A brief history
Ajit Sinha
An object or an activity is an ‘economic entity’ only if it has power to attract something in exchange. Thus it is fundamental for economics to understand how an object or an activity acquires exchange-value. The theories of value of heterodox economic traditions are rooted in classical political economy, which takes up this problem only with respect to commodities that are reproducible as they considered only those to be important in understanding an economic system. The classical economists were fundamentally interested in finding out the essential cause that gives rise to the exchange-value of commodities. The problem of exchange-value, however, also immediately raises the question of the scale by which it can be measured. As we shall see, the problem of the ultimate cause of value in the classical tradition gets entangled with the question of the scale of its measure—the cause must explain the change in value but at the same time must not affect the scale by which the change is measured. In this chapter we discuss three major developments in the history of value theory in heterodox economic traditions. First we discuss the problem as set up by Adam Smith, then criticized and developed by Ricardo and Marx and subsequently reconstructed by Sraffa, whose reconstruction removes the notion of equilibrium from the theory of value, which makes it most compatible with all hues of heterodox economics.
In the Wealth of Nations Adam Smith ([1776] 1981) devotes three short chapters (V, VI, and VII of Book I) to his theory of value, which set the ground for the classical theory of value and distribution. After establishing that the true wealth of a nation does not lie in the quantity of money-commodity a nation has accumulated but rather in the quantity of goods and services available per capita, Smith points out that the increase in the true wealth of a nation lies in two things: (i) improvements in the productivity of labor and (ii) the investment of savings in the employment of productive labor not unproductive labor, of which the former is by far the more important. Smith then goes on to argue that improvements in the productivity of labor largely depend on the extent of the division of labor applied in the production of any specific good, which in turn depends on the extent of its market. When the market for a good becomes very large, Smith argues, an opportunity arises for different aspects of the production of a commodity, which were earlier performed within a household or a factory, to be divided into independent trades and thus the division of labor at the level of a household or a factory grows into a social division of labor. It is the existence of the social division of labor that brings to the fore the question of commodity exchange.
However, instead of immediately posing the question of the principle that regulates the exchange ratios of commodities in an economy characterized by the social division of labor, Smith begins by raising the problem of the measurement of a commodity’s value or a nation’s wealth. Of course, if the problem is only to determine the exchange ratios of commodities then any commodity could serve the purpose of measuring the values of other commodities and thus the prevalent money-commodity, say gold or silver, would very well foot the bill. Thus it is clear that the theoretical problem posited by Smith is a different one. The problem is not of a measure of value at a point of time but rather of the measure of a change in value. For example, if the wealth of a nation is the availability of all goods and services at a point of time then their aggregate value in terms of money can be treated as a surrogate for the measurement of the wealth of a nation. But could the rise and fall in the total money-value of wealth be taken as a surrogate for measuring the rise and fall in a nation’s real wealth as the mercantilists had purportedly argued? Smith’s argument against such reasoning is that the value of money-commodity itself fluctuates independently of the aggregate of goods and services like the price of any other commodity. Therefore it cannot be a correct measure for measuring the changes in the wealth of a nation or the value of any other commodity over time.
This brings Adam Smith to the problem of the essential or the ultimate cause of value. What is it that causes a commodity to be valuable in the first place—that is, to command money or some other commodity in exchange? If one could find the ultimate cause that confers this property on a commodity then one would ipso facto know the measure to use for determining the changes in the real value of a commodity over time. Here we find that the question of a measure of value is intricately linked with the question of the essential or ultimate cause of value.
This takes Adam Smith deep into human history—that is, the ‘early and rude state of society.’ The basic idea is that primitive man must have had to wrest his subsistence from nature by working against nature with his bare hands. Thus production can be reduced to an exchange between man and nature. Adam Smith thought that this primitive exchange can also explain the exchange between man and man. Since the price paid for subsistence is the ‘toil and trouble’ of a certain period, possession of the subsistence produced can command or exchange for a certain period of toil and trouble of any other man. Thus the real measure of value is the ‘subsistence’ that buys the ‘toil and trouble’ or labor, which is the ultimate source of the value of a commodity.
