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Value: for many this term has a significance that is a little mystical, indicating a mysterious entity that is becoming a divinity that one can feel but cannot define. It is unnecessary to add that if one then searches to find what it is, one will effectively find no more than what Zeus found upon Olympus. …Value does not have one cause. It is as equally worth while to search for this cause in the cost of production as it is in the final degree of utility, in rareté or in any other entity. (Pareto 1901b [1982], pp. 4678) Around the same time, Pareto wrote a similar general introduction to mathematical economics which was published in the German encyclopaedia Encyklopädie der Mathematischen Wissenschaften in 1902. The article was subsequently translated by Guido Sensini and published as ‘Applicazioni della matematica all’economia politica’ (Pareto 1906b [1982]) in the Giornale degli Economisti. It is elegant overview of mathematical economics and covers both the hedonistic approach to pure theory and Pareto’s new choice approach, although in a truncated form. In 1902 and 1903, Pareto returned to the category of applied economics, where virtual movement is considered using mathematical methods derived from pure economics. The motivation for this was Gaetano Scorza’s review of Cassel’s Grundriss einer Elementaren Preislehre. This review was critical of Walras and Pareto, suggesting that Cassels’ work shows that the proposition that equilibrium under free competition is an economic maximum is nothing but ‘gross sophistry’. Pareto responded to this in ‘Di un nuovo errore nello interpretatre le teorie dell’economia matematica’ (Pareto 1902 [1982]), prompting Scorza to respond in “A proposto del massimo di ofelimità data della libera concorenza’ (Scorza 1902), with the debate concluding with Pareto’s ‘A proposito del massimo di ofelimità’ (Pareto 1903 [1982]). The author of this study has previously examined the ParetoScorza polemic in detail (McLure 2000). Consequently, it is only necessary to provide a brief overview on this occasion. As Pareto’s work on welfare economic had, until that time, focused on production, there was some basis to Scorza’s critique. Pareto’s reaction, while full of sarcasm and scorn, was also substantive as he extended his previous analysis of welfare to include both exchange and production. In the process, he provided economics with its first, analytically sound, firstorder demonstration of the first fundamental theorem of welfare economics. Scorza, however, was not satisfied, pointing to problems with second order conditions and the potential for multiple equilibria. Between 1900 and 1902, Pareto’s work in the Giornale degli Economisti continued to recognise the distinction between pure economics and applied economic, but it now had a curious element. Specifically, pure theory was choice theory, but applied economics that relied on mathematics to investigate virtual movement in commodity space, as in welfare economics, was expressed in terms of the hedonistic approach to theory. Pareto’s next article, ‘Il costo della produzione dell’uomo e il valore economico degli emigranti (A proposito di un articolo del Prof. F. Coletti)’ (Pareto 1905 [1982]), was again in the field of applied economics. It concerned the valuation of a man in society, and, the more complex issue, of how to measure the change in the economic state that will result from the emigration of a citizen to another nation. Pareto essentially pointed to the complexity of the issues, especially if reasoning is undertaken in term of ophelimity rather than monetary values. Next, Pareto responded to Vito Volterra’s review of the Manuale. Unlike the polemic with Scorza, this time Pareto treated his critic with respect in the reply article ‘L’ofelimità dei cicli non chiusi’ (Pareto 1906a [1982]), much of which was reproduced in the extended mathematical appendix to the Manuel. Volterra essentially reopened the question of path dependence within the ophelimity field by suggesting that the case of three goods or more requires further consideration than that provided in the Manuale, which tended to utilise two good specifications. Pareto had briefly touched on path dependence in the ‘Considerazioni’ and the ‘Sunto’ in discussion of the influence of the order of consumption on ophelimity, but had not dealt with the issue in a systematic manner because he considered it of some psychological interest but of little interest to economics. In ‘L’ofelimità dei cicli non chiusi’, Pareto developed an objective index of ophelimity from an arbitrary function of marginal ophelimity (determined from observed ratios of marginal utility), with the consequences for this index investigated for a circular consumption path in commodity space, from an initial arbitrary point that returns to that point. He used the term ‘closed circle’ when marginal ophelimity at the initial coordinates for a point in commodity space is unchanged following a circular consumption path and the term ‘open circle’ when a circular consumption path results in a change in marginal utility at the initial coordinates. That is, ophelimity is path independent when it is in a closed circle, and path dependent when it is in an open circle. Although Pareto did not establish the conditions for integrability in this, or other works, he concluded that equilibrium can be determined when elementary ophelimity is a closed circle, or