WICKSELL on WALRAS's EARLY TREATMENT of CAPITAL and INTEREST by ANDREA IMPERIA1, VINCENZO MAFFEO2 and FABIO RAVAGNANI3 Abstract

WICKSELL ON WALRAS'S EARLY TREATMENT OF CAPITAL AND

INTEREST

ANDREA IMPERIA1, VINCENZO MAFFEO2 AND FABIO RAVAGNANI3

Abstract

In this paper we examine the criticism that Knut Wicksell advanced against Walras’s treatment of capital and interest at the end of the nineteenth century, as well as the views of two distinguished followers of Walras concerning the points raised by the Swedish economist. As regards the first aspect, it should be noted that the criticism put forward by Wicksell at that time refers to the earlier editions of the Éléments, in which circulating capital is excluded from the analysis. We thus endeavour to clarify Wicksell’s remarks on the consequences of that exclusion for both the representation of the social production process and the determination of the interest rate. As to the second aspect, our discussion indicates that the appropriate way of treating the capitalistic element of production was an unsettled issue within the small circle of Walras’s followers at the end of the nineteenth century.

1: Department of Social and Economic Sciences, Sapienza University of Rome, Rome, Italy. Email: [email protected]. 2: Department of Social and Economic Sciences, Sapienza University of Rome, Rome, Italy. Email: [email protected]. 3: Department of Economics and Law, Sapienza University of Rome, Rome, Italy. E-mail: [email protected].

This “preprint” is the peer-reviewed and accepted typescript of an article that is forthcoming in revised form, after minor editorial changes, in the Journal of the History of Economic Thought (ISSN: 1053-8372), volume 40 (2018), issue TBA. Copyright to the journal’s articles is held by the History of Economics Society (HES), whose exclusive licensee and publisher for the journal is Cambridge University Press (https://www.cambridge.org/core/journals/journal-of-the- history-of-economic-thought ). This preprint may be used only for private research and study and is not to be distributed further.

The preprint may be cited as follows:

Imperia, Andrea, Maffeo, Vincenzo, and Ravagnani, Fabio. “Wicksell on Walras’s Early Treatment of Capital and Interest.” Journal of the History of Economic Thought 40 (forthcoming). Preprint at SocArXiv, osf.io/preprints/socarxiv 2

1. Introduction

Among the scholars of his time, Knut Wicksell was one of those who devoted more attention to Walras’s theory of capital and interest. As is known, for a long time he was highly critical of the French economist in that respect (cf., for example, Stigler 1948, pp. 252-254). In this paper we examine the criticism that Wicksell advanced against Walras’s treatment of capital and interest at the end of the nineteenth century, as well as the views of two distinguished followers of Walras concerning the points raised by Wicksell. As regards the first aspect, it should be noted that the criticism put forward by Wicksell at that time refers to the second and third edition of the Éléments, in which circulating capital is excluded from the analysis. We thus endeavour to clarify Wicksell’s remarks on the consequences of that exclusion for both the representation of the social production process and the determination of the interest rate. As to the second aspect, our discussion indicates that the appropriate way of treating the capitalistic element of production within the context of general equilibrium analysis was an unsettled issue among Walras’s followers at the end of the nineteenth century. The paper is organised as follows. Section 2 examines the critical assessment of Walras’s theory of capital and interest as put forward by Wicksell in Value, Capital and Rent (1893). Section 3 discusses Vilfredo Pareto’s views on one of the points raised by Wickell, as they emerge from the first volume of the Cours d’Economie Politique (1896), and Enrico Barone’s (1895, 1896) reply to Wicksell (a letter by Barone to Wicksell concerning this reply is reproduced, for the first time in its wholeness, in the Appendix). Section 4 documents the persistence of Wicksell’s criticism after Barone’s reply and offers an interpretation for this fact. Section 5 draws conclusions.

2. Wicksell’s early assessment of Walras’s theory of capital and interest: Value, Capital and Rent (1893)

2.1 Wicksell’s position on capital and distribution

In Value, Capital and Rent, Wicksell (1893, p. 94) ascribes to Walras the merit of having made, through “the equations of production”, the only successful attempt “to 3

do justice of [the] reciprocal relations” between the price and the cost of production of commodities; in other words, the merit of having treated those relations from the perspective of general economic equilibrium. At the same time, however, he contends that Walras’s concept of capital is “old-fashioned and one-sided” (1893, p. 21) and that the Walrasian analysis of production, distribution and exchange needs to be completed with Böhm-Bawerk’s theory of capital.1 As Wicksell points out, Böhm-Bawerk’s theory starts from the premise that production requires time. Capital is seen, in its essence, as a fund of means of subsistence that are advanced to workers and landowners for the whole period in which labour and land are employed directly and indirectly in the production of final consumer goods. At any given moment in time, this fund mostly appears in the economy in the form of raw materials, unfinished products and other capital goods that will be gradually transformed into consumption goods (Wicksell 1893, pp. 115- 116). In Wicksell’s (and Böhm-Bawerk’s) view, more indirect production methods are associated with longer periods of production. Moreover, it is held that the output per unit of labour increases with the length of the production period. Thus, the role of capital in production

