Walras and Ricardo
p. 967-985
Remerciements
An early version of this paper was presented by one of the authors at the conference in Lyon. The useful comments by people attending the session are gratefully acknowledged. We should also like to thank Christian Bidard, David Collard, John Eatwell, Christian Gehrke and Ian Steedman for helpful suggestions and remarks. The usual disclaimer applies.
Texte intégral
Introduction
1Most of Part VII of Léon Walras’s Elements of Pure Economics ( [1871] 1954) is devoted to a critical discussion of some of the views advocated by earlier schools of economic thought. In this paper we shall scrutinize Walras’s « exposition and refutation » of the classical authors. He accuses Smith, Ricardo and John Stuart Mill of having committed « fundamental errors ». In addition, Ricardo and his followers are criticized for having failed to develop « a unified general theory to determine the prices of all productive services in the same way » (ibid., p. 416).1 Such a unified general theory, Walras contends, has been elaborated by himself by generalising the principle of « scarcity », which the classical economists had limited to natural resources, to all goods and factors of production alike.
2While a large part of this paper is on Walras on Ricardo, we must also deal with what Ricardo wrote as opposed to what Walras interpreted him to have written. This explains the title of the present paper. Moreover, since Walras bases his criticism on a rational reconstruction of Ricardo’s argument we must closely inspect that reconstruction and compare it with more recent ones, which also claim to be faithful to Ricardo. We shall in particular deal with the contributions of Kaldor (1955-1956) and Pasinetti (1960) – which have been inspired by Sraffa (1951, 1960) – Samuelson (1959), and modem formulations of the « classical » approach to the theory of value and distribution (for a summary account, see Kurz and Salvadori, 1995). The composition of the paper follows closely the structure of Walras’s criticism of the classical economists. Section 2 deals with Lesson 38 which is devoted to the classical theory of value. The subject of Lesson 39, Ricardo’s theory of rent, will be discussed in Section 3. Finally, Section 4 will turn to Walras’s disquisition on the classical theory of wages and interest in Lesson 40. Section 5 contains some concluding remarks.
I. Walras on the ricardian theory of value
3Walras introduces Lesson 38 with a compliment to the classical authors: « The efforts of the English School to develop a theory of rent, wages and interest were far more sustained and thorough than those of the various French schools that came into existence after the Physiocrats » (§ 342, p. 398). He then recalls the Ricardian distinction between « commodities, the value of which is determined by their scarcity alone », because no « labour can increase the quantity of such goods, and therefore their value... varies with the varying wealth and inclinations of those who are desirous to possess them »; and commodities that « are procured by labour... and... may be multiplied, not in one country alone, but in many, almost without any assignable limit, if we are disposed to bestow the labour necessary to obtain them » (Works I, p. 12). The first set includes « rare statues and pictures, scarce books and coins, wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity »; these commodities are said to « form a very small part of the mass of commodities daily exchanged in the market » (ibid.). Walras also quotes a statement by J. S. Mill who contends with regard to the commodities of the second class that « there needs be no limit to the multiplication of the products » (Mill, 1909, p. 444).
4Walras identifies the first « fundamental error » as: « There are no products that can be multiplied without limit ». This is so, because « in the production of most things... land-services, labour and capital-services are found together. It follows, therefore, that all things constituting social wealth consist of land or personal faculties or the products of the services of land and personal faculties. » Now Mill and the classical authors have to admit « that land exists in limited quantities only. If that is also true of human faculties, how can products be multiplied without limit? » (§ 343, p. 399). The second « fundamental error » is that there is no « value of costs of production, which, having itself been determined, determines in turn the selling prices of products. » With regard to this error Walras is much more assertive than with regard to the other one (see § 344, pp. 399-400).
Alternative theories of value and distribution
5As to the first « fundamental error », it is questionable that Ricardo can be accused of having committed it. First, it should be noted that whereas Ricardo explicitly spoke of commodities that « may be multiplied, not in one country alone, but in many, almost without any assignable limit », Mill was less cautious. The target of Walras’s criticism is indeed Mill’s statement, not Ricardo’s. Ricardo was well aware of the fact that the quantities of the (reproducible) commodities effectually demanded generally have an impact on prices (and income distribution). The whole point of his theory of rent was the dependence of the price of com on the quantity of com produced. In a letter to Malthus dated 9 October 1820 he wrote: « You say demand and supply regulates value – this, I think, is saying nothing... it is supply which regulates value – and supply is itself controlled by comparative cost of production » (Works VIII, p. 279). And in his letter to Malthus of 24 November of the same year he added:
I shall not dispute another proposition in your letter « No wealth [ »] you say « can exist unless the demand, or the estimation in which the commodity is held exceeds the cost of production. » I have never disputed this. I do not dispute either the influence of demand on the price of com and on the price of all other things, but supply follows at its heels, and soon takes the power of regulating price in his own hands, and in regulating it he is determined by cost of production. I acknowledge the intervals on which you so exclusively dwell, but still they are only intervals (ibid., p. 302).
6Therefore, in Ricardo’s view demand and supply regulate the « market » prices of commodities, whereas the normal or « natural » prices are the prices which obtain in a cost-minimizing system of production, given the data (R1)– (R4) below. This does not mean that normal quantities (that is, « effectual demand ») do not affect normal prices: since they play a role in ascertaining the cost-minimizing technique, they co-determine prices.
