SOURCE: "Demaria on Pareto," in The Development of Economic Thought: Great Economists in Perspective, J. Wiley, 1952, pp. 628-51.

[In the following essay, which originally appeared in an Italian economic journal in 1949, Demaria examines Pareto's economic writings.]

I

By a consent which is nearly unanimous, Pareto has been given the honor title, "father of contemporary economic science." In order to appreciate the significance of the work of the great Italian thinker, we must pause for a moment to examine the stage at which economic science had arrived during the third quarter of the past century. At this period, economics abounded with historical interpretations which emphasized certain historical factors, claiming a fundamental character for each of these. This was often done in an arbitrary manner, on the basis of simple intuition, and in complete disregard of theoretical considerations. But during this period the reviewer also meets at every turn quantitative postulates and purely mathematical, that is, exclusively hypothetical, formula tions. These were usually expressed in the form of pseudo-universal absolutes, such as the doctrines advanced by English classical economics, and the doctrines of the continental hedonists, which were based on the assumption of personal interest, considered as causa causarum of economic activity, of cost as well as of utility.

We do not intend to discuss, in the present context, the original contributions which Pareto made in the realm of historical interpretations, such as his greatly admired Systèmes socialistes. However, it seems to us that the scientific appraisal of me position and even the general conceptual limitations of Pareto's original work in economics call for attention to me central point of his sociological system. The equilibrium of economic quantities, in its most general aspects, is interpreted as a historical phenomenon, which is not exclusively economic but political and sociological as well, based, in other words, on meta-economic judgments. From this it follows mat the deductive discipline of economics requires postulates and value scales of economic as well as sociological character, and that these in turn need to be supplemented, widi me help of the method of successive approximation, by research of the empirical, inductive, statistical, and historical variety. The old-line economic theorists, for the sake of clear exposition and coherent interpretation, had neglected the development of sociological categories designed to interpret the reality of economic life. It does not suffice, in fact, to speak intuitively of legal institutions, moral beliefs, and sentiments, which dominate the various social spheres, and to say that all mis is closely related to the hedonistic springs of action. In order to avoid a uniform and undifferentiated interpretation, it is also necessary to establish a classificatory scheme which embraces these matters. The empirical concepts of history and the no less inductive concepts of the old science of politics must be segregated and men re-aligned in coherent units. Only in mis manner can me complete truth be revealed. As Pareto indicated on the occasion of his anniversary at me University of Lausanne in July 1917, these sociological concepts make it possible to attain experimental truth and to find a way out of the impasse to which exclusive reliance on pure economics leads.

The two large volumes of P areto's Trattato di sociologia generale constitute the first contribution to the creation of a system, formed by theorems of mathematical precision, in which the elements of the sociological phenomena are considered by themselves. They also contain, and this concerns economics, a theoretical scheme, unequalled to the present day, for limited competition, oligopoly, and voluntary associations such as industrial combinations and labor unions—configurations which the recent economic theory, especially the English and American, misinterprets rashly in terms of "bargaining strength," "strategies," "minimax," and uncertainty, instead of interpreting them exclusively, as Pareto did, in terms of social causation, "non-logical actions," "derivations," "residues," "combinations," and "persistence of aggregates."

The specific as well as general economic policies pursued by oligopolists, polypolists, and combinations appear undoubtedly as a perpetual search for maximum conditions. Nevertheless, their dynamics, and even their statics, must be brought into close relation to sociological forces, more so, perhaps, than to purely economic forces. From this point of view, it is unfortunate indeed that Pareto's sociological work continues to be badly neglected by the pure economists. They fail to be aware of the hierarchy of sociological and economic values, concentrating their attention, as they do, on purely hedonistic behavior or, at best, limiting themselves to simple historical excursions—whenever they fail to rely exclusively on their precious gift of intuition. No doubt, this part of Pareto's work has a claim to definitiveness. The fundamental sociological categories which he reveals lead in a rational manner to the economic equilibrium of markets where exchangers are few. They present also characteristics so general that it is difficult to understand how they could have been neglected, in the absence of other investigations of similar profundity or of the formation of sociological rival systems. If they would not exist, it would be necessary to create them. Whatever their qualities, they constitute to this day doctrinal advances of the highest order. It seems indispensable for economists to understand them and to derive from them all conclusions which they are capable of yielding.

After having taken cognizance of the need for sociological expansion of economics along the lines developed by Pareto's genius, we shall now investigate the impetus given by his work to pure and applied economics. In this respect, as we shall see, all his fundamental contributions were published for the first time in the Giornale degli economisti, in numerous articles very characteristic for their intellectual strength. These writings were then reformulated in his three radically different books: Cours d'économie politique (Lausanne, 1896-1897); Manuale di economia politica (Milan, 1906); and Manuel d'économie politique (Paris, 1909). The French edition of the Manuale differs considerably from the Italian edition in the Mathematical Appendix. A remarkable summary of Pareto's economics is contained in his forty-page article in the Encyclopédie des sciences mathématiques.