“consists…simply and solely in making possible the introduction of a longer period of time between the beginning and the conclusion of the process of production of the commodity concerned and consequently the adoption of a more productive round-about method of production than would be possible if production were less strong in capital or totally devoid of capital” (Wicksell 1893, p. 115). It should be noted that in Value, Capital and Rent Wicksell develops his theory in the hypothesis of a stationary economy in which only circulating capital is employed. As regards the first aspect, he believes that, in a first phase, the theory of interest and the theory of accumulation should be taken into consideration separately, as is usually done for the theory of exchange and the theory of production (Wicksell 1893, p. 21). With that, he does not intend to deny that “the question of the origin of capital interest and that of the origin of interest-bearing capital itself…are related” (1893, p. 21). Wicksell seems merely to hold that the causes which determine the interest rate are broadly independent of those determining the accumulation of capital. In his view, the simplest way to treat the determination of the interest rate 1 The substance of the criticism put forward in Value, Capital and Rent as regards Walras’s theory of capital had been already expounded in Wicksell 1892; cf. Uhr 1962, p. 104. 4

separately from the theory of accumulation is to focus on the case of a “stationary economy in which capital and the other economic factors can be thought of as an approximately unalterable sum” (1893, p. 22). Wicksell seems to believe that in this hypothetical economy the determination of the interest rate must depend on the mere employment of a given quantity of capital in production, beside labour and land, and not on the conditions of its accumulation. As regards the hypothesis that only circulating capital is employed in production,2 in order to understand Wicksell’s position it is useful to consider his classification “of the different capitals…according to their durability” (1893, p. 105). Wicksell argues that “consumable or quickly exhausted” means of production, together with “the consumer goods [that] are not yet in the hands of consumers” and are therefore susceptible of being advanced to workers as means of subsistence, must be regarded as “capital in the narrower sense”. Then he distinguishes this first category of goods from the “highly durable goods” such as “productive buildings, factories, store-houses, railways, etc.”, which are remunerated only in proportion to their scarcity, without any noteworthy influence of the original costs of production. Wicksell states that the latter goods “must be placed, economically speaking, in the same category as landed property itself” and calls them rent-goods (1893, pp. 118- 119). Moreover, he asserts that rent-goods do not play any role in determining the rate of interest (1893, p. 119) and finally remarks that, in a stationary economy, rent- goods “are not produced at all, but kept in the same good condition” (1893, p. 162; emphasis added). In the foregoing classification, the machines of comparatively low durability are implicitly included among the “capital goods in the narrow sense” that are relevant for the determination of the interest rate (1893, p. 118). However, the treatment of comparatively short-lived machines was an unsettled issue to Wicksell. 3 This fact may explain why, in the subsequent development of the analysis, he does not take them into consideration but simply reasserts that rent-goods play no

2 In Wicksell’s theory all the means of productions, “once the production process is complete and the goods are ready,...are assumed to be worn out and valueless” (1893, p. 120). 3 As Wicksell himself will admit in the review of Åkerman’s study of durable capital, “[the problem created by durable capital] is so complex that the vast majority of economists, including the reviewer, have almost entirely passed it by as being much too difficult to be susceptible to analysis” (1923, p. 258; emphasis added). 5

essential role in the determination of the interest rate and gives the role of determining that rate to circulating capital only (1893, p. 163).

2.2 The criticism of Walras’s treatment of capital and interest

In view of both the conception of capital as a subsistence fund and the role attributed to circulating capital, it should come as no surprise that in Value, Capital and Rent Wicksell did not agree about Walras’s treatment of capital and interest. As is known, in the editions of the Éléments available at the time Walras refers his analysis to economies in which only endowments of fixed capital goods are assumed to exist, while the presence of stocks of raw materials, half-finished goods and means of subsistence is ruled out on the assumption that these goods are consumed as soon as they are produced and are not stocked in advance (cf. Walras 1954, p. 220; 1988, p.

278).4 According to Wicksell, the absence of circulating capital goods has two relevant consequences for Walras’s analysis, which are summarised at the end of Value, Capital and Rent. The first consequence is that

“[i]t is…implicitly assumed by Walras that workers and other producers maintain themselves during production and receive remuneration for their productive services from the proceeds of the products in question only after completion of the production” (Wicksell 1893, p. 167) . According to Wicksell, this tacit assumption “is obviously incorrect” since, as he remarks earlier in the book,

“[p]roduction requires time…and the sellers of the productive services will generally not be able or willing to await the completion of the commodities in order to secure their remuneration from the amount realized by the sale” (1893, p. 93). As far as realism in the representation of the social production process is concerned, we can say that Wicksell’s considerations point to a real weakness of the first formulations of the Éléments. Once it is acknowledged that some period of time must normally elapse between the moment in which primary inputs are employed and the moment in which the corresponding final products are ready for sale, the

4 It is only when the theory of exchange, production and capital formation has been fully developed on that assumption that Walras, in the second edition of the Éléments, briefly mentions the creation of inventories of nondurable goods in the economy (Walras 1889, pp. 312-14; cf. also Walker 1996, pp. 157-158 and 198-199). 6

maintenance of “workers and other producers” during the course of the social production process requires that at least one of the following conditions obtains. The first is that reserves of consumer goods are available in the economy. The second is that within the complex of the industries producing consumption goods and their direct and indirect means of production, productive processes are carried out side by side and co-ordinated in such a way as to ensure both the steady replacement of the capital goods used up and the emergence of a continuous flow of consumption goods. Neither condition is compatible, however, with the absence of stocks of circulating capital goods. This is obvious as regards the first condition. As to the second, it suffices to note that the production of a continuous flow of consumer goods presupposes that an aggregate of intermediate goods should be present in the economy at any moment in time. Moving now to the second consequence, Wicksell focuses his attention on the system of “equations of production and exchange” that, in all editions of the Éléments, constitutes an intermediate stage of Walras’s theory in the direction of the extended system with capital formation.5 In that intermediate system, Walras (1954, p. 238; 1988, pp. 302-303) assumes that the durable capital goods in existence are not subject to depreciation and, moreover, that the economy is “stationary” in the sense that additional quantities of capital goods are neither demanded nor produced (cf. also Van Daal and Jolink 1993, pp. 41-43; Walker 1996, p. 115). Wicksell (1893, p. 167) remarks that “these equations of production and exchange can give no information at all about the level of the rate of interest”, since

“[i]f only durable capital goods are regarded as capital, then a certain rent is fixed for each group of these [goods] by the above-mentioned equations, but not the capital value of the goods itself, nor, consequently, the rate of interest either, le ‘taux du revenu net’”.6 Then he states that this point “is explicitly admitted by Walras”, who “asserts that, in order to determine the level of interest, it is necessary to turn from the investigation of a stationary economy to the investigation of a progressive one, where new…capital goods are produced, whose capital value can be determined from the production costs”.