7Second, the case on which Ricardo focused attention is one in which the impact of the scarcity of land on relative prices is somewhat concealed: his theory of rent focuses mainly on the case of extensive diminishing returns, and thus extensive rent, which – as regards prices, wages and profits – allowed him to concentrate on the technical conditions of production on the marginal land. Ricardo discussed also the case of intensive diminishing returns and thus intensive rent. However, when analysing the relationship between wages and profits, the problem that concerned him most, he set aside the problem of rent. He justified this premise explicitly on grounds of the simplicity it gave to the problem under consideration and not on grounds of realism: « By getting rid of rent, ... the distribution between capitalist and labourer becomes a much more simple consideration » (Works VIII, p. 194). We may add that his approach could also derive some justification from the finding in the modem theory of production that even in the case of intensive diminishing returns there is a fictitious technique which can be obtained from the data of the problem (see Guichard, 1982), in which land does not appear.
8As to the second « fundamental error », Walras fails to see that Ricardo advocated an approach to the theory of value and distribution that differs fundamentally from his own approach. The data from which Walras typically starts in his fully developed general equilibrium analysis are (see the discussion in Kurz and Salvadori, 1995, pp. 21-6):
9(W1) the set of technical alternatives available to cost-minimizing producers;
10(W2) the preferences of consumers; and
11(W3) the initial endowments of the economy with all productive resources, including « capital goods proper ».
12Ricardo typically appears to approach the problem of value and distribution instead on the basis of the following givens:
13(R1) the set of technical alternatives available to cost-minimizing producers;
14(R2) the size and composition of the social product, reflecting the needs and wants of the different classes of society and the requirements of reproduction and capital accumulation;
15(R3) the ruling real wage rate for common labour; and
16(R4) the quantities of the different qualities of land available and the known stocks of depletable resources, such as mineral deposits.
17It is a first characteristic feature of Ricardo’s approach to the problem of value and distribution that the data contemplated all refer to magnitudes which, in principle, can be observed, measured or calculated. A second characteristic feature is that in Ricardo, contrary to the neoclassical approach of Walras, the wage rate is considered an independent variable and there is no initial endowment of capital, the relative « scarcity » of which would explain the rate of profit. It is this asymmetric treatment of the distributive variables, with profits as a dependent residual, which is the differentia specifica of classical theory as compared with neoclassical theory.
18Apparently, it did not occur to Walras that there could be a theory that is fundamentally different from, and not just a special and incoherent case of, his supply and demand theory. This explains why he assessed the classical economists not in terms of their own approach, but in terms of supply-and-demand theory. His main criticism was levelled at what he considered to be the particular causality entertained by the classical economists: in his view these authors took the prices of products to be determined by the prices of the « productive services ».
Three categories of products
19To Walras, simply reversing the causality from service prices to product prices is not good enough: both kinds of prices are determined simultaneously and symmetrically in terms of the supply of and the demand for the respective products and services. Walras devotes four more sections (§§ 345-8) to a discussion of the influence of the prices of « productive services » on the prices of the products. The first class of products is the one on which all agree: « the case of productive services which have passed out of existence [after having been used], for example, Ricardo’s “rare statues and pictures, scarce books and wines” » (§ 345, p. 400). He expounds: « The value of such products, as both Ricardo and Mill admit, is the result of the law of offer and demand alone » (ibid.).
20Section 346 is devoted to a second class of products: those produced by some « specific productive services ». This set includes Ricardo’s above example of « wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity ». In Walras’s view this set is much larger than the classical economists were inclined to think: « Had Ricardo and Mill been a little more methodical in their classification, they would have given examples of personal services which are no less specific than the land-services they mentioned, like the personal services of living artists, singers, eminent doctors and great surgeons » (ibid.). It appears to have escaped Walras’s attention that in Smith we find several references to the concept of « talent » and the remuneration paid for it, and that Ricardo was in agreement with Smith except whenever he explicitly said otherwise (see his Preface to Principles)2. What is intriguing is that Walras mentions « personal services » together with « land-services », but interestingly does not mention the services of « proper capitals ». In fact, in a long-period framework no capital good proper, or produced (and reproducible) means of production, can be the source of some « specific productive service » and yield its owner a scarcity rent: in the long run the self-seeking behaviour of producers will result in such proportions of the quantities of the different capitals goods proper that a uniform « rate of net income », Walras’s term for rate of profit, obtains. Hence, implicitly Walras shows some awareness that « proper capital » cannot be dealt with in strict analogy with the primary factors of production, land and labour.
21Section 347 is devoted to a third class of products: those produced by « unspecialised productive services », which « have competition to fear. » He adds, echoing Ricardo’s view, that this, « admittedly, is the most frequent case » (p. 401). In this case
A rise in the prices of unspecialised services will attract to production other similar services which exist in more or less large quantities. If the prices of the products [of unspecialised services] rise, the prices of the productive services will also rise, but only temporarily; for these will increase in quantity and hence the quantity of their products will also increase. The end result will be a slight rise in the price of both productive services in general and of products in general (§ 347, pp. 401-402; emphases added).
22It is not clear, why the « end result » would be a « slight » rise in both kinds of prices. The only possible rationalisation of this conclusion we can think of would have to be in terms of non-specific services of land and labour, whose available amounts are given, constant and scarce. Now, in Ricardo we certainly encounter the assumption that the quantities of the different qualities of land are given and (almost) constant, and, depending on the levels of production of the various commodities, some of these qualities of land may be scarce. Yet, as we have already seen, Ricardo, whose main concern was the relationship between the wages of labour and the profits of capital, was keen « to get rid of rent » by focusing attention on (non-intensively cultivated) marginal land. In this way he was also able to refute Smith’s doctrine that rent is a component part of price. However, whilst it is true that on Ricardo’s special premise rent does not enter into cost of production on marginal land, a change in the levels of production of commodities that are (directly or indirectly) produced by means of unspecialised qualities of land, will nevertheless generally affect which quality of land is marginal, and thus costs of production, prices, the rate of profit and the rents paid to the proprietors of intramarginal lands. Ricardo is very clear about this3.
