Discussions of inequality usually focus on the distribution of income. But Piketty’s most original and important arguments concern the distribution of wealth. That’s a significant choice, because when it comes to the income distribution, neoclassical economics has erected a towering theoretical apparatus that economists are permitted to embrace or extend but never question or disregard, except at the cost of ostracism and marginalization.

At the heart of the neoclassical apparatus lie the twin concepts of marginal productivity and the aggregate production function (more on these below), and as Thomas Palley has written, when it comes to these totems, “you are either in or out.” Thus, as soon as an economist who aspires to theoretical originality wishes to investigate the dynamics of income distribution, she’s liable to find herself swiftly tangled in a conservative straightjacket.

By stressing wealth distribution, rather than income, Piketty is able to do a partial end-run around the iron wall of marginal productivity, for there’s no canonical theory of wealth inequality with the same untouchable stature. The literature that does exist, and which Piketty draws on to yield his famous r > g, is far humbler and less central to economic theory than the marginalist doctrine.

This stream of analysis, which Joseph Stiglitz played a key role in developing in the 1960s, focuses on the essentially multiplicative nature of wealth accumulation — the fact that money begets money in compound fashion — and then studies how that process unfolds over time in the presence of random “shocks” to wealth (anything from wastrel heirs to disastrous family investments) that inevitably occur as the generations pass. It’s mostly a mathematical framework, adding relatively little in the way of economic content.

Piketty harnessed this framework to produce a three-fold discovery. First comes r > g: the fact that, all else equal, both the inequality of wealth and the importance of inherited wealth will converge to a very high level if the realized rate of return on private wealth stands higher than the economy’s growth rate. Coupled to this is an amazing empirical finding: that the “raw” rate of return (this is not Piketty’s term) has in fact always stood much higher than the growth rate. Astoundingly, it’s been largely steady for centuries.

Finally comes the third part of the syllogism. Piketty concludes that the only reason magnitudes of inheritance and wealth inequality in our own lifetime have been so much less than in the Gilded Age is that for an exceptional period in the twentieth century, while the growth rate was relatively high, the realized rate of return — the rate wealth owners actually get to keep, after capital losses and taxes — fell far below its “raw” rate.

And that was due to precipitous capital losses on real estate and bonds that accompanied strict postwar rent controls and financial repression, as well as high taxes and outright physical destruction — all exceptional factors in an era of world wars. From now on, Piketty argues, capitalism can be expected to slide back toward the nineteenth century norm.

What has made Piketty’s arguments about wealth distribution so explosive is the central place he gives to the phenomenon of rentier inheritance. If the past forty years have shown us anything, it’s that rich societies have a surprisingly elastic tolerance for spiraling income inequality. To be sure, readers of liberal weeklies and perusers of op-ed pages — in other words, the target market for Capital In the Twenty-First Century (and reviews about it) — encounter a lot of hand-wringing about inequality in their news diets and on their Facebook feeds. But alongside that disquiet, there’s also a deeply rooted embrace of meritocracy as an ideal, and a stubbornly pervasive inability to perceive modern capitalism as anything but meritocratic.

Piketty deliberately sets out to disturb that complacency by raising the specter of a return to the dynastic wealth of the Gilded Age. It’s this type of inequality he finds most troubling, as it “radically undermine[s] the meritocratic values on which democratic societies are based.” It was on these grounds, in fact, that the review of Capital in Libération, where Piketty himself writes a regular column, slashed it, only somewhat unfairly, for being built on a “conservative myth” seeking to distinguish earned from unearned privilege.

Thus, while there are many things to be found in the book, it’s this notion of r > g as a Marx-like “defect” at the heart of the capitalist system, driving the system toward its own discrediting, that seems to have caught the imagination of so many liberal readers and commentators.

“Piketty Explains Why It Took Until Now For An Economist To Expose The Flaw In Capitalism,” a Huffington Post headline blares. “The very structure of free-market capitalism insures the flow of wealth from the bottom to the top,” summarizes a Daily Kos blogger. And Piketty seems to encourage that interpretation; he speculates that it was the climate of Cold War ideological competition that prevented postwar economists from perceiving the mechanism he’s uncovered.

But Piketty’s professional reception has run into trouble. Now that the book’s arguments are being digested, the same liberal, MIT-style economists who did so much to thrust Piketty’s book into the spotlight are expressing serious doubts — and the reason goes back to marginal productivity theory. That theory might end up resembling less a wall that Piketty could circumvent than a maze in which he will find himself trapped.

