Value and distribution

The theory of value and distribution forms the backbone of all other economic theory in Ricardo. This explains why it was at the centre of debates ever since its inception. Our under­standing of Ricardo, and the classical authors more generally, has dramatically improved thanks to the publication of the Royal Economic Society (RES) edition of The Works and Correspondence of David Ricardo (Ricardo 1951-73), Piero Sraffa’s introductions, espe­cially to volume I of the edition, and the latter’s 1960 resumption of and elaboration on the “standpoint of the old classical economists from Adam Smith to Ricardo” (Sraffa 1960: v).

Market prices and “natural” prices As regards the assumed gravitation of the market levels of prices and the distributive variables to their “natural” levels, Ricardo closely followed Smith with perhaps a single, but important difference. This concerns the greater emphasis given to the decisions of profit-seeking capitalists and the role of the “moneyed class”, that is, financial capitalists, in particular. He stressed that the “restless desire on the part of all the employers of stock, to quit a less profitable for a more advantageous business, has a strong tendency to equalize the rate of profits of all” (Works I: 88). He then drew the attention to moneyed men and bankers. These are possessed of “a circu­lating capital [liquid funds] of a large amount”, and since “There is perhaps no manu­facturer, however rich, who limits his business to the extent that his own funds alone will allow: he has always some portion of this floating capital, increasing or diminishing according to the activity of the demand for his commodities” (ibid.).

The natural price of a commodity covers all necessary costs of production (wages, raw materials, and the wear and tear of fixed capital) plus the normal rate of return on the capital advanced. Costs reflect the “difficulty of production” of the commodity in given circumstances in terms of the inputs (means of subsistence and of production) that of necessity have to be used up in order to obtain the commodity. If the market price exceeds the natural price, typically above-normal profits will be obtained in the industry. Self-seeking behaviour will tend to eliminate the deviation: attracted by the above-normal profitability, capital (and labour) will move into the industry, increase productive capacity and output relative to effectual demand and thus lead to a falling market price, which eliminates above-normal profits; conversely in an industry that ini­tially exhibits below-normal profits.

In the simple case of single-product industries and thus circulating capital only, and normalizing gross output levels of the different industries as unity, the price equations Ricardo can be said to have aimed at can be written as

where p is the n-dimensional price vector (p₁, p₂,..., p_n)^T, r is the general rate of profits, M is the n ? n matrix of material means of production, S is the matrix of the necessary subsistence of workers and A = M + S. On the simplifying assumption of a given and uniform real wage per unit of labour employed in production, defined in terms of the number of units w of an elementary consumption bundle given by vector c = (c₁, c₂,..., c_n), and denoting the quantities of (direct) labour needed per unit of output in the different industries by l = (l₁, l₂,..., l_n)^T, S = ιvic', we can replace equation (1a) by

With M, l and c given, and taking a bundle of non-negative quantities of the different commodities d = (d₁, d₂,..., d_n)^T as the standard of value, that is,

the general rate of profits r and the prices in terms of the standard d can be ascertained, as Ricardo had maintained (see Sraffa 1960: ch.

The fundamental law of distribution “Profits come out of the surplus produce” (Works II: 128). What applies to a particular level of the real wage rate applies to all levels com­patible with a non-negative rate of profits. This led Ricardo to his fundamental law of distribution - the inverse relationship between the rate of profits (r) and wages (w), which was arguably one of his most important analytical discoveries. As he put it in a letter to McCulloch of 13 June 1820: “The greater the portion of the result of labour that is given to the labourer, the smaller must be the rate of profits, and vice versa” (Works VIII: 194). While the formalization above revolves around the real wage rate and implies ∂r∕∂w < 0, the argument applies also to the case with proportional wages.

A quick look at the path along which Ricardo gradually elaborated his remark­able propositions is in order. In his Introduction to the Principles in Works I, Sraffa interpreted Ricardo’s 1815 Essay on Profits as being based on the idea that there was a trade or sector in the economy that was “in the special condition of not employing the products of other trades while all the others must employ its product as capital” (Works I: xxxi; emphasis in the original). The sector under consideration is the growing of corn (wheat), a fact that led Sraffa to speak of the “corn-ratio theory”. It allows one to determine the rate of profit in the sector under consideration in purely material terms as the surplus (exclusive of rent) obtained in the sector, a quantity of corn, divided by the capital advanced in the sector, another quantity of corn - without any reference to values. However, the rate of profit so determined is also the general rate of profits since in the case of free competition all other trades or sectors which are supposed to need corn as an input yield the proprietors of capital the same rate of profits by an adjustment of the prices of their product relative to that of corn (see also Sraffa 1960: 93).

Sraffa draws the attention to Malthus’s criticism of “the fault of Mr. Ricardo’s table”, since circulating capital (which includes real wages) typically does not only consist of corn, but includes “tea sugar cloaths &c for the labourers” (ibid.: xxxii, n. 4). Ricardo stuck to his basic vision that the rate of profits could be conceived of in purely physical terms. A deeper analysis was needed than Malthus’s shallow proposi­tion that “the profits of the farmer no more regulate the profits of other trades, than the profits of other trades regulate the profits of the farmer” (Works VI: 104). This

proposition was of no use at all in understanding how that regulation was actually meant to work.

