The Giornale degli Economisti

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Pareto’s Major Scientific Contributions to the Giornale degli Economisti’

Pareto’s first entry in the Giornale degli Economisti, ‘L’insegnamento dell’economia politica’ (Pareto 1890 [1982]), was motivated by public policy issues and presented economic science as way of revealing the naked self interest of protectionism. The article commences:

Our protectionists have already done great and beautiful things. They have ruined Italy’s commercial exports; created artificial industries, such as the steel mills of Terni, that cannot survive without the largest government subsidies; they have raised the cost of living through custom duties on cereals, and helped increase the State’s spending out of all proportion to the economic power of the nation. Now they triumph. They enjoy their return, harm to everyone, and want to recreate in themselves a spirit of little ideal. They are disturbed by economic science, which does not want to justify that which gives them joy and pleasure: they are required to hear, and hear repeated, that protection is nothing if not the art of legally appropriating other people’s goods.

(Pareto 1890 [1982], p. 1)

The sarcasm of the above article became a feature of many of Pareto’s polemic writings. The article also served the purpose of putting a policy position which fully reflected the views of the editorial directors of the Giornale degli Economisti. In contrast, his final contribution to the Journal, the 1918 “Economia sperimentale” (Pareto 1918 [1980]), completely replaced normative concerns with discussion of the scientific basis of economic doctrines.

In this brief article I propose to investigate if, and to what extent, the doctrines of political economy, in the way they are usually expounded, are logico-experimental. I could just say logical, because, as far as I am concerned, logic is an experimental science like all other sciences. However, so as not to start with a dispute, which is, after all, unhelpful to the aim I have in mind, I will treat logic and experience as distinct.

(Pareto 1890 [1980], p. 719)

This last article finds that economics, ‘in the way that it is usually expounded’, is sadly wanting from a scientific perspective and then goes on to clarify how scientific economics is developed from the logico-experimental methodology. In the period between 1890 and 1918, Pareto contributions to the Giornale degli Economisti comprise 53 entries entitled ‘Cronaca’ and a further 39 articles. Most of his articles were concerned with scientific matters, although, as evident from the above quote from his first article, the early articles in the first few years had a foot in each camp: they considered economic science while also advocating non-interventionist public policy. By 1892, however, Pareto’s articles had become almost exclusively scientific. While the treatment of some economic issues in a scientific manner did have obvious policy implications, and these were generally consistent with the liberal philosophy espoused by the Journal, scientific demonstrations came to dominate considerations.

In the previous chapter, Pareto’s continuation to core scientific thought was considered in three sequential phases: an initial phase, an intermediate phase and the final phase. The following consideration of Pareto’s scientific contribution to the Giornale degli Economisti adopts the same approach.

The Initial Phase – 1890-1899

In this study, the initial phase of Pareto’s scientific work is characterised by placing Walras analysis of general equilibrium theory in the context of successive approximation. That is, pure theory concerns the primary phenomena of economic equilibrium, with applied economics considering: 1) uniformities in the real economic phenomenon from ‘disturbances’ not considered by pure theory; 2) study of virtual movements utilizing analysis developed in pure theory; and 3) identification of general empirical uniformities associated with the economic phenomenon.

During this initial phase, Pareto’s was in his most active period of collaboration with the Giornale degli Economisti on scientific matters. While the full methodological framework associated with successive approximations was developed in the Cours, ideas on the importance of founding economics on a positive basis and formative economic analysis which, in some cases, anticipated and, in other cases, influenced the Cours were first considered in the Giornale degli Economisti.

