The Delirium of Quantities

Thomas Piketty’s recent book Capital in the Twenty-First Century has leveraged current anxieties about rising inequality to re-awaken a discussion of capitalism, in a grand style rarely seen since the dawn of the 20th century. This is a book about the nature of capital, in its essentials, and thus about the fundamental structure of modern history. Irrespective of its ultimate persuasiveness, such lofty ambition is worthy of appreciation. Innumerable conversations of great interest have already been spun from it.

As a result of the excitement generated by Piketty’s book, its central formula r > g has become the most widely-recognized economic statement of our age. This post preserves strict neutrality in regards to the realism of r > g. It seeks to provide only a minimal elucidation, on the way to exploiting the formula, as a gateway into more general perplexities. (UF has nevertheless to endorse, if parenthetically here, Piketty’s remarkable conclusion: “… as I discovered, capital is an end in itself and no more.”)

What r > g describes abstractly is the functioning of capitalism as an engine of inequality. When ‘r‘ (the rate of return to capital) exceeds ‘g‘ (the rate of economic growth), the concentration of wealth intensifies. This is the normal capitalistic trend, Piketty argues, although it has been obscured in the last century by abnormal conditions of world war and massive capital destruction. Under more ‘typical’ conditions, the return to capital is roughly three times the rate of overall economic growth, and in lieu of catastrophe, some comparable disproportion can be expected the future of modernity. Furthermore, there is no natural equilibrium which would cancel the trend. It is mathematically possible, and socio-economically probable, for r > g to hold indefinitely, as capital accumulation outstrips aggregate economic growth, widening inequality without definite limit. (A sample of the subsequent disputation can be followed at the links provided.)

To make theoretical sense of Piketty’s formula, ‘r‘ and ‘g‘ have to be understood as distinct but commensurable quantities. Return to capital (‘r‘) is no different from capital itself, expressing the rate of capital accumulation in algebraic form. Since ‘r‘ and ‘g‘ are related through an arithmetical discrepancy, they are implicitly denominated in some common quantitative medium or currency, providing economic consistency, and enabling convenient conversion into monetary units. To state r > g, therefore, is to assert the semantic value of capitalist semiotics. Arithmetically-consistent monetary units effectively describe the global substance of the economy.

Unfortunately, the foundations of any such general economics remain profoundly obscure. As numerous commentators have remarked, the rigorous quantification of capital has been radically problematized at least since the Cambridge Capital Controversies. Cohen and Harcourt note:

Earlier [capital] controversies occurred at the turn of that century among Böhm-Bawerk, J.B. Clark, Irving Fisher, and Veblen and then in the 1930s among Knight, Hayek, and Kaldor. Similar issues recurred in all there controversies […] Looking back over this intellectual history, Solow (1963, p.10) suggested that “when a theoretical question remains debatable after 80 years there is a presumption that the question is badly posed — or very deep indeed.” Solow defended the “badly posed” answer, but we believe that the questions at issue in the recurring controversies are “very deep indeed.”

Piketty, then, serves to remind us that no coherent theory of capital accumulation exists. Bichler and Nitzan make this point forcefully in their essay Capital as power: Toward a new cosmology of capitalism:

Although most economists refuse to know it and few would ever admit it, the emergence of power destroyed their fundamental quantities. With power, it became patently clear that both utils and abstract labour were logically impossible and empirically unknowable. And, sure enough, no liberal economist has ever been able to measure the util contents of commodities, and no Marxist has ever been able to calculate their abstract labour contents – because neither can be done. This inability is existential: with no fundamental quantities, value theory becomes impossible, and with no value theory, economics disintegrates.

Among the possibilities — if not (necessarily) the firm expectations — of capital in the 21st century, is that we might finally learn what it is.

ADDED: From an Austrian perspective, ‘Steve’ at World Liberty News writes:

Piketty’s approach focuses on the quantity of capital and, more importantly, the rate of return on capital. But these concepts make little sense from the perspective of Austrian capital theory, which emphasizes the complexity, variety, and quality of the economy’s capital structure. There is no way to measure the quantity of capital, nor would such a number be meaningful. The value of heterogeneous capital goods depends on their place in an entrepreneur’s subjective production plan. Production is fraught with uncertainty. Entrepreneurs acquire, deploy, combine, and recombine capital goods in anticipation of profit, but there is no such thing as a “rate of return on invested capital.” […] Profits are amounts, not rates. The old notion of capital as a pool of funds that generates a rate of return automatically, just by existing, is incomprehensible from the perspective of modern production theory.

ADDED: On a tangential note, but one of special interest to this blog —

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