On September 6th, after I bemoaned the lack of things to blog about, Chris asked me whether I might do a tutorial on Volume III of CAPITAL. I responded with a post on the 10th briefly explaining why I did not think it would be much fun, and Chris immediately took exception to my explanation, citing and giving links to videos of lectures by Andrew Kliman, as well as to some publications. I am currently very busy with my Bennett project, and I simply do not have the time to watch the videos from start to finish and read the works referenced, so that I can give a serious reply. But it seems to me I owe Chris some answer, however fragmentary, so here goes.
As I suspected, Kliman is a student or follower of Richard Wolff and Steven Resnick, both of them old friends of mine from the UMass Economics Department. Rick and Steve have for more than thirty years been developing and teaching a systematic interpretation of Marx's economic theories. In true academic fashion, they have published books and articles, trained students, organized annual conferences, started a journal, and done all the other things that we do in the Academy to advance our views. I have enormous respect both for their work and for their dedication and energy, even though I do not agree with them about a number of things. Our specific disagreement over the so-called Transformation Problem is rather technical, but at the risk of losing everyone but Chris, I will spend a few paragraphs explaining what is at stake.
I have argued in my published writings on Marx and also on this blog that in CAPITAL, Volume I, Marx assumes equal organic composition of capital, only relaxing this assumption in Volumes II and III. Since Ricardo's version of the Labor Theory of Value is correct only under this severe constraint [as Ricardo himself was aware], this assumption allows Marx to focus on what he considers the more fundamental question that Ricardo cannot answer even in the special case in which his theory is true, namely why there is a positive rate of profit in a capitalist economy. Marx then introduces his distinction between labor and labor power to solve the problem, demonstrating thereby that capitalism rests essentially on the exploitation of the working class.
Mathematically speaking, the arguments by which the various propositions of Volume I are demonstrated -- at least on my interpretation of the book -- presuppose that competition establishes a uniform rate of profit throughout the economy. It is this assumption that yields the conclusion that input and output prices are identical for a given commodity. This way of analyzing things, which Kliman correctly labels a "simultaneous" approach, is widely adopted in the large international literature written by contemporary mathematical economists interested in casting Marx's arguments in modern dress. I am a big fan of this approach.
However, there is an alternative way of reading Volume I. If you give up the assumption that competition equilibrates the system by establishing a single economy-wide profit rate, then you can represent Marx's analysis as approaching such a uniform profit rate over time by way of a series of adjustments on the part of capitalists to the information presented by the market. In that analysis, input and output prices are not identical. This is not a simultaneous analysis, but a temporal analysis.
But I believe that the end result of these two modes of analysis is the same. The same relationships emerge between labor values and prices, and the same divergences of prices from labor values appear, which must be explained and analyzed by the same arguments that Marx invokes in Volume III. So I do not see how adopting Kliman's approach alters, in the end, our understanding either of capitalist economies or of Marx's text.
The second question, on which I am afraid I have nothing at all to say, is the dispute over Marx's claim that there is a tendency for the rate of profit to fall as more capital intensive techniques are introduced. I would have to read, or else watch on video, Kliman's analysis of that dispute, and I just have not done so yet.
Chris, I hope this at least demonstrates that I take your comments seriously, even if I am not now in a position to respond to them fully.