QUICK RESPONSES TO TWO COMMENTS

Jerry, there is so much to say about the evolution of rationales of exploitation that just talking about what Marx has to say on the subject would make this series of posts endless [which it well may be, anyway!]  Tomorrow I will say a bit about some of the really dopey explanations given by Marx's contemporaries for the existence of profit.  Speaking generally, Marx thinks [and I agree] that the principal task of philosophers, theologians, economists, and, I would add, political scientists in any era is to conjure up rationalisations for the manifest inequality in the distribution of the social product in that era.  To their great credit, Smith and Ricardo do not offer facile justifications, and that is one of the reasons why Marx thought so highly of them.  The rest he referred to as "vulgar economists."

Seth, I freely confess that I had never so much as encountered the word "holonomy" before reading your comment.  Can you say just a word about the sense in which profit is, as you call it, a "holonomy effect"?  Is it because it involves mapping a multi-dimensional magnitude onto a one-dimensional array?  As for the time I spend explaining things that are immediately obvious to some people, this is the price I pay for trying to weave together into a single narrative arguments taken from mathematical economics, history, sociology, philosophy, and literary criticism.  My deepest passion, during my entire life, has been to make difficult ideas clear and simple to anyone willing to follow the line of my exposition, with no assumptions made about their prior expertise.

THE SABBATH

After seven days posting installments of my integrated narrative, I am taking today off.  Back tomorrow.

WHAT HAVE I BEEN DOING -- PART SEVEN

Who Gets the Surplus?  It is Marx's view, confirmed by even the most cursory review of human history, that in every era and on every continent, we find a relatively small group of people who appropriate the lion's share of the surplus.  Kings and their entourages, emperors, landed aristocrats and their hangers-on in the churches and the law courts, there is always a class that gets the surplus, whether that surplus is in the form of foodstuffs, artworks, weapons, buildings, and fine clothing, or bags of gold, ingots of silver, copper coins, bank notes, and shares of stock.

What Do the Surplus Getters Do With the Surplus After They Get it?   [If I may reverse the order of the questions.]  This was actually a subject of the most intense concern for Smith, Ricardo, and the other classical Political Economists.  Smith in particular devoted a good deal of attention to the contrast between the entrepreneurs, who, he said, used their share of the surplus productively, by reinvesting it in expanding the scope of their production, and the landed gentry, who, in his view, wasted their share of the surplus [which came to them in the form of rent on their land] by supporting clouds of unproductive servants whose labor contributed nothing to the wealth of the nation but was in fact a drain upon it.  The worst nightmare of the classical school was something they called the "steady state," in which increased demand for food resulting from increases in population drove rents up so high that all of the available capital was absorbed in unproductive uses and economic growth ground to a halt.

Marx's answer [which, as we shall see, actually has a rather important mathematical significance] is that in a capitalist economy, entrepreneurs are compelled by competition to reinvest the surplus, which they receive in the form of money profits.  "Accumulate! accumulate!  That is Moses and the prophets!"  [Capital, Chapter XXIV, "Conversion of Surplus Value Into Capital."]  See The Gospel According to Luke, Chapter 24, verse 27:  "And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself."  It means going back to the foundation, the most basic texts.  It is characteristic that in writing about capitalist accumulation, Marx would invoke a catchphrase from biblical interpretation.

How Do the Surplus Getters Get the Surplus?  And so we come to the question that lies at the heart of Marx's economic theory.  In previous societies, it was not particularly difficult to figure out how the surplus getters got the surplus.  Sometimes they got it by naked force of arms, as for example was the technique of the Norsemen who, each Spring, would sail up the rivers of France and the Lowlands and simply steal the crops of the hard-working farmers along the river banks.  Military states like that of the Mongols got their share of the surplus by exacting taxes from those whom they conquered.  Feudal lords extracted a surplus from the serfs whose labor they could command on the lands they controlled.  And in slave economies, like that of ancient Rome or seventeenth, eighteenth, and nineteenth century America, the surplus getters got the surplus by compelling their slaves to work on their lands and in their shops and at their forges.

