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Table 1 Paretian Articles in the Giornale degli Economisti: 19001923 Pure Economics
(a) 12 articles on pure economics Public Finance and Sociology^{(a)(b)}
(b) 9 articles on public finance Applied Economics^{(c)}
(c) 4 articles on applied economics General^{(d)}
(a) 11 articles on general or miscellaneous matters Nevertheless, it should be recalled that the illustrative numerical example Pareto provided in the ‘Sunto’ specified the effect of obstacles on equilibrium as a linear equation and that variations in the obstacles using this equation were discussed entirely in terms of a variation in the consumer budget (Pareto 1900a [1982], pp.41923). Consequently, Boninsegni’s contribution to choice theory concerns the form of theory and not its substantial concepts. That is, he used Pareto’s ordinal conception and simplified numerical illustration of choice theory as the basis for presenting general consumer theory in isolation from the broader framework that Pareto used when formalising general economic theory. Curiously, some nonItalian economists overstate Boninsegni’s contribution. For example, Dooley has observed that “Boninsegni (1902) … is the nearly forgotten originator of the ordinal approach to indifference curve analysis” (Dooley 1998, p.89). This view no doubt derives from Pareto’s note in the Appendix to the Manuale when dealing with the equations that represent the system of indifference curves using index numbers: ‘For greater elucidation see P. Boninsegni, I fondamentali dell’economia pura, in the Giornale degli Economisti, Roma, February 1902’ (Pareto 1906 [1974], p.368). The same note is repeated in the Manuel (1909 [1971], p.392). It appears that Pareto actively promoted his talented protégé in the scientific community. Perceptions of his importance were also enhanced by Pareto’s reference to Boninsegni (1904) in the Manuale and Manuel when discussing the complexities of mathematical analysis based on ophelimity: In the Giornale degli Economisti, Roma, September 1904, Professor Boninsegni has published an excellent study which investigates ‘the functions of demand and supply in the case of barter, assuming that elementary ophelimity is linear’ (Pareto 1906 [1974], p376) In Italy, Boninsegni is recalled, but sometimes in dismissive terms. This is dicussed further in the next chapter. Another of Pareto’s students at Lausanne, Vladimir Furlan, attempted to generalise Pareto’s notion of ophelimity and choice theory in the Giornale degli Economisti. In ‘Cenni su una generalizzazione del concetto d’ofelimità’ (1908), Furlan introduced an axiom concerning human behaviour, by explicitly specifying that individuals maximise ophelimity through choice, with the choice of a preferred combination of goods yielding maximum ophelimity for the individual in question. Of the other major studies in pure economics from Table 1, Enrico Barone’s (1908a) ‘Il ministro della produzione nello stato collettivistà’ and Eugen Slutsky’s (1915) ‘Sulla teoria del bilancio del consumatore’, are the most important, but are too well known to devote much space to their propositions of each. However, it is appropriate to briefly consider the relationship between these studies and Pareto’s work. While Pareto is celebrated from his pioneering work on collective economic welfare, it is generally accepted that he still left gaps in the literature. In the Cours, Pareto’s discussion of socialism went some way to developing the second law of welfare economics, but he made an interpretive error. As John Chipman (1976, p.93) has pointed out, Pareto got the treatment of redistribution correct (unconditional lump sum transfers) but misinterpreted his analysis when concluding that the coefficients of production for a socialist state should remain unchanged from those under free competition. The change in the composition of demand resulting from the redistribution, efficiency dictates that coefficients of production will require different coefficients to maximise welfare: Pareto should have concluded that while the production functions are unchanged, the coefficients will change from those prevailing under free competition before the lump sum redistribution to those that would prevail if free competition were to operate under the new distribution of resources following the lump sum transfers. In the Manuale, Pareto (1906 [1974], p.2557) clarified his interpretation of this issue, but he did not provide the analysis to demonstrate the result. For the purpose of this study, the important thing is that ‘Il ministro della produzione nello stato collettivistà’ presented a competitive general equilibrium model that analysed welfare along the lines developed by Pareto, which Barone explicitly acknowledges. The resulting general equilibrium