Value in Use Versus Value in Exchange
Ricardo's Problem of an Invariable Measure of
In order to measure value at a specific time and place, one needs only a numeraire and any commodity will do. But if one wishes to make intertemporal or interlocal comparisons the problem of measuring value takes on formidable, and possibly insuperable, difficulty. David Ricardo who had what Keynes described as "the greatest mind that found economics worthy of its power"  wrestled with the problem and, despite concentrated mental effort, never found the invariable measure of value (IMV) that he sought. In his last letter to James Mill written less than a week before his death, he writes in reference to the problem, "I have been much thinking about the subject but without much improvement."  Although this admission has been quoted  to support the position that he left the problem unresolved, one must be careful about equating his not finding an IMV with his not resolving the issue. Reading the last letter in its entirety might lead one to the alternative conclusion that he resolved the problem of finding an IMV when he discovered that an IMV does not exist. He goes on to say in this last letter to Mill:
The issue of an IMV is something which in this day and age needs clarification. Frank Hahn, for one, admits that "for a modern economist it is almost incomprehensible."  The incomprehension is due to the modern use of value to mean strictly value in exchange, coupled with the recognition that exchange value is not measurable except under static, or non-varying, conditions. When we say, for example, that an apple exchanges for fifty peanuts we are only measuring the exchange value at a particular time and place. We can compare this exchange value with the rate of exchange of oranges for peanuts and make a statement about what has the greater exchange value--an apple or an orange--but the moment any change in market conditions occurs, the peanut measure ceases to be useful. If next week an apple exchanges for twenty-five peanuts, we cannot correctly infer that the exchange value of apples, in any general sense, has fallen.
An argument often adduced to demonstrate the impossibility of invariable measurement is that exchange value is not a quantity of a thing but is rather a relation between things. This distinction by itself, however, is not sufficient. As Keynes writes in an early essay:
What is needed to make the argument complete is the statement that the exchange value of a good in an n-good economy is not just a single relation (as in distance), but rather a set of n-1 relations.
Ricardo realized all this. In a pamphlet titled "Suggestions for a Secure and Economical Currency" (1816), he writes:
Ricardo's search for an IMV began only when working out the chapter on value for his Principles of Political Economy and Taxation (PPET), he developed an idea of what he called real, positive or absolute value--determining but distinct from exchange value. He writes to his friend Hutches Trower:
Formally, Ricardo is saying that if Vi represents the absolute value of good i and Pik represents the price of i in terms of good k, then: Vi: Vj = Pik: Pij for all i, j and k (1)
In Ricardo's scheme the absolute value of a good is determined by the quantity of labor expended in its production and the length of time that elapses from the time the labor is expended and the time the good is ready for sale. (I shall call this second consideration the time structure of production.) In the case of a constant wage and profit rate, the absolute value can be specified by: [Equation omited] (2)
where [omitted] is the proportionality constant, T is the number of periods between the first exertion of labor and the time the good is ready for sale, [omitted] is the quantity of labor expended in period T-t and r is the rate of profit.
Ricardo is sometimes described as being a proponent of the labor theory of value but this description can be highly misleading if the labor theory of value is interpreted to mean that the value of a good is proportional to the quantity of labor exerted in its production or: [Equation omitted] (3)
Although a number of Ricardo's less careful statements suggest such an interpretation, his numerical examples [11, 12], at least, should make it clear that he recognizes the importance of considering, as well as the quantity of labor, the time structure of production. Ricardo might have avoided much misinterpretation if he had followed through with tentative plans revealed to McCulloch in 1820. He writes:
Besides his tendency to slip into a crude labor theory of value, another unfortunate feature of Ricardo's exposition is his frequent use of the word value without prefix making it unclear whether he's referring to exchangeable or real value. When Trower comments on the reader's possible confusion, Ricardo only replies indignantly, saying:
Yet despite what he says the reader will find many unprefixed "values" dispersed throughout his work--an obvious example appearing every time he uses the term "invariable measure of value." Because of his admitted recognition that exchangeable value is not susceptible to invariable measurement, I shall assume that the invariable measure he seeks is of absolute value.
Marx, with some justice, writes that Ricardo's "problem of an 'invariable measure of value' was simply a spurious name for the quest for the concept, the nature, of value itself."  Ricardo was never able to exactly specify the function determing the relative or absolute value of commodities and acknowledged that if he were "in possession of the knowledge of the law which regulates the exchangeable value of commodities, we should be only one step from the discovery of the measure of absolute value."  In the case of a constant wage and profit rate, Ricardo's absolute value can be calculated easily by expression (2) above and then exchangeable value can be found by (1). But because Ricardo's essential theory is dynamic, seeking to explain movements through time of relative income shares, he could not be satisfied with a theory of value that assumed these movements away. Ricardo recognized that if the wage increased relative to the rate of profit, the exchange value of goods for which T was large would tend to fall relative to goods for which T was small. If, for example, there was a shift in distribution in favor of laborers last month, then cheese on market today that has aged a year will have been produced with cheaper labor and should thus fall in price relative to cheese that requires no aging. The result is that expressions (1) and (2) do not generate the correct exchange values under the condition of a changing distribution.