Pareto’s articles in the Journal between 1890 and 1891 can be largely set aside because they were more influenced by liberal political culture than scientific thought: ‘L’insegnamento dell’economia politica’ (Pareto 1890 [1982]) was a defence of liberalism in public policy; ‘Le industrie meccaniche e la protezione (Pareto 1891a [1975]) considered the impact of protectionism on industry; and ‘Lettera d’un Vignaiuolo’ (1891b [1975]), a letter written under the pseudonym Nando detto Marzocco, queried the contradictions of protection. These were all republished in volume 17 of Pareto’s complete works which collects his Political Writings. ‘Lasciate fare, lasciate passare’ (Pareto 1891c [1975]) was also republished in the same volume. It was essentially a review article of Gustave de Molinari’s Notions Fondamentales d’Economie Politique et Programme Èconomique (1891). While the economic program considered is discussed in terms of the liberal laizzez-faire tradition, thereby justifying its inclusion in the Political Writings volume of his complete works, it also dealt with the methodology of scientific thought. Pareto revealed considerable appreciation for de Molinari’s integration of evolution with economics and his general scheme of abstraction, suggesting that the treatment of economic actions by hedonistic homo œconomicus is very similar to the arrangement in mechanics. This was to prove influential in the emergence of the Cours, in which the mechanical analogy played a major role and applied economics is condition by the general state of social evolution and the prevailing ‘social physiology’ of society. Other themes reviewed in this article also reappear in a reworked form in Pareto’s Cours, such as the discussion of the economics of the production of man and the comments on positive, zero and negative rents from land use has similarities to the theory of rent that emerged in the Cours (although, in a much more general form, with rents extending to capital and economic factors).

Pareto’s most significant scientific contributions to the Giornale degli Economisti during the initial phase of his scientific economic thought commenced in 1892, with a remarkable sequence of papers on mathematical economics published in the Journal over the subsequent five years. The main theoretical contributions concerns equilibrium and value theory, although, given his economic motivation was driven by his support for liberal policy positions, it is not surprising that scientific analysis of international trade and protectionism also featured.

Pareto’s first essenrially scientific article was a reflection on mathematical economics: ‘Di un errore del Cournot nel trattare l’economia politica colla matematica’ (Pareto 1892a [1982]). He provided a critique of Cournot’s mathematical trade model in which free trade between two countries reduces the real income of the importing nation by the same value as the increase in real income of the exporting nation. In this paper, Pareto urged care in the application of mathematical economics, with the ‘error’ that Pareto successfully revealed being an error of interpretation: Cournot had demonstrated one thing and interpreted his results as demonstrating something else. In this regard, Pareto confirmed Cournot’s analysis can be maintained in aggregate across two trading countries, with the real income gain of the exporting country matching the real income loss of the importing country, but he rejected Cournot’s interpretation because it ignores the economic consequences that derive from the reduction in labour time (or resource costs generally) in the importing country that results from a move to free trade. Economic use of these freed resources will increase aggregate real income across the two countries.

This trade and protectionist theme was taken up again in ‘La teoria dei prezzi dei signori Auspitz e Lieben e le osservazioni del professore Walras’ (Pareto 1892b [1982]) and ‘Ancora della “Theorie des Preises” dei signori Auspitz e Lieben’ (Pareto 1892c [1982]), although this time Walras’ ideas were introduced. The analysis by Rudolf Auspitz and Richard Liebman (1889) utilized demand curves similar to Marshallian offer curves to argue in favour of protection (Chipman 1976 [1999], p.174). Pareto criticised this, using the Walrasian notion of interdependence in which variations in prices are considered with respect to all prices, including prices for the services of production. The analysis of Auspitz e Lieben was partial, with the numeraire for money assumed to have a constant marginal utility. While revealing limitations of the analysis by Auspitz and Lieben and showing that protection can be harmful, Pareto did not demonstrate that tariffs are necessarily harmful to the nations that impose them (Chipman 1976 [1999], p.175).

Perhaps the first sign that Pareto was a really exceptional talent in economics came with ‘Considerazioni sui principii fondamentale dell’economia politica pura’ (Pareto 1892-93 [1982]). This article was published in 5 parts between May 1892 and October 1893 and is important to the development of Paretian thought for a number of reasons. In terms of methodology, it gives a clear outline of the scope of pure economics and its relationship to the observed phenomenon, including rejection of the metaphysical concept of absolute perfection (a theme subsequently expounded upon with great effect in the Trattato). In terms of mathematics in economic theory, it makes clear that the objective of value theory is to explain and connect observable facts pertaining to prices, with the hedonistic basis of economic theory presented in that context. The main application of mathematics in this article concerned additive utility and the theory of value. The fundamental characteristic of pure economics is presented as the general proposition that the final degree of utility for goods, including instrumental goods, varies with the prices of consumable commodities and with other market conditions. In setting complementary and substitute (or what Pareto called fungible) goods temporarily aside, Pareto undertook analysis of exchange on the presumption that: the final degree of utility of a good is a function of the quantity of that good only; and that Daniel Bernouilli’s theorem, concerning diminishing final degree of utility, holds.