5 The “equations of production and exchange” mentioned in the text are introduced in Lesson 41 of the first edition of the Éléments and in Lesson 20 of the subsequent editions. 6 As concerns this aspect of Walras’s theory cf. Jaffé (1942, p. 143, n. 5), who underlines that “the theory of production gives the prices of the services of capital goods but not of the capital goods themselves”. 7

Finally, Wicksell argues that Walras’s assertion that the interest rate cannot be determined in the case of a stationary economy “is certainly incorrect” and ultimately can be traced back to the exclusion of circulating capital from analysis. His argument consists simply of recalling the results achieved through the alternative approach of Value, Capital and Rent, which show that

“[i]n the stationary economy, too…a rate of interest of the circulating capital will undoubtedly establish itself, precisely because the lengthier methods of production prove more profitable” (1893, p. 167). Let us examine more closely this second criticism raised in Value, Capital and Rent. On the one hand, the substance of the criticism is clear – according to Wicksell, Walras’s approach to the determination of the interest rate is seriously defective, as it is incapable of dealing with the basic case of a stationary economy (cf. also Stigler 1948, pp. 252-253). On the other hand, it should be noted that Wicksell’s critical argument implicitly relies on the view that Walras’s theory, when applied to a stationary economy, does not allow for the determination of the prices of capital goods on the basis of production costs. It is, however, unclear how this view can be held with regard to Walras’s extended system with capital formation. Considering that in that system Walras (1954, p. 268; 1988, p. 346) explicitly assumes that the fixed capital goods in existence are subject to wear and tear, it might be objected that durable capital goods must be normally produced even in a stationary economy in order to replace the means of production which are worn out. Why, then, does Wicksell ignore the extended system with capital formation and reason as if capital goods were assumed to be “indestructible” throughout Walras’s theory? We shall return to this issue after examining the views expressed by two eminent followers of Walras in the mid-1890s as regards the points raised by Wicksell.

3. Pareto and Barone on Walras’s treatment of capital

3.1 Pareto’s Cours d’Economie Politique

In the first volume of his Cours d’Economie Politique (1896) Pareto, without ever mentioning Wicksell, addresses in fact one of the questions raised by the Swedish economist, namely that, since production takes time, “the sellers of the productive 8

services will not be able or willing to await the completion of commodities in order to secure their remuneration”. After reinterpreting Walras’s definition of capital, Pareto introduces in his analysis a form of capital that is absent from Walras’s equations of production – the saving-capital, defined as “the saving used for the advances to production” that is fully worn out and restored at the end of each production process.7 In Pareto’s theoretical construction, the saving-capital available in the economy is employed by entrepreneurs to remunerate the sellers of productive services at the beginning of production processes: “it allows paying current production expenses through the product to come” (Pareto 1896, p. 304; our translation). The saving-capital is expressed by Pareto as a given amount of numeraire, but an equivalent stock of goods that can be employed for the advances to production must obviously exist in the economy.8 This means that the real remunerations of productive services consist of goods produced before the completion of the production processes in which they are employed. Thus, in the formulation of the cost of production of a generic commodity adopted in the Cours, besides the remunerations of labour and the other services, we find the price for the use of saving-capital, that is, essentially, the rate of interest (Pareto 1896, p. 44, n. 1). Once it is acknowledged that production takes time and that the sellers of productive services are paid before the completion of production processes, one should presume that the remuneration of saving-capital is proportional to the period of advance. In this respect, however, Pareto’s analysis is problematic. Let us consider his treatment of the raw materials used in the production of final goods. Raw materials do not appear as such in Pareto’s formulation of the production cost, but are ‘substituted’ by the quantities of services required for their own production: ‘raw materials break up in services’ (Pareto 1896, p. 46; our translation). In turn, those

7 Pareto 1896, p- 40; our translation, emphasis added. Walras’s original definition of capital ̶ “all the forms of social wealth which…can be used more than once” (Walras 1889, p. 197; our translation) ̶ is reinterpreted by Pareto as follows: “In order that an economic good may be a capital, it is not necessary that it can be materially used more than once in production; it must only be restored at the end of every period of production so that it can be economically used more than once” (Pareto 1896, p. 40; our translation). As a consequence, the definition of capital is now consistent with the presence of circulating capital in the economy. Saving-capital is just a form of circulating capital. 8 Failing this stock of goods, the remunerations of productive services would not find a corresponding volume of products to buy. Then, advances to production would be impossible. 9

quantities are simply added to the services directly employed in the production of final goods and are remunerated accordingly. In other words, the services required to produce raw materials are completely assimilated to the services employed in the direct production of final goods and, in fact, are considered to be advanced for just one period of production as the latter. This procedure seems at odds with the premise that production takes time, which implies that the services required to produce raw materials are used in a production period preceding that in which the services directly employed in producing final goods are applied. As we shall now see, a more consistent treatment can be found in Barone’s reply to Wicksell.