Smith realizes that in a capitalist economy the ‘subsistence’ that a worker receives for his ‘toil and trouble’ fluctuates over time. He maintains that such fluctuations in the values of the commodities that constitute the ‘subsistence basket’ as the ‘toil and trouble’—or the sacrifice made by the worker to receive the ‘subsistence basket’—remains the same and it is the sacrifice of the worker that measures the real cost of acquiring the commodity. This, of course, does not resolve the matter. The ‘toil and trouble’ represents the subjective notion of ‘sacrifice’ on the part of the worker which may not be measurable. But Smith insists that it can be measured by the ‘objective’ measure of hours of labor spent by the worker in the production process.
Adam Smith argues that in the ‘early and rude state of society’ laborers own their means of production or they produce the means of production from scratch. In this society Smith maintains that it would be natural for laborers to exchange their products in accordance with the total labor-time required to produce the respective commodities. In this case, the amount of labor that takes to produce a commodity is equal to the amount of labor that commodity can command of somebody else’s labor embodied in the other commodity. Thus the problem of the determination of the relative value of commodities coincides with the problem of the measure of value. According to Adam Smith, this coincidence, however, breaks down once the means of production becomes the private property of a class other than the laborers. Once a class of capitalists, who advance the means of production and the subsistence of the laborers during the production process, arrives on the scene and demands a share in the net product, it immediately creates a discrepancy between a commodity’s power to command the amount of labor-time and the amount of labor-time that is taken to produce that commodity—obviously the commodity’s command of labor must be higher than the labor-time it takes to produce the commodity if the capitalists’ share in the net output is to be positive. Thus, once the net output is distributed among two or more classes of people, Adam Smith argues, the principle of exchange of commodities (according to the total labor-time required to produce the respective commodities) no longer holds.
The alternative theory of value determination that Adam Smith proposes when net output is distributed to various classes is fundamentally a theory based on accounting. Smith argues that the size of the net output must be equal to the sum of total wages plus profits plus rents if the net output is divided into only three income categories. Similarly, the value of capital can in turn be broken down to wages, profits, and rents by going back into the chain of production. Thus adding up all the direct and indirect wages, profits, and rents will measure the total value of gross output. From this it follows that the price of a commodity is constituted by adding the aliquot parts of direct and indirect wages, profits, and rents that the production of that commodity generates.
Subsequently Smith argues that for any given economy at any given point in time there exists, as known data, a ‘natural’ rate of profits, wages, and rents. From the aggregation of these natural rates one can determine the ‘natural price’ or value of any commodity. These ‘natural’ rates are not the ‘actual’ rates that must exist at that moment however. They are the rates around which actual rates are at any given moment fluctuating—they can be thought of as averages of the past several years of actual rates although they are not just a statistical notion. These natural rates are those that specify the general equilibrium of the system—that is, if the ‘actual’ rates are equal to the ‘natural’ rates then the economy will be at rest. In other words, there will be no internal tendency for the economy to move from that position On the other hand, if the ‘actual’ rates are not equal to the ‘natural’ rates then there will be an inherent tendency—due to free competition in the economy—for the ‘actual’ rates to move toward the ‘natural rates.’ Hence the ‘natural’ rates generate a gravitational force that pulls towards the ‘actual’ rates.
