The Cambridge capital controversy
In 1960, Sraffa’s Production of Commodities points out the possibility of reswitching of techniques, already hinted at by Joan Robinson in the mentioned 1953-54 article (on whose limits see Petri 2004: 227-33).
This possibility, universally admitted after a 1966 Symposium in the Quarterly Journal of Economics, causes enormous surprise because it reveals that factor substitution need not work in the way until then unquestioned: a technique, abandoned in favour of others because the interest rate rises, may come back as being the most convenient as the rate of interest rises further; which means that if one switch of technique is in a direction supportive of marginalist theses, the other switch contradicts them. Thus, whatever way one measures the capital-labour proportion of different techniques, a rise of the interest rate need not cause a switch to a less capitalintensive technique. The impossibility of deciding unambiguously which techniques are more capital-intensive puts a final nail in the coffin of the idea that the observed methods of production entail the presence in the economy of a “quantity of capital” independent of distribution. Furthermore, a decrease of real wages may cause a switch to methods of production that decrease the amount of labour employed per unit of net product, and it may raise the normal relative price of the goods using more labour per unit of (value) capital: both the direct and the indirect factor substitution mechanisms are questioned. In value terms, a decrease of the rate of interest can cause the switch to a technique with a lower value of capital per unit of labour; this reverse capital deepening undermines the traditionally assumed negative interest elasticity of the demand for capital, and hence of investment too. Garegnani, in an influential article on Keynes (1964-65), argues that this possibility undermines faith in the rate of interest as capable of bringing investment into equality with savings; as a consequence one must reject Keynes’s investment function and the “neoclassical synthesis”. This, he concludes, strengthens Keynes’s principle of effective demand and the thesis that wage flexibility does not guarantee the tendency to full employment, and that growth depends on the evolution of the autonomous components of aggregate demand.One line of defence against the “Sraffian” criticisms is the argument that the likelihood of reswitching and of reverse capital deepening is low so their possibility can be neglected, as for Giffen goods. However, this attempted rehabilitation of traditional capital-labour substitution, besides being based on underestimation of the “likelihood” of reswitching (Petri 2011a), relies on a mistaken analogy: different from income effects, reswitching does not indicate a reason for multiple solutions in an otherwise consistent system of equations; it destroys the logical consistency of the conception of capital as a single factor and thus it destroys all legitimacy of determining equilibria based on capital treated as a single factor. The problem is not the likelihood of multiple or unstable such equilibria but the impossibility of determining them.
For this reason, the treatment of capital as a single value factor, still widely accepted in the early 1960s, undergoes a loss of theoretical legitimacy, and the main reaction to reswitching quickly becomes the claim that the “rigorous” versions of marginalist theory (by now more often called neoclassical theory) are the neo-Walrasian general equilibrium models that do not need capital the single factor; the one-good models (the sole versions by now that treat capital as a single factor, hiding its conception as a value factor under the thin disguise of the physical homogeneity obtained with the one-good assumption) are argued to be only simplifications, shortcuts to results that the “rigorous” theory would confirm, such as factor rentals inversely related to factor abundance, or supply-side-determined growth. This line of defence abounds with misunderstandings. Bliss (1975) and Hahn (1982) take it for granted that neo-Walrasian intertemporal equilibria are the only conceivable disaggregated theory of value and distribution.
