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Sunday, January 30, 2011


For reasons known only to himself, the buffoon Glen Beck has chosen to attack Frances Fox Piven, a creative and distinguished voice on the left for half a century, who with her husband Richard Cloward [now deceased] has worked tirelessly for the needs and interests of the poorest and most vulnerable among us. I had the great pleasure of having lunch with Piven forty years ago when I was trying, successfully, to persuade her to contribute an essay to a volume I was editing. Although I have not seen her since, I have always presumed on that brief acquaintance to consider her a friend. There is nothing I can do to stop Beck's attacks [which have led to death threats again this distinguished woman now approaching, as I am, her eighties], but I would be ashamed of myself if I did not at least speak up to defend her and condemn Beck's reckless, wanton, groundless, shameful attacks. It is at times like this that I bemoan my atheism. It would be comforting to believe that Beck and his like will earn an eternity of pain for the evil they spew into the public sphere. Since I am this morning also re-reading the portion of the REPUBLIC on which I shall be lecturing tomorrow, I am inclined to embrace Socrates' conviction that the greatest harm one can suffer is to be made a worse person. There may not be hellfire and damnation awaiting Beck the other side of the grave, but we can be sure that he has already harmed himself more than he and his epigones can ever harm Frances Piven.

Saturday, January 29, 2011


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.

Friday, January 28, 2011


[The absence of comments on the last two posts suggests that I have finally succeeded in boring you to death. But I am having such fun expounding this material, that I am going to press on, even posting twice in one day. Perhaps it is just as well that I cannot see your eyes glaze over.]

I guess you already figured out that I cooked the books to confirm Ricardo's hypothesis. If you want to check up on me, just alter the numbers a little -- a bit more iron needed in the corn sector, a trifle less corn in the iron sector, that sort of thing -- and solve the equations again, both for the labor values and for the prices. The first thing you will discover is that the price equations cannot be solved so nicely. It is still true that the wage and the profit rate vary inversely -- that is, as Jane Austen says, a "truth universally acknowledged." But until you specify a real wage [so much corn and so much iron per unit of labor] and plug it into the equations, the system will be underdetermined. And when you do, the nice neat proportionality between prices and labor values will not hold true.

What is happening? What is it about the little system I created that yields the nice neat Ricardo-confirming results? Well, in the jargon that Marx would introduce a half century after Ricardo published his great work, I created a system that exhibits "equal organic composition of capital." That means that the ratio of labor directly required to embodied labor [or labor indirectly required] is the same in all sectors lines of production. Check it out.

Another way of saying the same thing is that in some sectors of production, the labor indirectly required has been embodied in the non-labor inputs for a longer time, and hence, when we are figuring prices and profit rates, needs to be earning more profit. Suppose, for example, that one producer is making wine, which must sit in its cask for three years before it can be sold, while another producer is making bread that is sold hot out of the ovens. They may both have the same amount of capital bound up in production, but the wine maker has to get a price that compensates him for the time his capital has been tied up. Even if they are both getting 10% annually on their invested capital, the wine maker's capital must earn 10% a year over three years, which compounded is 33.1%, whereas the bread maker turns his capital over so rapidly that he need make only a fraction of one percent on each turnover to rack up a 10% annual rate of return. These differences will, when competition works its magic, drive the price of wine up above the price of bread. But since the labor values of the wine and bread are unaffected by the amount of time capital is tied up in production -- labor values only measure the quantity of labor directly or indirectly required -- the ratio of the price to the labor value of wine will diverge from the ratio of the labor value to the price of bread. This, for those of you who have ever wondered, is what is called "the transformation problem." [By the way, some of you may in your study of economics have come across the phrase "the roundaboutness of production." That phrase refers to the same thing we have been discussing.]

Now the really interesting thing is that Ricardo knew all about this problem, and spent a good deal of his life trying unsuccessfully to solve it. He was well aware that in the general case, prices are not proportional to labor values. But the problem stumped him. It was left to Marx to think the matter through more deeply and come up with a brilliant solution that is ALMOST, but not quite, satisfactory. It is going to be some days before I get to that part of the story, so hold the thought.

Strictly speaking, we have come to the end of our discussion of Ricardo, and are ready to move on to Marx, but there is one more little matter that I should like to discuss, namely rent. This is not part of Marx's story, because Marx knew that Ricardo had solved the problem of rent, and therefore he did not bother with it. Still, it was a brilliant coup on Ricardo's part, and we ought to be able to spare a few paragraphs to pay tribute to him.

The problem, in a nutshell, is this: Entrepreneurs [which in Ricardo's day frequently meant investors renting land on which to grow grain or raise sheep] pay rent for the land they use [to the landed aristocrats, those lazy bums]. That rent is one of their costs of production, as surely as the wages they pay or the money they shell out for seed and farm machinery. But land is not a produced commodity, and does not contain embodied labor that is passed along to or embodied in the commodities produced on it. That being so, it would seem that the Labor Theory of Value cannot hold true even in the special case of equal organic composition of capital. The theory can only be true if rent is NOT a cost of production. But how can that be? Certainly, if you ask an entrepreneur in the wool or corn trade, he will assure you that the rent he pays is very much a cost of production. Why would he pay it otherwise?!