Pareto’s analysis focused on the final degree of utility rather than total utility. He was of the view that people have a clear perception of variations in utility from some existing social state, but did not accept that people had a clear conception of total utility at the prevailing, or even an alternative, social state. As a result, he questioned whether total utility existed, settling for the view that in pure economic analysis, it is acceptable to assume that utility exists when the final degree of utility of a good is independent of other goods. Over his career, Pareto continued to make statements conditioned by the comment ‘if’ utility (or ophelimity from 1896 onwards) exists.

Inspired by Walrasian interdependence, Pareto’s ‘Considerazioni’ demonstrated the shortcomings of analysis that presumes the final degree of utility for money is held constant and, more importantly, demonstrated that the presumption was unnecessary. From his analysis of additive utility, Pareto derived a general downward sloping demand curve by undertaking comparative static analysis, involving the use of Hessian determinants, to find the solution to a general equilibrium system with diminishing final degree of utility in which the initial equations specify that: the relative prices of goods reflects their relative final degrees of utility; and markets fully clear for the given supply of consumer goods. Pareto also undertook extensive investigations of the potential form that functions for the final degree of utility could take if they were to conform with the findings of experience and observation. He utilised a range of functions of variables, and functions of logarithmic variables, some of which reveal characteristics of the Cobb-Douglas utility function (Weber 1998).

‘Considerazioni’ also laid the foundation for much of Pareto’s future work on pure economics. Being an early systematic work on the fundamentals of his approach to pure theory, it points to the issues that attracted most of his attention. If one single characteristic of this work stands out, it is the emphasis on the necessity for mathematical representation of pure theory to fundamentally conform with reality, as attested to by the long investigations of functional forms of marginal utility equations and the discussion of how these relate to theory and reality. It was his concern with these type of issue that lead Pareto to revisit economic equilibrium theory in the intermediate phase of his work, culminating in the development of choice theory.

Over the next four or five years, the ‘Considerazioni’ was followed by a succession of scientific articles that dealt mainly with what Pareto considered applied economics. His first scientific discussion of this character concerned population economics in ‘La mortalità infantile e il costo dell’uomo adulto’ (Pareto 1893 [1982]). This study considered the extent of economic advantage that a nation derives from a low infant mortality rate. It may be classified as concerning uniformities in the real economic phenomenon from disturbances which are outside the scope of pure economics. The basic goal of the article was to estimate the cost of producing a man while considering diverse infant mortality rates. To achieve this, Pareto utilised Samuel Engel’s work on population and the cost of raising children and introduced a general density function to represent the population distribution of surviving children between zero and twenty years of age. The primary finding is that the economic advantage enjoyed by nations with a low infant mortality rate is less than what is often assumed because of the costs of caring for non surviving infants. In this regard, nations with a low infant mortality rate may have a higher mortality rate for older children between fifteen and twenty years of age, for whom costs would accumulate over a longer period of time.

This general issue was to be dealt with again in the Cours, in the applied economics section dealing with ‘personal capital’ (Pareto 1896-97 [1987], pp. 305-319). It also laid the foundation for the broad treatment of demographic issues in the Cours, including the critical assessment of Malthusian views on population and investigation of the relationship between population growth and economic prosperity. The article is also relevant because it introduced a child population distribution function that was similar to the income distribution function which was given some prominent treatment in the Cours9

By 1894, Pareto’s contributions to economics had matured considerably, with attention returned to the formalization of general equilibrium theory of international trade and a profound contribution to welfare economics. Again, in this year his work primarily concerned applied economics, but of the analytical type where virtual movement is investigated in a manner that utilizes mathematical methods of analysis develop in pure theory.

The general equilibrium theory of international trade was developed in ‘Teoria matematica dei cambi forestieri’ (Pareto 1894a [1982]). It commences with an exposition of Walrasian theories of exchange and production, in which the provision of productive services is modelled on the presumption that coefficients of production are fixed. Pareto modifies Walras’ system to accommodate two markets (countries) for consumer goods. Quantities of consumer consumption sourced from domestic production and from imports are determined in equilibrium given the new exogenously given international prices, subject to the constraint that the value of exports equals the value of imports in each market.