when it is in an open circle but the path is determinate. Pareto’s contributions to the Giornale degli Economisti finish with a two part article entitled, ‘L’interpolazione per la ricerca delle leggi economiche’ parts 1 and 2, (Pareto 190708 [1982]), which deals with the analysis of time series data in economic and social research. He investigates how Cauchy’s interpolation equation could be employed to fit curves. This serves to reiterate Pareto consistent focus on positive methods, and the desire for statistical information to establish general empirical regularities as part of the second approximation along the lines of that developed for the Pareto distribution to estimate the general form of functions for pure theory. In regard to the latter point, Chipman (1976 [1999], p232) has already noted that these articles treat theoretical models as approximations with specification errors, and utilize a mixture of interpolation and least squares methods to account for both specification and measurement error. The second phase comes to an end with an appreciative obituary entry ‘L’opera scientifica di Leone Walras’ (Pareto 1910 [1982]). Like the first phase of his contribution to scientific thought, Pareto’s original, and internationally enduring, contribution in the intermediate phase started as development in the Giornale degli Economisti. His greatest single contribution to pure economics during this phase concerned pure theory: the development of choice theory. The ideas developed in this Journal on choice were contributed well before they reappeared in the Manuale. In the areas of applied mathematical economics, the Pareto Scorza polemic produced seminal and enduring contributions to welfare economics, with Pareto’s contribution over this time significantly influencing the Manuale and the Manuel. The Final Phase – 1912 onwards By the final phase in the development of Pareto’s scientific thought, his association with the Giornale degli Economisti had his scientific focus had now shifted almost entirely to sociology. Prior to the publication of the Trattato, Pareto contributed just one article, ‘Il Massimo di utilità per una collettività in sociologia’ (Pareto 1913 [1980]). However, this was a noteworthy extension of the nonadditive economic welfare theory, which does not require interpersonal comparisons of ophelimity, to a sociological theory of social welfare which specifies social utility in homogenous terms based on the interpersonal comparisons of individuals and government. The article is reproduced almost in its entirely in the Trattato, and has already been discussed in the previous chapter. Pareto’s last contribution to the Giornale degli Economisti was ‘Economia sperimentale’ (Pareto 1918 [1980]). It was published two yeas after the Trattato, and is essential reading for scholars seeking to appreciate Pareto’s view on economics in the final phase of his contribution to economic science. It differentiates between the economic part of the economic phenomenon, which is the subject of the science of economics, and the sociological part of the economic phenomenon, which is the subject of sociology. The critical point here is that this article defines the study of economic phenomena during the final phase of Pareto’s contribution to scientific thought. It is not often recognized that Pareto treated ‘experimental economics’ during this phase in a dualistic manner, with experimental economics utilizing economic science, to study the economic part of economic action, and sociology, to study the sociological part of economic action. This article is of some importance, and is given further consideration in chapter 6 and a translated version of the article has been included in Part II of the book. Pareto Inspired Articles in the Giornale degli Economisti before 1923 During the initial phase of Pareto’s work, he had no core followers writing in the Giornale degli Economisti, although there were some articles on themes initiated by Pareto. Most notably, Francis Ysidro Edgeworth (1897) and Rudolfo Benini (1897) considered economic aspects relating to the Pareto distribution and Enrico Barone had written articles on consumer demand, consumer surplus and production and distribution journal that had Paretian elements. Edgeworth clarified his critique of the Pareto distribution and Benini undertook empirical exercises in which he found α to be broadly in line with Pareto’s estimate, but did not use α as a measure of inequality. In ‘A proposito delle indagini del Fisher’, Barone (1894a) developed a critique of Marshall’s notion of demand and consumer surplus that confirmed Pareto’s finding in the ‘Considerazioni’ on the unnecessary presumption of constant marginal utility of money when the price of a commodity changes. In ‘Sopra un libro del Wicksell’ (Barone 1895), he not only adopted the commodity production functions that Pareto developed to investigate the welfare consequences of free competition in ‘Il massimo di utilità dato dalla libera concorenza’, he also enhanced them by considering the influence of scale of output and working capital on production (Dooley 1998, p. 76). Barone also drafted of a review of Wicksteed’s Essays on the Coordination of the Laws of Distribution (1894) which: pointed to Pareto’s use of production functions with variable coefficients of production; and developed the marginal theory of productivity further. He submitted his review to the Economic Journal, but it was