Here is Ricardo's answer: In any country, there are many different qualities of arable land, many variations in the productivity of the land. On some land, one need merely throw the grain at the ground and crops will spring up. On other land, some cultivation is required, on still other land fertilizer is needed to get a crop, and there is some land so arid and unproductive that one can scarcely grow anything on it at all. Now, at a given level of demand for corn [i.e., grain -- recall that "corn" is the English name for whatever is the dominant grain in a region, not for what we call corn, which the English call maize], entrepreneurs will compete for the best land, and they will offer rent to its owner, for they know that even after paying rent, they can make a profit on such fertile land. When all the best land has been rented, the remaining entrepreneurs will bid on the somewhat less fertile land. They will only be willing to pay lower rents, because they will not be able to compete against the investors who have snatched the best land, if they are forced to pay equally high rents. If demand presses on supply, and drives up prices in the market, more entrepreneurs will fan out and offer rents of the owners of even less fertile lands. The landowners are engaged in a parallel competition among themselves. The land is utterly useless to them unless it is rented out, so although they will press for the highest rents they can get, if push comes to shove, they will take whatever they can get.

At the margin, the least fertile plot of land will rent for virtually nothing per acre, for there is so little demand for it that the last entrepreneur who comes along and offers pennies an acre will succeed in striking a bargain. Remember, if you want to know why a landowner would rent his land out for so little, the answer is that anything is better than nothing.

Now, come harvest time, all these entrepreneurs who have been raising indistinguishable and interchangeable corn on lands of varying fertilities, on which they are paying varying rents, will bring their crops to the market, and there competition will ensure that every bushel of corn sells for the same price, REGARDLESS OF HOW MUCH OR LITTLE RENT HAS BEEN PAID FOR THE LAND ON WHICH IT WAS GROWN. That means that the corn grown on the least fertile land will fetch the same price in the market, and among the costs of production of the capitalist who grew his corn on that land, rent does not appear. Therefore, rent is NOT a cost of production.


The answer, Ricardo says, is that rent is a diversion into the pockets of the landowners of a portion of the profit earned by the capitalist class. It is, functionally speaking, identical with the money that is diverted today into the pockets of financiers, who drain the profits from capitalists just as the landed aristocracy did in the late eighteenth and early nineteenth centuries.

We are now ready to turn to Marx.


Using the variables defined at the end of the last Part, we can now set up a system of three simultaneous linear equations. Here they are:

100 + 2Lc + 16Li + 0Lb = 300Lc

90 + 9Lc + 12Li + 0Lb = 90Li

20 + 1Lc + 2Li + 2Lb = 40Lb

The first equation says that 100 units of labor directly applied to 2 units of corn, in which is embodied a quantity of labor two times the labor value of corn, and to 16 units of iron, in which is embodied sixteen times the labor value of iron, yields 300 units of corn, in which is embodied 300 times the labor value of corn. And so forth. Notice that the variable Lb does not appear in either of the first two equations. That means that an increase in the difficulty of producing theology books [problems with the proofs for the existence of God, perhaps] will have no effect whatsoever on the labor value of either corn or iron. It also means that we can treat the first two equations as a system of two linear equations in two unknowns, and after solving it we can simply plug the values of Lc and Lb into the third equation to find the value of Lb. [All of this is a mathematical representation of a very important set of facts about the economy, of course.]

So what is the solution to the first two equations? Well, if you will carry out the manipulations yourselves, you will find that Lc = 0.4 and Li = 1.2. Lb turns out to be equal to 0.6.

0.4 what? you may ask. 0.4 units of labor is the answer. That is how much direct and indirect labor ends up being embodied in one unit of corn. If the dimension of labor happens to be worker-years, and the dimension of corn happens to be metric tons, then the equations tell us that in this system it takes 0.4 worker-years of labor, directly and indirectly, to produce one metric ton of corn. [Real world factual plausibility is not an issue. We are doing economics here!]

We have now ascertained the labor values of the produced commodities in this system. Ricardo says that these labor values determine the natural or equilibrium prices at which these commodities sell in a laisser-faire marketplace. More precisely, he says that commodities exchange in proportion to their labor values. To find out whether he is right, we must still figure out what the equilibrium prices are, so that we can see whether they are proportional to the labor values.

In calculating labor values, we remained in the sphere of production, attending only to the quantities of inputs required for specified quantities of outputs, but now, as Marx would say, we move into the sphere of circulation. We must set up a new system of equations that is a bit more complicated to solve [second semester high school algebra], but before we can set up the equations, we must make a number of simplifying assumptions and behavioral assumptions about the capitalist economy in which all of this is taking place. Here are some of the things we must assume. [Marx, as we shall see eventually, has enormously insightful and important things to say about the historical, sociological, economic, and psychological conditions under which these assumptions are plausible, but I can only talk about one thing at a time, so they will have to wait for a while.]