In the Principles Ricardo suggested rendering heterogeneous commodities commen­surate in terms of the amounts of labour bestowed upon them in their production. The labour theory of value was the device by means of which he intended to overcome as best as he could the impasse in which he found himself, lacking a fully consistent and general theory of value. This was clearly seen by him as a makeshift solution, which, he opined, came close to the correct one he was unable to establish. Interestingly, the labour theory of value did not make him entirely abandon his conviction that the ques­tion of income distribution could be discussed independently of the theory of value: in all three editions of the Principles we encounter a numerical example that satisfies the homogeneity condition of output and capital, but now no longer with regard to a single industry (corn production) only, but with regard to the aggregate of several industries (corn, hats and coats) taken together (see Works I: 50, 64-6).

Ricardo was keen to avoid getting entangled in a myriad of complex relationships, whose precise form neither he nor anyone else knew at the time. In a letter to Malthus of 17 April 1815 he spoke of his “simple doctrine”, designed to “account for all the phe­nomena in an easy, natural manner” and thus stay away from “a labyrinth of difficulties” (Works VI: 214). Yet Ricardo obstinately insisted, as he wrote in a letter to McCulloch on 13 June 1820, that “After all[,] the great questions of Rent, Wages, and Profits must be explained by the proportions in which the whole produce is divided between land­lords, capitalists, and labourers, and which are not essentially connected with the doctrine of value” (Works VIII: 194; emphasis added). Ricardo was not able to prove the fruitful­ness of his remarkable intuition; a proof had to wait until Sraffa (1960: ch. IV).

The measure of value Intimately related to what has just been said, there is the remark­able fact that much of Ricardo’s thoughts and debates with friends, especially Malthus, revolved around the problem of an ideal or “invariable” measure of value. Originally the concept was designed to allow comparisons between one and the same economy at different times and between different economies at the same time, that is, intertemporal and interspatial comparisons.

After Ricardo had discovered that relative prices do not only depend on relative quan­tities of labour embodied in the different commodities, but also on income distribution, he had to adapt his concept of invariability. He struggled with the issue until the end of his life; see the draft and manuscript fragment on “Absolute Value and Exchangeable Value” written in 1823 (Works IV) shortly before he passed away. Since the time profiles of the quantities of labour bestowed on the various commodities typically differ from one another and since wage payments are to be discounted forward at the general rate of profits, a change in that rate (and a corresponding contrary change in wages) is bound to affect relative prices. Ricardo’s attention therefore focused on the “different circum­stances” under which commodities are produced (Works IV: 368). The extreme cases would be a commodity produced by direct labour alone, on the one hand, and a com­modity produced by means of a large amount of durable capital goods and hardly any direct labour at all, on the other. With a rise in the rate of profits and a corresponding fall in the real wage rate, the latter commodity would become more expensive compared with the former due to compound interest. A commodity, however, which exhibited the “medium between the extremes” (Works IV: 373), that is, the medium proportion of direct labour to means of production, would be a measure that is invariant with respect to changes in income distribution, because its profit component would rise by as much as its wage component would fall.

Ricardo’s arguments serve the purpose of elaborating a coherent theory of value and distribution. While Ricardo at first thought that he might be able to solve the two requirements of invariance of the measure of value - one concerning production, the other one distribution - in terms of a single commodity, he eventually understood that he was chasing a will-o’-the wisp, because the former referred to an environment with a changing and the latter with a given technology; see on this Kurz and Salvadori (1993). Only the latter problem of invariance can be solved analytically in a cogent way (pro­vided a solution exists), as Sraffa (1960) showed with his construction of the “Standard commodity”. The former problem requires the construction of index numbers.

Choice of technique In agreement with Adam Smith, Ricardo insisted that competitive conditions enforce cost-minimizing behaviour of producers. This means that a method of production will be chosen if it minimizes unit costs, that is, the amount of labour needed directly and indirectly in the production of one unit of the commodity. If new methods of production lead to “improvements” in the different sectors of the economy (agriculture, manufacturing, commerce, and trade) the following effects will result on the assumption that the real wage rate is given and constant. If the improvement concerns an industry that produces wage goods, that is, “necessaries”, or industries that directly or indirectly provide inputs for the production of wage goods, the price of the commodity will fall relative to the other commodities and the general rate of profits will rise. In the case of “luxuries” the improvement will lead only to a reduction in price, but leave the general rate of profits unaffected. If, Ricardo stressed,

by the extension of foreign trade, or by improvements in machinery, the food and necessaries of the labourer can be brought to market at a reduced price, profits will rise [,]... but if the com­modities obtained at a cheaper rate... be exclusively the commodities consumed by the rich, no alteration will take place in the rate of profits. (Works I: 132; see also 143)

The role of consumed commodities in Ricardo has been studied by D’Alessandro and Salvadori (2008) and Salvadori and Signorino (forthcoming). As Ricardo stressed: “the labouring class have no small interest in the manner in which the net income of the country is expended” (Works I: 392).

