of capitalism held long before capitalism: ‘The inequality r>g has clearly been true throughout most of human history, right up to the eve of World War One, and it will probably be true again in the 21st century.’ In a chart graphing the rate of return against ‘the growth rate, at the world level, of world output from Antiquity to 2100’, r hovers between 4 and 5 per cent until 1820, by which time the Industrial Revolution has spread beyond England. It plummets nearly as low as 1 per cent around the outbreak of the First World War, and then undertakes a steep climb throughout the 20th century before adjusting to a moderate slope that stretches up to and past our time into the indefinite and enduringly capitalist future. Across the same stretch of history, the global growth rate g ascends a gentle gradient until the mid-18th century, after which new summits beckon.

Piketty’s theoretical troubles may start with his definition of capital as wealth in general.

In his conclusion Piketty promotes r>g to the status of ‘the central contradiction of capitalism’. The phrase is meant to evoke Marx and the theory to better him.

At a distance Piketty’s central contradiction resembles Marx’s. Here too capital, ‘more and more dominant over those who own nothing but their labour’, overaccumulates relative to labour. But at least in formal terms, Marx’s theory is clearly superior. It proposes a genuine contradiction – capital accumulation undermines itself – and entails a mechanism specific to capitalism: the drive for profits through the exploitation of wage labour. Piketty’s r>g is not, by contrast, the ‘fundamental logical contradiction’ that he claims. Capital accumulation, left to outrun economic growth indefinitely, would create ‘an endless inegalitarian spiral’ threatening less to profitability than ‘to democratic societies and to the values of social justice on which they are based’.

Large fortunes would come to represent recent entrepreneurial feats more than the dumb luck of inheritance, and revenue from the tax could address public purposes neglected by private investors. Piketty hazards his ‘utopian idea’ as contemporary societies approach what he sees as a fork in the road. One way leads to concentrations of wealth incompatible with liberal democracy, the other to a redomesticated capitalism supporting ‘a social state for the 21st century’.

A recent study calculated that in the US the top 10 per cent of the income distribution enjoys an effect on political outcomes 15 times that of the remaining 90 per cent. Other countries are plutocratic to similar degrees. How are the executive committees of the ruling class in countries across the world to act in concert to impose Piketty’s tax on just this class?

But even without it, a rising capital/income ratio would no longer automatically deepen inequality. The notion of such a revolution – first in one country, then gatheringly international but not yet universal – is fanciful right now. But is it more so than a global capital tax requiring the co-ordination of virtually all nations? The longer global capitalism goes unreformed the more likely nations and regions are to reject it.

Piketty, ‘vaccinated for life against the conventional but lazy rhetoric of anticapitalism’ by the fall of the Berlin Wall, might consider such speculations an ideological relapse. He wants his tax on capital to ‘promote the general interest over private interests while preserving economic openness and the forces of competition’, and has said in interviews that the indispensable role of markets in complex economies justifies the persistence of capitalism.

Visions of a postcapitalist future, from Alec Nove’s Economics of Feasible Socialism (1983) to David Schweickart’s After Capitalism (2002), have more often been forms of market socialism. (Schweickart folds ‘a capital assets tax’ much like Piketty’s into a comprehensive transitional programme.) The private accumulation of capital would no longer drive the economy, even as the market still facilitated much private consumption and guided much public investment. Piketty might reject the idea in any or all varieties. For now he shows no awareness of it. The blindspot isn’t surprising in a writer who has boasted to the American press, perhaps not entirely disingenuously, of his unfamiliarity with Marx’s writing, and who in his book excuses his indifference to Marxist work generally by complaining that ‘one sometimes has the impression’ in reading Sartre, Althusser or Badiou that ‘questions of capital and class inequality are only of moderate interest to them.’ He would have done better to consult historians and economists than philosophers.

But the familiar equation of markets with capitalism lacks a historical or theoretical basis. It ignores the extensive markets in many precapitalist societies and the strong element of monopoly and state interference with markets throughout the history of capitalism.

Piketty’s appetite for and command over data, for one thing, are worth emulating. And surely if intelligent economists start reckoning with Marxian thought not as a historical curio but as a long and living tradition, they won’t simply ratify propositions about which Marxists don’t agree themselves. Investigated rather than ignored, Marxist ideas would be variously confirmed, refined or rejected. For the moment, however, mainstream economists, including the hero of the hour, seem reluctant to press their discoveries beyond the borders of the respectable. Their journalistic counterparts are if anything more timid.

The book is more exciting considered as a failure than as a triumph. Piketty has bid a lingering goodbye to the latter-day marginalism of mainstream economics but has not yet arrived at the reconstructed political economy foreseen at the outset. His theoretical reach fumbles where his statistical grasp is sure, and he leaves intact the questions of economic value, distributive justice and capitalist dynamics that he raises.