First of all, we must assume that the goods being produced have become standardized, so that one unit of corn or iron or books is much like another. If the society is still in the stage of craft production, with hand crafted furniture and artisanal loaves of bread or wheels of cheese, it will be impossible to represent the production process by our simple equations. The workers too must be standardized, and stripped of their inherited skills, so that one unit of labor directly applied is much like another. In the sphere of circulation, we must assume that competition establishes a single price for each kind of good, a single wage rate for labor, and a single rate of profit on invested capital [rent is not yet an issue.] All of these assumptions are hidden behind the simple price equations we shall shortly be setting down. Marx was the first economist [indeed, the first thinker of any sort] to recognize the enormous significance of these assumptions. Much of the first several chapters of CAPITAL is devoted to spelling them out and analyzing them. Later on, I shall have a good deal to say about them.

To formulate our equations, we need some new symbols for the unknowns. [I am limited, unfortunately, by the fonts available to me, so this will be clumsier than I would like.] First of all, we need a variable for each of the prices of the goods produced: Pc for the price of corn, Pi for the price of iron, and Pb for the price of books. We shall use W for the money wage, and R for the rate of profit. [Ordinarily one would use the Greek letter pi for the profit rate, but such is life in cyberspace.] Here are the equations read off from the same data that yielded the labor value equations:

(100W + 2Pc + 16Pi + 0Pb) (1 + R) = 300Pc

( 90W + 9Pc + 12Pi + 0Pb) (1 + R) = 90Pi

( 20W + 1Pc + 2Pi + 2Pb) (1 + R) = 40Pb

Why (1 + R)? you may ask. Because the money that the capitalists get from selling their output [300Pc in the case of the corn sector] must be enough to cover the cost of production [the 1] plus enough to yield the going rate of profit on that cost [the R]. Hence (1 + R).

This is a system of three equations in five unknowns. Mathematicians call such a system "underdetermined" [no, that is not what Althusser means by "underdetermined," but that is another matter entirely.] What to do? Well, the first step is to eliminate one of the price variables. Remember that what we are interested in is relative prices, which is to say exchange ratios between different commodities. The classical practice, employed by Smith, Ricardo, Marx and all other classical Political Economists, is to select one commodity as the money in the system, give one unit of it the price 1, and then express all other prices as multiples of that unit commodity, or as it is usually called, numeraire. This can be an ounce of gold, a pound of silver [the British Pound Sterling] or, if one is a Masaai warrior, one cow. In this case, we shall choose corn as our numeraire, and set the price of one unit of corn equal to 1. When we plug that assumption into our equations, we get:

(100W + 2 + 16Pi + 0Pb) (1 + R) = 300

( 90W + 9 + 12Pi + 0Pb) (1 + R) = 90Pi

( 20W + 1 + 2Pi + 2Pb) (1 + R) = 40Pb

This system is still undetermined, by one degree [as we say], because there are now three equations and four unknowns. Notice that once again, the first two equations can be treated separately, because the price of books, Pb, does not appear in them. They constitute a system of two equations in three unknowns: Pi, W, and R.

There are two things we can do. The first is to reduce the equations to one by eliminating the price of iron, so that we get a single equation in W and R. If we do this, we find with some algebraic manipulations [which I must simply assume you folks can do on your own] that there is the following inverse relationship between W and R:

(1 + R) = 6/(2W + 1)

Inspection reveals that as the wage rises, the profit rate falls, and vice versa, which nicely demonstrates the fundamental Classical thesis that the interests of the working class and the capitalist class are diametrically opposed.

But we can also try just to solve the two equations for the price of iron. In general, when you have a system of two equations in three unknowns, you cannot do this, but if you go ahead and try, you will discover, to your amazement, that the Wage and the Profit Rate drop out, and the two equations yield the result Pi = 3. This is an extraordinary result. It seems that in this system, the price of iron [and also the price of books, which turns out to be 1.5] is totally independent of the wage rate and the profit rate. No matter how those fluctuate in inverse relation to one another, the prices remain the same.

Well, Ricardo said that the prices at which goods exchange -- their natural prices or values -- are proportional to the quantities of labor required directly and indirectly for their production -- their labor values. Is he right? Let us see.

The price of corn is 1 and the labor value is 0.4, so the ratio is 1/.4 = 2.5

The price of iron is 3 and the labor value is 1.2, so the ratio is 3/1.2 = 2.5

The price of books is 1.5 and the labor value is 0.6 so the ratio is 1.5/.6 = 2.5


Ah well, if life were only that easy. Stay tuned. Tomorrow we shall discover the secret of this remarkable result.

Thursday, January 27, 2011


The table I posted is very small. To make it larger, and readable, hold down the control key and roll the wheel on your mouse up [or whatever else you do to change the size of things]. It will make it quite readable.

Not a perfect solution -- WallyVer has constructed a much more elaborate solution which I will try -- but at least it works. Think of this as an obstacle course deseigned to weed out the dilettantes from the hard core. :)


[All right, all right, so I am terminally stupid. Scroll down and read Segment One first. Then look at the table. Then come back to this and read it. Next time I will get it right. aaarrrggghhh!]

You will notice that I have constructed the sector devoted to the production of devotional literature so that iron, corn, and theology books are required as input. You may wonder in what sense theology books can be required as input into the production of theology books. Let us just suppose that the writers of the new books in each cycle of production read and re-read the existing books so assiduously that they wear them out. Analytically speaking, what matters here is that none of the output of the books sector is required as input into any other sector but itself. [For those of a more formal turn of mind, the square matrix of unit input coefficients is semi-positive and partially decomposable, with one of the submatrices representing the sector of basic commodities and another representing the sector of luxury commodities, but we need not go into that.]