Marginal productivity theory lies at the deep core of mainstream economics. It’s supposed to explain production and distribution, and together with utility theory, which deals with consumer preferences, it makes up something like neoclassical economics’ “operating system” — the language in which almost every proposition must be embedded in order to work.

As a theory stating that competitive capitalism rewards every participant with an income equal to the value of his or her contribution to the economy’s output, it’s also the essential basis on which conservatives like Gregory Mankiw morally justify the existing income distribution — though liberal adherents like Paul Krugman furiously insist it has no moral implications whatsoever.

But marginal productivity theory has not held up well to scrutiny. If you’ve read far enough into the reviews of Piketty’s book, you’ve probably already come across references to a mysterious academic debate of the 1950s and 1960s called the Cambridge Capital Controversies, which pitted MIT neoclassicals like Paul Samuelson and Robert Solow against a group of Cambridge University economists, including Joan Robinson and Piero Sraffa, who sought to revive and perfect aspects of the earlier classical approach of David Ricardo and Marx.

Popular attempts to recount that debate tend to get needlessly bogged down in the abstract. They typically focus on the brain-teaser question of whether it’s possible to quantify the “amount” of capital in the economy, given that this capital stock is made up of a vast number of heterogeneous goods, from jackhammers to hard drives. And that was, in fact, the issue that first got the debate started.

But what the argument was fundamentally about was whether the marginal productivity theory of income distribution — marginalism — is a logically coherent theory. Although carried out in technical terms, the debate had strong political overtones. (Note that Solow served in the Kennedy White House, whereas Sraffa had smuggled in the paper for Gramsci to write the Prison Notebooks).

At its heart, the controversy opposed two visions of the capitalist economy. In the neoclassical vision, the most fundamental forces shaping the division of society’s produce are the supply and demand for labor and capital, and behind them, the technical facts of technology, scarcity, and consumer tastes. In this vision, the income distribution can be explained by the old platitudes “when the price goes up, less is bought,” and “when more is supplied, the price goes down.”

In the Cambridge vision, social, historical, and political forces — class struggle — are the essential factors in setting the income distribution. Once that distribution is fixed, the rest of the economy adjusts around it.

Anyone who’s taken an intro economics course might remember the way marginal productivity is explained in textbooks. Usually it goes something like this: When an employer adds more workers to her fixed stock of capital, the workers’ marginal productivity — the amount of extra output made possible by adding the last extra worker — gets smaller and smaller as more workers are added. (Think of more and more workers crowding inefficiently around a lone machine.)

Result: the number of workers a firm is willing to employ will depend on the going wage in the marketplace; the higher the wage, the lower the desired employment. If the market wage is $10 an hour, a firm will keep hiring more workers, with each worker yielding a smaller marginal product than the last, until the last worker’s marginal product touches $10 (of output) per hour. Then the firm will stop. Any further workers would have marginal products less than their $10 wage, and thus would be unprofitable to hire. (Why pay a worker $10 an hour to get $9 an hour worth of output?)

If some non-market force were to push up the wage — a strike, a law — some number of existing workers would immediately be rendered unprofitable and these will be laid off. This mechanism supplies a rationale for applying the platitude “when the price goes up, less is bought” to the purchase of human labor.

In the Cambridge capital debate, this textbook theory was advanced by neither side. It’s a fairy tale told to undergraduates. Textbook writers are fond of it for two reasons. First, for its pedagogical utility, since it’s easier to explain than the real theory. Second, to indoctrinate the young in a certain style of thought. But as for the leading mid-century neoclassicals, they had long disavowed any claim that this story could logically explain the income distribution, for a simple reason: whether or not such marginal products actually exist in the real world is an entirely empirical question, and the answer is that they generally don’t.

Machines and tools are typically designed to be used by a fixed number of workers. On a given day, a machine might be used more intermittently, or more frequently, depending on how busy things get on the shop floor. But each machine will almost always have a normal capacity, based on an intended number of users, that firms naturally try not to exceed. A shovel is made to be used by one digger; a desktop computer by one mouse-wielder.

Today, empirical studies of manufacturing industries are unanimous in finding that per-worker productivity is constant, not diminishing, as more are put to work in a factory; while even in fast food joints (as this riveting online tutorial for McDonalds managers makes clear) the volume of sales per worker does not depend on how busy the store is, except maybe during the graveyard shift, due to a residuum of fixed labor costs.