23As regards the other primary factor of production, common labour, according to Ricardo there is no presumption that in the long run it may also be considered a scarce factor of production. (Things may obviously be different with regard to certain special talents). In the classical authors the required size of the common work force is taken to be generated within the accumulation process. Therefore, while due to an abundance or a « scarcity of hands », to use Ricardo’s expression, in the short run wages may fall below or rise above their normal or « natural » level, in the long run a sufficient amount of labour will be forthcoming.
24Interestingly, in Walras we encounter a similar point of view. In Lesson 36 he states: « In a progressive economy, the price of labour (wages) remaining substantially unchanged, the price of land-services (rent) will rise appreciably and the rate of net income will fall appreciably » (pp. 390-1; emphasis in the original). Morishima (1977, p. 5) has stressed the thoroughly Ricardian flavour of this statement. Note in particular that according to Walras in the long run any tendency of the wage rate to rise as capital accumulates and the demand for labour increases is effectively offset by an expansion of the supply of labour. In other words, very much like in Ricardo the size of the workforce is considered an endogenous variable. Walras assumes in fact: « Population... does increase, for such an increase is implicit in our definition of progress; and thus additional labour, naturally proportional [?] to the additional future output, is assured » (p. 386). This makes Walras’s above objection to Ricardo’s long-period theory that not only land, but also human faculties exist in limited quantities, all the more puzzling (p. 399). In § 348 Walras summarizes his argument why, « in reality, there is no absolute antithesis between the two cases distinguished by Ricardo and Mill » (see § 348, p. 402).
25It is clear at this point, notwithstanding appearances to the contrary, that here there is no real logical disagreement between Walras and Ricardo. The difference between the two concerns the theory and thus the givens in terms of which the problem of value and distribution ought to be tackled. Ricardo based his explanation of relative prices and income distribution as much as possible on observable magnitudes; in contradistinction to Walras, he tried to avoid non-observable magnitudes, such as « utility » and the like.
II. Walras on the ricardian theory of rent
26Lesson 39 is devoted to an « exposition and refutation » of the Ricardian theory of rent. Sections 352-3 are devoted to a geometrical exposition in which each (incremental) investment involves an amount of £ 1,000 (which may be considered the unit of account in money terms in which the analysis is conducted)4. He objects that in Ricardo’s presentation of extensive rent (see Works I, pp. 70-1) it is not clear what is meant by « equal amounts of capital and labour »: « Ricardo does not state expressly in what terms these employments of capital are evaluated or what their value is; but in the second part he explicitly supposes that they are evaluated in terms of money [ “numeraire”] and that their value is £1,000 each » (§ 352, p. 405). In § 354 Walras then criticizes Ricardo: instead of proceeding in terms of increments of capital worth £1,000, he should have argued in terms of infinitesimals and should have supposed « that every time the capital used is increased by an infinitely small quantity, the rate of yield must decrease by an infinitely small quantity » (§ 354, p. 408). He illustrates his argument geometrically and then, in § 355, complements it by an algebraic formulation.
27Walras’s reconstruction of Ricardo’s theory of rent is challenging and deserves to be compared with the more recent reconstruction by Kaldor (1955-1956). There are three main differences. First, in his diagrammatic illustrations Walras puts on the horizontal axis « Capital Employed » whereas Kaldor puts « Labour ». In the literature subsequent to Kaldor we find also the expression « Labour-cum-capital » to indicate that whilst the unit of measurement is a unit of labour, the measure refers to the capital advanced, which includes not only the labour paid the given real wage, but also the « seed capital » used by one worker. Second, Walras draws a diagram for each quality of land, whereas Kaldor draws one single diagram for the whole com sector. Third, the curves drawn by Walras represent the derivative (or the increment) of « the excess per hectare of the total number of units of product over the number of units necessary for the payment of wages [on each kind of land, respectively] » (§ 355, p. 409), whereas the curve drawn by Kaldor gives the marginal productivity of labour (reflecting the amount of capital employed). Let us consider these three differences in turn.
28As regards the first difference, it is best to begin by recalling Ricardo’s first two consecutive attempts to simplify the problem of distribution (see Sraffa, 1951). The first step consisted of getting rid of rent in terms of the theory of extensive rent in the Essay on Profits (see Works IV); this allowed Ricardo to focus attention on marginal (in the sense of no-rent) land. In Sraffa’s interpretation (1951, p. xxxi), the second step consisted of trying to get rid of the problem of value by assuming the « corn model ». The assumptions underlying this model are:
- There is only one type of agricultural product, called « corn » .
- Corn is the only wage-good.
- Capital consists entirely of the wage-bill, i.e. com is produced by labour and land only.
29In this case the rate of profit obtained in com production can be ascertained directly as a ratio of quantities of com – that of the surplus product to the wage-bill advanced – without any need of having recourse to prices. With com entering (directly or indirectly) the production of all other commodities (as the only wage good and possibly also as an input) the prices of these commodities would have to adjust such that the same competitive rate of return could be earned in their production.
30It is obvious that in an economy satisfying assumptions (i)– (iii) there is no problem to construct production functions and plot marginal productivity of capital schedules for each quality of land. It is even possible to construct a production function and the corresponding marginal productivity of capital schedule for agriculture as a whole, even if land is diversified in quality5 However, in the case in which com enters into the production of com not only as a wage good, but also, as it is natural to assume, as a means of production, i.e. seed, it is no longer possible to plot the conventional marginal productivity schedules or to construct an aggregate production function for agriculture as a whole, unless one is willing to replace assumption (iii) by the following assumption:
31(iv) Capital consists of seed com and wages, and the seed corn input is strictly proportional to the labour input6.