II

As we have noted, Pareto's economic work made its appearance toward the end of the nineteenth century, at a stage of development of economic science of which the doctrines of the English classicists and the continental hedonists were characteristic. It is well known that these doctrines had arrived at a point at which they had become particular and specific, having turned, in the last analysis, into a mere series of dissociated problems which were integrated in a singularly formal manner. The doctrines of the English classicists had been made comprehensive with the help of a pretentious generalization which presented every economic fact as a phenomenon of absolute cost and the whole of economic facts as a comparative table of absolute costs. The doctrines of the continental hedonists had been made comprehensive with the help of a no less trite panutilitarianism which vested exclusive power of explanation in a neat and subtle theory of utility. These two constructions attach an exaggerated significance to a few economic phenomena, whereas other factors, much more numerous and important, are either relegated to a shadowy existence or cast out altogether from the conceptual framework of the doctrine.

The scientific position of the two doctrines has so often been examined that it would not be interesting to resume the discussion in the present context. It is equally well known that the germ of the concept of general economic equilibrium existed already in the theories of the classical economists and utilitarian authors, and that the first, highly ingenious attempt at the coordination of the classical and utilitarian doctrines was undertaken by Alfred Marshall, dating from the period of his two widely studied works, The Economics of Industry (1879), and Principles of Economics (1890). But, in reality, there had been no "coordination." The classical doctrine of cost is an empirical universe which denies the utilitarian solution. The hedonistic doctrine itself must also be characterized as a pseudo-logical concept, excluding, as it does, the historical reality of cost. How can one talk of coordination when the problem of the unity of the two explanations claiming universality is resolved by a mere juxta-position, exclusively empirical, full of precarious casuistry—when it is impossible to say which of the two spheres of judgment is the decisive one?

No doubt, intuition, which infers general conclusions ex posteriori on the basis of observed facts, comparing and assembling partial truths, is an artificial construction. Practical, as it is, it nevertheless is a psuedo-concept, leading to a mirage and to deceptive reasoning—as is always true of a posteriori rather than theoreticalreasoning. This was indeed the path followed by Cournot, Marshall, and Edgeworth, which led to laws—and this is important to note—valid only under the ceteris paribus condition, "others being equal."

It was Walras who cast light on the fundamental aspect of economic equilibrium—the mutual dependence of a series of closely aligned relations. As Enrico Barone has pointed out, this construction was not a mere continuation of the first attempts, highly meritorious as they were, of Cournot and Marshall. Instead, it was a veritable jump forward, accomplished in an original and masterly fashion, in the field of pure economics. It is the imperishable merit of Leon Walras—which Pareto in no way shares—of having applied his powerful mind to the development of the framework of the relations of general interdependence. But it is fitting—and this observation is of major importance—to underline the decisive character of the advance of the problem of interdependence due to Pareto's work. The classical economists, and, before them, the authors of fragmentary works written in the course of the seventeenth and eighteenth centuries, had a clear perception of economic interdependence but were unable to visualize it as a whole, even in the form of a rough sketch. To present it as the momentous discovery of Pareto would thus contradict a variety of testimony. It is true indeed that the great Walras was the first to give a demonstration of it in mathematical language and that he incorporated it safely into his own theoretical system. But Pareto, by insisting on the subjective character of interdependence, went farther. And he also may claim technical priority for having presented, for the first time, competitive and purely monopolistic relationships under the same head in an interdependent system, although he overlooked the problem of a larger number of dependent monopolies. But, apart from this, it must be emphasized that Pareto always interpreted his system as a complex of necessarily individual relations. To him, all relations which appear as aggregate today but not from today on—and which lead to the so-called macro-economics—are considered as accidental, ephemeral, and impermanent, only approximately universal or not universal at all.

It is not intended to repeat here what has been said a hundred times about Pareto's work in the histories of economic thought and elsewhere. Instead, we shall try to go beyond the limits of the traditional appraisals of Pareto's work. It seems that nobody has ever observed, or, at least, has paid adequate attention to the fact that Pareto always presents interdependence as a subjective datum, that is, that the activities and value judgments of individuals, not the activities and judgments of the mass, constitute the economic problem. To be sure, numerous economists do not deny this principle, but they believe that in practice they can neglect it with impunity. It suffices to recall only two readily available interpretations, those of Marshall and Walras. In the first edition of his Principles Marshall points out that the many subtle points which are required for giving precision to the most general and abstract economic doctrines have only a very limited practical significance. He thereby intended to defend the methodological legitimacy of partial equilibria, of the notions of aggregate demand and supply, and of the representative firm. In the work of the Cambridge school, the idea of general equilibrium ends up in an empirical and approximative formula. If economic analysis progresses in this direction, it will never emancipate itself from Marshall's empirical and, thus, alogical foundation. Partial equilibria provide insight into detail, useful, no doubt, but unable to open up an exact view of the economic system as a whole: the observer is faced by problems which all are indeterminate. Partial-equilibrium analysis obscures the facts and leads to sophisms and erroneous conclusions. Pareto always considered Marshall a great man, because, "on the basis of a small number of principles, he constructed economic science." This is as far as his admiration went. He immediately emphasizes that "Walras and his school had gone very much farther."