Ricardo ([1821] 1951) criticizes Adam Smith for both his choice of the wage-unit as the ‘invari-able’ measure of value as well as his so-called ‘additive’ theory of value. First of all, Ricardo points out that real wages do fluctuate over time and, hence, there is nothing inherent in wage-units, compared to any arbitrary commodity, to be claimed as an ‘invariable’ measure of value. As we have seen, Adam Smith had of course recognized that wages do fluctuate over time which he defends from the standpoint of the laborer. Smith argues that if we compare eight hours of work by a laborer over two time periods, the ‘sacrifice’ or hardship that the laborer endures in both time periods remain the same and that is the real price the laborer pays in exchange for his or her subsistence. Now, if the subsistence basket contains more or less of commodities then—as far as the laborer is concerned—it is the value of those commodities that are falling or rising because the laborer is buying more or less for the same amount of payment she makes for acquiring the subsistence. This ‘measure’ may be sensible for measuring the changes in the wealth of a nation on the grounds of welfare. Given that the class of laborers constitutes the majority of population, a measure of a rise or fall in the wealth of a nation must represent the improvement or worsening of the conditions of its working force. Yet, it is not a ‘scientific’ measure that would ensure that when a change in the value of a commodity is measured against this yardstick it always measures the changes that have occurred in the commodity and not in the yardstick itself. That was Ricardo’s main objection to it.
With respect to Adam Smith’s ‘additive’ theory of value, Ricardo argues that it was logically flawed—if the net output of an economy is distributed or divided among three classes then it cannot be claimed that its size is determined by adding up independently determined wages, profits, and rents. Since if wages and profits are given from outside then rents have to be the residual and cannot also be from outside. In other words, according to Ricardo, Adam Smith fails to recognize that there is a constraint binding the size of the total income. Elsewhere (Sinha 2010a, b) I have argued that this is not a justified criticism of Adam Smith as he does acknowledge the constraint binding net output and determined rent as the residual.
In Ricardo’s opinion, however, Adam Smith errs to think that his labor theory of value was only valid for the ‘early and rude state of society.’ Ricardo argues that the labor theory of value remains a ‘correct’ theory for value determination even in a capitalist society where the net output is distributed between two or three classes. Let us suppose that there are no landlords but a class of capitalists exists who advance the subsistence and implements to workers who produce two commodities and demand a rate of profit on their capital investment. Ricardo shows that, as long as the ratio of labor-time taken to produce the implements used (that is, indirect labor) and the direct labor-time to produce the two commodities remains the same, it does not matter what rate of profits (which must be uniform in a competitive economy) the respective capitalists receive. The exchange ratio between the two commodities will not be affected—that is, they would still exchange in the ratio of the total labor-time needed to produce the respective commodities. Ricardo also argues that the rent of land is determined by a principle that makes it irrelevant for the determination of relative values of commodities. Thus, Ricardo contends that Adam Smith was wrong in thinking that the labor theory of value is invalidated once an income category other than wages emerges.
Ricardo, however, acknowledges that when the ratios of direct to indirect labor-time in various industries are not equal then the competitive condition of a uniform rate of profits across industries comes into contradiction with the principle of the labor theory of value. When wages are reduced from their full share of net output, the various industries release income in proportion to the number of workers they directly employ. Now if the ratio of direct to indirect labor of various industries is not equal then industry-wide release or transfer of income from their wage bills will give lower rate of profits for industries that are relatively ‘capital intensive’ and vice versa. Thus the competitive condition of equalization of the rate of profits across industries must result in modifying the exchange ratios of commodities from their original labor-time ratios.
How much must the labor theory of value be ‘modified’ in the face of heterogeneous ratios of direct to indirect labor-time across industries? Ricardo offers no answer. Adam Smith set the problem in terms of measuring the changes in the wealth of a nation over periods of time, Ricardo also set the problem of measuring the changes in the distribution of income over periods of time. In this context, Ricardo argues that with population growth more food must be produced. Given diminishing returns on land, it takes more labor-time to produce the same wage basket, which amounts to proportionately more labor-time devoted to producing wages on the marginal land and proportionately less labor-time devoted to producing what amounts to profits. Therefore, this should lead to a fall in the rate of profits. The idea was to show that the changes in the relative distribution of income over time can be explained exclusively through changes in the labor-time needed to produce the commodities, which Ricardo also considers to be the ultimate cause of value.