Now, let us get to it. According to Ricardo, the natural price, or value, of a commodity [which is to say, something reproducible, like corn or iron, not something non-reproducible, like land or an Old Master] is determined by the quantity of labor that is required, directly or indirectly, to produce it. By labor indirectly required Ricardo means the labor that was required to produce the non-labor inputs into its production. If we look at the Corn Sector in the little model above, we will see that 100 units of labor are required to produce 300 units of corn, so each unit of corn requires one-third of a unit of labor directly. But each unit of corn also requires 1/150 of a unit of corn, as seed presumably [I get this number by dividing the left hand side of the Corn Sector line through by 300, to find out what are called the "unit input requirements" of the Corn Sector.] Now, we have just seen that each unit of corn requires 1/3 of a unit of labor, so the corn that is used up in the production process of the Corn Sector must have required 1/450 of a unit of labor in the previous cycle of production. This labor is described by Ricardo as being "embodied" in the seed corn, and as being transferred to the output when the seed corn is used in the production process. The same sort of calculation shows that a unit of corn requires 4/75 of a unit of iron. Now, looking at the Iron Sector, we find that each unit of iron requires one unit of labor to be produced, so that means that the iron that goes into one unit of corn production must itself have required 4/75 of a unit of labor in the previous cycle of production. So, thus far, we see that a unit of corn requires 1/3 of a unit of labor directly, and (1/450 + 4/75) or 1/18 of a unit of labor indirectly -- 1/18 of a unit of embodied labor.

But wait, you will protest [and you will be right], in that previous cycle of production to which you have been alluding, corn and iron, as well as labor, were required to produce the corn and iron that are being used in this cycle, so there are some extra little bits of embodied labor carried over from an even earlier cycle, that must be added in. It doesn't take much mathematical imagination to see that we have here the makings of an infinite sum of bits of embodied labor. Two questions immediately present themselves: First, does this infinite sum converge on some finite quantity? and Second, if it does, what does it converge on? How much total labor, directly and indirectly, does it take to produce one unit of corn? Or, as we have learned to say, What is the Labor Value of Corn?

Well, it turns out that we have here a problem whose answer can be arrived at by setting up and solving a little system of simultaneous linear equations. The Table we have been working with gives us a great deal of information about the production of corn, iron, and theology books, but there are three quantities that it does not directly tell us about. namely, the Labor Values of corn, iron, and theology books. These are, as they say in elementary algebra classes, the unknowns [or, as Donald Rumsfeld would say, the known unknowns.] So, I am going to choose three symbols to stand for these unknowns. Let us let Lc stand for the labor value of corn, which is to say the total amount of labor directly and indirectly required for the production of one unit of corn. Li will stand for the labor value of iron, and Lb for the labor value of books. Three unknowns, three equations pretty easily arrived at. We can solve that baby! Tomorrow, I will show you the equations [back to the scanner -- ugh], tell you what the solution is [you are going to have to work out that bit of elementary math yourselves], and move on to the next step in the process of checking to see whether Ricardo's Labor Theory of Value is true.


WARNING: I will have to introduce some more tables, and also some little systems of equations, and I have not solved the problem of doing this gracefully in a blog. So I will scan the tables or equations and put them into the blog as pictures. My blog program insists on putting these scans at the beginning of the post rather than where I want them to be, so each time I need to insert one, I will close the blog post, post it, then create a separate post containing only the table or equations, post that, and then continue my text in yet another post. This is too stupid even to contemplate, but it is the only solution I can think of. My granddaughter is, alas, otherwise occupied. :)

We are now ready to engage with Ricardo's version of the Labor Theory of Natural Price [or Value], to see what it means, and to ascertain whether it is correct. For a variety of reasons, it is useful to change my original corn/iron model a bit by assuming that the surplus getters [capitalists, in this case] use a portion of the physical surplus to underwrite a sector devoted to the production of luxury goods. Technically, these are goods that require inputs of various sorts, but whose output is not required as input into either the corn or the iron sector. They are, in modern terminology, final goods. We could, of course, posit a sector devoted to the production of luxurious clothing or sporty cars or gourmet breakfast foods, but since we are explicating Ricardo, and therefore presumably analyzing the doings of stern, upright, seriously religious Protestant businessmen, I shall assume that the luxury good to which they choose to devote a portion of their surplus is theology books. By the way, some of you may be wondering why Corn Flakes and frozen Macaroni and Cheese dinners do not count as luxury goods, even though they, like theology books, are not used as inputs into any line of production, and thus are also final goods. The answer -- and it turns out to be super important, theoretically -- is that Corn Flakes and frozen Macaroni and Cheese dinners are wage goods -- i.e., things consumed by the labor producing sector, which is to say by the workers. Thus they do enter indirectly into the production of all the other sectors, because labor does. Way down the road, this is going to allow me to invoke a nifty theorem proved by John von Neumann to demonstrate exactly when Marx's sophisticated version of the Labor Theory of Value is true. I say this now just to keep up the spirits of the cognoscenti among you who may be yawning and wondering when I am going to get to the good stuff.