The next article published was the seminal ‘Il massimo di utilità dato dalla libera concorenza’ (Pareto 1894b [1982]). The Walrasian system of production again provides the starting point, but the theory of exchange is largely set aside. The resulting analysis represents the definitive nineteenth century study of production efficiency. It is also significant for introducing variable coefficients of production to economics for the first time, which facilited his demonstration of the theorem that a point of equilibrium under free competition must yield an economic maximum when the cost of productive services is minimized by the competitive process. If society moves from an initial state that is not a point of free equilibrium to a subsequent state that is a point of free equilibrium, an economic residual (surplus) is generated from the more efficient use of productive services.

Importantly, Pareto also makes the point in this article that social welfare is increased when the coefficients of production are altered in a manner that increases the product returned to each individual member of society but harms no one. Consequently, this article posited both the basic Pareto principle and the first theorem in welfare economics (an economic maximum in terms of the Pareto principle is given by a point of equilibrium under free competition). The article is also suggestive of the second law of welfare economics (any point of economic maximum can be realized under conditions of free exchange), through its discussion of the socialist economies and the role of the Ministry of Production in setting coefficients of production. As Chipman (1976 [1999], p178) has perceptively pointed out, the ‘compensation principle’ is introduced in this article when Pareto discusses variation in the coefficients of production in socialist economies. In this regard, he indicated that the coefficients of production could be altered even when someone is harmed provided that a quantity of the numeraire good is taken away from those who have experienced a gain and used to ‘compensate’ those who have experienced a loss. This would yield an equilibrium that could be achieved under free competition with the appropriate initial resource endowment.

This analysis of welfare generally, and welfare in socialist countries in particular, is further developed in the Cours (Pareto 1896-97 [1987], pp. 722-34). However, the weakness of the article is also preserved in the Cours, with analysis focusing on production (albeit with variable coefficients of production) while largely ignoring the issue of exchange, which is necessary for a general specification of the fundamental theorems of welfare economics.

In 1895, Pareto contributed 3 scientific articles to the Giornale degli Economisti on applied economics: ‘La legge della domanda’ (1895a [1982]), ‘Teoria matematica del commercio internazionale’ (Pareto 1895b [1982]) and ‘Per la verità’ (Pareto 1895c [1982]).

‘La legge della domanda’ (Pareto 1895a [1982]) considers the impact of income on demand. Pareto employed ‘a simple empirical law’ on the distribution of income that he says will be presented in some detail in the Cours. The proposed distribution is:

While similar to the simplified version of the Pareto distribution that appeared in the Cours, it is not the same: y is the ordinate for number of taxpayers with a particular income x, not the sum of the number of people with an income of x or above. Consequently the h parameter has an average value of 2.5, higher than the 1.5 average for α. Nevertheless, as an indicator of inequality of income distribution, Pareto used h in the same way as α. That is, he considered a reduction in the inequality of income as being represented by a reduction in h. He then considered the demand for a product, in this case wheat, as a function of its price and income to estimate the parameters necessary to reproduce the relationship between the price of wheat and the wheat harvest that Gregory King had estimated in the seventeenth century. While finding tentative support for this law, the important point for the development of Pareto’s work was the recognition that an individual’s demand was influenced by their income, and that market demand was constrained by broad contextual factors that influence the degree of inequality in the distribution of income.

The quantity h depends on all the quantities which qualify the economic state, so when the quantity of economic goods demanded varies, so does h. However, using a procedure that is well known in mathematics, we can start by assuming that h is constant, and then take its change into account.

(Pareto 1895a [1982], p. 300)

As such, ‘La legge della domanda’ provides insight into the relationship between Pareto’s interest in the relationship between general empirical uniformities associated with the economic phenomenon and pure economic theory. Specifically, he regarded inequality of income distribution as a parameter to be estimated when considering demand, although as income inequality was relatively stable (with changes only occurring over long periods) it could be considered as a constant rather that a variable influence, at least over the medium term. While the Pareto distribution itself did not appear in this article or elsewhere in the Giornale degli Economisti prior to appearing in the Cours, Pareto’s explorations into child population distributions, income distribution and demand in the Journal played a formative role in the development of Pareto’s law.