There are two ways of expressing Ricardo's dilemma. One is that he regarded exchangeable value as always proportional to absolute value so that the problem lies in the correct specification of the absolute value function. The other is that expression (2) always correctly describes absolute value and his problem lies in transforming absolute value into exchangeable value. It's not clear from his writings how Ricardo would have expressed the puzzle but since the two expressions, for our purposes, amount to the same thing and since Sraffa  has set a precedent of adopting the latter one, I shall follow suit and do the same.
With the emergence of the marginalist revolution, the notion of absolute, positive, or real value as a quality inherent in a commodity fell out of view, having been discarded by the neoclassical economists as an unnecessary and obfuscating theoretical construct. Jevons, for example, writes:
Yet despite the neoclassical economist's unfamiliarity with any notion of absolute value distinct from exchange value, its apprehension is necessary is we are to make sense of the core of Ricardo's work--that is, his theory of the secular trends in distribution between laborers, landlords, and capitalists. This core theory can be separated into three strands: (1) the theory that in the long-run the wage falls to the subsistence level; (2) what has become to be known as the Ricardian theory of rent (although Ricardo rewards credit to Malthus and Edward West); and (3) the one doctrine for which Ricardo claims originality, his theory of the falling rate of profit. This last doctrine proceeds as follows: As the economy grows and less fertile land is cultivated, the required labor input, and consequently the absolute value, of agricultural produce increases. The result is that the absolute value of the subsistence bundle, or the natural wage, increases. Now, in the agricultural sector where the input and output can be approximately measured in the same commodity, diminishing marginal returns imply a falling rate of profit directly--being deduced, as Sraffa has pointed out , independently of value considerations. However, in extending the theory to apply to the rate of profit in the manufacturing sector, Ricardo cannot, and does not, avoid reference to value. To arrive at a falling rate of profit in industries not dependent directly on the fertility of the land, he argues that as the economy grows, the absolute value of the ultimate input (labor) is increasing, while at the same time, the absolute value of the output--barring technological innovation--remains the same. Thus the difference between the two--the absolute value of the profits--falls.
The important point to note about Ricardo's theory of the falling rate of profit is that he works it out in absolute value terms. If the reader were to miss the role of absolute value in the argument, he would wonder (especially if he were brought up with a Smithian adding-up theory of price), why Ricardo has ruled out the possibility of the higher wages being passed on in higher prices of manufactured goods, leaving profit margins unchanged. This is a natural confusions because, in framing his theory, Ricardo has adopted money as an IMV: thus when he says the price of a good remains constant, he really means the absolute value has remained constant. He writes in a crucial footnote at the beginning of his chapter on profits:
The IMV bridges Ricardo's abstract theory running in terms of absolute value with the real observable world that he sought to influence. As with any theory that hopes to be convincing, Ricardo's requires conclusions that can be compared with and corroborated by observation. It would be wrong to regard Ricardo's problem of an IMV as merely a minor analytical puzzle auxiliary to his main theory and the policy recommendations arising out of it: in fulfilling the role as a link between his purely theoretical concept of absolute value and the phenomena that he attempts to analyze, diagnose, and remedy, the IMV is as crucial as any other element in his schemata. Its importance is compounded with the recognition that of all the elements in his theory, it was with his IMV that Ricardo was the most dissatisfied.
In 1823, Malthus published a small book entitled The Measure of Value Stated and Illustrated in which he criticizes Ricardo's IMV and adopts Adam Smith's idea that the value of a good is best measured by the amount of labor it can purchase. The two criticisms that Malthus lodges against Ricardo's gold measure are: (1) both gold discoveries and improved mining technology would affect the conditions of production of gold and thus its absolute value and (2) changes in distribution would affect the exchange value of the gold relative to goods with different time structures of production.
Ricardo, of course, could not answer these criticisms. In deciding on gold as an IMV, he had recognized the limitations but had reasoned that gold has the least of these limitations shared by all goods, including labor. Ricardo argued in response to the first criticism that the conditions of production and the supply of gold do not fluctuate any more than of those of other goods. In response to the second, his argument was that gold stands somewhere between the two extremes of those goods, like shrimp, produced primarily with immediate labor and those, like old oak trees, produced primarily with accumulated labor; and thus although not demonstrably the best measure, it was, at least on this count, better than many others.