Here is the revised model:


Wednesday, January 26, 2011


The theoretically most interesting and problematic of the doctrines of the Classical Political Economists is their explanation of how prices are determined in a laisser-faire capitalist economy. Why, you may wonder, is that so important a question? Well you may ask. I myself asked that same question of John Eatwell [currently Baron Eatwell and President of Queen's College, Cambridge], when as a young man in his thirties he taught a brilliant graduate course on Value Theory in the UMass Economics Department in the semester when I was first acquainting myself with economic theory. He was rather startled by the question, not anticipating that a total naif would be sitting in on his very advanced seminar, but the answer is quite simple. The two great questions of Classical Political Economy are, First, how is the annual social product [the "wealth of nations," in Smith's words] divided up among the three classes of society -- the landed aristocracy, the entrepreneurs, and the laboring class? and Second, what are the conditions of sustained economic growth? Growth and distribution are the alpha and omega of the classical school. It is what makes their theories, otherwise so out of date, interesting today. Now, in a laisser-faire money economy, the social product is apportioned to each class by the intermediation of money. Each class receives a share of the social product in the form of the money that it manages to lay its hands on. The landed aristocracy is paid a price for the use of its land -- we call it rent. The entrepreneurial class is paid a price for the use of its capital -- we call it profit. And the laboring class is paid a price for its laboring [or, as Marx will say, for the use of its Labor Power -- but that gets ahead of our story.] -- we call it wages. These prices -- rent, profits, and wages -- determine the distribution of the annual social product. The same processes of competition that determine the prices of corn and iron, cloth and coal, eggs and cattle fodder also determine rents, profits, and wages.

Confronted with this question, Adam Smith makes a series of brilliant conceptual moves that virtually define the discipline of economics ever after. [Aside: I have just re-read Chapter Two of my book, UNDERSTANDING MARX, in which I set forth Smith's innovative conceptual moves in some detail. If anyone is really interested in this subject, I strongly recommend looking at what I have written there. It is simply too detailed to reproduce here.]

He begins by observing that there is an ambiguity in the term "value," for sometimes we mean by the value of a good its usefulness to us in satisfying some want or enabling us to advance some undertaking. Water slakes our thirst. Cloth protects us from the elements. This aspect of any good Smith calls its "value in use," or, as we have learned to say, its use value. But goods may also be exchanged for other goods, and this aspect of them Smith calls their "value in exchange," or exchange value. When we consume some good, it is its use value that concerns us -- will this apple satisfy my hunger? Will that lump of coal burn well and provide warmth or energy to drive a machine? But in the marketplace, our concern is for the exchange value of a good. How many apples can I get in exchange for this bolt of cloth? How many bushels of corn for a ton of coal?

Drawing on the notion of nature as a system of universal laws -- an idea well-established in the late eighteenth century as a consequence of the manifest success of Newton and others in articulating that system in elegant mathematical form -- Smith suggests that society is a second nature, governed, as is physical nature, by universal laws. Instead of gravitation as the key to these laws, Smith offers the universal tendency of men to "truck and bargain" in the marketplace. [See David Hume's TREATISE OF HUMAN NATURE for a similar conceptual move -- in Hume's case, the principle of the association of ideas. Hume and Smith, of course, were good friends.]

We observe, Smith says, that in any given neighborhood or marketplace, there is a customary or usual price at which goods sell, and also a customary or usual wage paid to laborers, rent paid to land owners, and profit earned by entrepreneurs. These customary or usual prices may, of course, vary on a particular day as a consequence of momentary factors, such as a glut of corn one day or a scarcity of cloth the next. Smith, like Ricardo and Marx after him, was quite aware of what have come to be called the "laws of supply and demand," but he, as did they, considered these to be ephemera, not underlying determinants of the system of society. To those customary prices Smith gives the name "natural prices," calling the momentary fluctuations "market prices." The natural prices act, he says, like centers of gravity, drawing the fluctuating market prices to them [you see the influence of Newton.] From that day forward, one of the central tasks of Economics became the discovery of the determinants of natural price. Those of you who have studied economics will be familiar with the notion of natural price under its modern label, equilibrium price.

What then determines the natural price of a good in the market? Smith is actually rather confused about this question, and offers three answers without seeming to understand that they are different from, and in fact incompatible with, one another. One source of his confusion is his belief, which Ricardo shared, that in order to understand what happens when the relative prices [exchange ratios] of two goods change, one needs to find in the circle of exchanging goods one whose natural price never changes, so that any change can be traced to some alteration in the conditions under which the other good is produced. All of this is fascinating, but much too complex to go into here. [Once again, see my book.]

What matters is that Smith advances a seminal idea, on which all subsequent Classical Political Economy rests. The natural price of a good, Smith proposes, is determined by the amount of labor that is required to produce it.

Now, a small but important terminological matter. In the eighteenth and early nineteenth centuries, the term "value" was used interchangeably with "natural price." The value in exchange, or exchange value, of a good in the market was called either its natural price or its value. Thus, when Smith advanced the hypothesis that the natural price of a good is determined by the quantity of labor needed to produce it, he was offering a Labor Theory of Natural Price, or, what was to him the same thing, a Labor Theory of Value. That, just so you know, is the origin of this famous and controversial phrase.

