Understanding Sraffa

[Red.Jack.Philly]

Hello. This is my first post on this forum. A comrade and I are trying to wrap our heads around the so-called "Cambridge Capital Controversy (http://en.wikipedia.org/wiki/Cambridge_capital_controversy)." While he's a little more well-versed than I am in economics, I'm going to speak for myself here.

Here's my background: I've taken two college economics courses (macro and micro.) I've read quite a bit on Marxian econ and have a decent grasp on the topic. I've heard many Marxist criticisms of marginalism, but from what others have told me and from what I've gathered by reading about the topic, the most devastating critique of it comes from Sraffa in his The Production of Commodities by Means of Commodities. In it, he shows that bourgeois economics falls apart on its own terms.

The problem for my comrade and I is that we don't really understand the argument. It seems like it's very technical and we haven't been able to find an accessible explaination of it (Wikipedia hasn't helped either.) The best we've done is this Chris Harman article Called "The Crisis of Bourgeois Economics." (http://www.marxists.org/archive/harman/1996/06/bourgecon.htm)

Here's an excerpt:

The radical Keynesians at Cambridge took up Sraffa’s point, insisting that the neo-classical economists’ elaborate algebraic calculations and geometrical curves rested on a tautology as meaningless as that which says, ‘An egg is an egg.’ The neo-classicists said profits and interest were ‘rewards’ for ‘abstention’, ‘waiting’ or ‘production time’, and were equal to the increase in value (‘marginal product’) produced by extra capital. So the rate of profit was marginal product divided by the value of the total capital. But how was the value of that capital to be measured? It could not be arrived at by adding together the different physical measurements of goods that made up the means and materials of production (tons of iron, gallons of oil, kilowatts of electricity, etc.). In fact, it depended, according to marginalist theory, on the value of the marginal product – the same thing that the measurement of profit depended on. In that case, there was no way of arriving at a figure for the ratio of the profit to the capital, that is, at the rate of profit. Or, to put it another way, the rate of profit and interest depended on the amount of capital, and the amount of capital depended on the rate of profit and interest.

Could anyone please either:
1.) Provide a detailed, yet accessible explanation of the "Cambridge Capital Controversy" and the implications of Sraffa's work for marginalism...
or
2.) Provide a work which gives a detailed, yet accessible explanation to people with my background.

Thanks!

Comradely,
Red Jack

[ComradeRed]

Could anyone please either:
1.) Provide a detailed, yet accessible explanation of the "Cambridge Capital Controversy" and the implications of Sraffa's work for marginalism...
or
2.) Provide a work which gives a detailed, yet accessible explanation to people with my background. Basically, Sraffa treats marginalism as a "word problem" and does all the work from there.

Steve Keen summarizes up Sraffa's points thus:

Sraffa’s technique was to eschew the initial aggregation of capital, and to say, in place of ‘factors of production produce goods’, that ‘goods produce goods’ – in concert with labour. Sraffa then used this ‘assumption-free’ model of production to show that the economic theories of price and of income distribution were invalid.

The essential point in his analysis was that capital does not exist as an easily definable entity, yet such an existence is necessary for the simple parable that profit represents the marginal productivity of capital to be true. He made this point by constructing a series of models that directly confronted the true complexity of a system of commodity production.
Sraffa worked with an economy in equilibrium, which is empirically incorrect but economists use it mathematically as an axiom.

A more elaborate explanation from The Economics Anti-Textbook (pp 181--83):


Consider the textbook story about the determination of the return to capital. This postulates an aggregate production function with capital as one input. From this we determine the marginal product of capital, which in equilibrium
equals the real rate of interest. But how do we add up all the different kinds of capital – all the different tools, machines and structures – to get one measure of capital to put into the production function? The answer is that we must add everything up in dollar value terms. But this means that the value of capital must be known before it enters the production function, and hence before the value of capital can be determined.

This circularity is not, however, the telling point. There are many examples of simultaneous mutual dependence in economics that can be routinely solved. The telling point is that during the ‘Cambridge capital controversies’ it was shown that there may be no unique equilibrium solution. Because of the mutual dependence between the value of capital and the interest rate, it can be shown that one method of production – call it technique A – can be cheaper at both high and low interest rates, while another method – call it technique B – is cheaper at intermediate rates of interest. This is known as the ‘reswitching result’, and it implies that the demand for capital can have a backward-bending segment, implying the possibility of multiple equilibria, as shown in Figure 8.6. [not shown, imagine a dollar sign $ plotted]

If the possibility of multiple equilibria means that the impersonal force of marginal productivity isn’t enough to determine the interest rate, then what does determine it? Suddenly, the door is open for all kinds of other social forces to matter: social norms, relative power, bargaining, government policies, and so on.

The neoclassical economists responded by arguing that the aggregate model is used only as a simplifying device – they know it isn’t intellectually respectable, so showing that it’s false isn’t damaging their core theory. Rather, the intellectually respectable version is the extremely disaggregated (and complex) general equilibrium theory. In this theory, each disaggregated factor must earn a reward equal to its marginal product and the model economy is Pareto-efficient. Unfortunately, as the critics were quick to point out, these models provide no support for a ‘relative scarcity theory of distribution’. For example, one cannot assert that, ceteris paribus, an increase in the supply of capital causes real interest rates to fall, as is implied in the right-hand diagram of Figure 8.5. Nor can one assert that, ceteris paribus, an increase in the supply of labour causes real wages to fall, as is implied in the left-hand diagram of Figure 8.5. As Cohen and Harcourt (2003: 207) put it:


[T]he switch to general equilibrium, rather than saving the neoclassical parables, abandoned them for simultaneous equation price systems ... Relinquished, however, were one-way causal claims about unambiguously signed differences in the interest rate associated with differences in the quantity of capital.

Furthermore, general equilibrium theory itself is plagued by difficulties in showing uniqueness and stability (see Ackerman 2002, and the addendum to Chapter 6). It seems that there is something fundamentally wrong with the neoclassical ideal world of perfect competition.