Pareto did not endorse the assumption of constant marginal utility of money, perfectly arbitrary as it is, although convenient and necessary for operations with two-dimensional curves. These times "have passed." In an essay published in 1892 he stated, in connection with arguments based on constant marginal utility of money, and in opposition to Jevons' point of view: "It is peculiar that he made this assumption, since he himself had correctly emphasized the necessity of regarding it as variable. If one considers it as constant, one is unable to deal properly with the most important points of economic science."

Similar observations can be found in an earlier study relating to Auspitz and Lieben's theory of prices: "To start out with an examination of certain aspects, while assuming other economic quantities as constant—this is not merely a question of method. Such a method conforms to the disposition of the human mind; but it is a mistake nevertheless because it promotes the search for a simple expression of phenomena which are so highly complex that one cannot represent them with the help of a curve." It is indeed impossible to draw the curve of the production cost of a commodity on the assumption that equilibrium continues to prevail with respect to other goods. Effects which appear as secondary may be essential; variations of the value of one element may not only modify the value of all unknown quantities but may also change the known quantities in the equations. The dependence among economic quantities is so pronounced that each degree of utility depends upon several quantities. Moreover, in order to carry studies of this sort to their successful conclusion, it is necessary always to observe that the degrees of utility are related to the costs. Thus, the ceteris paribus method will never result in an appropriate treatment, not even in a coherent treatment, because it never leads to theorems and rigorous corollaries.

It was the highest aim of Pareto's speculation to retrace all relations and correlations among the economic facts, to cast light on the real economic process from its beginning to its end, and to reveal the successive movements which never terminate, which cannot be separated from each other, and which reappear incessantly. In comparison with the thought of Walras, this aim was achieved in an even more complete and masterly fashion.

These are the words with which Pareto honored the memory of Walras shortly after the latter's death:

Walras' name will endure in science, and his reputation will continuously grow. The evolution which tends to turn political economy into an exact science is not going to be stopped, just as the parallel movements have not been stopped which wrested all modern sciences from empiricism. Once a true science has emerged from literary economics, one will not fail to go back to Walras' work when dating its origin.

The principal merit of this scientist, his very great merit, is based on the study, which he undertook as the first, of a general case of economic equilibrium. Thereby he led economic science on a path which can best be compared with the path opened up to rational mechanics by Lagrange.

Jevons, and later Marshall and Edgeworth, applied mathematics to political economy at the same time as this was done by Walras. But, unlike Walras, these authors did not consider the general hypothesis of economic equilibrium. It is exactly in this case that the application of mathematics becomes useful. If the investigator restricts himself to particular problems, the use of mathematics can lead to interesting results but it cannot cause the science to advance.

General economic equilibrium, on the other hand, casts light upon the great principle of mutual dependence, which requires the use of a special logic, that is, of mathematical logic. In the works of Walras we find the first comprehensive conception of the economic phenomenon, just as the theory of universal attraction entailed, for the first time, a comprehensive conception of the movements of the celestial bodies.

There is, perhaps, no other statement by Pareto which would illustrate better and more succinctly the historical significance of the Walrasian construction. What then is this general hypothesis of economic equilibrium which was studied by Walras for the first time? Pareto surely did not intend to allude to the general assumption of competition, or of constant coefficients of production. Pareto's words, uttered under delicate circumstances, are not of the type employed in a commonplace judgment. Having to attach himself to the Walrasian tradition and to emphasize his personal affinity with it, he had to place in bold relief the point where his own system diverged from that of Walras. Everything finds an explanation if we recall what we have noted before: Pareto presents the fact of interdependence as a complex of necessarily individual relations. To be sure, Walras had considered and systematized the individualistic aspect of reality. But he did so with the view of deriving therefrom the aggregative or synthetic categories of total demand, total supply, and total saving, adding up the algebraic sums of the various partial supplies and demands. The Walrasian system does not always rest on the double foundation of individual valuations and individual actions. In certain moments it is based directly on mass actions. It suffices to open up the definitive edition of Walras' Éléments to demonstrate this and to appreciate the change brought about by Pareto. At a certain stage of his construction, Walras' work ceases to be theoretical and becomes mere description. Walras does not always recognize that the individual, and his relationships, must invariably remain the primary element. He yields to the mechanism of synthetic functions or synthetic methodological procedures. He considers it legitimate to add up the algebraic sum of the various partial supplies and demands. At this stage, a break, in the nature of a genuine discontinuity, occurs in his system. Before long, the consequences of this were to make themselves felt in the scientific development of the schools of thought which do not belong to the Lausanne group. These were to refer to the high authority of Walras in order to justify systematically what today tends to become a universally fashionable approach to economic science—a fashionable approach but not an essential method.

