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The problem is not mathematics as such, but the junk economics and junk statistics used by the mathematicians who have captured the discipline of economics. For contrast, one need only turn to the 19th century’s rich toolbox of economic concepts developed to analyze today’s most pressing problems.

The overburden of public debt prompted Adam Smith to comment that year that no government ever had repaid its debts, and to propose means to keep it in check by freeing the American colonies that were a major source of conflict with France, for instance, and most of all, by paying for wars out of current taxation so that populations would feel their immediate cost rather than running into debt to international bankers such as the Dutch.

The early 19th-century French reformer St. Simon proposed that banks shift from making straight interest-bearing loans to “equity” loans, taking payment in dividends rather than stipulated interest charges so that debt service would be kept within the means to pay. (Islamic law already had banned interest.) This became the inspiration for the industrial banking policies developed in continental Europe later in the century. St. Simon influenced Marx, whose manuscript notes for what became Vol. III of Capital and Theories of Surplus Value collected what he read from Martin Luther to Richard Price on how debts multiplied by purely mathematical laws independently of the “real” economy¹s ability to produce a surplus. The classical concept of productive credit was to provide borrowers with the means to pay. Unproductive debts had to be paid out of revenue obtained elsewhere.

Interest paid by consumers was treated as a psychological choice, while industrial profit was treated as a return for the widening time it presumably took to produce capital-intensive goods and services. The ideas of “time preference” and the “roundabout” cycle of production were substituted for the simpler idea of charging a price for credit without any out-of-pocket cost or real risk undertaken by bankers. The world in which economic theorists operated was becoming increasingly speculative and hypothetical.

After the Napoleonic wars ended in 1815, Britain’s leading bank spokesman, David Ricardo, applied the concept of economic rent to the land in the process of arguing against the agricultural tariffs (the protectionist Corn Laws) in his 1817 Principles of Political Economy and Taxation. His treatment deftly sidestepped what had been the “original” discussion of rentier income squeezed out by the financial sector.

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.

Where only transactions for money are recognised as belonging to "the economy", the vast amount of unpaid labour – as conducted for instance in families and local areas – goes uncounted and unvalued. We need to question that familiar categorisation of the economy as a space into which people enter in order to reluctantly undertake unwelcome and unpleasing "work", in return for material rewards which they can use for consuming.

Above all, we need to bring economic vocabulary back into political contention, and to question the very way we think about the economy in the first place. For something new to be imagined, let alone to be born, our current economic "common sense" needs to be challenged root and branch.

How do you think protestors in today’s society can more effectively disrupt urban economies? Harvey: Hurricane Sandy really disrupted the lives of those living in New York City. So, I don’t see why organized social movements couldn’t disrupt life as usual in big cities and therefore cause damage to ruling-class interests. We have seen many historical examples of this. For example, in the 1960s, the disruptions that occurred in many cities in the United States caused massive disruptions to business. The political and business classes were quick to respond because of the level of disruption and destruction. I mention in the book the immigrant workers demonstrations in the spring of 2006. The demonstrations were in response to Congress attempting to criminalize illegal immigrants. Subsequently, people mobilized in places like Los Angeles and Chicago, and significantly disrupted city business.

Participatory budgeting is currently happening in Porto Alegre, Brazil, where the Workers Party developed a system through which local populations and assemblies decide what their tax money should be spent on. Thus, they hold popular assemblies, and so forth, which decide how to utilize public funds and services. Again, here’s a democratic reform that initially took place in Porto Alegre, but has since been passed along to European cities.

In Chapter Five, you write, “In the Marxist tradition, urban struggles are often ignored or dismissed as being devoid of revolutionary potential or significance.

I take it as symbolic importance that the first two acts of the Paris Commune were to abolish night work in the bakeries, a labor question, and to impose a moratorium on rent, an urban question.” Can you talk about the privileging of industrial workers in Marxist ideology? 

This idea of a vanguard struggle leading to a new society has been around for some time. However, what’s fascinating is the lack of alternatives to this vision, or at least variants of its intent and purpose. Of course, a lot of this comes from Marx’s Vol. I of Capital — emphasizing the factory worker. This idea that the vanguard workers party is going to take us to the new promise land of anti-capitalist, let’s call it ‘communist’ society has been persistent for over one hundred years. I’ve always felt that this is too limited a conception of who is the proletariat and who’s in the ‘vanguard.’ Also, I’ve always been interested in class-struggle dynamics and their relationships with urban social movements.

When you look at the wide range of urban social movements, you’ll find some are anti-capitalist and others are the opposite. But I would make the same remark about some forms of traditional union organizing. For example, there are some unions who look at organizing as a way to privilege the privileged workers of society. Of course I don’t like this idea. Then, there are others who are creating a more just and equitable world.

That way, in Gramsci’s thinking, they could get a better picture of what the entire working-class looks like, not just those who are organized in factories and so forth. Including people like the unemployed, temporary workers and all of the people you previously mentioned who were not in traditional industrial sector jobs. So, Gramsci proposed that these two kinds of political organizing methods should be intertwined in order to truly represent the proletariat. In essence, my thinking reflects Gramsci’s in this regard. How do we begin to care for all of the working people within a city? Who does this? Traditional unions tend not to do this.

an you talk about some of those cities, such as Al Alto, Bolivia? Also, I was in Madison, Wisconsin in 2011 during the labor protests, and I must say, it’s been interesting and utterly frustrating to experience the internal dynamics of the labor movement, and how it interacts with non- unionized workers and citizens. Unfortunately,  the union movement stifles serious dissent and resistance.

The reason I mentioned Trumka was because I think Trumka and many of those within the organized union movement understand that they can no longer go it alone; they require the help of the entire workforce, unionized or otherwise. This is always the challenge when organizing: How much support do we want from these large entities? And how much of what they’re doing is out of a true sense of solidarity? How much of it is for personal gain? My own experience in Baltimore, surrounding living wage campaigns, mirrors your experience to some extent. The unions were generally hostile to these campaigns and didn’t help, generally speaking. However, we did receive a lot of help from local unions.

There’s a moment in the film that’s somewhat funny: The guys can’t picket anymore because of the Taft-Hartley legislation, so the women take over the picketing because there’s nothing banning them from joining the protests. Then, the men have to take over the household jobs. Interestingly, the men quickly begin to understand why the women were asking for running water, and other things from their employer that would make daily life much easier.