The point should be underlined: if workers’ productivity stays constant rather than diminishing as more are employed in a firm, then it would be irrational for a firm to lay off some workers just because, say, a strike or a minimum wage law hiked up their wage. The employer would get the worst of both worlds: a lower profit margin on every unit of output produced (because of the higher wage) and fewer units produced (because of the laid-off workers). Rather, her best option would be to keep producing as much as she can manage to sell while simply accepting the lower profit rate, assuming profits are still being made. Analyzed in this way, there’s no necessary reason why the platitude “when the price goes up, less is bought” ought to apply to human labor.

But the neoclassical economists on the MIT side of the Cambridge debate already knew all that. They were defending a more sophisticated version of marginal productivity theory that was subtler and, in a way, simpler.

It argued as follows: when the wage is hiked up — again, think of a strike or a law — labor-intensive goods get relatively more costly to produce, while capital-intensive goods get relatively cheaper to produce. (And the opposite happens when the wage goes down, or when the interest rate — the cost of capital — falls, perhaps due to higher savings.) As a result, consumers switch their purchases from labor-intensive to capital-intensive goods, while firms and entrepreneurs building new lines of business choose more capital-intensive, rather than labor-intensive, techniques.

It is these shifts in buying that should (not immediately, but in the long run) cause demand for labor to fall — resulting in higher unemployment, and ultimately pushing the wage back down again. In other words, when consumers and businesses choose what to buy, they are exerting demand for labor or capital through their purchases, and naturally they choose the cheapest options. This was how Samuelson, Solow, and the others on the neoclassical side of the Cambridge controversy hoped to apply the platitude “when the price goes up, less is bought” to human labor or to capital.

And this was the argument that the Cambridge University side defeated — most fundamentally Piero Sraffa in his 1960 book Production of Commodities By Means of Commodities. The problem with the neoclassicals’ argument was that it treated “capital” as if it were a homogenous substance distinguishable from labor. In reality, capital consists of many different capital goods, which are themselves produced by labor — as well as by other capital goods, which are in turn produced by other labor and other capital goods, and so on forever.

Thus, when a consumer buys a consumer good, or a firm buys a capital good, they are not simply exerting demand for that specific good. They are also implicitly demanding a whole chain of other inputs: the labor needed to produce that good, as well as the capital goods needed to produce it, as well as the labor and capital goods needed to produce those capital goods, and so on. (Hence the title of Sraffa’s book.)

In other words, the problem with heterogeneous capital goods is not so much that they’re heterogeneous; it’s that each capital input was once an output, and had its own inputs in turn.

Once capital is correctly analyzed in this way, it becomes clear that a rise in the wage does not necessarily make labor-intensive goods relatively more costly to produce, as the neoclassicals had assumed. It will certainly make the labor they require more expensive. But what about the (specific) capital goods they require? The answer is, it all depends on the complex pattern of input-output relations in the economy as a whole — how many units of good A it takes to produce good B, how many of good B to produce good C, etc., for all the millions of goods in the economy.

This casts fundamental doubt on the MIT neoclassicals’ method of applying the old platitudes to labor. Once this neoclassical story — where the relative demands for labor and capital are dependent on their relative prices — is “debunked,” to use Paul Samuelson’s contrite term, the competitive market economy no longer contains any necessary mechanism pushing the various wage rates or the profit rate to any determinate level.¹

Rather, history and custom, as well as politics, laws and struggle, will determine who gets what. It’s a system of grab what you can.

But mainstream economics never really absorbed the lessons of the Cambridge capital debate. For one thing, most economists these days are only dimly aware of the controversy — usually via stray comments heard from professors in grad school, or throwaway lines in advanced textbooks. For another, those comments are not necessarily innocuous: The Cambridge controversy was a powerful moment of collective identity-formation for the intellectual tradition Paul Krugman calls “saltwater economics.” (It was in a paper doing battle with Joan Robinson that Samuelson first invoked an “MIT school” of economics.)

In that sense, it’s unsurprising we should find marginal productivity to be the point where Piketty’s sweeping vision of modern inequality would run into trouble with the economics mainstream.