3.2 Barone’s articles of 1895 and 1896

Wicksell’s criticisms spurred the reflection of Enrico Barone, who responded with an article published in 1895. Some relevant aspects of his reply, as we shall see, are spelled out in a subsequent article (Barone 1896). As regards Wicksell’s first criticism, Barone contends that in Walras’s theory it is not tacitly assumed that workers support themselves with their own resources during the course of the productive process. In his opinion,

“Walras clearly states that the entrepreneur needs not only the services of land, labour and (durable) capital, but also the use of a certain quantity of numeraire [in order] to advance the wages, to buy the necessary raw materials…etc.” (Barone 1895, p. 535; our translation). Among the production costs that the entrepreneur must bear is therefore included

“the price for the use of [that] quantity of numeraire, [which in turn] represents the interest that Wicksell believed was left out of Walras’s theory” (1895, p. 535; our translation). However, Barone does not explain to which passages of the Éléments he is referring. As we shall presently see, his very intention is to show how Walras's analysis can be developed so as to take Wicksell's first criticism into account.9 To clarify this point let us examine, in the essential lines, how Barone determines the amount of numeraire that is needed for the production of a generic consumption good. Since Barone does not dwell on this aspect in the reply of 1895,

9 According to Jaffé (1965, p. 650), in the two passages quoted in the text Barone is “interpreting [Léon Walras’s] theory generously, completing and correcting it in detail”. 10

we shall refer to the illustrative example presented in his subsequent article (1896, pp. 134-136), which can be conveniently summarised as follows. Barone assumes that all the stages of the direct and indirect production of the generic consumer good are carried out within a single factory by employing only labour and circulating capital goods. More precisely, he assumes that the factory is composed of four sections and, moreover, that the production of both the consumption good and its direct and indirect means of production takes place under the following conditions. In the first section, L1 workers produce good (A) ; in the second, L2 workers transform (A) into good (B) ; in the third, L3 workers transform (B) into good (C), and, finally, in the fourth section, L4 workers transform (C) into the consumption good (D). It is assumed that the production processes of the four sections are carried out side by side and synchronised in such a way as to ensure both the steady replacement of the circulating capital goods used up and the emergence of a batch of the final consumption good (D) at the end of each week. Under the above-mentioned assumptions, Barone focuses on the initial four weeks during which the different sections of the factory are activated in succession in order to obtain the first batch of final product. He points out that the total quantity of numeraire required in that initial phase in order to advance the wages to the workers progressively employed does not amount to Z = 4s(L1+L2+L3+L4), where s denotes the weekly wage rate, but only to a fraction of Z. Considering that in the first week only the L1 workers of the first section are employed, that in the second week only the (L1+L2) workers of the first and second sections are employed, and so on, Barone (1896, p. 136) concludes that the fund of numeraire required in order to advance the wages in the initial phase under examination is N = s(4L1+3L2+2L3+L4) = (1/ε)Z. Then he remarks that, once the initial phase has been completed, the fund of numeraire N originally used for advancing the wages must remain permanently invested in the factory, as it corresponds to the value of the aggregate of circulating capital goods that is constantly required in order to regularly continue production (1896, p. 119). The foregoing example elicits two considerations. To begin with, we have seen that Barone, in order to counter Wicksell’s first criticism, introduces the assumption that all the stages of the direct and indirect production of consumption goods are carried out simultaneously and coordinated so as to yield a continuous flow of those 11

goods. This assumption takes into account the fact that production is time- consuming, allows for consistent analytical treatment of raw materials and other intermediate products and, finally, it explains how workers can regularly receive the necessary means of subsistence during the course of the social production process. As remarked in Section 2 and shown by the example just examined, however, the assumption of “continuous production” presupposes that a stock of intermediate goods should be constantly present in the economy. It can therefore be concluded that Barone, in his attempt to defend Walras from Wicksell’s first criticism, is in fact admitting that Walras’s theory needs to be completed through the introduction of circulating capital. This may explain why, in his reply to Wicksell, Barone (1895, p. 534) acknowledges that the analysis put forward in the first editions of the Éléments cannot be regarded as “definitive”. The second consideration to be made is that Barone, in his attempt to complete Walras’s analysis, comes very close to Böhm-Bawerk’s (and Wicksell’s) conception of capital. To substantiate this claim, let us return to Barone’s example. As has been seen, the fund of numeraire that, under Barone’s assumptions, must remain permanently invested in the factory amounts to

N = (1/ε)Z (1)

Recalling that Z = 4s (L1+L2+L3+L4), equation (1) can be written

N = (4/ε) Ls (2) where L = (L1+L2+L3+L4) is the total number of workers continuously employed in the production of both the consumption good and its direct and indirect means of production. Now, it is readily ascertained that the coefficient (4/ε) in equation (2) coincides with Böhm-Bawerk’s average period of production calculated for the example under discussion.10 Taking this fact into account, equation (2) reveals that

10 Note first of all that equation (2) implies

4/ε = N/Ls = (4L1+3L2+2L3+L4)/(L1+L2+L3+L4) (2’) Then redefine the quantities of labour in the right-hand side of (2’) so that, for each quantity, the deponent indicates the number of weeks that must elapse between the moment in which the quantity of labour is remunerated and the moment in which the corresponding final product is ready for sale.

This can be done by denoting the quantities of labour by L1 , L2 , L3 and L4 , where L1 = L4,

L2 = L3, L3 = L2, L4 = L1 . Under this modified notation, equation (2’) can be written

4/ε = ( L1 + 2 L2 + 3 L3 + 4 L4 )/ ( L1 + L2 + L3 + L4 ) 12

the fund of circulating capital that the entrepreneur must keep permanently invested in the factory is equal, under Barone’s assumptions, to the total amount of wages paid to the L workers continuously employed multiplied by the average period of production. We can finally come to Wicksell’s second criticism, i.e. that Walras’s theory does not allow for the determination of the prices of capital goods, and therefore of the interest rate, in the case of a stationary economy. In replying to this criticism, Barone (1895, p. 538) raises the very objection mentioned at the end of Section 2, i.e. that fixed capital goods are subject to wear and tear and are therefore normally replaced by newly produced goods:

“Durable capital goods are not imperishable and, if for no other reason than keeping them at the statu quo, a continuous production of them is required” (our translation).

