MARX BOOK DAY THREE

 

                                       David Ricardo and the

Labour Theory of Natural Price

 

The theoretical problem bequeathed by Adam Smith forty-one years earlier was how to analyse the determination of prices, and thereby of rents, wages, and profits, in that developed state of the economy which results from the “appropriation of land and the accumulation of stock.” In analytical terms, this meant producing a satisfactory theoretical treatment of rents and of capital stock (which is to say capital other than outlays for wages). In addition, Ricardo needed to put forward a theory of the determination of the wage, for although he had made some remarks on the subject in the Essay on Profits, he did not yet have a coherent explanation for the magnitude and movement of wages.

 

To handle the problem of rent, Ricardo adopted the analysis that had been developed by his contemporaries West, Torrens, and Malthus.  Interesting though that is, there is no part of a story so I shall leave it to one side. Ricardo assimilated the determination of the wage to the general problem of price determination by means of Malthus’ theory of the pressure of population on the food supply. That is rather more directly related to Marx’s views and I shall return to it later.   We are left, then, with the core analytical problem: how to take account of the role played in production, and thereby in the determination of natural price, by the accumulation of stock, in the form of cleared fields, buildings, tools, factories, raw materials, machinery, and so forth.

 

Ricardo’s solution is to extend the principle which Smith invokes for the simple case of the “early and rude state.” The title of section three of the first chapter (“Of Value”) of Ricardo’s Principles reads:  Not only the labour applied immediately to commodities affects their value, but the labour also which is bestowed on the implements, tools, and buildings, with which such labour is assisted.

 

Commenting on Smith’s beaver/deer example, Ricardo observes that even in so simple a case, some capital will be necessary in the form of weapons.

 

Suppose the weapon necessary to kill the beaver, was constructed with much more labour than that necessary to kill the deer, on account of the greater difficulty of approaching near to the former animal, and the consequent necessity of its being more true to its mark: one beaver, [Ricardo reasons] would naturally be of more value than two deer, and precisely for this reason, that more labour would, on the whole, be necessary to its destruction. Or suppose that the same quantity of labour was necessary to make both weapons, but that they were of very unequal durability; of the durable implement only a small portion of its value would be transferred to the commodity, a much greater portion of the value of the less durable implement would be realised in the commodity which it contributed to produce.

 

The phrase, “only a small portion of its value would be transferred to the commodity,” introduces us to the central concept on which both the Ricardian and the Marxian theories of natural price are based. Ricardo speaks most often of the labour “bestowed” upon a commodity, meaning by this not only the labour directly employed in fashioning the commodity, but also the labour indirectly required, for example to produce the raw materials and tools which are used in making the commodity, or the labour which is expended in bringing those raw materials and tools to the place of manufacture, or the labour employed in building the ships which bear the raw materials and tools to the place of manufacture, and so on.

 

It has become common practice to speak of the labour directly or indirectly required for the production of a commodity as labour “embodied” in the commodity, and this locution ineluctably draws us into thinking of a commodity as a container in which labour has been stored up. Ricardo encourages this way of thinking by speaking of a “portion of the value” of a tool being “transferred” to the commodity which is produced with its assistance. We are clearly invited, by this language, to suppose that as a tool or implement wears out over the course of its useful life, the value stored within it – which is to say, the labour bestowed upon it in the past – is slowly shifted over to  the commodities produced with its aid, until finally, at the moment when the tool ceases to be useful, its store of embodied labour, or value, is exhausted.

 

Thus construed, the notion of “embodied labour” is clearly crackbrained – the rankest sort of bad metaphysics. However, the concept of a quantity of labour directly or indirectly required for the production of a commodity is, under certain assumptions, perfectly coherent and meaningful, and quite susceptible to precise calculation.

 

At issue here more generally is what accountants and economists call the problem of imputation. When a factor of production is employed in the production of a number of units of some commodity, the question arises of how to impute or attribute or credit the cost of that factor to the several units of output for the purpose of determining how much each unit has cost to produce. One brief example will illustrate some of the complexities of the subject.