Now, anyone with eyes to see could tell that in mid-nineteenth century England, an enormous surplus was being generated on the land and in the factories, and it was obvious that most of that surplus was being regularly appropriated by entrepreneurs, capitalists, businessmen, call them what you will.  Every commentator on the passing scene was powerfully struck by the phenomenon of "new men," who began life as apprentices or small merchants and seemingly in no time became wealthy nabobs in fine houses, marrying their daughters off to impecunious young men sporting ancient titles.

But though it was clear that a surplus was being generated each year larger than any that had been seen in previous eras, and it was manifest who was getting the surplus, it was extremely unclear how these surplus getters were getting their share of the surplus.  Marx's recognition that capitalism mystifies the process of the appropriation of the surplus and his analysis of that mystified process is the theoretical heart of his entire theory.  Smith and Ricardo, despite their enormous theoretical contributions, did not even realize that there was a question to be answered.  Because Marx was convinced that the identification of this question and its answer was more important and more fundamental than the problem with which Ricardo had wrestled in his final years -- the problem of the deviation of prices from labor values -- he chose to set aside Ricardo's question in Volume I by writing the entire volume on the assumption of equal organic composition of capital, a condition in which the deviation does not take place.  Only after he had laid bare the complete dependence of capitalism upon exploitation would he complicate his story by taking up Ricardo's secondary puzzle.

The puzzle is this:  If equals truly exchange for equals in a marketplace free of the distortions either of law or custom, then the inputs that the capitalist purchases at their value at the beginning of the production process must pass their value on to the product that emerges at the end of that process, but no more.  When the capitalist sells his product, once more at its value, he will recoup every bit of money that he has laid out to his suppliers.  But how is it that he exits this cycle of purchase, production, and sale with more money than he had when he began?  How does the capitalist make a profit? 

WHAT I HAVE BEEN DOING -- PART SIX

Before answering the question I posed at the end of yesterday's installment [I do feel, sometimes, as though I am writing episodes of that old movie serial thriller, "The Perils of Pauline," which I would watch goggle-eyed each Saturday at the Main Street Theater in Kew Gardens Hills, along with two feature films, a raft of cartoons, and The News of the Week in Review], there is an arcane technical matter that I need to address.  This is really, really important, but has somewhat the feel of inside baseball, so those of you who don't much like Economics will have to be patient.

The classical economists assumed that there was, at any given historical moment, a single dominant technique for the production of each commodity, which could be characterized by listing the quantities of labor and non-labor inputs required per unit of output.  There would of course be some old-fashioned less efficient techniques hanging around, in use by some manufacturers, but competition in the marketplace would pretty quickly eliminate them, for the capitalists using those old techniques would have higher costs but be forced to sell at whatever was the going rate in the market.  There were usually also a couple of hotshot manufacturers trying out innovative techniques, and if any of those proved to be super-efficient, those manufacturers would have an edge in the market.  They would be able to undersell the competition and still make a profit.  Once again, as word got round, their competitors would be forced to switch to the new technique.  Abstracting from these temporary complications, the classicals conceived of an economy as consisting of a number of industries in each of which one technique ruled.  Ricardo and the others did not themselves use mathematics to analyze this situation, but in the twentieth century [thanks, in the first instance, to the great Russian-American economist Wassily Liontief], economists found that the Classical approach to economics could be captured quite nicely by systems of simultaneous linear equations.  That is why, when I began my four decades long engagement with the thought of Karl Marx, my first task was to acquaint myself with Linear Algebra.

In the 1870's, when Karl Menger, Léon Walras, and Stanley Jevons transformed Economics by introducing considerations of marginal productivity and such, economists did a complete flip.  Instead of simplifying and idealizing the object of their study by positing a single dominant production technique for each commodity, they chose the opposite simplification and posited an infinity of alternative production techniques, each represented by a different quantitative combination of inputs.  To make their lives simple and their theories exciting, they assumed that the relationship between a set of inputs and a quantity of output was a continuous twice differentiable production function, and Economics was off to the races.  Before long, they were talking about supply and demand curves, marginal productivities, general equilibria, and all manner of sexy technical innovations that allowed them to suppose that they were not humanists at all, but scientists.  [Okay, okay, so I am not the most sympathetic and enthusiastic student of modern economic theory.]