Still, Malthus's book had the effect of stimulating Ricardo to rethink the problem of an IMV and to attempt to come up with a better solution. Yet after a great deal of discussion of the problem with Malthus and others in the months succeeding the publication of A Measure of Value Stated and Illustrated, and preceding his death, Ricardo reached the conclusion summed up in a letter to Malthus dated 15 August 1823. He writes:
One solution to Ricardo's problem that might suggest itself to a modern economist is to use as an IMV, money adjusted by some index like the CPI. By doing so one would be able to track what we today call the "real value" of a good, or what the classical economists called "the power of purchasing the necessaries and conveniences of life." But our concept of real value differs from Ricardo's notion of absolute value in important respects. For Ricardo, absolute value was to have certain characteristics--it was to be proportional with exchange value and dependant on only the amount of labor input, the time structure of production, and distribution. A necessary feature of an IMV for Ricardo was its capacity to measure changes in value arising from, and only from, changes in these three specified determinants. But a CPI-adjusted real price is only indirectly linked with these determinants. Moreover, it involves the somewhat arbitrary concoction of a composite commodity; and given Ricardo's predilection for strict deductive reasoning, he would probably agree with Keynes that "the proper place for such things ... lies within the field of historical and statistical description, a purpose for which perfect precision--such as our causal analysis requires ...--is neither usual or necessary."  In response to the idea of using some sort of composite bundle to measure value Ricardo writes:
There are two positions that can be taken regarding Ricardo's problem of an IMV. One is that is of purely antiquarian interest and that as a live issue was extinguished once and for all by Jevons' unequivocal assertions that value can be nothing but a ratio of exchange and thus not, strictly speaking, susceptible to invariable measurement. According to this view, any intertemporal or interlocal comparison of value must be done using the necessarily approximate method of index numbers. The other position is that Ricardo was on the right track to identify a "notion of real or absolute value underlying and contrasted with exchangeable or relative value" . If this view is taken the question of whether and how absolute value can be measured remains open.
Sraffa in his Production of Commodities by Means of Commodities (PCBMC) adopts this second position of retaining a notion of value distinct from exchange value. Although he never undertakes an explicit discussion of this concept, the fact that he has an invariable measure of it in his Standard Commodity, indicates his belief in its existence. But if we read closely to discover what exactly it is that the Standard Commodity is measuring when there is a change in distribution the most we find is the vague "peculiarities of production." If there is a change in distribution and the standard commodity price of iron, say, changes by a given percentage, we can be assured that this price change is solely due to the "peculiarities of production" of iron and not to those of the standard commodity. Sraffa's idea of value associated with peculiarities of production is better than a crude labor theory of value because it allows for the necessity of considering the time structure of production or of "dating" labor inputs. In addition, by employing the standard commodity to measure value, Sraffa maintains the proportionality between absolute and exchange value and thus resolves one of Ricardo's difficulties. The catch, however, is that he resolves the difficulty only by ruling out, through assumption, all changes except for changes in distribution.
In his Preface to Ricardo's PPET, Sraffa distinguishes two roles that Ricardo insisted his IMV must serve: one is that it must capture changes in value arising out of changes in the technical coefficients of production and the other is that it must capture changes arising out of changes in distribution. In his PCBMC, Sraffa presents a model that contains an IMV fulfilling the second, but not the first, of these roles. Writing of Ricardo's problem and Sraffa's relation to it, Roncaglia says, "Sraffa shows that the problem can be solved only if the two functions are distinguished and that the first, indeed, must be abandoned." 
Important differences exist, however, between Ricardo's and Sraffa's theory so it is not obvious how much relevance the Sraffian solution has to the Ricardian problem. The fact that it fulfills only the second of the two roles suggests that Ricardo would not think it useful; Sraffa's standard is incapable of measuring changes in the value of the natural wage arising from diminishing productivity in agriculture--changes which represent an essential part of Ricardo's theory. Furthermore, while Ricardo did express the necessity of an IMV capturing the effect of a changing distribution, he adds, "The reader should remark that this cause is comparatively slight in effect"  and also, "In estimating ... the cause of the variations in the value of commodities, although it would be wrong wholly to omit the consideration of the effect produced by a rise or fall of [the value of] labor, it would be equally incorrect to attach much importance to it." 
One point in common between the Ricardian and Sraffain theories is the conclusion that there exists a trade-off between the wage and the rate of profit. Sraffa shows that if the wage (w) is measured in the Standard Commodity, then the equation r = R(1-w), where r is the rate of profit and R is the Standard Ratio, expresses the distribution relation. One might argue that it is in this relation that we find the solution to Ricardo's problems of convincing his practical-minded colleagues who refused to believe in Absolute Value that the rate of profit varies inversely with the wage. But Sraffa's "factor price frontier" is irrelevant to Ricardo's problem for the reason that it is based on an assumption that contradicts the cornerstone of the Ricardian theory. Sraffa's relation applies to an economy that is reproducing itself exactly--item for item--employing unchanging techniques to obtain unchanging results; Ricardo's theory, on the other hand, is of an expanding economy that is experiencing diminishing marginal returns in the agricultural sector.
In contrast with Sraffa's construction in his PCBMC, Ricardo's is a model of an economy in which the technical coefficients of production are changing through time; and it is for such an economy that the problem of finding an IMV takes on a far greater challenge. Evidence of the immense difficulty of the task Ricardo set himself is that in over a century and a half since his death no one has found a solution--although it must be admitted part of the reason is that mainstream economists stopped looking when they decided that value was to mean strictly a ratio of exchange. If Ricardo were summoned up now to review and comment on progress with his problem since 1823, he might appropriately respond by echoing his last words to Mill and say:
If defeat in the face of the problem is admitted,
Ricardo's next step would have been to draw the
implications for his theory of retaining within the
predictive results, statements framed in terms of a
concept that cannot be measured.