 

Suppose Diana is uncertain how much of the cost of her bow to impute or attribute to each of the deer she kills, in order to determine what price to charge for them. Clearly she must impute something, for otherwise she will be failing to take account of the labour it cost her to acquire the bow, over and above the labour she expended directly in the hunt. Were she to forego the imputation, she would find, when the bow finally wore out, that she had failed to accumulate a sinking fund for the replacement of the used-up implement. She can simply divide the original cost of the bow by the average number of deer killable with one bow, and then impute the resulting fraction to the price of each deer. Or, she can take account of the fact that a bow requires some breaking-in before it is maximally functional, and so charge a larger fraction of the cost to those deer killed during the sub-efficient breaking-in period. Or, she can take into consideration the appearance in the weapons market of new, more efficient bows, and impute to each deer only as much as it would cost her per deer were she using one of the more efficient bows (thus explicitly acknowledging the sound accounting principle that it is the cost of replacement at current prices and levels of technology that governs the imputation of costs). Indeed, should she have an armamentarium of bows of various ages, dating from different periods in, and price structures of, the weapons market, she could impute her costs using the first in first out (FIFO) method, or alternatively the last in first out (LIFO) method, and so forth.

 

At this point, I shall introduce a little three sector model of an economy that produces corn, iron, and theology books. Remember that everything I say about this little model can be proved rigorously for models of any finite number of sectors, using the techniques of linear algebra. I apologize for the fact that the table is labeled Table 3 and the system is called System C.  I have copied this from a file of my book, Understanding Marx, and I am insufficiently technically adept to figure out how to edit it once I have copied into this text.

 

Let us return to the simple corn/iron/theology books model, System C, which we imagined to arise as the consequence of the emergence of a physical surplus in the production of corn and iron. The structure of System C, it will be recalled, is as shown in Table 3.

 

According to Ricardo, the value (i.e., the natural price) of these commodities is affected (i.e., determined, or at least primarily determined) by the amount of labour indirectly as well as directly bestowed upon them. This means that as between two commodities, say corn and iron, their prices will stand in the same ratio to one another as do the amounts of labour directly and indirectly required for their production.

 

Leaving to one side for the moment the very important qualification “or at least primarily determined,” what we have here is a theory of the determination of natural price. The theory states that the natural price of a commodity is proportional to the quantity of labour directly and indirectly required for its production.

 

How can we ascertain whether this theory is confirmed by System C? Clearly, we must find some way to calculate the quantities of labour directly and indirectly required for the production of each of the three commodities produced by the system – corn, iron, and theology books. Then we must find some independent way to calculate the natural prices of these same commodities – which is to say, the prices that prevail when the supply and demand for each commodity are in balance, and a uniform rate of profit is therefore returned on the value of capital invested throughout the system. Finally, we must form the ratios of labour required to natural price for each commodity and see whether they are indeed equal to one another.

 

Before we can determine the correctness of Ricardo’s thesis, we must find some way to make it precise. To this end, let us adopt a series of notational conventions, of the sort customarily used by mathematicians and economists. First of all, we shall define a number of variables standing for the prices of the commodities produced in System C. Specifically, let pc stand for the natural or equilibrium price of corn, let pi stand for the natural price of iron, and let pb stand for the natural price of books (“p” for “price”). Then, let us define variables standing for the quantity of labour directly or indirectly required for the production of single units of corn, iron, and books. Following what has become a tradition in the literature on this subject, we shall use the Greek letter lambda to stand for this quantity. Thus, λc, λi, and λb shall stand for the quantities of labour directly and indirectly bestowed upon, or required in the production of, one unit of corn, iron, and books respectively.

 

With this notation in place, we can now restate Ricardo’s thesis in the form of an algebraic equation. When Ricardo says that commodities exchange in proportion to the quantities of labour directly or indirectly bestowed upon them in production, he is, in effect, asserting:

 

(λc/pc) = (λi/pi) = (λb/pb)        (1)

 

If we wish to determine whether (1) is true for the commodities in System C, we must find some way to calculate the values of the price variables pc, pi and pb, and the “labour value” variables (as they are usually called), λc, λi, λb. Then we can substitute those values into (1) and see whether the equality holds.