The notion of long-period disaggregated equilibrium such as Wicksell’s is totally forgotten; the problems with “capital aggregation” are misunderstood as identical with those posed by aggregation (in production functions) of heterogeneous labour or land, without perceiving the fundamental difference consisting of the insufficient persistency of the endowments of the several capital goods that makes it nonsensical to take them as given, a problem not arising for different qualities of land or of specialized labour, whose quantities are persistent and accordingly can be treated as different factors. The possibility of a theory of income distribution not based on factor supply-and-demand equilibration is not considered at all. This makes Hahn present Sraffa’s prices as a very special case of intertemporal general equilibrium prices (the case when initial endowments cause equilibrium relative prices not to change from one period to the next), to be contrasted with the capacity of general equilibrium theory to deal with any given initial endowments: absent is any recognition that Sraffa is not assuming full employment, or that his prices are the same normal prices that not only Ricardo but also Wicksell tried to determine, necessarily associated with an endogenous determination of the composition of capital.This helps to explain why the undermining of the notion of capital the single factor does not bring about an abandonment of the entire supply-and-demand approach. Hicks’s misrepresentation of long-period equilibria as secularly stationary equilibria has favoured an inability to understand the long-period method; the new generations of economists, acquainted only with neo-Walrasian equilibria, have grown accustomed to the auctioneer, are unaware that, for example, in Wicksell complete disaggregation has gone together with the treatment of capital as a single value factor of variable “form”, and do not understand the reasons for such a treatment of capital; the impossibility to treat capital as a single factor is viewed as questioning only the use of aggregate production functions.
Garegnani’s 1960 book, that discusses Wicksell at length, concluding that the impossibility of determining the capital endowment of long-period equilibria undermines the entire marginalist approach, is not very widely read (it is not translated into English), but above all it is not found decisive because neo-Walrasian equilibria do not require - it is argued - capital the single factor.Garegnani (1976, and then in greater detail in 1990) tries to re-establish an understanding of the evolution of neoclassical capital theory, remembering the method of normal positions, and the marginalist need for a given endowment of capital the single value factor of variable “form” in spite of complete disaggregation if the aim is to determine a normal-position (that is, a long-period) equilibrium, because the several endowments of capital goods must then be variables. He argues that the shift to the neo-Walrasian treatment of the capital endowment was due to the indefensibility of the value-capital factor, with an example from Hicks. He proceeds to stress three new problems of neo-Walrasian equilibria owing to the vectorial specification of the capital endowment:
1. Impermanence problem. Some of the data determining the equilibrium (endowments of the several capital goods and also, in temporary equilibria, expectation functions) lack persistence, being changed by disequilibrium decisions; the auctioneer is only a fairy tale; therefore before the repetition of transactions may correct or compensate the deviations from equilibrium, the equilibrium’s data may have changed considerably; then, since the theory is silent on what happens in disequilibrium and therefore offers no reason to exclude a cumulation of deviations of the actual path from the path traced by the sequence of equilibria (even assuming this sequence does not itself suffer from indeterminacy), the actual path remains undetermined.
2. Substitutability problem. There is almost no substitutability among factors, because different production methods generally require different capital goods, not the same goods in different proportions; thus the demand for labour will be extremely inelastic and the equilibrium real wage may easily be totally implausible.
3. Price-change problem. Since equilibrium relative prices cannot be assumed persistent, consideration of price changes must be allowed but only two equally indefensible roads are available: intertemporal equilibria require the absurdity of complete futures markets or perfect foresight, which means that, clearly, real economies will behave differently; temporary equilibria suffer from an indefiniteness problem because the single equilibrium as well as the path followed by a sequence of temporary equilibria come to depend upon arbitrary assumptions on unknowable initial expectations and on how these evolve over time.
However, Garegnani (1990) continues, these new problems, that drastically undermine the capacity of these equilibria to indicate the behaviour of actual economies, are incurred to no avail, because the need for the traditional conception of substitutability between labour and capital the value factor has not been removed. A persistent change in the rate of interest necessarily causes a tendency of prices over time toward the corresponding long-period relative prices, and hence it causes changes in technical choices and in consumer choices tending to those studied by long-period analysis. The full employment assumed by neo-Walrasian equilibria requires that these changes be such as to ensure that, if the value of decisions to save were to exceed that of decisions to invest, a reduction of the rate of interest would induce firms to absorb the excess savings by coupling the existing labour supply with capital goods of greater value. This is what the validity of the conception of capital as an amount of value and yet behaving like a technical factor would ensure, but reverse capital deepening refutes it. So the shift to the neo-Walrasian versions represents a cosmetic change only; the old conception of capital is still implicitly and illegitimately assumed to be valid if it is claimed that neo-Walrasian equilibria mimic tendencies of actual economies.