In his ‘Theory of International Values’, Edgeworth (1894, p. 442) indicated that he was unaware of any additional conclusions when trade theory was taken beyond a 2 good model. In the footnote to this comment, Edgeworth was critical of ‘Teoria matematica dei cambi forestieri’ (Pareto 1894a [1982]) because the net advantages to counties from trade need to be considered with respect to ‘total utility’ and not by the final degree of utility. In response, Pareto wrote ‘Teoria matematica del commercio internazionale’ (Pareto 1895b [1982]) and attempted to extend his work in the previous year on welfare issues to the subject of international trade. His starting point, which became typical of his subsequent work on welfare theory, was an equilibrium state, but in this case the equilibrium provides for free international trade in consumer goods. He then considered the imposition of trade restriction, and calculated the additional cost that a country would incur to maintain the level of consumption that was prevailing under free exchange.10 Again, this discussion was influential in the subsequent but fuller treatment of international trade and welfare maximization in the Cours (Pareto 1896-97 [1987], pp 879-84). Later in the year Pareto wrote a brief note, ‘Per la verità’ (Pareto 1895c [1982]) in which he defended the use of Walras rarità and Jevon’s final degree of utility in economic theory, and point to its consistency with respect to Francesco Ferrara’s theory of the cost of reproduction.

Pareto’s contributions to the Giornale degli Economisti in 1896 and 1897 fell into two categories: (i) methodology; and (ii) the Pareto distribution.

In regard to the first issue, ‘Il modo di figurare i fenomeni economici’ (Pareto 1896a [1982]), ‘L’uomo delinquente di Cesare Lombroso’ (Pareto 1896b [1982]) and ‘Polemica col Prof. Lombroso’ (Pareto 1897b [1982]) all emphasise the experimental character of science, be it economics, criminology or the study of the relationship between economic phenomena and criminal activity.

In regard to the second issue, Pareto utilized the Journal to respond to Edgeworth’s (1896 [1999]) comments on the originality of the Pareto distribution, especially the suggestion that it has some similarities with Pearson’s probability distribution. While Edgeworth admitted that this similarity is more apparent than real, he nevertheless pointed to the lack of theoretical rationale for Pareto’s distribution. When this is taken together with statistical merit of Pearson’s equation and Pearson’s status in the scientific community, Edgeworth reveals a strong preference for adopting Pearson’s probability density function ahead of the Pareto distribution.

Pareto’s responses in the Giornale degli Economisti, ‘La curva delle entrate e le osservazioni del prof. Edgeworth’ (Pareto 1896c [1982]) and ‘Aggiunta allo studio sulla curva delle entrate’ (Pareto 1897a [1982]), were ill-tempered as he saw Edgeworth’s comments as a ‘thinly veiled accusation of plagiarism’ (Chipman 1976 [1999], p.210). Pareto also suggested that the rational basis for his distribution would follow, but went on to indicate that Otto Ammon’s theory of ‘social heterogeneity’ may provide the answer. In terms of the emergence of Paretian thought, the relevant point is that Pareto was, in the Cours, in the early stages of developing his theory of elites (aristocracies in the Cours). It is likely that the bitterness of his reaction to Edgeworth’s comments on his income distribution function, motivated Pareto to further develop his theory of elites during the next phase of his scientific work and present it, in part, as a rational and empirical explanation for his income distribution curve.

During this initial phase, Pareto’s contributions to pure theory are largely represented by the five part ‘Considerazioni’. These contributions informed the representation of pure theory in the Cours, but the discussion of the relationship between particular functions and the observable economy went beyond the Cours, and can be seen as motivating developments that Pareto made to pure economics in the Manuel during the subsequent phase in the development of Paretian thought. In regard to applied economics, the same pattern of contributions evident in the Cours is also evident in his articles in the Giornale degli Economisti. Uniformities related to the real economic phenomenon from ‘disturbance’ not considered in pure theory are examined, as in the case of demographics and population economics. Virtual movements utilizing mathematical methods of analysis developed in pure theory are consider, as in the case of trade theory and welfare theory. General empirical regularities associated with the economic phenomenon, in conjunction with their relevance for interpreting pure theory, are also considered, as in the case of preliminary studies of income distribution, and the defence of the Pareto distribution once it had been developed. In short, many of Pareto’s most original contribution to applied economics were developed and showcased in the Giornale degli Economisti prior to appearing in the Cours.

The Intermediate Phase – 1900-1911

In the intermediate phase, Pareto’s association with the Giornale degli Economisti diminished notably, largely to make time for his increasing efforts in sociology, such as his work on elite theory in ‘Un’applicazione di teoria sociologiche’ (Pareto 1900a [1980]) for the Rivista Italiana di Sociologia and, of course, to write the Systémes Socialistes. However, the work that he did contribute was primarily focused on pure theory, with formative contributions to choice theory first introduced to economics through the Giornale degli Economisti.