 

Let us begin by attempting to determine how much labour is required in System C, directly and indirectly, to produce 1 unit of corn. In short, let us try to calculate the value of λc. The  information available to us is the data on inputs and outputs summarised in Table 3. This tells us that 100 units of labour are employed directly in the production of 300 units of corn. Consequently, 1 unit of corn requires 1/3 unit of “direct labour.” Thus, λc, the quantity of labour required directly or indirectly for the production of 1 unit of corn, must be at least 1/3. We can express this by the incomplete expression

 

λc  = 1/3 +

 

indicating that more labour than the 1/3 unit of direct labour may be required.

 

But Table 3 also tells us that 2 units of corn are required in order for the 300 units of corn to be produced as output, and 16 units of iron as well. It follows that the production of a single unit of corn requires 1/150 of a unit of corn and 4/75 of a unit of iron.

 

Now 1/150 of a unit of corn will require for its production (1/150)(1/3) units of labour directly applied, so the original unit of corn manifestly requires an additional 1/450 of a unit of corn indirectly for its production. The 4/75 of a unit of iron will require in turn (4/75)(l) = 4/75 of a unit of labour for its production, for as the input/output proportions in the iron industry show, it takes 1 unit of labour directly applied to produce 1 unit of iron. We see therefore that we must add some labour indirectly required to the 1/3 unit of labour directly required for the production of a unit of corn. In short:

 

λc  = 1/3 + 1/450 + 4/75 +

 

Thus far, we have a total of 7/18 of a unit of labour directly and indirectly required to produce 1 unit of corn. But we are not done, for of course the 1/150 of a unit of corn required to produce the original unit of corn itself requires corn and iron for its production, as do the 4/75 of a unit of iron, and these in turn require some labour for their production, and so on. Quite obviously, we have here an unending series of quantities of labour more and more indirectly required for the production of the original unit of corn, in addition to the 1/3 of a unit of labour directly required. What are we to do?

 

As it happens, this series “converges,” as mathematicians say. That is, it gets closer and closer to some finite amount, the more terms we add. And there are ways to figure out what that finite amount is – what the “limit” is of the infinite sum. But we need not carry out any such summation in order to arrive at the total amount of labour directly and indirectly required for the production of a single unit of corn in System C. Instead, we may make use of a mode of calculation that derives from the input/output analysis of the Russian-American economist Wassily Leontief, and which has now become universally accepted as the correct analytic reconstruction of Ricardo’s notion of a quantity of labour “bestowed” upon a commodity.

 

The central idea of the modern method of “required labour” calculations is simply that the total quantity of labour embodied in a certain physical magnitude of output exactly equals the quantity of labour directly bestowed upon it in the course of production plus the quantity of labour indirectly bestowed upon it by way of the non-labour inputs which are used up in the production process. Continuing to use λc, λi and λb to stand for the quantities of labour directly and indirectly required for the production of one unit of corn, iron, and books respectively, we are now able to translate the conditions of production defined in System C into a series of equations.

 

The input/output data for the corn industry specify that 100 units of labour are directly required, together with 2 units of corn and 16 units of iron, in order to produce 300 units of corn as output. The 100 units of labour contribute 100 units of embodied labour to the output, obviously. Each unit of corn input embodies λc units of labour, according to the convention we have adopted (we don’t yet know how much labour that is, of course – finding that out is the point of this exercise). Therefore, the 2 units of corn used as input must contribute 2λc units of labour to the end product. Similarly, the 16 units of iron must contribute 16λi units of labour. The output, which consists of 300 units of corn, must embody 300λc units of labour. So, putting this all together, we can translate the conditions of production in the corn sector into the following “labour value equation”:

 

100 + 2λc  + 16λi + 0λb = 300λc.        (2)

 

By exactly the same process of reasoning, we can translate the conditions of production in the iron and books industries into two more labour value equations, namely:

 

90 + 9λc + 12λi + 0λb  = 90λi (3)

 

and

 

20 + λc + 2λi + 2λb  = 40λb    (4)

 

Equation (2) asserts that 100 units of labour directly bestowed on 300 units of corn output plus 2 times the amount of labour “embodied in” a unit of corn (and hence “transferred” to the output in the production of which it is totally used up) plus 16 times the amount of labour “embodied in” a unit of iron equals 300 times the amount of labour bestowed on, and thereby “embodied in” a single unit of produced porn. And similarly for equations (3) and (4).