The analogy Ricardo drew between improvements and foreign trade explains why he advocated free trade: it will cheapen many commodities, which benefits consumers, and it will frequently imply a rise in the rate of profits, given the real wage rate, which can be expected to speed up capital accumulation and economic growth and, as a consequence, increase wages.

Ricardo insisted that technical progress, by itself, never decreases the rate of profits. Marx tried to disprove him in this regard, but failed (see Kurz 2010). Ricardo may be said to have anticipated what became known as the “Okishio theorem”: for a given real wage rate cost-minimizing behaviour implies that new methods of production will be adopted if and only if they raise the general rate of profits or leave it constant (in the case of non-basics) (see also Bortkiewicz 1906-07; Samuelson 1959; Sraffa 1960).

Rent theory Up until now we have put on one side scarce natural resources such as land, which Ricardo assumed to be possessed of “original and indestructible powers” (Works I: 69). In chapter I of the Principles he abstracted from them on the ground that his argument applied to no-rent (later called: “marginal”) land, on which the level of the rate of profits was decided for any given level of (real or proportional) wages. In chapter II, “On Rent”, he then elaborated the principles of extensive and intensive diminishing returns in agriculture, reflecting a growing scarcity of land. While Ricardo was not the first to discover these principles, he deserves credit for having incorporated them into a fairly coherent system of political economy whose main aim was the deter­mination of the general rate of profits.

With extensive diminishing returns, lands of different quality (or location) can be brought into a ranking of natural “fertility” that corresponds to the order according to which the different qualities of land will be cultivated. With low levels of produc­tion of corn, only land of the highest fertility (that is, lowest unit cost) will be cultivated and there will be no rent, for essentially the same reason “why nothing is given for the use of air and water, or for any other of the gifts of nature which exist in boundless quantity” (Works I: 69). It is only as capital accumulates and population grows that land of second, third and so on quality will have to be cultivated in order to satisfy a growing social demand. As a consequence, the price of corn will rise relative to that of other commodities. The price being determined by costs of production (includ­ing profits at the normal rate) on no-rent-bearing land, the owners of intra-marginal lands obtain differential rents reflecting lower unit costs. From this Ricardo concluded against Smith that rent “cannot enter in the least degree as a component part of its price” (Works I: 77). Rent was not an expression of the generosity of nature, as Smith had argued echoing the Physiocratic doctrine, but of its “niggardliness”: it was not the cause, but the effect of a high price of corn.

With intensive diminishing returns, the amount of labour and other inputs will be increased per acre of a given quality of land; it will result in an increase in output per acre, though at a diminishing rate. (The case of intensive diminishing returns was later generalized by marginalist authors indiscriminately to all factors of production and all industries alike. In this way all prices and distributive variables were taken to be subject to a single principle only: that of universal scarcity or marginal productivity. However, as Knut Wicksell already understood, this generalization meets with considerable difficulties; see Kurz and Salvadori 1995: ch. 14; Kurz 2000).

Ricardo dealt also with exhaustible natural resources, such as coal or metals, especially in chapter XXIV of the Principles, “Doctrine of Adam Smith Concerning the Rent of Land”. He criticized Smith for confounding profits and rents, which ought to be carefully distinguished, because in the course of the development of a country, and setting aside technical progress, they typically move in opposite directions. Ricardo was, of course, aware of the principal exhaustibility of certain resources, but did not think that the problem was imminent: first, because “new and more productive mines may be discovered”; second, because “Improvements may be made in the implements and machinery used in mining, which may considerably abridge labour”; and third, because “the facilities of bringing [the resource] to the market may be increased” (Works I: 86). While these factors tend to reduce the value of the metal, “the increasing difficulty of obtaining [it], occasioned by the greater depth at which the mine must be worked [and so on]” (ibid.), tend to increase it.

All things considered, Ricardo felt entitled to approach the problem of exhaustible resources in terms of his theory of differential rent. Since there will generally be deposits of different fertility, the working of each of which is subject to a capacity constraint that limits the amount of the resource that can be extracted per unit of time, effectual demand will typically be met by working several deposits simultaneously. As in the theory of the rent of land, there will be a marginal, no-rent, deposit worked together with several intra­marginal deposits that will yield their proprietors differential rents, which are higher the lower the costs of extraction are of one unit of the resource. (For a comparison of Ricardo’s approach with the Hotelling model, see Kurz and Salvadori (2009, 2011). The Hotelling rule maintains that in competitive conditions the preservation of a resource must yield its proprietor the same general rate of profits as is obtained in production and trade, which implies that the price of the resource in situ, which is capital to the proprie­tor, will have to rise with that rate. Empirically, the Hotelling rule does not perform well and precisely for the reasons given by Ricardo.)