model, in which initial endowments and coefficients of production are exogenous, but individuals’ tastes are directly observed is able to analyse welfare effects for individuals, competitive collectives and socialist collectives in terms of a numeraire indicator. It is also able to make provisional assessments of welfare from distributional changes. The influence of Pareto’s goal for experimental equilibrium analysis is clear and the article was cited favourably by Pareto in the appendix to the Manuel. Under the heading of equilibrium for one individual with any number of goods and constant prices, Pareto discussion of how experiments can be used to deduce the theory of economic equilibrium and concludes with a note that: ‘This point of view is developed in a scholarly article by E. Barone. See Giornale degli Economisti, Rome, September 1908’ (Pareto 1909 [1971], p. 416). Barone’s main advance in this article was his clarification of the relationship between the first and second theorems of modern welfare economics. By relying on experimental observations of tastes he was able to further develop the ‘compensation’ principle that Pareto introduced in ‘Il Massimo do utilità dato della libera concorrenza’ (1904b) to make compare different states. As Chipman and Moore (1978, 548) have noted, Barone mentioned the compensation principle no less than four times. However, this classic article has also been criticised for not fully accounting for the impact of choice on the unique system of processes used in the welfare analysis, with Allais, who was most impressed by Pareto’s equivalent surplus notion of welfare, arguing that: ‘From a scientific point of view, Barone’s article was a step down from the summits reached by Pareto’ (Allais 1975 [1999] p. 457, italics from the original text). However, the equivalent surplus approach to welfare comparisons for which Pareto is justifiably famous was not included in the Manuale, published before Barone’s article, but in the Manuel (Pareto 1909 [1971], pp. 4745), which was published one year after Barone’s article. It appears likely that, after reflecting on Barone’s article, Pareto was inspired to reconsider how measurement issues associated the compensation principle, which he himself had developed twelve years earlier, could provide the basis for a surplus approach to welfare. It should also be noted that Barone made significant contributions to fiscal theory in articles published in the Giornale degli Economisti. Most notably, his two part article ‘Studi di economia finanziaria’ (1912) investigated incomes and fiscal burden, taxation theory, tax shifting and the excess burden from indirect taxation. However, this extended economic analysis to individual fiscal events that went well beyond the level of economic analysis of fiscal events that Pareto would contemplate and could not be considered Paretian in the strict sense. Amoroso’s ‘Sulla teoria delle curve di utilità’ (1916) is of some historical interest because it reviewed William Ernest Johnson’s ‘The pure theory of utility curves’ (1913) published in the Economic Journal. Amoroso pointed out that the ordinal theory presented by Johnson was developed without any prior knowledge of Pareto’s work on the subject, and lamented that this lack of knowledge on Pareto is not limited to Johnson, but extends to his entire area. The issue of Johnson and Pareto on ordinal utility theory is discussed in a well researched paper by Ivan Moscati (2005). In spite of the limited penetration of Pareto’s ideas on utility in the United Kingdom, the development of demand theory in the Giornale degli Economisti did attract attention in some European centres. While a faculty member of the Kiev Institute of Commerce, Eugen Slutsky wrote his famous ‘Sulla teoria del bilancio del consumatore’ (1915). This article extended Pareto’s derivation of a downward sloping demand curve from his investigation of general utility functions in ‘Considerazioni sui principii fondamentale dell’economia politica pura’ (Pareto 189293d [1982]). Slutsky’s great achievement was to extend Pareto’s contribution by respecifying the analysis for a generally ordinal specification of utility and to then isolate the income and substitution effects. Pareto (189293d [1982]) considered utility as independent and additive and did not isolate these two effects. Moreover, his subsequent treatment of the issue in the Manuel did not achieve full ordinal specification. Perhaps in light of this, R.G.D. Allen was to reflect that ‘the present theory of the consumer’s behaviour, as developed by Hicks and others, is essentially as much a development of Slutsky’s work as it is of Pareto’s’ (Allen 1950, pp. 2101). The relative contribution of Pareto and Slutsky to the development of consumer theory has been the subject of some