Ricardo announces the theme of class conflict in the opening sentences of the Preface to the Principles:
"The produce of the earth—all that is derived from its surface by the united application of labour, machinery, and capital, is divided among three classes of the community; namely, the proprietor of the land, the owner of the stock or capital necessary for its cultivation, and the labourers by whose industry it is cultivated.
"But in different stages of society, the proportions of the whole produce of the earth which will be allotted to each of these classes, under the names of rent, profit, and wages, will be essentially different; depending mainly on the actual fertility of the soil, on the accumulation of capital and population, and on the skill, ingenuity, and instruments employed in agriculture.
"To determine the laws which regulate this distribution, is the principal problem in Political Economy."
And right here we have the answer to my naive question in John Eatwell's class. Why do we want to know how prices are determined in a capitalist economy? Not because we care how much it costs to buy a yard of cloth or a bushel of wheat or a peck of potatoes. No, those are not the prices we really care about as Political Economists. We want to know the price of land, labour, and capital, which is to say rents, wages, and profits, because it is through the intermediation of those prices that the annual social product is divided up among the "three classes of the community," landowners, workers, and entrepreneurs.
Most modern students of Economics probably imagine that what distinguishes the old guys -- Smith, Ricardo, Mill, and Marx -- from the new hotshots -- Walras, Jevons, Menger, Marshall, Samuelson, Malinvaud, and Minkiw [well, no, not Minkiw] -- is the fact that the old guys use addition and subtraction and multiplication and division, with sometimes a foray into the taking of averages, while the new hotshots use the calculus and all that cool stuff. Not so. The real distinction is that the two groups of theorists ask different questions and are interested in different issues.
The classical Political Economists were concerned, above all else, about two things: Distribution and Growth. They wanted to know how and why the annual social product got divided up among the three great classes of society in the way that it did, and they wanted to know under what conditions that annual social product would expand year by year, and under what conditions it would not. As we shall see in a bit, their mathematical intuitions were in fact quite acute, even though their mathematical tools were rather primitive, and it is not difficult, with some modern math [linear algebra, mostly, not the calculus] to present their arguments in a quite mathematically rigorous fashion.
What are modern so-called "neo-classical" economists concerned with [never mind why "neo-classical"]? Here is a standard answer from Chapter One of Nobel Laureate Paul Samuelson's famous Economics text. [My edition, the ninth, was published in 1973. According to Amazon.com, the current edition is the eighteenth. Samuelson died two years ago, but his textbook, like the evil that men do, lives after him.]
"Economics is the study of how men and society end up choosing, with or without the use of money, to employ scarce productive resources that could have alternative uses, to produce various commodities and distribute them for consumption, now or in the future, among various people and groups in society. It analyzes the costs and benefits of improving patterns of resource allocation."
Or, as Lord Lionel Robbins rather more succinctly put it in his 1932 classic, An Essay on the Nature and Significance of Economic Science:
"Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses."
The classical Political economists were quite capable of considering the efficient allocation of scarce resources with alternative uses, but that was not what they were interested in. And modern economists can discuss growth and distribution, but their treatment of those problems tends to be clumsy and ad hoc because that is not the principal focus of their attention. I shall have more to say about this later on.
The real methodological difference between the two schools is in the nature of the simplifications they posit in order to bring their analytical tools to bear on the analysis of a capitalist economy. Economics is quite unlike, for example, History as a discipline. Historians revel in particularity [which is why Aristotle consider History inferior to Poetry, but that is another matter.] Even ideologically driven historians will lavish time and attention on the irreducible specificity of an historical moment, positively relishing the details their archival research have unearthed. Two good examples among my very most favorite works of historiography are Georges Lefebvre's great work, La Revolution Franҫaise, and Leon Litwack's Been in the Storm so Long: The Aftermath of Slavery. Lefebvre was a Marxist, and he begins his work with a brief preface in which he lays out a standard Marxian line about the French Revolution as an episode in the rise to power of the bourgeoisie. But once that is out of the way, we are treated to a meticulously detailed account of the revolution, in which the details of the doings of particular people in particular regions of France quite obscure the ideological message. Litwack's work is equally informed by his impassioned moral and ideological commitment, but as one turns the pages, one finds story after story recovered from archives and other literary remains of the ways in which particular former slaves reacted to their new-found freedom.
Economists construct radically simplified models of an economy in order to carry out logical and mathematical deductions. There is nothing wrong with this way of proceeding. The same thing is done by geneticists, climatologists, physicists, and [of course] logicians. What is interesting is the fact that the classicals and the neo-classicals choose exactly opposite simplifications. To put it in a phrase, the classicals assume there is one dominant technique of production for each category of commodity, and the neo-classicals assume there are an infinite number, so arrayed that a function relating the vector of inputs to a quantity of outputs is continuous and twice differentiable. As a consequence of these alternative simplifications, the arguments of the classicals are best rendered mathematically by means of linear algebra, and the arguments of the neo-classicals are best rendered by the differential calculus.
The classicals and neo-classicals also differ in the way in which they model the real wage, which is to say the actual physical bundle of goods and services that the workers consume. The classicals, writing at a time when the condition of the working class was quite miserable, assume that there is a single quite plain market basket of goods that each worker and his or her family purchase with their money wage. For some purposes, as we shall see, Ricardo even goes so far as to assume that this market basket contains a single commodity -- grain [or "corn," as the English would say. When I first read about the dispute over the Corn Laws, which were tariffs on imported corn, I was mystified, because to me "corn" refers to maize, or as we say, "corn on the cob." But the English don't eat corn on the cob. It turns out "corn" is the British term for whatever is the dominant grain of a locality. Hence when the first English settlers got to the Americas and discovered the locals eating maize, they called it "corn."]
The neo-classicals, writing at a later time, assume that workers will make a series of choices about how to spend their money wage, and a good deal of their most mathematically sophisticated manipulations are devoted to relating those choices to their subjective preferences.
My own personal opinion is that the classical simplification is closer to the underlying reality than that of the neo-classicals. But what really interests me is the fact that the classical simplification makes it much easier and more perspicuous to study the structure of the distribution of the annual social product. It becomes trivially easy to demonstrate formally that the money wage rate and the money profit rate vary inversely to one another, which is a mathematical way of saying that the interests of the working class of irreducibly opposed to those of the capitalist class. It is, of course, possible to show this in the neo-classical model -- the thing about properly constructed mathematical models is that they are always inter-translatable -- but the opposition between Labor and Capital is hidden rather than made manifest in the neo-classical models.
In these days when mouthpieces for Capital cry "class warfare" at the slightest suggestion that what goes into the pockets of the rich comes out of the pockets of the poor, it is convenient to employ a model of the economy in which this fact is impossible to miss.