 

Assuming that these equations correctly capture Ricardo’s intuitive notion of labour bestowed on the output of a process of production, we can now proceed with little difficulty to ascertain how much labour is required directly or indirectly for the production of a single unit of corn, iron, or books. All we must do is find the values of the variables λc, λi, and λb. Now, equations (1) through (4) constitute a system of three independent linear equations in three unknowns.  There is precisely one set of values of the variables that satisfies all three equations. Elementary algebra permits us to solve the system of equations. As the reader can check, by substituting back into the equations to see whether they balance, the values of the variables that solve the equations are:

 

λc  = .4

λi  = 1.2

λb  = .6

 

What this means in economic terms is that 4 units of labour (measured in hours, weeks, years, or whatever) are required, directly and indirectly, to produce 1 unit of corn in System C, and that 1.2 units and 6 units of labour respectively are required directly and indirectly to produce single units of iron and books. These quantities are customarily referred to as the “labour values” of corn, iron, and books in System C.

 

We are thus in a position to determine how much labour is required to produce corn, iron, and theology books, despite the fact that inputs other than labour are employed in the production process.

 

A closer look at equations (2) through (4) reveals that although they do indeed form a system of three independent linear equations in three unknowns, equations (2) and (3) actually form a subsystem of two independent linear equations in two unknowns. Theology books enter into the production only of themselves. They play no role in the production of corn and iron, although corn and iron do play a role in their production. The values of the variables λc and λi are thus entirely determined by equations (2) and (3). No change in equation (4) can affect the values of those variables. This corresponds to the economic fact that the labour values of corn and iron are entirely determined by the combined conditions of production in the corn and iron sectors. A change in the conditions of production of either corn or iron could be expected to have an effect on the labour values of corn, iron, and theology books, but a change in the conditions of production of theology books will affect only the labour value of the theology books themselves.

 

It is a good deal more difficult to determine the natural prices of corn, iron, and books in System C. To calculate the labour values, we required only the input/output physical data contained in Table 3. Hence our results are valid for-any economy employing the technology summarised in the table. But before we can calculate the natural prices that would rule in a system having the physical proportions of System C, we must introduce a number of assumptions concerning the knowledge available to economic agents, the rules or principles that guide their choices, and the institutional and legal setting within which they act economically.

 

Modern economists are more explicitly self-conscious about their behavioural and institutional presuppositions than were Smith, Ricardo, and the other classical theorists. Nevertheless, with the benefits of hindsight, we can reconstruct a number of basic background assumptions implicit in their arguments.

 

The first assumption on which Smith and Ricardo build their theories of distribution and growth is that the economic actors in a capitalist system – the workers, landlords, entrepreneurs, and consumers – have perfect knowledge, or at least tend to acquire perfect knowledge, concerning the characteristics of commodities, market prices, wage and profit rates, opportunities for increased return, and so forth. Producers are assumed to know what the ruling technique of production is, what prices are being charged for labour and raw materials, what prices they can expect to sell their output for, and what rental they will be charged for agricultural land. They are also assumed to know, or at least to learn pretty quickly, when one of their number starts to make an unusually high return on an investment.

 

The point of these assumptions, which are theoretical simplifications rather than realistic descriptions, is to factor out of the picture any of the complications that result from industrial secrets, imperfect or uneven distribution of market information, duplicity, etc. We can think of these assumptions, and others to be discussed, as playing the same role in the classical theory of the market as is played by the assumptions of point masses or frictionless surfaces in Newtonian mechanics.

 

The second assumption is that everyone in the system is motivated by self-interest defined in a narrowly economic sense. Workers seek the highest wage, regardless of where it is offered or in what line of work, and they exhibit very little hesitation about leaving one job and moving to another. Capitalists seek the highest rate of return on their capital, regardless of whether it is derived from the manufacture of luxury cars or the collection of garbage. Consumers seek the lowest price, unhampered by loyalty to one vendor rather than another.