debate. Dooley (1983 [1999]) has pointed out that Slutsky followed Pareto’s procedure and demonstrated that Pareto’s solution for the partial derivative of the quantity of a good with respect to its own price is mathematically the same as Slutsky’s equation, it just does not isolate the two effects. This suggests that ‘Pareto was the true master, Slutsky the gifted disciple, who improved the master’s work’ (Dooley 1983 [1999], p292). Christian Weber (1999), however, pointed out that Pareto had no intention of systematically examining the effect of income on demand. From the text of the Manuale (1906 [1974], p. 193), it is clear that Pareto fully appreciated that the change in demand for a good following an increase in income my take any sign (positive, negative or zero). In view of this, and in light of Pareto’s methodology, Weber suggests that Pareto may have considered the theoretical representation of the effect of income changes on demand as a waste of time: If the mathematical analysis yields a definite sign, the theory was contradicted by facts. If it yielded an uncertain sign, nothing new had been learned, so what is the point? (Weber 1999, p.581) Weber’s suggestion is indeed plausible and, on this basis, Slutsky should be considered as more than a disciple following the master. While he followed Pareto in terms of procedure, at least in part, he investigated an issue that was to become attractive to formal consumer theory in the twentieth century, but in a manner that represented something of a departure from acceptable experimental relationship between fact and theory within Pareto’s methodology of science.^{14} The Italian reaction to this issue was to jointly recognise the contributions of both scholars by, as Dooley and Weber have both noted, referring to the ‘ParetoSlutsky’ analysis of demand, as in D’Albergo (1949). The substantive fact of all these contributions to pure economics is that they derive from the intermediate phase of Pareto’s scientific contributions, with Amoroso, Barone, Boninsegni and Furlan (and Sensini, as discussed below) directly following Paretian methodology and theory of studies in pure economics and Slutsky following Pareto mathematically but not necessarily methodologically. However, if these scientific contributions to pure economics are considered in isolation, a strong case for a ‘Pareto school’ does not emerge. Walker’s assessment is basically correct and it would be appropriate to use the term Lausanne school. Dooley (2001) too refers to the Lausanne School (whose core members he descrives as Walras, Pareto and Barone) in his discussion of production theory and the theory of the firm, and his classification is difficult to fault. This is not changed when Paretian studies of an applied nature are considered. Even empirical work on Pareto distribution of income was primarily concerned with statistical investigation of a possible empirical regularity: the particular Paretian character emerges in its complete form when income distribution is linked to the circulation of elites and sociological theory. General studies provide some insight into what may define the Pareto school. The relationship between mathematics and science features strongly in the studies of Murray and Amoroso. Also, the studies of rent by Sensini are a direct extension of the unique relationship between production and rent that Pareto developed in his Cours and Manuale. However, it is only when the field of public finance is consider does the grounds for referring to a Pareto school clearly emerge, as it is in this are that the broadest treatment of equilibrium that Pareto developed in his final phase of scientific thought. That is, it is in the field of public finance that the influence of sociological phenomena on economic equilibrium and the social state emerged in a uniquely Paretian line. The main contributors were Roberto Murray, Guido Sensini and Gino Borgatta, although Murray’s association with Pareto was, to some degree, self assessed. Without the scholarship of this group of fiscal scholars, the basis for suggesting that a Pareto school, in the fullest sense, developed in Italy is difficult to sustain. However, these fiscal scholars do not form a homogenous group in the second decade of the twentieth century. Murray was the first to initiate developments in fiscal studies along a Paretian line, but his approach was soon overtaken by developments contributed by Sensini and Borgatta. Along the way, Borgatta and Murray were at odds over the relevance of methodological individualism in fiscal studies. As Paretian fiscal sociology, which emerged in the immediate post World War I period, is the primary subject of subsequent chapters, developments in this area are not discussed here. 
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