3.3 A letter to Wicksell

In his review of Value, Capital and Rent Barone used a rather harsh tone towards Wicksell, to the point of qualifying him as one of those who “aim at catching the masters out over some trifle, in order, then, to demolish them”, thus contributing “to bring discredit on the science and its scholars” (Barone 1895, p. 539; our translation). In a private letter to Wicksell dated November 23rd 1895 and written in Italian, however, Barone took on a different attitude. In that letter, which is reproduced in full in the Appendix to this paper with a translation into English,11 Barone admits that he had “gone too far” in taking Walras’s side. He justifies the tone used in the review of Wicksell’s book with the desire of preserving the internal unity of mathematical economists, who were at the time a minority scarcely appreciated in academic circles:12

“we mathematical economists are so few, we are looked on with so much suspicion…that we have the absolute duty not to harm each other, in order not to prevent or delay the success of our method” (our translation).

where the term on the right-hand side is precisely Böhm-Bawerk’s average period of production. 11 Parts of the letter have been formerly reproduced, without translation, in Jaffé 1965, pp. 603, n. 3 and 662, n. 3. 12 On the widespread hostility to the use of mathematical methods in economics during the years between the end of the 19th century and the beginning of the 20th, cf. Schumpeter 1954, p. 957. 13

Moreover, in the letter Barone admits quite explicitly his closeness to Wicksell’s views as regards capital:

“I am pleased to tell you that I am presently engaged in some studies on the Theory of Distribution and having nearly completed the first of these studies… I had to convince myself that we absolutely agree on several points and arrive through slightly different routes to almost identical results. This is the case, for example, in all that relates to capital and the role that it plays in the advance of rent; and this is the case in all that relates to the wages-fund theory” (our translation). These assertions are followed by a passage in which Barone states his admiration and appreciation for Böhm-Bawerk’s treatment of capital and interest. He stresses, however, his resolve to follow Walrasian doctrine, which he aimed to “simplify, complete and develop”. The last assertion confirms that Barone did not regard Walras’s analysis as definitive, but thought it was susceptible of being completed and improved, as he intended to do as concerns circulating capital (following in this particular case, as we have seen, an approach analogous to Böhm-Bawerk’s one).

4. The persistence of Wicksell’s criticism in the years following Barone’s reply: an interpretation.

In the review of Pareto’s Cours, Wicksell (1897, p. 141) asserts that the theoretical considerations presented by the French-Swiss economist do not sufficiently improve upon “some of the less successful ideas of the classical Walrasian work”. Thus, as regards the theories of production and capital, he acknowledges that Pareto “emphasizes more strongly than [Walras] the capital aspect even of consumable commodities” (1897, pp. 144-5). At the same time, however, he criticizes the way in which, as we have seen, Pareto takes raw materials into account in his formulation of production cost. In this connection, Wicksell (1897, p. 145) correctly remarks that “it is impossible to enter [the services used for producing raw materials] on the accounts for the current year”, since those services “were applied not in the year in question but in a previous year”. In the same review, Wicksell (1897, p. 146) approvingly mentions the first part of Barone’s reply, which he correctly interprets as an attempt to improve on Walras’s theory: 14

“E. Barone has recently shown in a really brilliant manner how Walras’s theory of production may be completed, so that all theoretical blemishes are removed…This is accomplished simply by adding another relation to the ‘logical relations’ formulated by Walras for the quantities concerned; that is to say, by relating them to the length of the production period or the investment period, thus bringing to the foreground this exceedingly fruitful idea, which was…first exploited to the full by Böhm-Bawerk”. In that review, however, the objection raised by Barone against Wicksell’s second criticism – i.e. that fixed capital goods must be reproduced also in a stationary economy – is not even mentioned. An indication of how Wicksell considered Barone’s objection can be found in the second edition of the Lectures on Political Economy published in Swedish in 1911. Consider, in particular, the following passage:

“In the Walras-Pareto theory…capital and interest rank equally with land and rent; in other words, it remains a theory of production under essentially non- capitalistic conditions, even though the existence of durable, but apparently indestructible instruments, is taken into account” (Wicksell 1911, p. 176; our translation). This passage shows that Barone’s objection had no effect on Wicksell, who in the Lectures continues to regard the fixed capital goods appearing in Walras’s theory as indestructible means of production. On the other hand, Wicksell also asserts in that passage that, in Walras’s theory, capital is assimilated to land and interest to rent. This suggests that, in his opinion, the fixed capital goods of the Éléments are nothing but the rent-goods mentioned in Value, Capital and Rent, i.e. highly durable means of production that in a stationary economy are not produced at all but are simply maintained in the same good condition. Under this interpretation it is clear why Wicksell held the view that Walras’s equations, when applied to stationary economies, do not allow for the determination of the prices of capital goods on the basis of production costs. Moreover, it is clear why Wicksell dismissed Barone’s remark that the replacement of fixed capital must also take place in a stationary economy: according to Wicksell that remark, although correct in general terms, is not applicable to the particular “durable instruments” considered in the Éléments and can therefore be ignored. It may, however, be contended that a brief passage from Wicksell’s Lectures is not sufficient to support the above-mentioned interpretation. Two issues accordingly arise at this point in our discussion. To begin with, did Wicksell have 15

some reason for regarding the fixed capital goods of the Éléments as rent-goods? Secondly, can further evidence in favour of the suggested interpretation be found in Wicksell’s writings? We shall now argue that, in both cases, the answer is affirmative. As regards the first issue, let us examine the condition that the selling price P of a newly produced, fixed capital good must fulfil within Walras’s system of equations with capital formation. From the second edition of the Éléments Walras assumes that the annual amortization quota charged on the capital good is a given and constant fraction µ of P. Moreover, he assumes that an annual insurance premium νP will be charged on that good, where ν is itself a given and constant fraction. Under these assumptions, Walras states that in equilibrium the selling price P must comply with the following condition:

p P = (3) i    where p is the gross price for the yearly service of the capital good and i is the yearly rate of net income obtainable on all capital goods (i.e. the equilibrium rate of interest). Assuming ν= 0 for simplicity, equation (3) can be written

p  P  P = = i i (3’) where π = (p – µP) is the annual net income obtainable from the capital good. It should be noted that, in equation (3’), the selling price of the capital good is calculated as the present value of a perpetual flow of net incomes of constant amount π, where the flow is discounted at the current rate of interest i (cf. Jaffé 1942, p. 146). It can therefore be argued that, under Walras’s assumptions, the amortization of the generic fixed capital good takes in fact the form of a steady annual “maintenance” through which the capital good can be made to last forever with constant efficiency (Garegnani 2008, p. 369, n. 9; cf. also Walker 1996, p. 165, Dvoskin and Lazzarini 2013, p. 127). This in turn provides a basis for assimilating the durable capital goods of the Éléments to rent-goods. Coming now to the second issue, textual evidence shows that throughout his life Wicksell continued to regard the fixed capital goods of the Éléments as rent- 16

goods. For example, in the review of Pareto’s Manuel d’economie politique, Wicksell (1913, p. 171) writes:

“[Pareto’s] theory of production, like that of Walras, deals solely with the concept of production without capital. The technical aids to production are regarded as inexhaustible funds, so that they could as well be described as some peculiar types of fertile soils”. A more explicit statement is put forward ten years later in the comment on Åkerman’s analysis of fixed capital:

“Walras essentially regards capital-goods as indestructible or as constituted in such a way that they can be kept intact with a given amount of maintenance… costs” (Wicksell 1923, p. 258).

5. Conclusions

In this paper we have examined some central aspects of the critique that Wicksell advanced against Walras’s treatment of capital and interest at the end of the nineteenth century. In particular, attention has been focused on the criticisms originated by the exclusion of circulating capital from the analysis in the first editions of the Éléments. We first looked at Wicksell’s criticism that the exclusion of circulating capital forces Walras to tacitly assume that workers and other producers support themselves with their own resources during the course of production. In this connection it has been argued that Wicksell’s remark points to an actual inadequacy of the description of the social production process in the first editions of the Éléments. We have also observed that, shortly after the publication of Value, Capital and Rent, the question of the maintenance of the workers raised by Wicksell was addressed by two distinguished followers of Walras. Thus we have pointed out that Pareto, in the first volume of the Cours, attempted to deal with that question by introducing a form of capital – the “saving-capital”, used for the advances to production – that was not present in Walras’s production equations. Moreover, we have noticed that Barone admitted that Walras’s theory needed to be completed through the introduction of circulating capital and came quite close to Böhm-Bawerk’s conception of capital in the attempt to show how that element could be taken into account. Our discussion 17

thus indicates that the appropriate treatment of the capitalistic element of production was an unsettled issue within the small circle of Walras’s followers at the end of the nineteenth century. Then we moved on to consider a second criticism advanced by Wicksell, i.e. that Walras’s theory cannot determine the prices of capital goods, and therefore the rate of interest, in the case of stationary economies. We have argued that this criticism ultimately relies on Wicksell’s view that the durable capital goods appearing in the Éléments can be assimilated to the “rent-goods” discussed in Value, Capital and Rent. Moreover, we have pointed out that Walras’s peculiar assumption concerning the amortization of fixed capital goods provides a justification for that view. After the publication of Value, Capital and Rent, Wicksell maintained a critical stance regarding Walras’s theory of capital for many years, although significant changes occurred in those years in the analytical framework of the Éléments (for example, the inclusion of circulating capital goods in the fourth edition). Then, in the last part of his life, Wicksell apparently changed his attitude (cf., for example, Stigler 1948, p. 253; Uhr 1962, pp. 106-107). The evolution of Wicksell’s views about Walras’s capital theory was therefore quite complex. The present paper, which is exclusively focused on Wicksell’s initial position, should be seen as just a first step towards a thorough reconstruction of that evolution.

References

Barone, Enrico. 1895. “Sopra un libro del Wicksell”, Giornale degli Economisti 5 (11): 524- 539. Barone, Enrico. 1896. “Studi sulla distribuzione”, Giornale degli Economisti 6 (12): 107- 155 and 235-252. Diemer, Arnaud, and Jean-Pierre Potier, eds. 2013. Léon Walras: un siècle après (1910- 2010), Bruxelles: P.I.E. Peter Lang.

Dvoskin, Ariel and Andrés Lazzarini. 2013. “On Walras’s Concept of Equilibrium”, Review of Political Economy, 25 (1): 117-138. Garegnani, Pierangelo. 2008. “On Walras’s Theory of Capital (Provisional draft 1962)”, Journal of the History of Economic Thought, 30 (3): 367-384. 18