Yet again Ricardo faces the problem that changes in wages or the rate of profits modifies the relative values of commodities. Therefore the measure of changes in value—in terms of any arbitrary commodity—may nullify or reverse the effect caused by the changes in the labor-time used to produce the commodities. This led Ricardo to search for a commodity that would remain ‘invariant’ in the face of changes in the rate of profits. He did not find or theoretically construct any commodity that would fulfill such a requirement. All he did is to assume that (i) his money-commodity ‘gold’ was always produced by the same amount of labor-time and that (ii) the composition of its direct and indirect labor-time was somewhere near the middle of most of the commodities produced. Thus the effect of changes in the rate of profits on the values of most commodities, when measured against gold, remained small enough to be ignored. Sraffa (1951) argues that Ricardo was searching for an ‘average’ commodity as a yardstick such that the price changes (due to changes in the rate of profits) would be such that the total value of the net output will remain constant before and after the change in the rate of profits—that is, the size of the pie remains constant when it is cut in different proportions.
Elsewhere (Sinha 2010a, c) I have argued that Ricardo’s ‘invariable measure of value’ was designed to show that changes in the rate of profits have no effect on the values of commodities when measured against this particular yardstick. Thus it could be established that labor-time is the sole or ultimate cause of the change in values and the distribution of income, and that the apparent changes in value due to changes in the rate of profits is solely due to the arbitrary nature of the money-commodity that we have to choose as a measuring yardstick for changes in values. This idea is, however, illogical as changes in the rate of profits affect relative values of commodities and therefore there cannot be any commodity either in reality or theory against which relative values of commodities would not change. Ricardo finally comes to this realization, as six days before his untimely death he wrote to James Mill:
I have been thinking a good deal on this subject lately but without much improvement— I see the same difficulties as before and am more confirmed than ever that strictly speaking there is not in nature any correct measure of value nor can any ingenuity suggest one, for what constitutes a correct measure for some things is a reason why it cannot be a correct one for other.
Ricardo [1823] 1952: 372, dated Sept. 5, 1823
Marx ([1905–10] 1963) criticizes Ricardo for getting bogged down by a ‘secondary’ problem of searching for an ‘invariable measure of value.’ Marx argues that classical economists such as Adam Smith and David Ricardo are unable to solve the problem of value because they are unable to understand the nature of profit in the capitalist system. Marx’s central criticism of classical economics is that it is unable to penetrate through the appearances to get to the essence of capitalism. Marx ([1867] 1977) argues that the wealth of a capitalist nation appears as an immense collection of commodities, which in his opinion is akin to a ‘cell’ of a living organism and therefore an understanding of this living organism must begin with an analysis of its ‘cell,’ meaning a commodity in singular. In its appearance a commodity has two characteristics: (i) it has some use to someone in society—that is, it has use-value, and (ii) it always stands in a relation of exchange with some other commodity (the money-commodity)—that is, it has exchange-value. Marx argues that though use-value is necessary for a commodity to have an exchange-value, it is not something that explains the quantitative relation that exchange-value represents, since use-values of two commodities cannot be quantitatively compared.
The next step in Marx’s argument is that an exchange relation between two commodities represents a relation of equality, that is, something equal in quantity changes hands. He further argues the only thing that is common to both the commodities is that they are both products of labor. At this stage Marx argues that labor itself has two aspects: (i) concrete labor and (ii) abstract labor. Concrete labor represents the actual laboring process that ends up in the production of a particular use-value such as the laboring activity of an ironsmith that produces a sword. Abstract labor, on the other hand, represents the expenditure of energy by the ironsmith in the laboring process. In this case there is no qualitative distinction between the labor of an ironsmith or a goldsmith. It is the pure expenditure of human energy and can be quantitatively compared irrespective of the form in which it is spent.