The problem for the book is that its gloomy forecast of a return to “patrimonial capitalism” is based on the prediction that over the next decades, the gap between r and g will widen due to a fall in the growth rate (g). No one has a problem with the prediction of falling growth — all else equal, this will happen simply if population growth slows, as it almost certainly will. The problem is that if growth slows while the rate of saving (i.e. investment) stays constant, capital will start accumulating faster than output is rising, meaning the measured capital-output ratio will increase.

But marginal productivity theory sees a rise in the capital-output ratio as an increase in the “supply of capital,” which, in classic supply-and-demand logic, ought to bring about a reduction in its “price” — that is, a fall in r. According to the theory, this should neutralize the effect on the r–g gap.

In his faint-praise review of Piketty’s book, Larry Summers was unyielding on this point: “Economists universally believe in the law of diminishing returns,” he insisted, in a line resounding with the thud of a fist pounding a lectern. Piketty’s forecast of rising r – g must be rejected, Summers concluded, because “as capital accumulates, the incremental return on an additional unit of capital declines.”

Piketty had of course been aware of this issue when he wrote the book, and he made an attempt to reconcile his argument with conventional theory. He contended that as growth slows and the capital-output ratio rises, r might decline (as theory predicts) but the magnitude of the decline might still be small enough to permit a net widening in the r – g gap.

The technical term for the quantitative relationship involved (that is, between the size of a change in the capital-output ratio and the size of the change in r that supposedly results, or vice versa) is the elasticity of substitution: the higher the elasticity, the smaller the “response” of r to a given change in the volume of capital. When the elasticity is higher, it’s taken to signify that the force of diminishing returns to capital is weaker, due to richer technological opportunities for labor-saving investment.

As Summers pointed out in his review, “economists have tried forever to estimate elasticities of substitution with many types of data,” so there’s a large literature on the subject. This is the so-called production function literature, which tries to apply marginal productivity theory empirically by estimating the supposed causal relationships between quantities of labor and capital inputs, on the one hand, and the quantity of output on the other. Piketty’s argument was that the elasticity needed for his forecast to come true isn’t all that much higher than at least a few of the estimates found in the existing production function literature.

But in saying so, he made a crucial error. He confused two different ways of measuring the elasticity: the usual (gross) measure, which counts depreciation as part of the return to capital, and his own (net) measure, which doesn’t.

When this discrepancy is accounted for, the elasticity Piketty requires turns out to be far, far higher than any known estimate. This was first pointed out in mid-April by Matt Rognlie, an MIT graduate student and blogger. The problem was ruefully acknowledged by Brad DeLong, the former Clinton administration economist, who is sympathetic to Piketty’s project.

Summers’s review a month later in the journal Democracy sealed the judgment: Piketty “misreads the literature by conflating gross and net returns to capital,” Summers wrote. “I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1, and I know of quite a few suggesting the contrary.”

A reader at this point could be forgiven for feeling confused. Didn’t Piketty gather his own data? He did, of course. That Herculean effort by him and his team of international colleagues, compiling statistics on historical rates of return and capital volumes in many countries going back to the eighteenth century, is the one point on which all reviews are unanimous in their praise.

As Piketty makes clear, those data — which he’s made freely available on the internet for anyone to check — are indeed “explained” by a net elasticity of 1.3–1.6, which would indicate an extremely weak force of diminishing returns to capital. Yet it’s also true that this figure is far higher than any found in the existing literature — probably more than twice as high as the highest typical estimates.

What should we make of this?

First, Piketty’s estimate of the elasticity of substitution can’t really be compared with those in the literature. His is based on economy-wide data covering decades and centuries while estimates in the literature typically cover only a few years, and often just a few industries. Moreover, his pertain to all private wealth, while the literature focuses narrowly on production capital. These are very different concepts.

But most importantly, given the flawed marginalist theory behind it, and its even more flawed basis of measurement — a subject there’s no space to go into here, but which marks a fundamental critique of the production function literature advanced in an important book published just two months before Piketty’s — the elasticity of substitution simply cannot be regarded as a meaningful measure of an economy’s technology (or anything else), or as providing any clue to its future.

What’s essential, rather, is Piketty’s empirical demonstration that the rate of return on wealth has been remarkably stable over centuries — and, contra Summers, with no visible tendency to vary in any consistent way against the “supply of capital.”

Therefore, if we expect growth to slow, the most reasonable expectation is that the r – g gap will in fact increase, and inherited wealth will expand.