Choice theory was initially developed in a two part article, ‘Sunto di alcuni capitoli di un nuovo trattato di economia pura’ (Pareto 1900b [1982]). In this article, Pareto demonstrated that, for a system of indifference curves in which each curve is labelled by an index number, the shape of the indifference curves is unaltered when an arbitrary transformation function is used to change the index numbers. The system of index numbers applied to different consumption bundles could reflect the (cardinal) measure of pleasure as a quantity, but this would be just one of an infinite range of possible index number systems, none of which would alter the shape of indifference curves. When the transformation function is constrained by the requirement that the value of index numbers increases when passing from one indifference curve to another that corresponds to a more favoured preference, Pareto demonstrated that the outcome of equilibrium analysis in which the index represents pleasure as a quantity is identical to the outcome achieved when index numbers increase in (monotonic) relation to preference ordering. In both cased, the equilibrium is given by the tangent between indifference curve, with the highest index number, and the curve of obstacles.

The ‘Sunto’ is superior to the subsequent Manuale and Manuel in one significant respect: the text of the article contains a flawless literal exposition of an ordinal approach to ophelimity and equilibrium and the appended ‘analytical solution to the problem’ contains a near flawless mathematical formalisation of an ordinalist system, with just one cardinal condition retained (McLure 2005). Complexities associated with the greater range of additional issues addressed in Pareto’s post ‘Sunto’ studies contributed to a diminution of his emphasis on ordinalism in economic theory.

However, the introduction of ordinalist indexes was not ‘an end’, rather, it was a means to make economics experimental by focusing on the ‘fact of choice’ and dispensing with considerations on the motives for choice. The statistical problem presented here depends on data from the observation of choice and, through interpolation, estimation of the equation for indifference curves in the area that is close to equilibrium, with index numbers included in the equation which increase with preferred combinations of goods (Pareto 1990b [1982], p. 413). This goes some way to providing the foundation for a revealed preference approach to equilibrium, but the formalism is not axiomatic and the focus remains on indifference curves.

The “Sunto” was followed by a series of open letters in the Giornale degli Economisti written by Pareto, in ‘Sul fenomeno economico: lettera a Benedetto Croce’ (1900c [1999]) and ‘Sul principio economico’ 1901a [1999]), and Benedetto Croce, in ‘Sul fenomeno economico: lettera a Vilfredo Pareto (1900 [1999]) and ‘Replica all’articolo del Professore Pareto’ (1901 [1999]).11 This exchange was one of the few occasions that Pareto treated his opponent in a scientific debate with great respect. Methodologically these articles are important for the provisional introduction of the Pareto’s distinction between logical and non-logical action, highlighting the positive basis of his work, by emphasizing the study of the ‘economic phenomenon’ ahead of the specification of ‘economic principles’, and for clarifications that he made to choice theory. In regard to choice theory, Croce regarded human will as the appropriate basis for considering economics, which Pareto had set aside in his focus on the fact of choice in the ‘Sunto’. In response, Pareto differentiated two types of choice, real choice and potential choice, which Martin Gross and Vincent Tarascio (1998) suggest provided the basis for two complementary approaches to choice theory. The ‘real’ approach relies on observation of human choice. This largely reflects the system outlined in the “Sunto”, although discussion of preference order in the article is also suggestive of a potential choice approach. The ‘potential’ approach provisionally outlined in his open letters to Croce, was subsequently clarified in the Manuale (1906 [1974], pp. 120-1) as the basis for binary choice experiments (Georgescu-Roegen 1975 [1999], pp. 491-95).

Pareto’s next article in this phase also dealt with pure theory and methodology. The text of ‘Le nuove teorie economiche: Appunti’ (Pareto 1901b [1982]) is largely an introductory review of the goals and objectives of marginalist economics, the role of mathematics in economics and the relevance of non-mathematical economics. It also included a mathematical appendix which contained his first attempt to specify dynamic equilibrium in equation form by accounting for variation is the level of savings in violation of Walras’ Law. However, the success of this was limited, as variations in ophelimity functions over time were not accommodated. Perhaps the issue of most historical relevance in this article is the linking of the concept of value with non-scientific notion, as subsequently mentioned in the Manuale and which came to exert a very significant influence over his direct followers:

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