Marx argues that what changes hands in equal quantity, in an exchange relation, is the abstract labor that is embodied in the two commodities. Here Marx makes a distinction between (a) the value and (b) the exchange-value of a commodity. The amount of abstract labor embodied in a commodity is called the value of a commodity, which is an absolute category—it exists in a singular commodity. Marx’s contention is that the value of a commodity manifests itself only in relation to an exchange with another commodity. Thus exchange-value is an outward appearance of the essence of a commodity, which is its value.
Marx then poses the question: if exchange-value represents the exchange of equal values then where does profit come from? In a capitalist system, a capitalist begins with a certain amount of money capital with which she buys raw materials, machines, etc. and also hires workers for a wage to produce a commodity which she sells in the market to recoup her money. Now, if the quantity of money the capitalist ends up with equals the quantity of money she started with (that is, M-C-M) then the whole process would be irrational from the point of view of the capitalist. Thus for this system to be meaningful the capitalist must end up with more money than she started with (that is, M-C-M′, where M′ > M). But the problem is: if the exchange involved represents an exchange of equal values then where does more money come from?
Marx’s answer is this. When the capitalist pays wages to the worker this appears to be a price paid for the laboring activity that the worker performs in the production process and so all costs are fully paid. But actually what the worker exchanges with the capitalist for a wage is not laboring activity but the worker’s capacity to work, which Marx calls ‘labor-power’ in contradistinction to ‘labor’ as such. The value of labor-power is also determined by the same principle as the value of any other commodity—that is, its value is determined by the amount of abstract labor-time needed to produce and reproduce the worker’s capacity to work at any given socio-historical moment. Thus given the wage basket, the value of labor-power is derived by reducing the wage-basket to the total abstract labor-time embodied in those commodities.
Marx contends that capitalism as a mode of production survives only because the value of labor-power turns out to be less than the labor-time that workers expend in the production process. This is the part of laboring activity that turns into profits for the capitalists. Thus the value of a commodity can be analyzed first into two distinct parts and then into three distinct parts: first, the value of a commodity is made up of the abstract labor-time embodied in all the raw materials, machines, etc. used up in producing the commodity—the indirect labor-time of the classical economists, which Marx called ‘constant capital’ (c), plus the direct laboring activity performed by the worker in producing the commodity—the classical economists’ direct labor-time.
It is Marx’s contention that though the classical economists analyzed the process of production in these two separate parts in the context of their labor theory of value, they failed to take the decisive step of analyzing the laboring activity itself in its two component parts: (i) the value of labor-power, which Marx called ‘variable capital’ (v), and (ii) the remaining laboring activity, which Marx called ‘surplus labor’ or ‘surplus value’ (s). Thus the value of a commodity is made up of c + v + s, where c + v represents the value of capital investment by the capitalist for producing the commodity and [s/ (c + v)] the rate of profit received by the capitalist on the sale of the commodity, which explains M′ > M of the circuit of capital.
Let us suppose that a commodity’s value is given by λi, then λi = ci + vi + si and therefore the rate of profits in terms of the value produced in this industry is given by si/(ci + vi). This can be written as (si/vi)/(ci/vi + 1). Similarly for other commodities, such as j, k, etc., the value of their rate of profits can be written as (sj/vj)/(cj/vj +1), (sk/vk)/(ck/vk + 1), etc. The ratio si/vi is called the ‘rate of surplus value’ or the rate of exploitation-it is the ratio in which the total direct labor-time is divided between what goes to the capitalists and what goes to the workers. In general one assumes that this ratio should be uniform across industries as the length of a working day is generally fixed conventionally or by law, and wages are determined at the level of the whole economy and not at an individual industry level. The ratio ci/vi is the ratio of the value of the total capital invested between its non-human (raw materials, machines, etc.) and human components. This ratio is a Marxian surrogate for the classical indirect to direct labor ratio and there is no reason to think that it should be uniform across industries as it represents specific techniques onf producing different use-values.