Jaffé, William. 1942. “Léon Walras Theory of Capital Accumulation”, reprinted in Donald A. Walker, ed., William Jaffé’s Essays on Walras. Cambridge: Cambridge University Press, 1983, pp. 139-150. Jaffé, William, ed. 1965. Correspondence of Léon Walras and Related Papers, vol. II. Amsterdam: North Holland. Jaffé, William. 1980. “Walras’s Economics as Others See It”, reprinted in Donald A. Walker, ed., William Jaffé’s Essays on Walras. Cambridge: Cambridge University Press, 1983, pp. 343-370. Pareto, Vilfredo. 1896. Cours d’Économie Politique, vol. I. Lausanne: Rouge. Schumpeter, Joseph. A. 1954. History of Economic Analysis. Oxford: Oxford University Press. Stigler, George J. 1948. Production and Distribution Theories. New York: The Macmillan Company. Uhr, Carl G. 1962. Economic Doctrines of Knut Wicksell. Berkeley and Los Angeles: University of California Press. Van Daal, Jan, and Albert Jolink. 1993. The Equilibrium Economics of Léon Walras. London: Routledge. Walker, Donald A. 1996. Walras’s Market Models. Cambridge: Cambridge University Press. Walras, Léon. 1889. Éléments d’Économie Politique Pure ou Théorie de la Richesse Sociale. Lausanne: F. Rouge. Walras, Léon. 1954. Elements of Pure Economics or the Theory of Social Wealth. Translated and edited by William Jaffé. London: George Allen & Unwin. Walras, Léon. 1988. Éléments d’Économie Politique Pure. In Pierre Dockès, Pierre-Henri Goutte, Claude Hébert, Claude Mouchot, Jean-Pierre Potier and Jean-Michel Servet, eds., Auguste et Léon Walras. Œuvres Economiques Complètes, vol. VIII. Paris: Economica. Wicksell, Knut. 1892. “Kapitalzins und Arbeitslohn”. Jahrbücher für Nationalökonomie und Statistik 59: 852-874. Wicksell, Knut. 1893. Über Wert, Kapital und Rente nach den neuren nationalökonomie Theorien. Jena: G. Fisher. Translated as Value, Capital and Rent, London: George Allen & Unwin, 1954. Wicksell, Knut. 1897. “V. Pareto, Cours d’Économie Politique”, 1st part. Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, 6: 159-166. Translated as “Vilfredo Pareto’s Cours d’Économie Politique”, in Knut Wicksell, Selected Papers on Economic Theory, edited by Erik Lindhal, Cambridge (Mass.): Harvard University Press, 1958, pp. 141-58. Wicksell, Knut. 1911. Föreläsningar i nationalekonomi, Häft I. Lund: Berlingska Boktryckeriet. Wicksell, Knut. 1913. “V. Pareto, Manuel d’Économie Politique”. Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, 22: 132-151. Translated as “Vilfredo Pareto’s Manuel d’Économie Politique”, in Knut Wicksell, Selected Papers on Economic Theory, edited by Erik Lindhal, Cambridge (Mass.): Harvard University Press, 1958, pp. 159-75. 19

Wicksell, Knut. 1923. “Realkapital och kapitalränta”, Ekonomisk Tidskrift, 25: 145-180. Translated as ‘Real Capital and Interest’, in K. Wicksell, Lectures on Political Economy, Vol. I: General Theory, edited by Lionel Robbins, London: Routledge, 1934, pp. 258-99.

Appendix: Barone’s letter to Wicksell of 23rd November 1895

I. The original text in Italian

Roma, 23 Novembre 1895 Egregio Signore, La ringrazio del lavoro sull’incidenza della imposta, che Ella ha voluto compiacersi di spedirmi: l’ho già quasi tutto letto, ed in massima siamo d’accordo nelle conclusioni. A mia volta Le ho spedito un mio scritto sul “Trattamento di quistioni dinamiche” già comparso nel Giornale degli Economisti: in esso vedrà che già avevo fatto un tentativo di soluzione generale del problema dell’incidenza: o meglio, avevo accennato a questo tentativo, giacché in quello studio, il quale, come Ella vedrà, ha uno scopo più largo, la quistione dell’incidenza dell’imposta era trattata a titolo di semplice esempio. Le dirò, con compiacimento, che trovandomi ora a svolgere alcuni studi sulla Teoria della Distribuzione, ed avendo già quasi compiuto il primo di questi studi, che nel fascicolo di Gennaio del Giornale degli Economisti sarà pubblicato, ho dovuto convincermi che in parecchi punti noi siamo assolutamente d’accordo e giungiamo per via un po’ diversa a risultati quasi identici. Così per esempio in tutto ciò che si riferisce al capitale ed alla parte che esso ha nella anticipazione della rendita; così in tutto ciò che si riferisce alla teoria del fondo-salari. Soltanto io non seguo il Böhm-Bawerk, del quale ammiro ed apprezzo la teoria del capitale e dell’interesse beneinteso. Io seguo piuttosto il Walras, la cui mirabile dottrina miro a semplificare, completare e sviluppare, per mezzo della teoria della produttività marginale. Ciò che del resto Ella tra poco vedrà. Ed a proposito del Walras appunto, mi è caro di significarle che come Ella è dolente di avere un po’ ecceduto forse nella critica del suo sistema – il quale, come Ella ha visto nel mio scritto, permette benissimo di tener conto anche del fondo di anticipazioni – così sono dolente, da parte mia, che la difesa del mio maestro mi abbia fatto un po’ eccedere. Questo Le dichiaro senza esitazioni, perché noblesse oblige. Veda, caro Signore. Noi economisti matematici siamo così pochi, siamo guardati con tanta diffidenza da questa folla d’ignoranti presuntuosi i quali usurpano il nome di economisti, che abbiamo il dovere assoluto di non danneggiarci a vicenda, per non impedire o ritardare la vittoria del nostro metodo – che è l’unico possibile in quistioni quantitative. Io sinceramente e profondamente deploro le controversie eccessive fra il mio maestro ed il Prof. Marshall ed il Prof. Edgeworth, tanto che, come Ella avrà visto, l’opera scientifica mia è stata in parte rivolta fino ad ora a mettere pace fra di essi. Io vorrei che coteste controversie eccessive cessassero, pur senza rinunciare, ciascuno di noi economisti matematici, a quella completa libertà di giudizio nel giudicare l’opera altrui, senza la quale non vi è possibilità di vero progresso scientifico. Noi economisti matematici dobbiamo aiutarci a vicenda pel progresso della scienza e pel trionfo del nostro metodo: ed essere concordi sopra tutto in questo: nel far vedere come la mancanza di conoscenze matematiche abbia condotto codesti sedicenti economisti ai più grossolani errori. Se voi desiderate di essere conosciuto in Italia, lasciate a me la cura, certo che per la Germania farete altrettanto per me. Se desiderate di pubblicare qualche cosa sul Giornale degli Economisti, io che sono intimo amico del Prof. Pantaleoni, sono a vostra disposizione. Scrivete in francese ed io mi prenderò la cura di tradurre il vostro scritto, come affiderò a voi 20