32Hence, both Walras’s and Kaldor’s construction (and, of course, those by Samuelson (1959), and Pasinetti (1960), which is similar to Kaldor’s) are correct if and only if either of the following sets of highly restrictive assumptions apply: (i), (ii) and (iii); or (i), (ii) and (iv).
33The second difference mentioned above is thus also dealt with. Once it is clear that a presentation in terms of the marginal productivity of capital is admissible only when there is a single commodity ( « corn ») and com-inputs are proportional to labour-inputs, it is indeed possible to work in terms of a single curve representing agricultural (corn) production in the economy as a whole.
34The third difference reflects Walras’s deviation from, or, as Stigler (1941) argued some time ago, misunderstanding of, Ricardo’s treatment of the wages of labour. In Ricardo wages are included in the capital advanced at the beginning of the uniform period of production: they form an integral part of the dose of capital-cum-labour. Walras instead reckons wages as a part of the net product. Hence in Ricardo wage-goods, and especially corn, are « necessaries » both from the point of view of the single worker and from the point of view of the productive system as a whole. Below we shall see that in Walras’s interpretation of Ricardo’s theory of rent, strangely enough com does not enter (directly or indirectly) into its own production (seed). Therefore Walras’s reasoning cannot be based on either of the two sets of assumptions specified above. The « capital » employed in com production he talks about cannot be corn, but must be some other commodity or bundle of commodities. However, this is left in the dark, so that it remains unclear on which foundation his « rigorous formulation » of the English theory of rent (p. 411) rests.
Walras’s formalisation of classical rent theory
35In order to facilitate the exposition, let us summarize Walras’s algebraic argument. Let hi be the excess product per hectare of land of quality i over the payment of wages, xi the « amount of capital » in terms of the numéraire (and exclusive of the wages of labour) employed per hectare on land of that quality, and t the « rate of interest charges expressed in terms of [physical] units of product » (p. 409), then the rent per hectare of land of quality i, ri, is given by ri = hi – Xi t, (i = 1, 2,..., s) (1)
36where s is the number of the different qualities of land available, each of which is in given supply ni, and where hi is assumed to depend exclusively on Xi, that is,
37hi = Fi (xi). (i= 1, 2,..., s) (2)
38In a long-period equilibrium each quality of cultivated land must earn the same physical return per unit of capital employed, t. In the case in which qualities 1 to m are cultivated (m ˂ s), we have
39t = F1’ (x1) = F2’ (x2) =... = Fm’ (xm). (3)
40Counting the number of equations and unknowns in (1)– (3), Walras observes that there are only 3m equations but 3m+1 unknowns: the unknowns are r1..., rm; h1..., hm; x1..., xm; and t. Hence there is a degree of freedom. How to close the system?
41Another equation is needed. We can, without deviating in any way from a faithful interpretation of Ricardo’s theory, write the following equation which is analogous to those given in §§ 242 and 248:
42njXj + n2x2+ n3x3+... =X. (4)
43According to Ricardo, it seems that in every economy there is a certain amount of capital... At any given moment, the amount of capital is determinate. Let us call such a determinate amount X, and let us distribute it among the different kinds of land in such a way that the rate of yield is the same on all lands (ibid., p. 410; emphasis added).
44Walras thus interprets Ricardo as closing the system in terms of a given « quantity » of social capital.
45From what has been said in the above, this interpretation is difficult to sustain. Moreover, to take X as given is by no means necessitated by the desire to get a determinate system. This becomes clear when we give a closer look to the exact role played by the above closure of Walras’s Ricardesque model. In order to be able to determine the rents of land and the rate of profit, given the real wage rate, what we need to specify is the size of corn production. This can be done in several ways. In a model in which com is the only capital good, there is no harm in fixing total com production in terms of the amount of com capital employed in the growing of com. This is indeed the assumption needed in order for Walras’s reasoning to make sense. In this case equation (4) would provide the required information. However, there are more direct, and less ambiguous, ways to specify the size of com production, one of which is, of course, giving the overall level of com production. Alternatively, the level of corn production except the wage bill could be given, and so on. The latter alternative would imply an equation like
46n1h1 + n2h2+ n3h3 +...– H, (4’)
47where H is the excess product of com over the payment of wages. Clearly, equation (4’) would do the job equally well as equation (4), and in addition, it may be contended, is more faithful to Ricardo.
The dubious assumption of a given « quantity of capital »
48The fact that Walras’s interpretation is inconclusive follows also from a critical scrutiny of his claim that equation (4) is « analogous » to the equation given in §§ 242 and 248. While the two are formally very similar – logically they are very different. In contradistinction to equation (4), the allegedly « analogous » equation in §§ 242 and 248 is not just an equation fixing the total amount of com produced, but an equilibrium equation in which E (which plays the role played by X above) is the « algebraic sum of the individual excesses of income over consumption » (§ 242, p. 275). E is therefore not a given, but a magnitude to be determined endogenously: it has the role of relating investment to saving and of rendering the two equal to one another. In short, it refers to a savings-investment equilibrium.
49Going back to Lesson 39, Walras then proceeds to determine t for a given X by first solving equations (3) for given values of t, which gives him the xi’s corresponding to the different values of t, or x; = j; (t). He stresses: ‘ « The lands for which F’ (0) ˂ t will not be cultivated; only those for which F’ (0) > t will be brought under cultivation » (§ 355, pp. 410-11). Replacing the xi’s by the ji (t)’s in equation (4) gives him one equation for the only unknown t. Alternatively, it is easily checked that replacing the hi’s by the Fi (ji (t))’s in equation (4’) gives once again one equation for the only unknown t. Once t is determined, the other variables can be ascertained.