rejected. As Barone had noted that Pareto’s work on variable coefficients of production predated Wicksteed’s work, this rejection contributed to the souring of relations between Pareto and Edgeworth (Chipman 1976 p. 90). Barone also outlined a marginal theory of productivity in which coefficients of production varied with the scale of production as well as factor combinations, which influenced the structure of his seminal Studi sulla distribuzione (Barone 1896). While his contribution to the marginal theory of productivity is closely related to Pareto’s analysis, the fundamental idea was conceived independently of Pareto (Dooley 1998, p. 77). In this regard, Pareto (189697 [1971], p. 723) came to object to the marginal theory of production because an increase in one productive service is not necessarily ‘compensated’ for by a decrease in other productive services. Some productive services are fixed, others are variable, some are partially fixed and partly variable and all this is constrained by the state of technology. Consequently, by 1896 Pareto came to the view that basing production theory on the presumption of perfect substitution of productive services was too approximate for economic theory, even though that is what he effectively did in earlier studies (Pareto 1894b [1982]). Interestingly, Pareto also convinced Barone of the main flaws in the marginal product theory of distribution (Schultz 1929 [1999] p. 432)^{12}. On balance, in the last decade of the nineteenth century Barone is most properly considered an eminent contemporary of Pareto, rather than his follower. Like Pareto, his interest was focused in the implications of Walras’ work. He was an independent thinker who also investigated issues in a manner that Pareto did not. In particular, he was interested in partial equilibrium to a much greater extent than Pareto, even taking steps to define the relationship between the two approaches. For example, in ‘Sulla consumer’s rent’ (Barone 1894b), he presented the partial equilibrium approach to consumer surplus of Marshall as a reasonable approximation to the more rigorous the general equilibrium approach to consumer demand of Walras and in ‘Sul trattamento di questioni dinamiche’ (Barone 1894c) he utilised Marshallian type analysis of equilibrium adjustments. None of these issues are Paretian in character. . It was not until the intermediate phase of Pareto’s scientific work, when his major contribution to pure theory was developed, that a discernable circle of specifically Paretian scholars emerge. Between 1900 and Pareto’s death in 1923, there were 40 articles published in the Giornale degli Economisti that dealt with Paretian themes, of which 6 were critical assessments or book reviews. The themes can be broadly categorized as pure economics, fiscal studies which draw on sociology, applied economics, and other general studies. Articles pertaining to these themes are chronologically listed in Table 1.^{13} In the field of pure economics, Pareto’s followers mainly worked on issues associated with the intermediate phase of Pareto’s scientific contributions. Of these, the most influential were by Pasquale Boninsegni, Enrico Barone and, of course, Eugen Slutsky. Luigi Amoroso’s pure economics at this relatively early stage of his career work was also important, although ,ainly as impressive precursors to his Lezioni di economia matematica (Amoroso 1921) and other studies after Pareto’s death. Boninsegni’s initial articles (1901a, 1901b) attacked the notion of ‘economic convenience’ developed and defended by Ulisse Gobbi (1900, 1901), where both means and ends associated with heterogeneous actions are analysed in monetary terms using mathematical functions. Gobbi’s approach is not only rejected for lacking rigour, but for being a backward step that is fundamentally at odds with mathematical economics. In short, Boninsegni used his criticism of one formulation of pure economics to highlight the strength of mathematical economics along the lines of Pareto (Mornati 1999). In ‘I fondamenti dell’economia pura: a proposto di un libero del sig. A. Aupetit’, Boninsegni (1902) also took the opportunity of criticising Essai sur la théorie générale de la monnaie by Aupetit (1901), in which money is directly incorporated into general equilibrium theory, to highlight, and extend, Pareto’s analysis. Boninsegni objected that there were not enough equations to determine the elementary ophelimity of the numeraire (or money) as well as the goods exchanged. More importantly, he contrasted the Paretian approach with the monetary theory of choice being developed by Aupetit. Fiorenzo Mornati observed that Boninsegni also modified Parteo’s approach to choice in the ‘Sunto’ in an original manner (Mornati 1999, pp. 1646). Specifically, while following Pareto in finding equilibrium at the point of tangency between indifference curves (with different index numbers that are a arbitrary function of tastes) and the function for obstacles, Boninsegni represented obstacle as a linear budget constraint, whereas Pareto used nonlinear constant output curves derived from his obstacles’ functions. As such, Boninsegni presented choice theory in the context of the consumer, whereas Pareto presented it in the concurrent context of exchange and production. As such, Mornati finds that Boninsegni’s enhancement is similar to that subsequently developed by Hicks and Allan (1934). 
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