Before launching into what will undoubtedly be a very long and complex discussion of Marx's theories, I thought I might pause just for a day to catch my breath, make an observation, respond to several [but not all] of the comments, and devote a few paragraphs to a minor matter that is not, strictly speaking, part of my story, but is nonetheless interesting.
So, taking a deep breath, first the observation. As I have mentioned on this blog, I am currently teaching a course at Duke University in a Learning in Retirement program there called the Osher Lifelong Learning Institute [OLLI], on Plato's REPUBLIC. This is a program that caters mostly to seniors like myself, and is taught by volunteers, of whom I am one. Last Monday, I was lecturing on Book I of the REPUBLIC. At one point in the lengthy exchange with Thrasymachus, Socrates distinguishes between the activities of a doctor or ship captain or shepherd as such, and the accidental fact that each of them, while pursuing the techne or craft of medicine, etc., also earns wages. The earning of wages is no part of the essence of the techne, he observes [and Thrasymachus agrees.] As I was explicating this passage, I suddenly realized that as I participated in the OLLI program, I was acting purely as a teacher, because I receive no wages for my teaching. Well, the same thing is true of this tutorial, and all the other tutorials and such that I have from time to time posted on my blog. Since I receive no wages for this labor, it is truly a labor of pure unadulterated pedagogy. I rather like that thought.
Now, as to Ricardo on slavery. I did not recall Ricardo discussing the subject, so I consulted my ten volume edition of the complete works and writings of Ricardo, edited by Sraffa with the assistance of none other than Maurice Dobb. In the index [which is the eleventh volume], I found only three listings under "slavery," all to speeches Ricardo gave in Parliament in 1823. It is clear from one of them that he was opposed to slavery [as were all of his circle, including his close friend James Mill, John Stuart's father], but he seems not to have been moved to discuss the subject in any systematic manner. Indeed , one of the three speeches is much more concerned with the depredations of white ants on the sugar plantations in the East Indies.
As for the matter of the mathematics, I am sure the solution of simultaneous equations was well understood in Ricardo's day, but neither he nor other economists seem to have thought to use it to analyse the vexing problems of the Labor Theory of Value. It was I think Leontieff's Input-Output analysis that first used mathematics in this way, though I may be wrong about that. Marx himself struggles in CAPITAL to analyse the subject, and gets things badly wrong, as many people have pointed out. There is actually a large specialist literature on this subject, with some people devising strategies for defending what Marx does as a sort of iterated approximation, but Marx himself pretty clearly did not conceptualize the subject in this manner. As we shall see, Marx's insights and intuitions are brilliant, but his exposition leaves a good deal to be desired in this area.
And now to the minor but interesting side note. I have been talking about Adam Smith and David Ricardo, but probably the most widely read political economist in the middle of the 19th century was John Stuart Mill. We remember Mill for his classic work ON LIBERTY, and also [if we are philosophers] for his essay UTILITARIANISM. In his own day, however, Mill was very widely known for a two volume exposition of classical Political Economy, PRINCIPLES OF POLITICAL ECONOMY, which first appeared in 1848 and went through seven editions, the last in 1871. My copy, which runs to almost 1200 pages in two volumes, is an 1897 reprint of the 5th edition, which I picked up for $2.50 in a second hand book store more than half a century ago. Book II of Mill's PRINCIPLES is called Distribution [Book I is of course Production], and Chapter iv of Book II is entitled "Of Competition and Custom." In this chapter, Mill offers an observation that is at one and the same time obvious and indisputable, but also freighted with the greatest theoretical significance. In the marketplace, he points out, competition does not always operate alone to determine the prices at which commodities exchange. Sometimes sheer custom or habit shapes consumer choices. A piece of land may have commanded a certain rent for several generations, and that fact alone will incline prospective renters to be willing to pay that rent even though competition might, working alone, drive the rent higher or lower. Those shopping for consumer goods may be influenced by a preference for a local market run by someone with whom they have established a personal relationship, even though identical goods may be available at a lower price literally next door. And so on.
One can, of course, always explain this behavior by supposing that the consumer has, and is engaged in maximizing, a utility function that takes as arguments interpersonal relations as well as market prices. But the significance of Mill's observation is this. If consumers are influenced only by price [as between two identical instances of the same good], then it is possible to calculate their behavior ex ante, not simply account for it ex post. On the basis of such ex ante or a priori calculations, one can then deduce powerful theorems about the determination of natural or equilibrium prices. That, after all, is what I did when I solved the price equations for our little corn iron books model. But if custom [or, what is in some sense irrational factors] plays a role in the determination of consumer behavior, it is impossible to incorporate it as a factor ex ante into one's calculations. The most one can do is to build dummy variables into one's equations representing the "custom" factor. Then, one can collect data about past consumer behavior -- what economists call time series -- and make a series of estimations or predictions about what values those dummy variables will take on in the future.
In short [since this is already getting too long], one can stop doing microeconomics and start doing macroeconomics. This is why, among economists, microeconomics is considered purer and classier than macroeconomics, for all that macroeconomists win Nobel Prizes too. If I may wrap this up with another reference to the REPUBLIC, macroeconomists are like the people chained to the floor of Plato's cave, predicting the shadows as they pass by on the wall where they are thrown by the fires illuminating the objects carried behind a parapet by slaves.