One of the consequences of this shift in theoretical model building, not exactly unintentionally, by the way, was that the class struggle over the division of the social product, which had been the centerpiece of Classical Political Economy, completely disappeared from view, to be replaced by anodyne theoretical discussions of Pareto Optimality and production frontiers.

Well, enough talk.  It is time to introduce some mathematics.  I am going to make this as easy and stress free as possible.  Let us imagine a very simple economy -- one in which only three goods are produced:  corn, iron, and theology books.  With not the slightest attention to the real conditions under which these three goods could actually be produced [thus showing myself to be a true economist!], I shall assume that the chart displayed below represents the amounts of each input required for the production of a certain amount of output.  If the idea of an economy with only three commodities strains your credulity, you may think of this as a model of an economy with an agricultural sector, and industrial sector, and a luxury goods sector. [The theology books are thought of here as luxury goods produced for the amusement and edification of the moneyed classes, the assumption being that the capitalists are upstanding Puritans of the sort studied by Max Weber in his classic work, the Protestant Ethic and the Spirit of Capitalism.] 

Corn, Iron, Theology Books System

­­­­­­­­­­­­­­­­­­­­­­­­­­­-------------------------------------------------------------------------------------

                                      Labor     Corn     Iron     Books                Output

                                      Input      Input     Input   Input

--------------------------------------------------------------------------------------

          Labor                                    42          21        0                          210

          Corn Sector           100            2          16        0                          300

          Iron Sector              90            9          12        0                            90

          Books Sector            20            1           2         2                            40

 

          Total Input            210           54          51        2

Since I am going to draw very deep and important conclusions from this little model, let me take a moment to make sure everyone understands what it says.  Look first at the Corn Sector.  The chart tells us that it takes one hundred units of labor, two units of corn, sixteen units of iron, and no theology books at all, to produce in this economy three hundred units of corn.  Analogous conclusions can be drawn from examining the numbers in the Iron Sector and the Books Sector.  The line labeled "Labor" says that the workers must consume forty-two units of corn and twenty-one units of iron to "produce" two hundred ten units of labor [which is to say, to enable them to labor for two hundred and ten units of time, inasmuch as labor is measured in minutes, hours, weeks, months, or years.]

The first thing we see is that Books are not required by inputs in any industry save the one in which they themselves are produced.  This, as it happens, marks a fundamental distinction between what Sraffa called "basic" and "non-basic" commodities.

The second thing we notice is that a physical surplus of corn, iron, and theology books is produced in the economy.  That is to say, when we take the annual product and subtract from it what is needed to run the system at the same level of operation the next year, a good deal of stuff is left over -- to be precise, there is a surplus of 246 units of corn, 49 units of iron, and 38 units of books.  This way of conceptualizing the economy immediately presents us with three simple questions.  The three questions are: 

1.  Who Gets the Surplus?

2.  How do the Surplus Getters get the Surplus?  and
3.  What do the Surplus Getters do With the Surplus After They Get It?

A little reflection will convince you that a good deal of Theology, Philosophy, History, Political Science, Sociology, Anthropology, and of course Economics is devoted to answering these three questions.

 

THE OLD PHILOSOPHER SCREWS UP AGAIN

It is of course Brian Leiter, not Bruce Leiter.   I was confusing him with Bruce Wayne.  :)

WHAT I HAVE BEEN DOING -- PART FIVE

Before continuing this exposition and explication of the evolution of the Smith/Ricardo/Marx Labor Theory of Value, let me just note that none of these luminaries made the slightest use of even the relatively elementary algebra readily available in their day.  It is simply extraordinary that without the aid of correctly worked-through quantitative examples, they were able to intuit very deep formal truths.  [Marx tried to carry out a numerical example in Capital, but got it wrong, even though the deeper proposition he was attempting to prove is, as it happens, true.]