But so what? Suppose it all comes true: growth slows, the r – g gap widens, and both wealth inequality and inheritance balloon. What real difference would that make in a world already swimming in inequality? Piketty thinks a return to dynastic wealth will fatally erode capitalism’s legitimacy. I’m not so optimistic.

One hundred years ago, as Arno Mayer and Sven Beckert have shown us, rich bourgeois both in Europe and America projected an aristocratic image of cultivated leisure. When Thorstein Veblen called his era’s rich a leisure class in 1899, he didn’t even feel the need to provide evidence. Today, by contrast, the rich have ostentatiously aligned themselves with the popular insistence that work must attend wealth.

The phenomenon is documented by the sociologist Shamus Khan in his recent ethnography of St. Paul’s, the elite New England boarding school that once educated generations of Vanderbilts and Rockefellers. Khan found that the mores of today’s students (and their parents and teachers) bear little resemblance to those of the past:

[T]he new elite are not an entitled group of boys who rely on family wealth and slide through trust-funded lives. The new elite feel their heritage is not sufficient to guarantee a seat at the top of the social hierarchy, nor should their lives require the exclusion of others. Instead, in certain fundamental ways they are like the rest of twenty-first-century America: they firmly believe in the importance of the hard work required to achieve their position at a place like St. Paul’s and the continued hard work it will take to maintain their advantaged position. Like new immigrants and middle-class Americans, they believe that anyone can achieve what they have, that upward mobility is a perpetual American possibility. And looking around at their many-hued peers, they are provided with experiential, though anecdotal, evidence that they are correct.

However much richer the rich may get in the coming years, it seems unlikely that they’ll ever revert to the old-regime social values of the monocle-and-tuxedo era. No matter how many millions they bequeath to their children, they will raise them to work; they will muster their accumulated advantages to secure them the best jobs; and they will urge their children to “do what they love.” Those offspring will be visible to the public mainly as the occupants of prestigious posts with high salaries, rather than as possessors of trust funds (much less titles).

All of which suggests that an increase in r – g, if it comes, may merely represent a glacial deepening of the current pattern of inequality, rather than some shocking qualitative change.

And that brings us to a lacuna in Piketty’s analysis that Paul Krugman and other reviewers of Capital have rightly pointed to. The skyrocketing of top-end income inequality we’ve actually witnessed so far in the English-speaking world has mainly come in the form of inflated “labor” earnings, rather than pure capital income.

Those earnings accrue mostly to those Piketty calls “supermanagers” — that is, corporate higher-ups. But Piketty has little new to say about what determines their incomes, and Krugman charges that in that sense the book falls short as an overall analysis of modern inequality.

Before tackling the question of why managers’ incomes have ballooned, we should pause to note an important fact: “earned incomes,” like those of the supermanagers, can bring about a rise in inherited wealth even without any increase in r – g.

Think about how r – g works: it increases the pace of wealth accumulation for capital income earners relative to labor income earners, for any given pattern of saving rates between the two groups. But the same logic can apply within the universe of labor-earners — that is, between the top earners (say, the top 1% or 5%) and everyone else. To the extent that the growth rate of labor income at the top exceeds that for the bottom — call it t > b — the relative pace of wealth accumulation for the top group will be faster than for the bottom (for any given pattern of saving rates). And as long as the children of top labor earners are disproportionately likely to become top labor earners themselves — which is true in spades — then top wealth will accumulate across generations, not just over lifetimes, and top labor earners will become not only high-paid “workers” but heirs as well.

On the surface, this dynamic differs from Piketty’s r > g scenario in that Piketty’s rentiers can be totally idle, rather than being worker-heirs. But if we admit that mores have changed, and that tomorrow’s heirs will most likely work even if they don’t “need” to, the distinction between r > g and t > b collapses.

At least in the United States, then, we’re probably already living in the early years of Piketty’s dystopia. There’s no need to quibble over elasticities of substitution.

Which brings us back to marginal productivity theory. Manacled to that concept as their “baseline” theory of income distribution, most liberal economists have done no better than Piketty in their efforts to account for the elephantine growth of these managerial incomes. They’ve had to depict that growth as the result of “rents,” due to imperfections located within specific managerial labor markets, causing incomes there to diverge anomalously from supposed marginal products.

For example, many (including Piketty himself) have argued that rising managerial income is due to distorted bargaining over executive pay within publicly traded corporations, where millions of dispersed shareholders must delegate the job of executive wage bargaining to boards with cronyish relationships to their own CEOs. Another tack is to emphasize the role of the finance industry and the rents its workers earn from excessive Wall Street risk-taking, spurred by high leverage and faulty regulation.