 

Finally, we assume a system of private property, in which each actor is free to make legally binding contracts for the sale of goods and services, including labour services, without constraints on the terms of those contracts save that they be legally voluntary.

 

A number of useful conclusions follow from these assumptions. First of all, as a consequence of the behaviour of consumers and producers, a single economy-wide set of prices for commodities will come to prevail. If corn is being sold for less in one shop than in another, consumers will know about it (the knowledge assumption), and they will hurry over to buy the cheaper corn (behaviour assumption). Capitalists who have been charging a higher price will lower their price in order to avoid losing all their sales (behaviour assumption), and no government agency or local ordinance will stop them from doing so (institutional assumption).

 

In a similar manner, a single economy-wide wage will rule, because workers will know whether an employer is offering more than the going wage (knowledge assumption), will look for jobs wherever higher wages are being offered (behaviour assumption), and will be free to make the best wage bargain they can (institutional assumption).

 

Most important (and most complicated) of all, capitalists will tend to earn the same rate of return on their invested capital, for they will learn about any industry in which higher returns are being earned (knowledge assumption), they will shift their capital as soon as they can to that industry (behaviour assumption), they will be unconstrained by law or custom in the reinvestment of their capital (institutional assumption), the additional output they contribute to the market will drive down the market price (knowledge, behaviour, and institutional assumptions), and as a consequence the rate of return will tend to approximate the economy- wide rate.

 

On the basis of these assumptions, we can translate the input/output data of Table 3 into a number of new equations expressing the relation between the price a capitalist must pay for his labour and materials, the profit mark-up he puts on his costs, and the price at which he sells his output in the market.

 

Since there is a single price for each commodity, we can assume that each capitalist, no matter in what line of production, pays the same amount for a unit of corn, iron, or books, and that this is also the price at which he sells a unit of each.

 

As in equation (1), we will let pc stand for the price of corn, pi for the price of iron, and pb for the price of books. In addition, we can let w stand for the wage, for our assumptions imply that all workers earn the same amount per unit of time that they work.

 

Finally, since all capitalists earn the same rate of return, we can define the Greek letter π as the uniform rate of return on the value of invested capital.

 

With these five variables: the three prices, the wage, and the profit rate, symbolised by pc, pi, pb, w, and π, we can now translate the data of Table 3 into equations expressing the relation between a capitalist’s costs, his profit mark-up, and the price at which he sells his output. In the corn industry, for example, the capitalists as a group pay 100w for their labour, 2pc for their corn inputs, and 16pi for their iron inputs. They put a (1 + π) mark-up on their costs, in order to net a rate of return of n, and all of this must equal 300pc, which is what they sell their output for. In short:

 

(100w + 2pc + 16pi + 0pb)(l + π) = 300pc      (5)

 

By the same process, we can arrive at price equations for the iron and books industry, namely: (90w + 9pc + 12pi + 0pb)(1 + π) = 90pi;       (6)

and

 

(20w + pc+ 2pi  + 2pb)(l + π) = 40pb (7)

 

Equations (5) through (7) form a system of three equations in five unknowns. Consequently, there cannot possibly be a single set of values of the variables that uniquely satisfies all three equations. Instead, there is an infinite number of such sets of values. In order to make the system determinate, we must somehow introduce more information, and thereby reduce the number of variables.

 

A first step (standard in the analysis of models of this sort) is to appeal to the fact that we do not really need three price variables. A system of prices is usually expressed in terms of one commodity, which is chosen as the unit of money in the system. For example, a pound of silver may be chosen as the unit of money, or “numeraire,” and all other prices may then be expressed as multiples or fractions of pounds sterling. Or an ounce of gold may be selected as the unit of money. Or, in System C, a unit of corn may serve. When this is done, the “price” of a unit of the commodity functioning as money is arbitrarily set equal to 1. (This is mathematically the equivalent of dividing all of the other prices by the price of the money-commodity.)