50Walras’s aim seems to be to establish the price equation
51pb = btpt + bpPp + bp’pP’ + bp” pP” +... + bkpk + bk’Pk’ + bk” pk” +... (5)
52where pb is the price of the product (b is the abbreviation of the French word for corn: ble), the b’s are technical coefficients of production, pt is the rate of rent in terms of the numeraire, the pp’s are the prices of « personal services », i.e. wages, and the pk’s are the prices of « capital service », i.e. interest charges. The b’s are variables, because there is a choice of technique, and all the p’s need to be determined by the theory. It is interesting to note that this equation is precisely one of the equations one encounters in the modem theory of rent of classical derivation (see, for instance, Kurz and Salvadori, 1995, p. 298). It therefore cannot be a source of disagreement between us and Walras. The real disagreement between Walras on the one hand and us (following Ricardo) on the other concerns the way in which he attempts to determine the rate of profit: he conceives of it as reflecting the scarcity of a factor called « capital proper ». However, as we have seen, he himself occasionally showed signs of awareness that this was perhaps not possible in a long-period equilibrium framework in which the natural assumption appears to be that the quantities of the different capital goods have had time to adjust such that a uniform rate of profit obtains. The disagreement concerns once again the substance of the theory reflected in the data from which to start: in the model presented by us (see Kurz and Salvadori, 1995) there is no equation or inequality relating to the available « quantity of capital » (or that of labour); instead one of the distributive variables (the real wage rate or, alternatively, as in our formalisation, the rate of profit) is considered as given. As we have seen, Walras advocated a different approach, which, however, ran into difficulties as Walras by the time of the fourth edition of the Elements began to recognise7.
Walras’s misunderstandings of Ricardo’s theory of rent
53As mentioned in footnote 4, in § 352 Walras remarks that in the quoted passage on extensive rent « Ricardo does not state expressly in what terms these employments of capital are evaluated or what their value is; but in the second part he explicitly supposes that they are evaluated in terms of money [ “numeraire”] and that their value is £1,000 each » (p. 405). In his formalisation of Ricardo’s theory Walras instead measures the outputs hi, the rates of rent ri, and « the rate of interest charges expressed in terms of [physical] units of product » t in terms of product. He therefore feels the need to come back to this issue, not least because it is at the centre of his criticism. In § 357 he restates equation (1) when all variables are expressed in terms of numeraire (the i’s are dropped for the sake of simplicity):

54where i is here « the rate of net income in terms of numeraire »8 and therefore r = p/pb and t = i/pb.
55In our interpretation, with the doses of £1,000 Ricardo intends to refer to the units of account, that is, units of corn, in terms of which he conducts his analysis, and the fact that they are expressed as if they were « in money terms » does not affect the substance of the argument. Walras, on the contrary, infers from the fact that they are expressed in money, i.e. numeraire: « Since each application always amounts to £1,000, it follows that the prices of the capital goods in question are determinate and constant » (§ 359, p. 414). This is a non sequitur. Walras recognises that « Ricardo obviously could not have argued that the product obtained depended on the capital employed no matter how this capital was employed, even if it was employed absurdly » (ibid.). Then, how can he presume that in Ricardo a given amount of capital implies « certain determinate quantities of definite kinds of capital goods » and thus « certain determinate quantities of definite kinds of services » (ibid.), irrespective of the quality of land and the method of production adopted to cultivate it? Walras’s argument lacks conviction9.
56He continues: « This hypothesis has important consequences » (§ 360, p. 414). In his opinion « It led Ricardo to base the existence, the origin and the growth of rent on the increasing dearness of products. Indeed, in his view, cost of production determines selling price » (ibid.). Walras overlooks that there is at least one element amongst the ingredients of com production, whose price is bound to rise, namely that of corn itself: com needed as seed and com to feed workers. Surprisingly, Walras misses the important aspect of circular flow of production in Ricardo.
57The main argument developed by Walras in this regard is totally unconvincing. Walras first argues that

58then he adds: « if we ignore variations in i, this last ratio will increase indefinitely as t decreases, which is the basis of the theory » (§ 360, p. 415). How can one ignore variations in i? How is it possible that an increase in the price of corn, given the prices of the capital items and given i, could be said to be « the basis of the theory » of the English economists? The contrary comes closer to the truth. Walras summarizes his interpretation as follows: « Thus, the English theory can only determine the price of land-services and demonstrate its residual character on the twofold assumption that the prices of personal capital, the prices of capital goods proper and the rate of net income are predetermined and constant, and that, therefore, the prices of the services of personal capital and capital goods proper are also predetermined and constant » (§ 361, p. 415).
59Walras refrains from substantiating his surprising claim in terms of some evidence from Ricardo’s Principles. In fact, no such substantiation can be provided. In Ricardo the falling tendency of the rate of interest is inextricably intertwined with the theory of rent. To assume that the rents of land go up, but the rate of profit stays constant, misses the whole point of Ricardo’s explanation of the tendency of the rate of profit to fall. It is astonishing how Walras could go astray so much. He continues: « We may ask... why the English School determines rent by the quantities of labour and capital-services employed, rather than wages and interest by the quantities of land-services employed; or why this school does not try to formulate a unified general theory to determine the prices of all productive services in the same way » (p. 416). This is indeed the crucial question: Is it possible to generalize the principle of rent to an explanation of all kinds of income in the same way and thus interpret the wages of labour as well as the profits of capital as scarcity prices of the respective factors of production, labour and capital? Walras thinks that this is indeed possible. In his concluding words of Lesson 39: Thus, all that remains of Ricardo’s theory after a rigorous critical analysis is that rent is not a component part, but a result, of the price of products. But the same thing can be said of wages and interest. Hence, rent, wages, interest, the prices of products, and the coefficients of production are all unknowns within the same problem; they must always be determined together and not independently of one another (p. 418).