In support of his hypothesis, Smith now sketches a little story in which is actually embodied a theorem in rational choice theory. Here is the entire passage, from Book I, Chapter 6 of WEALTH OF NATIONS.

"In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another. If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day's or one hour's labour.

And there it is! The Labor Theory of Value, in its first appearance on the world stage. It won't do in the form in which he presents it, of course, and Smith knows that. Indeed, in the very first phrase of the first sentence, he indicates why it won't do. This simple theory may hold for situations in which there is no accumulation of stock [hence no tools, farm animals, or other inputs into production] and no appropriation of land [hence no rent charged for the use of the land], but in the real world, all economic activity relies upon both "the accumulation of stock" and the "appropriation of land."

Just so we are clear, let me spell out the problem, even at the risk of being a trifle tedious. Suppose the deer hunters use bows and arrows to hunt the deer, while the beaver hunters use beaver traps to catch the beaver. [Bows and arrows and beaver traps are "stock."] Now, it takes labor to make a bow and arrows and also to make a beaver trap. Clearly, in deciding in what ratios they will exchange the deer for the beavers, both groups of hunters need to take into account that labor as well as the actual labor of hunting or checking the traps. It might be, for example, that beaver traps take only a few moments to make, but really can be used only once [the beavers wreck them trying to escape], whereas bows and arrows take many days to make, but can be re-used for years. In some way or other, this indirectly required labor will have to be taken account of if the two groups of hunters are to succeed in making rational decisions when they enter into bargaining with one another.

Smith pretty much gave up on this problem, and there things stood for forty-one years. Enter David Ricardo, arguably one of the three or four greatest economists of all time. The solution to the problem, Ricardo proposed, is to think of the stock -- the tools, raw materials, etc. used in the process of production -- as though they had embodied in them the labor that had been expended at an earlier time in making them or gathering them. When workers use those tools and machines as they worked up the raw materials into the finished products ready to be sold in the marketplace, we can think of them as transferring that embodied labor, along with their own labor, to the finished product. Thus, the natural price, or value, of the end product is really determined by the sum of the labor directly required in the production process and by the labor indirectly required in earlier periods of production. The sum -- of embodied labor and direct labor -- is the true determinant of natural price or value. This in a nutshell is Ricardo's version of the Labor Theory of Value, and it is, as we shall see, a dramatic advance on Smith's hypothesis, even though it is still not quite right.

At this point, I am going to stop, because in the next Part, I must incorporate some little systems of equations into the text, and despite the helpful suggestions of a number of you, I have not quite figured out how to do that. Also, I must lecture this afternoon to my graduate seminar, and I think I ought at least to make a show of preparing for my lecture. See you all tomorrow, if I succeed in sorting out the technical details of incorporating equations into the text.

Tuesday, January 25, 2011


Who gets the surplus?

In virtually every known society, the surplus is appropriated -- taken -- by some relatively small subset of the population, with the result that the members of that subset live better than the rest of the members of the society. We know these appropriators as kings, princes, oligarchs, pharaohs, priests, generals, landed aristocrats, tyrants -- and as entrepreneurs, merchants, advertising executives, lawyers, professors, and elected politicians. Almost always, the appropriators trick out their appropriations with justifications, rationales [or rationalizations] designed to persuade those from whom the surplus is taken of the rightness of the appropriation. The surplus getters suggest that they are bigger, stronger, more handsome, more charismatic, smarter, more productive, blessed by the Gods, sanctified by immemorial tradition, chosen by a vote of the people, riding the wave of history. And for the most part, those from whom the surplus has been taken -- the expropriated -- accept these rationales, sometimes grudgingly, quite often willingly or even enthusiastically.

The surplus comes in many forms. It is extra grain harvested from the fields, over and above what is needed to keep alive those who grow and harvest the grain. It is cloaks and mantles over and above what is needed to shelter from the weather those who shear the sheep, card and spin the wool, and weave the cloth for the cloaks and mantles. Sometimes it takes the form of swords made from iron that would otherwise provide additional plowshares or in the form of spears that could better serve as pruning hooks. [A little biblical reference there, for those of a religious turn of mind.]

In some societies, the conditions of life of those who get the surplus are only slightly more comfortable than those from whom the surplus is taken, but in many societies, the differences are so great that after a while the two groups of people seem not even to be of the same species or from the same world. The producers of the surplus are short, thin, careworn, illiterate, and short lived. The surplus getters are tall, handsome, healthy, cheerful, well-educated, and long-lived. The surplus producers struggle to keep their children from starving to death. The surplus getters send their children to Ivy League schools and on to the Grand Tour of Europe. Life is good for the surplus getters; not so good for those who produce the surplus.

How do the surplus getters get the surplus?

In many ways. Sometimes, like the Vikings of early medieval Europe, they simply sail up the rivers of Western Europe from the coast each Fall and steal the harvest as the peasants reap it. Or they ride into town as the bandits of the Southwest did and take the harvest at the point of a gun. At first, this is, and is understood to be, simple theft. But as the bandits return, year after year, the peasants become accustomed to the raids, and in an effort to avoid bloodshed, prepare the harvest for the stealing. This is then called taxes. Eventually, one lone bandit rides into town, not even wearing a gun, to collect the money the peasants have managed to acquire by selling their crops. The state has arrived.