 

Suppose that we choose corn as numeraire in System C and set its price equal to 1, thereby making all the other prices “corn prices,” or prices expressed in units of corn. If we now substitute into equations (5) through (7) the new information, pc = 1, we have:

 

(100w + 2 + 16pi)( 1 + π) = 300,        (5’)

 

(90w + 9 + 12pi)(l + π) = 90pi,           (6’)

 

and

 

(20w + 1 + 2pi  + 2pb)(l + π) = 40pb. (7’)

 

This is a system of three equations in four unknowns: the relative prices of iron and theology books, the money wage in units of corn, and the profit rate (which is a pure number, or percentage, and hence is unaffected by choice of units). This is better, but our system still has one degree of freedom (one more variable than equations), and hence does not have a unique solution. What new information can we add to this model to advance our analysis?

 

Modern theorists recognise two economically meaningful ways to analyse this system. The first is to close the system by specifying the wage exogenously (i.e., from outside the system), which has the effect of reducing the system to three equations in three unknowns. Once we have added this new information about the wage, the remaining variables do in fact become

determinate. The second way is to reduce the system to a single equation in two unknowns, the wage and the profit rate, and then to study the relationship between them.

 

Ricardo’s original idea was rather deeper than either of these. He was convinced that prices were determined solely by the technical conditions of production, whereas the wage and the profit rate – the distributional variables – were determined by an ongoing struggle between the labouring class and the entrepreneurial class. The implication of this idea was that a system of equations like (5’) through (7’) should be soluble for the relative prices without specifying the wage or the profit rate. In fact, System C has deliberately been constructed to exemplify Ricardo’s conjecture, as the following algebraic manipulations demonstrate:

 

(100w + 2 + 16pi)(l + π) = 300.          (5’)

 

(90w + 9 + 12pi)(l + π) = 90pi.           (6’)

 

From (5’)

 

1 + π = 300/(100w + 2 + 16pi).

 

Substituting in (6’)

 

90pi = 10(30w + 3 + 4pi)/(100w + 2+ 16pi)

 

or

 

 

i

100wpi + 2pi + 16p ² = 300w + 30 + 40pi. 16pi2 + (l00w – 38)pi – (300w + 30) = 0

We can solve this equation, using the quadratic formula. Since the unknown quantity is a price, negative values of the variable have no economic meaning.

 

Pi = { – (100w) – 38) ± [(100w – 38)² + (4)(16) (300w + 30)]^1/2}/32

 

Pi = { – (100w – 38) ± [(100w + 58)²]^1/2}/32

 

Pi = (– 100w + 38 4-100w + 58)/32

 

Pi = 96/32

 

Pi = 3

Thus, the wage drops out of the computation, showing thereby that relative prices are determined by the technical conditions of production, independently of the distributional variables.

 

Finally, we are in a position to determine whether Ricardo’s theory of natural price holds in System C. According to Ricardo, as we have interpreted him, natural prices are proportional to labour values, which is to say:

 

λc/pc  = λi/pi = λb/pb   (1)

 

Substituting the values we have obtained for these six variables we have:

 

1/.4 = 3/1.2 = 1.5/.6,

 

which is true. So, in System C, Ricardo’s labour theory of natural price, as we may call it, holds. What we have done, let me repeat, is to use the input/output technical data summarised in Table 3 to determine the labour values of the commodities produced in System C. Then we have used the same data, together with a number of powerful knowledge, behavioural, and institutional assumptions to determine the relative prices of the commodities. And finally, we have used the values and prices thus arrived at to test Ricardo’s theory of price in System C.

 

If we substitute the values of pc and pi back into (5’), we can, by a few manipulations, arrive at the expression,

 

1 + π = 6/(2w + 1),

 

which exhibits the relationship between the wage and the profit rate. As w rises, (2w + 1) rises, and hence 6/(2w + 1) falls. Therefore π falls. And conversely. We can immediately conclude that the distributional variables, π and w, are inversely related. This relationship, to which Ricardo attached great importance, is very difficult to observe when the interactions of prices, wages, and profit rates are analysed verbally. In algebraic form, however, it is immediately manifest. It is the formal reflection of the necessary conflict of interest between the capitalist and labouring classes.