With the aid of the linear algebra that I taught myself that cold Northampton January, I was able to read and grasp the mathematical reconstruction and reinterpretation of classical Political Economy carried out around the world in the 60's to 80's of the last century by a score of gifted economists.  Indeed, I was even able to offer formal proofs of a few interesting propositions myself, although, alas, the most important of them was anticipated by a year by a Spanish economist [a fact pointed out in print by the most mathematically gifted of the American Marxist economists, John Roemer.  So much for immortality.]

 

Ricardo claimed that equilibrium prices [or "natural prices," as the classicals called them] are determined by the quantities of labor directly and indirectly required for their production.  He quite well understood that this explanation excluded such scarce goods as Old Masters and "wine grown on a particular side of the hill."  [Ricardo had a rather comfortable lifestyle.]  In mathematical terms, this means that the prices of commodities would be proportional to their labor values.  Since a good deal hinges on this simple claim, let me, at the risk of totally alienating the innumerate among my readers, take a moment to explain exactly what Ricardo was asserting.

Each of the commodities bought and sold in the marketplace has a natural value, or, as modern economists would say, an equilibrium price.  [The economy is equilibrated by movements of capital and of prices until there is a single set of prices and a single profit rate throughout.]  Suppose we use the lowercase letter p to represent price, with subscripts to indicate which commodity we are referring to.  Thus p_c will stand for the natural price of corn, p_l will stand for the natural price of linen, and so forth.  Let us also adopt the modern convention of using the lowercase Greek letter lambda, or λ, to represent the quantity of labor directly or indirectly required to produce a unit of a commodity, which is to say the labor value of that commodity, with subscripts employed in the same fashion.  If corn is measured in bushels, linen in yards, money in shillings, and labor in hours, then Ricardo's Labor Theory of Value asserts that:

The price in shillings of a bushel of corn is to the price in shillings of a yard of linen as the labor value in hours of a bushel of corn is to the labor value in hours of a yard of linen, which, using our newly defined symbols, can be stated succinctly as:    p_c/p_{l =}  λ_c/λ_l.

Even though Ricardo never translated his claims into convenient symbols of this sort, he grasped intuitively, and with great insight, that this proposition, which he himself had asserted, is not in general true!  What is more, he understood exactly what had to be the case in order for it to be true.  Briefly, the natural prices of commodities are proportional to their labor values only when the ratio of the quantity of labor directly required to the quantity of labor indirectly required is the same in all lines of production.  This is the situation that Marx was later to call "equal organic composition of capital."  The point is that some production techniques are what we have come to call "labor intensive" while others are "capital intensive."  In an economy with production techniques of both sorts being employed, prices will in some industries lie above their labor values and in other industries below their labor values.  [As is perhaps obvious by now, I find this whole subject absolutely fascinating, but I am quite well aware that not everyone, to quote the old joke about philosophers, wants to know "that much about rainbows."  Readers who share my geekish enthusiasms are invited to consult the relevant chapters of Understanding Marx.]

After publishing the Principles of Political Economy and Taxation in 1817, Ricardo spent the remaining six years of his life struggling unsuccessfully with this deep problem with his Labor Theory of Value.  Marx was well aware of this, and in Capital Volume Three offers a brilliant solution that is almost [but not quite] correct.  And yet, despite the fact that the materials of his entire hauptwerk were worked out before 1867, Marx chose to write all of Volume One on the assumption of equal organic composition of capital!  Why on earth would he make so odd a choice, considering that he had in his back pocket, as it were, a solution to Ricardo's problem?  Tomorrow I shall answer that question and carry our story forward into Capital Volume One itself.

DOES ANYONE KNOW WHAT IS GOING ON?

As I have observed before, every so often Bruce Leiter, Professor of Law and Philosophy at the University of Chicago and author of the most widely read blog in the academic field of Philosophy, gives my little blog a hat tip and link, and suddenly my daily visits, as recorded by Google, shoot up from five or six hundred to two thousand or more.  Then things settle down, the visitors depart, and my small community of faithful readers slogs along.  Yesterday, visits suddenly jumped to 1474 [at least so far as Google is able to tell], and today, at not yet ten in the morning, the number has hit 2167.  I checked Leiter's blog, but not a peep.  Either someone else has granted me fifteen minutes of fame, or the world is hungrier than I thought for anything on Karl Marx.  Does anyone know what is going on?