There are probably few criticisms of neoclassical economics that have been both so universally acknowledged to be valid, and yet so completely ignored, as the Cambridge Capital Controversy (CCC). Chapter 7 of Steve Keen’s Debunking Economics provides an overview of this debate about the nature of capital.
Basic economic analysis teaches that capital, like other factors of production, is paid in proportion to its productivity – the so called ‘Marginal Product of Capital (MPC),’ which is presumed to be equal to the rate of profit. Keen gives two good criticisms before he delves fully into the CCC:
First, the MPC assumes that other factor inputs are fixed when capital is employed, which leads to our first problem: since capital is (rightly) assumed to be the least variable input, any time period in which you can employ more capital is surely one in which you can employ more labour, too? Once again we are forced to face the reality that firms tend to vary all inputs employed at once.
Second, in an industry as broadly defined as ‘the capital market’ we run into familiar Ceteris Paribus problems, where varying inputs will create effects on wages and the existing capital stock that alter the rate of profit. For small and medium sized firms these effects will be negligible, but when analysing the biggest firms and entire industries the feedback between them will create collateral effects that undermine partial equilibrium methodology.
However, even ignoring these criticisms, there are serious issues with the neoclassical treatment of capital.
Capital is often measured in units. There are obvious problems with this: capital includes brooms, blast furnaces, buckets, string and potentially any commodity you care to think of, so a single unit of measurement is difficult to justify. Generally economists either leave capital in undefined units or measure it by price. The former treatment does not deserve to be criticised formally – something that poorly defined is, like utility, Not Even Wrong. As for the latter, Keen notes that there is an “obvious circularity” to the definition. The value of capital is based on the expected profit from it, which is partly based on the price of capital. Thus the use of price as a unit of measurement is not particularly enlightening.
Piero Sraffa’s Devastating Critique of the Neoclassical Treatment of Capital
As always, Piero Sraffa offered the most fully fleshed out and devastating critique of the neoclassical theory.
Sraffa proposed that, instead of treating one factor of production as a mysterious substance called ‘capital,’ we instead supposed that goods produce other goods, when combined with labour (hence the title of his Magnum Opus, Production of Commodities by Means of Commodities). He rigorously derived an internally consistent model with the sole aim of invalidating neoclassical economics on its own terms. There is some debate about the empirical applicability of his conclusions, but logic is sufficient to invalidate the neoclassical theories, which are based on the same premises.
Sraffa builds up a complex model step by step, starting simple. In the first statement of the model, there are a few firms, whose only inputs are the goods produced by other firms and themselves. So firm A needs a certain amount of commodities x, y and z to produce commodity x, whilst firm B needs a different combination to produce commodity y, and firm C a different combination to produce commodity z. Each firm produces just enough of their respective commodities for economy-wide production to continue at the same level in the next period. Sraffa’s next step is to alter the model so that each firm produces more than they need to in order to continue production – a profit.
The first conclusion he comes to is that the relative production of factor inputs,and the rate of profit, is not based on supply and demand, but on ‘the conditions of production’ – the amount of inputs required to keep a firm or industry going.
Sraffa then explicitly incorporates labour into his model. He notes that wages are obviously an inverse function of profit: the higher they are, the lower profit will have to be, and vice versa. He then proposes a new method of measuring capital: treat it as the dated value of the labour required to produce it (wages), plus the profit made from it since it was produced, plus the value of the commodity that was combined with the labour to produce it. This ‘residual commodity’ can then be further reduced to labour times profit, plus another commodity, and so forth:
commodity a = ((labour input at time x)*((1+rate of profit)^(time periods since time x))) + commodity b
As Sraffa himself points out, there will always be residual commodity left out if you break down a commodity into the labour and commodity required to create it. However, as you do this again and again, the resultant term becomes smaller and smaller until it can be negated. This type of reasoning is far more scientific than the neoclassical approach and actually closely resembles the perturbation methods used by mathematicians and engineers, where a function is split into an infinite amount of terms of decreasing value, but only the first few are used in calculations.
In the equation above, there are two competing effects: profits and wages. As one rises, the other must decrease. It is easy to see in this in equation that there is a peak value for capital somewhere in the middle; either side of this the reduction in one term will overwhelm the other and the measured value of capital will decrease.
This creates an interesting phenomenon known as capital reswitching. Consider two production techniques, A and B, which involve inputting different amounts of labour at different times – a common example is creating wine through ageing it (A) or through a chemical process (B). A requires more labour input in the distant past; B requires more labour input in the near past. At a zero rate of profit, both techniques are identical. As the rate of profit rises, technique A, which relies on more distant, fewer labour inputs, will remain cheaper and therefore more viable. However, as the effect of the rising rate of profit compounds due to the time delay, technique A will become more and more expensive, and technique B will take over.*
The point of this approach is to show a few things:
(1) The value of capital varies depending on the rate of profit, as the rate of profit is a variable in the equation for measuring capital. Since the measured amount of capital depends on the rate of profit, profit cannot simply be said to be the ‘Marginal Product of Capital.’
(2) There is no easy to discern relationship between profitability and the amount of capital employed. Generally, neoclassical economics teaches that output is simply a concave but increasing function of the amount of capital employed, much like any other demand/utility curve. Capital reswitching destroys this idea.
(3) We cannot calculate prices without first knowing the distribution between wages and profits. The measured price of inputs depends on income distribution, not the other way round.
Many might be struck by the sheer level of abstraction in Sraffa’s approach. It’s worth noting that in Commodities, he adds many more levels of realism past those that Keen explores. But, as I said before, the basic point was taking on neoclassicism with its own logic, rather than presenting an alternative. By the end of the debate, Samuelson and Solow had both conceded that the criticisms were valid, and their models were wrong or incomplete.
Discussions of the CCC since then have tended to assume the standard neoclassical tactic of asserting the objections have been incorporated. But this stuff was 50 years ago. Why do undergraduate and postgraduate programs still teach concepts like the MPC? The Solow-Swan growth model, which depends on an aggregated capital stock K, subject to diminishing returns? As Robert Vienneau says, if neoclassicism were really revising itself to the extent that’s needed, we’d expect some of the modifications to filter down over time. But the fact is that they haven’t.
In fact, what seems to have happened is that economists have done a fairly typical dance – weaving between ‘that is unimportant’ and ‘that has been incorporated:’
Aggregative models were deployed for the purposes of teaching and policymaking, while the Arrow-Debreu model became the retreat of neoclassical authors when questioned about the logical consistency of their models. In this response, a harsh tradeoff between logical consistency and relevance was cultivated in the very core of mainstream economics.
This sort of evasiveness is common – there will always be a paper written recently that attempts to shoehorn any objection one cares to think of into the neoclassical paradigm. But these objections are incorporated one at a time, rarely find their way into the core teachings, and never involve questioning the foundations of neoclassicism on any substantive level. The reality is that, when the problems are as deep as the ones highlighted in the CCC, we need a meaningful overhaul rather than mere ad-hoc modifications.
*For those interested, the linked Wikipedia article has a fairly simple numerical example where the most effective method goes from A to B and back to A again.