Sometimes the surplus getters hold the producers in bondage, forcing them to labor on the lands owned by the surplus getters. Instead of seizing the surplus after it has been produced, they forcibly command the labor of the producers, allowing to the producers only so much of the annual product as is needed to keep them alive and allow them to raise up their replacements when they wear out -- their children. This is known as slavery. The condition of the slaves is often very little different from that of the nominally free producers whose surplus is taken from them, or appropriated.

How do the surplus getters get the surplus in a capitalist society. in which all men are free [we pass over in silence for the moment the condition of women], and all exchanges in the marketplace voluntary and based on mutual self-interest? That there are surplus getters even in this "very Eden of the innate rights of man" [CAPITAL, last page of Chapter VI] is manifest, for cheek by jowl with the slums of Manchester, Liverpool, and London are great mansions in which live the getters of the capitalist surplus. But HOW they get it is a mystery that eludes even the greatest minds of the Classical tradition in Political Economy. It is to the solution of this great puzzle that Marx devotes much of Volumes One, Two, and Three of CAPITAL, and we shall return to this question shortly, for at its heart lies the secret of capitalism.

What do the surplus getters do with the surplus when they get it?

This is actually the question that exercised Smith and Ricardo the most. In their view, entrepreneurs used the surplus [in the form of profits] to expand the scope of production, reinvesting it in an expanded labor force, new machinery, more fields under cultivation, and so on. The landed aristocrats, by contrast, used their share of the surplus [which came to them in the form of rents] to employ crowds of liveried servants, give lavish balls, maintain gilded carriages, consuming the surplus unproductively. Smith in particular was worried that as the demand for grain pressed on the available land and rents rose, so much of the annual surplus would be transferred to these unproductive expenditures that growth would come to a halt and the dreaded "stationary state" would result. It is worth noting that the notion of class conflict was central to classical political economy, and was not in any way original with Marx.

A share of the social surplus in most societies is consumed buttressing, protecting, and rationalizing the privileged position of the surplus getters. Some of that share is used to support a substantial military and police force which is available to put down any dangerous protests from those who are being denied the fruits of their productive labors. Some supports priests and churches, in which the virtues of submission and the promise of plenty in the next life serve to dull the resentment of the expropriated producers. Some must be devoted to maintaining lawyers and judges who can be counted on to resolve all disputes in a manner favorable to the surplus getters' interests. And there is even a bit of this share left over to keep in comfortable unproductivity artists to provide amusements for the surplus getters and philosophers to explain why all is for the best in the best of all possible worlds.

The secret of the explosive power of capitalism, as Smith, Ricardo, and Marx well understood, is that it alone, among all the forms of economy and society that history reveals to us, relentlessly allocates as much as possible of the social surplus to reinvestment for the purpose of expanding yet further the magnitude of the surplus. "Accumulate! Accumulate! That is Moses and the Prophets to the capitalists," as Marx writes in one of many brilliant passages in volume I of CAPITAL.

There are of course books to be written on every one of the observations in the preceding paragraphs, and Marx wrote a good many of them himself. But in the interest of brevity, I shall concentrate here on one question among all those that have been raised or intimated, namely, How in a capitalist economy does it come about that entrepreneurs exit from the market ever richer? Exactly how is it that in a capitalist economy the annual surplus is appropriated by one class, the entrepreneurs, or capitalists?

To answer this question, Marx must wrestle with and finally solve a technical puzzle concerning the determinants of the prices of commodities in the marketplace that had baffled Smith and in the end stumped Ricardo.

In the next post, we shall begin our discussion of this famous puzzle, leading finally to Marx's version of that centerpiece of Classical Political Economy, the Labor Theory of Value.

Monday, January 24, 2011


Once again, I am being defeated by this damned blog. Is there anyone who can figure out how I can put a table into a blog so that it looks the way it ought to look? I cannot figure out why the blog does not accept hard spaces so that I can space things out appropriately. Rats!


We come now to the heart of this tutorial, Marx's economic theories. It is worth noting that the subtitle of CAPITAL is "A Critique of Political Economy." Marx's work is as much a critique of previous economic theories as it is an analysis of the economic reality of capitalism. Karl Marx was, at one and the same time, the greatest of the classical political economists, bringing to completion more than a century of brilliant theorizing, and also the greatest critic of classical Political Economy, devastatingly exposing the inner contradictions and inadequacies of the classical tradition. In order to understand what he is talking about in CAPITAL, therefore, we must spend a little time tracing the evolution of classical Political Economy from its origins in France in the middle of the eighteenth century to the work of its greatest exponents, Adam Smith and David Ricardo, against whom and in continuation of whom, Marx wrote.