60In terms of which data can this be accomplished? This is the question! Walras and neoclassical economists in general assume that the supplies of labour and « capital » must be among the givens also in a long-period framework. Classical economists argue that in the long period either the wage rate or the rate of profit must be among the givens, because there is no possibility to consider the « capital endowment » as a datum in long-period analysis. But this problem transcends the scope of this paper. The interested reader is invited to consult, for example, Garegnani (1990) and Kurz and Salvadori (1995, ch. 14).
III. Walras on the ricardian theory of wages and profits
61In Lesson 40 Walras deals with the classical theory of wages and profits. The lesson is almost exclusively devoted to a criticism of John Stuart Mill and especially his wage fund doctrine. Since Ricardo was no advocate of that theory (cf. Stirati, 1994), these parts need not concern us here. There is only one section which is somewhat related to Ricardo’s way of thinking and which deserves to be commented upon. We quote § 368 in full:
Let P be the aggregate price received for the products of an enterprise; let S, I and F be respectively the wages, interest charges and rent laid out by the entrepreneurs, in the course of production, to pay for the services of personal faculties, capital and land. Let us recall now that, according to the English School, the selling price of products is determined by their costs of production, that is to say, it is equal to the cost of the productive services employed. Thus we have the equation
P = S + I + F, [(6)]
and P is determined for us. It remains only to determine S, I and F. Surely, if it is not the price of the products that determines the price of productive services, but the price of productive services that determines the price of the products, we must be told what determines the price of the services. That is precisely what the English economists try to do. To this end, they construct a theory of rent according to which rent is not included in the expenses of production, thus changing the above equation to
P = S + I.
Having done this, they determine S directly by the theory of wages. Then, finally, they tell us that « the amount of interest or profit is the excess of the aggregate price received for the products over the wages expended on their production », in other words, that it is determined by the equation
I = P-S.
It is clear now that the English economists are completely baffled by the problem of price determination; for it is impossible for I to determine P at the same time that P determines I. In the language of mathematics one equation cannot be used to determine two unknowns. This objection is raised without any reference to our position on the manner in which the English School eliminates rent before setting out to determine wages.
62Before we enter into a discussion of this criticism two observations should be made. First, essentially the same objection was put forward by William Stanley Jevons: Walras in fact essentially reiterates Jevons’s criticism (see Jevons, [1871] 1911, pp. 268-269). Second, the claim that Ricardo tried to determine two unknowns with a single equation is perhaps the expression that comes closest in these authors to admitting that the classical approach is fundamentally different from their own marginalist approach. In the way Jevons put the claim, the degree of freedom in classical analysis as regards distribution is put into sharp relief: as we know, that degree is filled by fixing the level of the real wage rate (see axiom (R3) above).
63Once this is seen, it becomes clear that Walras’s (and Jevons’s) criticism cannot be sustained. It was explicitly refuted by the Russian mathematical economist Vladimir K. Dmitriev ( [1898] 1974, pp. 51 ssq.), who showed that Ricardo gave a definite solution to the problem of the determination of the distributive variables and relative prices. In the following we shall provide an argument that is logically identical to Dmitriev’s, but which refers also to other parts of the Elements. In this way we intend to throw some additional light on certain aspects of Walras’s thought which do not always seem to have been properly understood (see also Kurz and Salvadori, 1995, pp. 25-26).
64Equation (6) is nothing else than equations (4) in § 203 of the Elements (p. 240), which are here presented using matrix notation:
65p = Cq + Ew + Ay,
66where p is the vector of prices of output (Walras assumes that the first element of p equals unity because the first commodity acts as the numeraire), C is the matrix of the production coefficients of land inputs of the operated processes, q is the vector of prices of land services (i.e., the rent rates), E is the matrix of the production coefficients of labour inputs of the operated processes, w is the vector of prices of personal services (i.e., the wage rates), A is the matrix of the production coefficients of the inputs of capital goods proper of the operated processes, and y is the vector of prices of the services of capital goods proper10. If, following Ricardo, as mentioned by Walras himself, we take account only of the technology used at the margin (either extensive or intensive)11 and if we assume for simplicity that there is only one quality of labour, we obtain the equation
67p = wl + Ay. (7)
68Finally, assume that all capital goods proper are circulating capital, so that the depreciation charges equal the corresponding prices, and that the insurance premiums are nought, then
69y = (1 +i) p,
70where i is the « rate of net income »,12 and equation (7) becomes
71p = wl + (1 + i) Ap. (8)
72This is a system of n equations in n + 1 unknowns, since by definition the first element of p equals unity, where n is the number of products, some (or all) of which could be capital goods proper13.
73Taking (with Ricardo) the real wage rate as given, we get the n + 1st equation needed to determine prices and distribution. In fact if
74w = bTp,
75where b is a given vector defining the real wage rate, and assuming (with Walras) that wages are paid post factum, equation (8) becomes
76p = IbTp + (1 + i) Ap, (9)
77and if the elements of b are small enough, then matrix I – bTp is invertible with a semipositive inverse and
78p = (1 +i) (I-bT)-1 Ap.
79That is, 1/ (1 + i) is the Perron-Frobenius eigenvalue of matrix (I – lbT)-1A and p is the corresponding eigenvector whose first element equals unity.