 

The central purpose of a theory of natural price, it will be recalled, is to assist us in analysing the distribution of the physical surplus of commodities generated by the productive activities of the economy. In our original discussion of System C, we treated the food, clothing, and shelter consumed by the workers as part of the inputs required to keep the economy going. Modern economists tend to treat wages as a share of the surplus (speaking, in modern terminology, of the “net national product” as being “gross of wages”). But we shall continue

to treat worker consumption as part of the physical requirements of the system, for that is how it was understood by Ricardo and Marx.

 

In order to study the allocation of the physical surplus, therefore, we must first specify how much corn, iron, and theology books are required in each cycle of production to reproduce the working class. The workers, of course, receive their wages in the form of money, and then buy their food, clothing, and shelter in the market at going prices. But if we are to determine the size and composition of the physical surplus, we must make some assumptions about precisely how they spend their wages.

 

Ricardo, and Marx after him, argued that workers by and large received wages adequate only for subsistence living, and that as a class they spent their money in pretty much the same way, for plain food, plain clothing, and simple lodging. They also assumed that as a class workers do not save. Since we have broken the economy of System C into only three sectors – corn (or food), iron (or non-agricultural necessities and capital goods), and theology books (somewhat facetiously construed as luxury items) – we may, following Ricardo and Marx, suppose that each worker spends his or her money wage for the same quantity of food, clothing, and shelter (corn and iron) with nothing left over for luxuries (theology books).42 Since we are making no particular effort at historical realism in the analysis of System C, we may simply assume that workers receive a money wage of .5 per unit of labour (where the wage is measured in terms of the numeraire, corn), and that they all spend their wage on .2 units of corn (costing .2) and.1 units of iron (costing .3). The actual market basket of commodities, (.2 corn, .1 iron), purchased with the money wage is called by economists the real wage. Thus, we are assuming that in System C, the real wage is .2 units of corn and .1 units of iron per unit of labour delivered by the workers to the capitalists.

 

As we saw earlier, in System C the relationship between the money wage and the profit rate is given by the equation

 

(1 + π) = 6/(2w + 1).

 

It follows that with a money wage of .5/unit of labour, the profit rate, n, is 200 percent. (No attempt has been made to achieve historical realism!) Since we have assumed that (.2 corn, .1 iron)/unit of labour is a subsistence wage, it follows that the entire physical surplus is appropriated by the capitalists. To determine the size of the physical surplus, we must subtract the physical inputs, including those required by the workers as food, clothing, and shelter, from the gross outputs of corn, iron, and theology books. The result is a physical surplus of 246 units of corn, 39 units of iron, and 38 theology books.

 

At the natural prices prevailing in the system, this surplus has a value, in corn-money units, of: (246 × 1) + (39 × 3) + (38 × 1.5) = 420.

 

The total profit earned in all sectors can be ascertained by multiplying the price of all inputs by the profit mark-up. As Table 3 shows, a total of 210 units of labour, 12 units of corn, 30 units of iron, and 2 units of books are consumed as inputs throughout the system. Hence, the total profit appropriated by all capitalists, with the prices we have calculated and a profit rate of 200 percent is:

 

(210w + 12pc + 30pi + 2pb) × π = 420.

 

As expected, the profit appropriated by the capitalists just suffices to purchase the physical surplus remaining after the inputs for the next cycle have been deducted.

 

With this analysis before us, it is now possible to give a preliminary account of Ricardo’s answer to the three questions posed by the emergence of a physical surplus in an economy periodically reproducing itself. Who gets the surplus? The capitalists, or entrepreneurs get the surplus. (We have not yet introduced Ricardo’s villain, the landlord). How does the surplus- getter get the surplus? That is not quite so clear. The entrepreneur buys inputs, including labour, combines them, and sells the output at a profit. The simple answer, therefore, is that the capitalist class appropriates the physical surplus by making a money profit and then using it to buy the physical surplus. But it is not yet clear, as Marx was quite dramatically to point out, how it comes about that the capitalists make a profit. Finally, Ricardo, following Smith, argues that capitalists use their share of the physical surplus to expand the scope of production, thereby generating economic growth. Landlords, on the other hand, spend whatever money they can get on luxuries, drawing a portion of the physical surplus away from production and restricting economic growth.