Political Economy begins with the effort of Turgot and Quesney to understand the French economy in the eighteenth century. These two theorists, who, with their fellows, have come to be referred to as the Physiocrats, conceived agriculture as central to the wealth of Old Regime France, so much so that they disparaged the productive efforts of artisans and craftsmen. Their great contribution to the field, and to subsequent theorists, was their recognition that the on-going productive economic activities of a nation must be conceptualized as an endless cyclical process of REPRODUCTION. The output of the nation at one point in time becomes the input of the productive process at a later point in time, so that there is a cycle of inputs and outputs, a cycle of reproduction. This season's harvest provides the seed corn for next season's planting. The iron ore dug from the mines this year becomes the shovels used to dig iron ore next year, and so on. [This is the origin of the title of Piero Sraffa's seminal little book, PRODUCTION OF COMMODITIES BY MEANS OF COMMODITIES.] There are, of course, some goods that are by their nature not reproducible -- old master paintings, for example, whose value lies not only in their beauty but also in their scarcity. Somewhat more importantly, one essential input into production -- land -- is not in general reproducible [although it is of course possible, on the margins, to carry out landfill operations that increase the available land, such as the project that created the ile St. Louis in the Seine in the middle of Paris.] This latter element in the process of production set for the classical theorists the problem of providing an adequate analysis of land rents, a problem that was solved by Ricardo in one of the most brilliant achievements of the classical school.

Although the Phsyiocrats did not themselves call attention to it, the concept of reproduction can be usefully applied even to that input into production on which we shall focus most of our attention, namely labor, for this generation's output of the production process [the children] becomes the next generation's inputs [the parents], thus justifying the use of the word "reproduction" to apply to that process as well. There is even a third sort of reproduction of which we shall have to take account eventually as our exposition goes forward, namely the reproduction of the social relationships and cultural institutions and ideological formations that constitute a society. But we are getting ahead of ourselves.

And now, a word of caution before we begin. This is a complex subject, and I have found it useful to proceed slowly when expounding it, starting with elementary concepts and postponing until later the introduction of the complexities and complications that are a part of the finished story. So please, before you write long comments asking why I have not mentioned these essential complexities, show a little patience. If you really want to know whether I am just ignorant of those complexities, then read my two books on Marx before you rush to comment. Thank you.

In order to have before use a numerical example of the process of reproduction, I am now going to introduce a little model of a very elementary economy. Like all models, its construction requires a good deal of abstraction.

Let us begin by imagining an economy in which there are only two produced goods [or, if you prefer, two categories of produced goods], corn and iron [or agricultural goods and industrial goods]. Each good requires inputs of corn, iron, and labor [forget about land for the moment], and in each sector of production, the combination of these inputs results in a certain quantity of output of one good or the other. [In deference to Marx's brilliant analysis of the commodity, I am not yet referring to these goods as "commodities."] Since all of these theorists lived in the temperate zone of the Northern Hemisphere. they all assume an annual growing cycle, and we shall follow that tradition. Here is a simple numerical representation of the economy we are describing. I choose to treat the reproduction of labor on a par with the reproduction of corn and iron because that is the way Marx thought about it [as did Ricardo, by the way]. Sraffa's approach is different, although either way is convertible to the other easily enough. Call this System A:

Labor Input Corn Input Iron Input Output

Labor Sector 38 units 19 units 190 units

Corn Sector 100 units 2 units 16 units 300 units

Iron Sector 90 units 9 units 12 units 90 units

Total Input 190 units 49 units 47 units

A few preliminary observations about System A;

1. The size of the units is not indicated, but since this is supposed to be an annual cycle of reproduction, presumably they are pretty big [millions of tons of corn, or something like that.]

2. There is not the slightest indication of what technology of production is being used. Important though that obviously is, it is irrelevant for the purposes to which we are going to put this model. Following the Classical Political Economists, we assume that there is one and only one dominant technique used for the production of each good. If some entrepreneur introduces a new and more efficient technique, the pressure of competition pretty soon forces all the other entrepreneurs in that line to adopt it, and it becomes the new standard.

3. Notice [this is crucially important] that both corn and iron are required as inputs in each line of production.

4. I could make the model somewhat more elaborate, in an effort to do a better job of mimicking reality, but that would not change the theoretical analysis. It would just require us to use rather more sophisticated mathematics. I prefer the transparency of the simple model. In a more complex model, there might be hundreds of sectors of production, and in some of them [this too is crucial] some goods might not be used as inputs, but they might be used in the production of goods that were themselves used in the production process, and so we could say that they were indirectly required. In general, there will be a distinction [also crucial -- there is a lot of crucial stuff here] between those goods that are directly or indirectly required in every single line of production, and those goods that are not directly or indirectly required in every line of production. For reasons that will become clear, we shall call the first group of goods basic Goods, and the second group Luxury Goods. In System A, iron and corn are both Basic Goods.

5. This model is deliberately so simple that it even ignores fixed capital, which lasts through more than one cycle of production, and joint production, a situation in which a given technique of production has two or more salable outputs. As I said earlier, I am going to creep up on the more complicated cases.

Even the most cursory inspection of System A reveals that in each cycle of production, there is more output than is required for the next cycle's input -- 251 units of corn and 43 units of iron, to be precise. [The fact that there is, at this point, no extra labor produced is actually analytically important -- wait for it.] If we meditate on this fact for a bit, three questions should occur to us. All of Economics, Sociology, History, and Political Science is nothing more than attempts to answer these three questions.

The first question is: WHO GETS THE SURPLUS?



Tomorrow we shall begin answering these questions, in the course of which we shall hear about Natural Price, Productive and Unproductive Labor, Necessary Labor and Surplus Labor, Base, Superstructure, Ideology, The Labor Theory of Value, and other arcana. Stay tuned.