The problem with these arguments is that neither financiers nor public company executives have led the swelling of high-end incomes over the past several decades. Rather, the single largest contributor has been the income growth of managers in closely-held corporations outside the finance sector — that is, firms with only a few shareholders, where the controlling owners are almost always the managers themselves, usually family members. Think of the Koch brothers: as executives and 84% owners of Koch Industries, they may or may not pay themselves a salary, but it hardly matters, since most of the money would be coming out of their own pockets anyway.

Thus it turns out that at both the individual and the aggregate levels, the incomes of supermanagers are in fact an inseparable blend of “labor” and “capital” income. At the aggregate level, the increase in top 1% incomes since 1979 has shown up in the data as a fairly even mix of higher salaries (41%) and higher self-employment profits (36%), with the rest being mostly pure capital income.

As for the individual level, the only comprehensive evidence comes from a well-known 2009 paper by John Bakija and his colleagues, using IRS data on the occupations of taxpayers in the highest income groups. When they examined the top 0.1% of earners — who far more than doubled their share of national income between 1979 and 2005 — they found that 70% of that increase indeed went to corporate managers and financial workers. But of that 70%, more than half (37%) went specifically to owner-managers in closely-held nonfinancial corporations, like the Koch brothers, while only a tenth (8%) went to salaried managers in public traded nonfinancial companies, i.e. those who face absentee shareholders. The rest (25%) went to owners, managers, and workers in the finance industry.

As for finance, there’s been no tendency for its executives’ pay to outpace that of nonfinancial executives. On the contrary: even during the bubble years of the mid-2000s, top 0.1% finance executives in public companies saw their pay rise by 52%, while nonfinancial executives’ rose 58%. The industries with the biggest pay hikes were not banks, but transport, restaurants, and wholesale trade.

The statistical image that emerges from these numbers is neither Piketty’s vision of rising returns to “capital” as such, nor Krugman’s picture of an increase in returns to managerial “labor.” Rather, we see the burgeoning of a general surplus: an excess of national income over and above what’s needed to pay the nation’s non-managerial workers, appropriated broadly by all those who control capital — whether as shareholders, managers, or financiers. The picture looks something like this chart, based on data from a forthcoming paper by Simon Mohun of the University of London, which roughly estimates the share of US national product paid out to non-managerial workers in all industries since 1964:

Here we return to the vision of the classical economists — Adam Smith, Ricardo and Marx — who saw the income distribution as the outcome of a historical struggle between capitalists and those they employ, with no “equilibrium solution” possible.

The history this chart evokes has been told before, by writers like Doug Henwood and J.W. Mason, though maybe the definitive version still waits to be told: how resurgent capitalists in the 1970s and 1980s, emboldened by a weakened working class, drafted managers tightly into their ranks using the tools and personnel of Wall Street, and reshaped the economic landscape. (Note the sheer size of the shift in this chart: had it not occurred, the average non-managerial worker’s compensation would be more than 20% higher today.)

Just how the spoils of that twentieth-century victory get handed down to future generations is a matter that will no doubt depend on the multiplicative dynamics of capital in the twenty-first century, as Piketty claims. But whether those numbers spell a social crisis or just more of the same will depend on how the next chapter of the struggle is written.

1. In a tour de force reconstruction of the history of distribution theory, Michael Mandler has shown that even using the neoclassical general equilibrium approach, it’s impossible to build a model without arbitrary restrictions in which wage and profit rates can be pinned down by technologies, preferences and endowments, unless at least one of two key features of real capitalist production is omitted: fixed production coefficients and capital accumulation over time. (The latter is usually omitted.) That’s why to the end of his life Paul Samuelson pinned his faith in marginal productivity on the dubious possibility that perhaps real-world production might not be so well described by fixed coefficients after all.
2. Even if we accepted Summers’s beliefs about diminishing returns, there would be good reason to doubt their relevance to Piketty’s forecast of r – g. Diminishing returns to capital will only affect r – g under the assumption that the predicted growth slowdown will have no effect on the saving-investment rate. That’s the neoclassical assumption, which sees investment (“in the long run”) as driven purely by individual saving preferences. Piketty plays along with this story, but in reality slower population growth will likely mean less investment.