Now, if si/vi, sj/vj, sk/vk are equal and ci/vi, cj/v, ck/vk are not equal, then their respective value rate of profits, say ri, rj, rk, would not be equal either. If equal values change hands in exchange, then it is clear that the rate of profits received in various industries will not be equal. But Marx, following Adam Smith and other classical economists, maintains that in a competitive capitalist economy the rate of profits must be equal across sectors in a state of equilibrium. The problem is one of how to reconcile this contradiction.
Marx’s ([1894] 1991) proposed solution is as follows: at the level of value analysis we know it is the surplus value that is appropriated by the capitalists. So we add up all the surplus values produced by all industries, which gives us the total value appropriated by the capitalist class as a whole. If we divide this total surplus value produced in the economic system, say S, by the total constant plus variable capital of the system, say (C + V), then the ratio S/(C + V) gives us the average rate of profit of the economic system, which is the rate of profits that must be received by all industries. Mathematically, Marx’s argument can be presented thus:
In other words, the competitive mechanism of the capitalist system amounts to an exercise of pooling all the surplus value produced in the economic system into one pond and then redistributing it equally to all individual industries in proportion to their relative capital investment. This process takes place by establishing the exchange ratios of commodities such that all industries end up receiving an equal rate of profit. Thus the exchange-values do not represent an exchange of equal values. As a matter of fact, the industries whose rates of profits are higher must exchange more values against less value from the industries with lower value rates of profits—that is, Pi/Pj is not equal to λi/λj. However, ΣPi = Σλi and Σri (ci+vi) = S, that is, the total prices of production are equal to total value, and total profits are equal to total surplus value. Thus value is the ‘stuff’ of capitalism which circulates, gets exchanged, and divided between classes but the competitive mechanism of capitalism creates an appearance of this ‘stuff’ in such a way that its true nature is obscured.
There are two fundamental problems with Marx’s analysis. Böhm-Bawerk ([1896] 1949) argues that Marx’s conclusion contradicts his premise. Recall that Marx argues that the exchange of two commodities represents the change of hands of something equal. This was the premise from which he derives that it was an equal amount of abstract labor-time embodied in the two commodities that changed hands in the process of exchanging commodities. But in conclusion Marx claims that actually equal abstract labor-time does not change hands in an exchange relation, which contradicts the premise. The only way to overcome this criticism is to scrap the premise as unnecessary. One could simply claim that the total labor-time in terms of human energy expenditure represented by simple unskilled homogeneous labor-time embodied in a commodity, say λ, can be analyzed into three component parts, c + v + s. On the basis of this one can determine the rate of profits and the exchange ratios of the economic system in equilibrium.
Bortkiewicz ([1907] 1949), however, raises a more serious problem with Marx’s transformation of values to the prices of production. Bortkiewicz argues that Marx makes a mistake in measuring capital. If the production prices of commodities are not equal to their values then the relevant measure of capital must also be in terms of the prices of production and not in terms of values. Thus the average rate of profits derived by Marx is not the correct average rate of profits and so the measure of those prices of production are also incorrect. What it amounts to is that Marx’s system of equations is not well defined.
Once we allow the prices of production to appear on the left-hand side of the equations as well, then we return to Ricardo’s world and Marx’s analysis of a singular commodity as value loses all analytical significance—we are in the world of relative values and profits to begin with. Once values are replaced by unknown prices of production on the left-hand side of the equations, it becomes clear that Marx’s system of equations is underdetermined because it has more unknowns to solve than it has independent equations. In this system an extra equation for the numéraire—the measuring yardstick—can be added from outside the system and then the equations can be solved for an equal rate of profits and relative prices. If one puts the condition that the total prices of production must equal total values in the system, which satisfies Marx’s yardstick of maintaining all deviations of prices of production from value to be zero, then there is no reason to assume that the total profits in the system would be equal to total surplus value (see Seton 1957). So Marx’s value analysis of a commodity no longer appears to reveal the essence of exchange-values and profits.