l’incarico di tradurre in tedesco se mi accadrà di dover pubblicare qualche cosa in giornali o riviste tedesche. E poiché siamo a discorrere, io desidererei di conoscere qualche cosa di voi, come ora io vi comunico qualche cosa di me. Neppure io sono professore. Io ho 35 anni e son Maggiore di Stato Maggiore (Major in dem Generalstabe) nell’Esercito. Otterrò quanto prima il diploma di Privat-Docent: ma non insegnerò pubblicamente, perché la mia qualità di ufficiale me lo vieta. Benché affezionatissimo alla carriera delle armi, tuttavia la mia passione per gli studi d’economia, siano matematici o non matematici, è così forte, che io forse mi deciderò a lasciare l’Esercito, se, come mi han fatto sperare, otterrò fuori d’Italia una cattedra d’economia. Qui in Italia molti giovani mi seguirebbero nel metodo matematico se io avessi tempo e modo di dar pubbliche lezioni. Dei professori già di grido non v’è che il Pantaleoni, il quale sia un cultore intelligente dell’Economia matematica. Anche il Prof. Bodio, direttore generale della nostra Statistica, si interessa dell’Economia matematica e mi è stato sempre largo di incoraggiamento e di aiuto. Che età avete? Che fate? Quali sono le vostre aspirazioni? Vostro Maggiore Enrico Barone via Salaria 36 – Roma ______

P. S. Vi prego di indicarmi se nei „Jahrbücher ...„ il Conrad pubblica scritti d’economia matematica; e se pure ne pubblica il Böhm-Bawerk nella stessa Rivista. Sareste disposto, qualora ciò fosse, di scrivere di me a cotesti signori, come io son disposto a farlo per voi presso le molte conoscenza che ho?

II. English translation

Rome, 23rd November 1895 Dear Sir, Thank you for the work on tax incidence that you kindly sent me: I have already read it almost entirely, and in general we share the same conclusions. In turn, I have sent you a paper of mine concerning the ‘Treatment of dynamic issues’, which has already appeared in the Giornale degli Economisti. In this you will see that I had already made an attempt to put forward a general answer to the incidence question: to be more precise, I had touched upon this attempt in this work, which, as you will notice, has a broader aim and the issue of tax incidence was dealt with as a mere example. I am pleased to tell you that I am presently engaged in some studies on the Theory of Distribution and having nearly completed the first of these studies, which will be published in the January issue of the Giornale degli Economisti, I had to convince myself that we absolutely agree on several points and arrive through slightly different routes to almost identical results. This is the case, for example, in all that relates to capital and the role that it plays in the advance of rent; and this is the case in all that relates to the wages-fund theory. Only I do not follow Böhm-Bawerk, whose theory of capital and interest I admire and appreciate, of course. I rather follow Walras, whose admirable doctrine I aim to simplify, complete and develop through the theory of marginal productivity. All of this, on the other hand, you will see soon. And while speaking of Walras, I wish to say that, just as you regret for having perhaps gone a little too far in the criticism of his system – which, as you saw in my paper, perfectly allows taking also the advance fund into account – so I am sorry for having gone a little too far in defense of my master. This I declare without hesitation, because noblesse oblige. 21

You see, dear Sir, we mathematical economists are so few, we are looked on with so much suspicion by this crowd of ignorant and conceited people who usurp the name of economists, that we have the absolute duty not to harm each other, in order not to prevent or delay the success of our method – which is the only possible method in quantitative questions. I truly and deeply deplore the excessive disputes between my master and Professor Marshall and Professor Edgeworth, so much so that, as you will have seen, my scientific work has been partly addressed so far to make peace among them. I hope that these excessive controversies cease, at the same time without giving up, for each of us as mathematical economists, that complete freedom of judgment in evaluating other people’s work, without which there can be no real scientific progress. We mathematical economists must help one other for the progress of science and for the victory of our method, and must agree above all on this: on showing how the lack of mathematical knowledge has led those self-proclaimed economists to the grossest mistakes. If you wish to be known in Italy, leave this matter to me. I am sure that you will do the same for me in Germany. As a close friend of Professor Pantaleoni, I am at your disposal in case you wish to publish something in the Giornale degli Economisti. Write in French and I will take care of translating your paper, just as I will entrust you with the task of translating into German should I have something to be published in German journals or reviews. And since we are talking, I would like to know something about you, as I am going to tell you something about myself. Indeed, I am not a professor. I am 35 years old and I am a Major of the General Staff (Major in dem Generalstabe) in the Army. As soon as possible I will obtain the Privat- Docent diploma, but I will not teach publicly, since my position as an officer forbids that. Though I am very fond of the military career, my passion for economic studies, be they mathematical or not, is so strong that I will perhaps take the decision to leave the Army, if, as I was led to believe, I obtain a Chair of Economics outside Italy. Here in Italy many young people would follow me in embracing the mathematical method, if I had the time and the opportunity to teach publicly. Among already renowned professors, there is no intelligent scholar of Mathematical Economics besides Pantaleoni. Also Professor Bodio, general director of our Statistical Office, is interested in Mathematical Economics and was always of great encouragement and help to me. How old are you? What do you do? What are your ambitions?

Yours Maggiore Enrico Barone via Salaria 36 – Roma ______

P.S. Please tell me if Conrad publishes papers in mathematical economics in the ‘Jahrbücher ...’; and if Böhm-Bawerk too publishes in the same Review. Should that be the case, would you be willing to write to those gentlemen about me, as I am willing to do the same for you with the several acquaintances that I have?