I published Understanding Marx thirty-one years ago. In the intervening three decades, although I have of course looked at the book from time to time, I have never read it with the care I am now giving it as I prepare my lectures on it for my Marx course. Last Wednesday and next Wednesday, I am covering the first three chapters, roughly half of the book, dealing with the theories of Adam Smith and David Ricardo. Last week, while carefully re-reading the chapter on Smith, I discovered a mistake. It is a small mistake, which is in fact corrected in the next paragraph, so it has no impact on the argument. But it is a flat out mistake. Having quoted Smith as stating that it takes Diana one day to catch a deer while it takes Orion two days to catch a beaver, I go on to say that when they meet in a clearing in the woods after two weeks of hunting, Diana is carrying five deer and Orion is carrying ten beaver. Aaaarrrggghhh!!!! I think it just seemed intuitively obvious to me that deer are harder to catch than beaver [but what do I know?]. In the next paragraph, I say that after some bargaining, they agree to exchange two deer for one beaver [which is correct]. Thus is born the Labor Theory of Value.
I challenged the class to tell me where I had gone wrong, and after a few minutes one of the students correctly identified the error. O.K. Cute. Shows the Professor has humility, right?
Sigh. Today, I have been working on my lecture on Ricardo's version of the Labor Theory of Value [embodied labor and all that good stuff], preparing to go through a rather more complicated example of the calculation of prices, for which purposes I must invoke the dreaded quadratic formula of high school algebra fame. [You all recall it, no doubt: "x equals minus b plus or minus the square root of b squared minus four ac, all over 2a." Sound familiar?]
The example is designed to illustrate Ricardo's important claim that the wage and the profit rate are independent of commodity prices, a claim that is in fact true for the special case that Marx later dubbed "equal organic composition of capital." The algebraic manipulations, although conceptually elementary, are actually a trifle complex, since one carries along terms with the wage rate, w, in them that then miraculously drop out at the end.
In my book, I did what all serious economists and mathematicians do -- I left out half of the steps, relying on the reader to supply them. And since I wrote the book three decades ago, I had of course long since forgotten those steps. But it occurred to me that if I were going to stand up before a class and teach this stuff, I had better reconstruct them, in case some alert student asked me to fill in the gaps.
Out came a pad and a pen, and I began. Things did not go well, and I finally discovered that in my book, I had neglected to factor out 90 from one side of the equation when I factored it out of the other side. Now, this is not a total disaster, because the solution I got for the equation is in fact correct. It is merely an editing error, right?
Once, I can smile and get away with this sort of thing. But twice? I live in terror of what I shall find when I get to the mathematical examples of Marx's theory in the next chapter.