Marx was aware that his method of deriving the rate of profits and prices of production had some problems and that he needed to replace values with the unknown prices of production on the left-hand side of the equations as well (see Marx [1894] 1991: 264–265). In this case, he came to the conclusion that he can only make a much weaker claim that the rate of profits would be positive if and only if the rate of surplus value is positive—a proposition that is valid and was later christened as ‘fundamental Marxian Theorem’ by Morishima (1973). But, as Samuelson (1974) shows, after Sraffa (1960) we know that prices and the rate of profits can be directly determined from the physical input-output data without going through value determination. In that case it can be shown that positive surplus value exists if and only if there is a positive rate of profits. In other words, the arrow of causation can go both ways, which amounts to saying that no arrow of causation can be drawn.
For Sraffa (1960) one major distinction between the classical theory of value and the orthodox one lies in their attitude to the measurability of the variables on which the theory depends. Sraffa thinks that a scientific theory must be based only on objectively observable and measurable variables. Thus, he was of the view that classical and Marxian economics include only those variables that can be objectively and directly measured on some scale, whereas orthodox theory bases itself on the subjectivities of agents, which cannot be directly measured. On this basis Sraffa develops a theory of value that is based on only objectively given physical input and output data. However, he rejected the classical idea of finding the essential or ultimate cause of value. Instead, he developed a geometrical theory, which establishes exact relations that must prevail between the theoretical variables at any given moment and not the discovery of the cause of their existence. Sraffa’s commitment to basing his theory solely on observed data at any given moment also led him to reject the classical idea of the center of gravitation or equilibrium, since such notions are ideal and not observable at any given moment. Functional relations of orthodox economics that generate causal forces for variables to move in certain prescribed directions are also rejected on the grounds that, at any given moment, functions do not exist; at best, only a point exists.
Sraffa’s approach to the problem of value follows Adam Smith’s general approach of looking at it as an accounting problem. If we start with an economic system with workers and wages as the only income category (as in Adam Smith’s ‘early and rude state of society’) then total net income must be appropriated by workers as wages. The assumption that uniform labor receives uniform wages leads to a solution of exchange-values as relative values must be equal to relative total labor-time embodied in respective commodities. If wages are reduced then some net output will be released. If this net output must be appropriated by a class of capitalists such that every capitalist receives a uniform rate of profits on capital invested then the question is: what exchange-values must prevail that would account for the values of industrial capital investments and the values of their net outputs such that the ratios of their net output values to capital investments are equal and the value of total net output released by reducing wages is accounted for as total profits in the system? Sraffa showed that the system needs no additional information (for example, demand) to solve for a set of relative values and a uniform rate of profits that would account for the net output released as profits.
We have seen that Adam Smith claims the ‘natural’ rates of wages, profits, and rents are given independently of values and that prices only account for those given rates at any moment. In Sraffa’s opinion another major line of demarcation between classical theory and orthodox theory is that the distribution of income in terms of the rates of wages, profits, and rents is determined independently of the determination of exchange-values, whereas the orthodox theory determines simultaneously these distributional variables with exchange-values. In Sraffa’s theory of value determination described above, the rate of profits is simultaneously determined with prices. So the question is: how does it rehabilitate the classical theory? The answer to this lies in the fact that the above description of Sraffa’s price theory is not yet complete.
Sraffa goes on to show that there exists one and only one set of multipliers (which can be discovered from the observed actual system of production) that would convert it into a system such that the physical composition of its net output and total capital is the same. Sraffa calls it the standard system. In this case, the ratio of the net output to total capital or the maximum rate of profits of the system (R) can be determined by the physical system independently of exchange-values. If the net output of the standard system, which he called the Standard commodity, is used as the measuring yardstick to measure given wages and values then it can be shown that in the observed actual system there exists a relationship between the rate of wages (w), the rate of profits (r), and the maximum rate of profits (R) given by r = R(1 – w), which holds for all the values of w. Since R is independent of both r and w as well as the values of commodities and w is taken to be given from outside the system of equations, it follows that r can be determined independently of exchange-values. This establishes the classical and Marxian position that the theory of distribution can be separated from the theory of value.