80We may thus conclude that Walras’s criticism is untenable: Ricardo cannot be accused of having attempted « to solve two unknowns with one equation ». Ricardo’s system is perfectly determinate. The data, or independent variables, from which he starts his analysis of the problem of value and distribution (R1)– (R4) suffice to determine the unknowns, or dependent variables, that is, the general rate of profit, the rent rates and prices in terms of the given numeraire. No other data, such as utility or demand functions, are needed. In his reading of Ricardo Walras was misled by the idea that there is only a single kind of theory in economics: supply and demand theory. Assessed in terms of his own theory, Ricardo’s was bound to look somewhat strange. Had Walras given a closer look to Ricardo’s construction he would have found out that there was no indeterminacy.
Concluding remarks
81In this paper we have scrutinized Walras’s criticism, in Part VII of the Elements, of the classical theory of value and distribution, paying special attention to Ricardo’s contribution. We have shown that on the one hand Walras succeeded in pointing out several weaknesses and unnecessarily restrictive assumptions in Ricardo’s theory of rent and that certain aspects of his interpretation may be said to foreshadow the later ones by Nicholas Kaldor, Luigi Pasinetti and Paul A. Samuelson. However, Walras does not appear to have been aware of the fact that in order to be able to draw marginal productivity curves of capital with regard to each quality of land, exceptionally restrictive assumptions must hold in corn production. In particular, the only capital good employed has to be corn, that is, an input identical with the output. That Walras did not assume this becomes clear when we turn to Walras’s misinterpretations of Ricardo. First, there are misunderstandings of specific elements of Ricardo’s theory. These include Ricardo’s treatment of the wages of labour as a part of the capital advanced at the beginning of the period of production; instead Walras considers them as a part of the net product. Then there is a lack of understanding on Walras’s part of the circular flow of production in Ricardo and especially of the fact that com is considered a product that enters into its own production (via the wages of labour and seed capital) and, besides this, also into the production of other commodities. This implies, among other things, that the capital employed in com production in his attempted formalisation of Ricardo’s rent theory cannot be physically identical with the product. It follows that Walras was not entitled to draw the marginal productivity curves as he did.
82More important, Walras fails to see that the classical approach to the theory of value and distribution is fundamentally different from his own supply-and-demand approach. He treats Ricardo’s theory as if it was just an early and rude version of his own elaborate neoclassical general equilibrium theory. This theory attempts to determine quantities, relative prices of goods and income distribution in terms of the following data: (W1) technical alternatives; (W2) preferences; and (W3) initial endowments of factors of production, including capital. Ricardo in his theory is said to start essentially from the same sets of data, but to impose unnecessary restrictions on them and in addition to commit logical blunders. Entirely in line with his neoclassical perspective of Ricardo, Walras believes to be faithful to the English economist when « closing » his model of the Ricardian theory of rent in terms of a given « quantity of capital ». He misses the fact that the data of the classical theory are: (R1) technical alternatives; (R2) the size and composition of the social product; (R3) the real wage rate; and (R4) the quantities of land available. He also misses the fact that in terms of these data the dependent variables – the rate of profit, the rent rates and relative prices – are fully determinate. There is no need, and indeed no possibility, to add some further givens, such as the capital endowment of the economy or utility. Walras’s objection that Ricardo tried « to determine two unknowns with one equation », involving that his system is underdetermined, is false.
83Walras’s attack on Ricardo is challenging. It was meant to clear away the classical theory of value and distribution and establish the superiority of his own – the only and « truly scientific theory of social wealth » (p. 428). While some of Walras’s criticisms are pertinent, his interpretation taken as a whole reflects a lack of understanding of the nature of Ricardo’s approach to the theory of value and distribution, which is fundamentally different from the supply-and-demand approach. To Walras there is only the latter and Ricardo’s contribution has to be assessed in terms of it. Not surprisingly, Walras finds fault with Ricardo’s treatment of the real wage rate as a known magnitude. To Walras all prices and all distributive variables are to be explained simultaneously and symmetrically in terms of supply and demand. The asymmetric treatment of the distributive variables in the classical authors, who took the real wage rate as given and determined all shares of income other than wages residually, is extraneous to his way of thinking. In this regard Walras’s interpretation of Ricardo does not differ much from that of other neoclassical authors, for example Jevons. They showed similar difficulties to apprehend and appreciate the distinct character of the classical analysis which had gradually been « submerged and forgotten since the advent of the marginal method » (Sraffa, 1960, p. v).
Bibliographie
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References bibliographiques
Dmitriev V. K. (1974), Economic Essays on Value, Competition and Utility, English translation of a collection of Dmitriev’s essays published in 1904 in Russian, edited by D. M. Nuti, Cambridge: Cambridge University Press. Dmitriev’s essay on Ricardo’s theory of value was originally published in 1898.
Freni G. (1991), « Capitale tecnico nei modelli dinamici ricardiani », Studi Economici, 44, pp. 141-59.
10.1007/978-1-349-20861-6 :Garegnani P. (1990), « Quantity of Capital », in: J. Eatwell, M. Milgate and P. Newman (eds), Capital Theory, London: Macmillan, pp. 1-78.
Guichard J. P. (1982), « La Rente différentielle intensive, expression d’un processus d’intensification de cultures », in: R. Arena et alii (eds), Études d’economie classique et neoricardienne, Paris: PUF, pp. 115-38.
10.1057/9781137374158 :Jevons W. S. (1911), The Theory of Political Economy, first ed. 1871, London: Macmillan. Fourth ed., London: Macmillan.
10.2307/2296292 :Kaldor, N. (1955-6), « Alternative Theories of Distribution », Review of Economic Studies, 23, pp. 83-100.
Kurz H. D. and Salvadori N. (1992), « Morishima on Ricardo: A Review Article », Cambridge Journal of Economics, 16, pp. 227-47.
10.1017/CBO9780511625770 :Kurz H. D. and Salvadori N. (1995), Theory of Production. A Long-period Analysis, Cambridge, Melbourne and New York: Cambridge University Press.
10.1002/9781118011690.ch20 :Mill J. S. (1909), Principles of Political Economy, Ashley ed., London: Longmans, Green and Co.
Morishima M. (1977), Walras’s Economics. A Pure Theory of Capital and Money, Cambridge: Cambridge University Press.
10.2307/2296129 :Pasinetti L. L. (1960), « A Mathematical Formulation of the Ricardian System », Review of Economic Studies, 27, pp. 78-98.
Ricardo D. (1951-73), The Works and Correspondence of David Ricardo, edited by Piero Sraffa with the collaboration of M. H. Dobb, 11 vols, Cambridge: Cambridge University Press. In the text refereed to as Works, volume number.
Samuelson P. A. (1959), « A Modem Treatment of the Ricardian Economy: I. The Pricing of Goods and of Labor and Land Services », Quarterly Journal of Economics, 73, pp. 1-35.
Psraffa P. (1951), « Introduction », in: Ricardo (1951), Works I, pp. xiii-lxii.
Sraffa P. (1960), Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory, Cambridge: Cambridge University Press.
10.4324/9781315127477 :Stigler G. J. (1941), Production and Distribution Theories, New York: Macmillan.
Stirati A. (1994), The Theory of Wages in Classical Economics. A Study of Adam Smith, David Ricardo and their Contemporaries, Aidershot: Edward Elgar.
10.4324/9781315888958 :Walras L. (1954), Elements of Pure Economics, London: Allen and Unwin. English translation by W. Jaffé of the definitive edition of Éléments d’économie politique pure, first published 1874, Lausanne.
Notes de bas de page
1 In the following all isolated pages given refer to the Jaffé edition of the Elements.
2 For a discussion of the classical theory of wage differentials, see Kurz and Salvadori (1995, ch. 11).
3 Therefore, Walras’s verdict that the proposition that rent does not enter into cost of production « proved to be the rock on which the English theory of rent finally foundered » (§ 361, p. 417) appears to be untenable.
4 Walras emphasises that this measure is in terms of money (numeraire), and, as we will see later, this creates some complications in the exposition, but the recent literature seems to be inclined to interpret the « £ 1,000 » mentioned by Ricardo just as the unit of account in terms of which the analysis is carried out, taking it for granted that the sum represents a certain amount of « corn ».
5 For a demonstration, see Freni (1991), whose results on this point are reported by Kurz and Salvadori (1992, pp. 230-5).
6 If neither assumption (iii) nor assumption (iv) hold, then neither a production function for each quality of land nor a production function for the whole economy can be built up. Freni (1991) has provided an example (the reader unable to read Italian can consult Kurz and Salvadori, 1995, p. 313) in which there is only one quality of land (so that there is no question of the existence of a production function for each quality of land or for the agricultural sector as a whole), one product (com), one quality of labour, and com does enter into the production of itself but not in proportion to labour inputs (i.e., seed-capital is not proportional to the wage-bill). In this example, for a given rate of profit (interest), a given amount of land and a given amount of com to be produced over and above the amount required as an input, there are three possible solutions.
7 A discussion of these difficulties is beyond the scope of this paper. See therefore the summary account of the deficiency of Walras’s approach in Kurz and Salvadori (1995, chs. 1 and 14)
8 The definition of the rate of net income i is given in § 233 (pp. 268-9) and from it we see immediately that i is a pure number. However, curiously, when referring to the rate of net income, Walras insists to add: « in terms of numeraire ».
9 Ricardo was very clear about the fact that in general (i.e. setting aside the case of the « com model ») the concept of « capital » is a difficult one. In a letter to McCulloch he wrote: « I would ask what means you have of ascertaining the equal value of capitals?... These capitals are not the same in kind – what will employ one set of workmen, is not precisely the same as will employ another set... » (Works IX, pp. 359-360; see also his letter to Torrens, Works IV, pp. 393-4). And William Blake he asked: « In what shape does this capital exist which is to be devoted to expenditure? » (Works IV, p. 346).
10 In accordance with Walras rents and wages are taken to be paid at the end of the uniform period of production.
11 For the intensive margin we have to follow the procedure provided by Guichard (1982).
12 Walras stresses that in equilibrium conditions the rate of net income « is the same for all capital goods » (§ 233, p. 269; see also §§ 238 and 249).
13 In § 238 (similarly § 232) Walras asserts that if Pk is the price of a capital good proper, its depreciation charge and its insurance premium are respectively mkPk and nkPk. If the mentioned capital good is a circulating one, then mk = 1; and if the insurance premium on it is nought, then nk = 0. These assumptions are adopted only for the sake of simplicity. If, on the contrary, M. is the diagonal matrix with the exogenously given depreciation charges on the main diagonal and V is the diagonal matrix with the given insurance premiums on the main diagonal, then y = (M + V + iI) p,
and equations (8) and (9) become p = wl + A (M + V + iI) p (8’)
and p = lbTp + A (M + V + il) p, (9’)
respectively. Finally 1/i is determined as the Perron-Frobenius eigenvalue of matrix (I – 1bT – AM – AV)-1A
and p as the corresponding eigenvector whose first element equals unity. What prevented us from using these equations in the text is this: the modem treatment of fixed capital has clarified that a correct analysis cannot consider the depreciation charges as given independently of the rate of profit (or interest); see Kurz and Salvadori (1995, p. 210, and in general chapters 7 and 9). Therefore, Walras’s approach to fixed capital cannot be sustained.
Auteurs
-
Heinz D. Kurz
Université de Graz
-
Neri Salvadori
Université de Pise
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