The last point in this context is the condition of the equal rate of profits in Sraffa’s equations. As we know in the classical tradition this is used as the condition of equilibrium (that is, an ideal) of the system. But Sraffa’s system of equations represents an observed actual system of inputs and outputs at any moment. So how can one reconcile the empirical system with the ideal position? One way is to assume constant returns to scale for all industries but Sraffa emphatically denies making any such assumption. It is my contention (see Sinha 2010a, 2012, 2016) that no reconciliation is needed. Sraffa’s standard system reveals the average rate of profits of the observed empirical system as a ‘non-price phenomenon.’ It is the mathematical property of the ‘average’ that leads to the conclusion that whatever is leftover of the net output after the payment of wages in terms of the Standard commodity must be distributed according to a uniform rate of profits—this is not a condition of equilibrium of the economic system however. Thus we have for the first time a theory of value that does not rely on the notion of equilibrium.
In this chapter we have traced out three major theoretical developments in the theory of value, beginning with Adam Smith and then to Ricardo and Marx and finally the reconstruction of this tradition by Sraffa. Two theoretical problems have been highlighted: (i) the question of the scale by which the value of a commodity can be measured and (ii) what causes a commodity to acquire value to begin with. Adam Smith poses the question of the measure of value prior to the question of the cause of value. This was because the problem of value was posed in the context of change in the value of a commodity over time. The question was: what scale is to be used to measure the change? It was the search for this scale that led Adam Smith to the question of the ultimate cause of value.
Adam Smith argues that the ultimate cause of value lies in the primordial productive activity when man works against nature directly. There are two aspects to this primary exchange between man and nature: (i) it is a laboring activity where man sacrifices his ease and comfort and (ii) it results in the appropriation of income. How these two elements of the primordial exchange between man and nature relate to the value of a commodity is the source of most of the confusion and controversies in the classical tradition of value. Adam Smith argues that in the primordial state the two aspects of the exchange are united in the same individual, which results in a simple rule of exchange for commodities; but once appropriation gets disconnected from the laboring activity, no such simple rule of exchange holds any longer. Smith emphasizes the relation of the appropriation of income with value and develops a theory of value which is mainly a problem of accounting for income given its rule of distribution from outside.
Ricardo, in opposition to Adam Smith, emphasizes the relation of laboring activity with value. He argues that even though, in general, it cannot be established that the laboring activity per se determines the value of a commodity at a point of time, one could argue that changes in value of a commodity can be directly related to changes in laboring activity. It was in this context that Ricardo faces the problem of the scale or the ‘invariable measure’ of value—a problem that he was not able to resolve.
Marx goes a step further than Ricardo and argues that one can establish a direct relation between the exchange-values of commodities at a point of time with the laboring activity. Marx argues that the classical economists, particularly Ricardo, could not solve the problem of the determination of exchange-values of commodities on the basis of the data on laboring activity alone because they did not ask the question: where do profits come from? His answer in terms of surplus labor or the surplus value, however, failed to solve the problem as he left the question of the scale unresolved.
Sraffa reconstructs the classical paradigm by going back to Adam Smith in the sense of formulating the problem of value in terms of accounting for a given net output and its distribution in terms of wages, profits, and rents. In this context Sraffa showed that income distribution can be taken as given from outside independently of the exchange ratios of commodities and it can be shown that the exchange ratios of commodities are completely determined once income distribution is specified. In this context Sraffa needed a scale of measure that would not be affected by changes in distribution, which he discovered in the Standard commodity.
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