One can understand the temptation created by the employment of mass categories. The human mind is easily thrown into confusion when confronted by an infinitely complex reality. It feels the spontaneous need for representative schemes which are as simple as possible, that is, synthetic. But what is the result of this? One enters the realm of the deceptive mechanism of synthetic economics, presented at one time in the form of the naive constructions of Moore or Cassei, generated by massive trends which are surreptitiously or openly introduced as assumptions or as a priori historical postulates. Similar considerations apply to later developments, such as the "condensed" functions of Keynes and his school, and the functions based on the distinction between wage goods and non-wage goods, elaborated by Pigou and his followers. These constructions are the most formal and the most empirical ones which one can imagine. In a first stage they favor explicative clarification, but they are dialectically erroneous, leading, as they do, to conclusions which are contained in the basic assumptions themselves: within the realm of the hypothesis one moves from the prologue to the epilogue, traversing the whole development from the statement of the problem to its solution. This is true of the hypotheses of extrapolated trends, of algebraic sums, of ex ante collective propensities to save and to invest, of discounted profit rates, of the ex ante behavior of the interest rate, etc., which lose themselves in precarious casuistry. The march of science eventually comes to a standstill. Science finds itself abandoned to intuition rather than to logic, and confusion results, since only practice, not theory, can determine which of the different hypotheses is the correct one. An irreconcilable opposition arises between the various constructions and potential reality, with the latter continuously and inexorably contradicting the former. True science does not artificially smooth the difficult points in order to resolve them. True science proceeds with the help of pure rather than statistical hypotheses, of hypotheses which do not need to be modified every moment. Pure hypotheses do not need to be changed—otherwise one faces mere pseudo-concepts, arbitrary constructions, sophisms.

Pareto indeed does appreciate the importance of the hypotheses. He recognizes that the conclusions can only be functions of the hypotheses. For this reason his hypotheses are truly universal, being based on the elementary activities of individuals and kept free from historical qualifications. Specific qualifications are provided only in the light of a sociological system. Pareto thus maintains neatly the difference between science and history, insisting that the equilibrium is always and exclusively a complex of relations among individuals. Since contents which are so divers—and lacking in homogeneity, as is the case of individuals, their actions and evaluations—cannot be measured and enumerated, the synthetic categories are not the result of proper reasoning and cannot be universal. In brief, the synthetic categories either serve to express an a posteriori synthesis of historical character, or they are intellectual manipulations of reality, helpful, perhaps, in the explanation of reality but without ever shedding the character of arbitrary exteriority.

It is our opinion that the absolute and fundamental character of the individual element, which Pareto places at the basis of his general construction of equilibrium and which he consistently retains, constitutes the major contribution of Paretian scientific speculation. After this contribution was made, it failed to yield all the fruit it is capable of bearing. Only those economists who understand its message will know how to reap this rich harvest. All other theorems discovered by Pareto are only of relatively secondary importance if compared with this fore-most and most profound contribution.

III

It is much less difficult now than it was in 1924 to indicate which of Pareto's secondary contributions are the most important ones and how they are to be ranked according to their systematic significance. This is much easier now than it was at the time of Maffeo Pantaleoni, when he refused to indicate the influence of these contributions on subsequent studies. In Pantaleoni's opinion, Pareto's sociological studies represented an alpha, whereas his work in pure economics was in the nature of an omega, bringing a cycle to conclusion and terminating all opportunities for further research aiming at higher generalization. After the passage of a quarter century this judgment seems an inadequate half-truth. Today, mathematical generalization is a sovereign fact, advancing, as it does, irrepressibly in the modern economic literature, which is so rich of controversy rather than of conclusions. At a certain point even the most capable "literary" economists lose heart in the face of so complex a play of economic activities, and feel the spontaneous need for recourse to mathematics, being unable to resign themselves to the historical method with its mere registration of events. Pareto's merit does not rest upon the fact that he expressed himself in the language of mathematics, with the power of one who

sopra gli altri come aquila vola.

There were other powerful minds, Cournot and Edge-worth, for example, who were his equals in the use of mathematics. But, to Pareto, the use of mathematics did not serve exclusively as a means to satisfy the desire to give greater precision to concepts and to delineate the meaning of assumptions with the view of producing a more rigorous demonstration. His use of mathematics was equally inspired by the intention to prove that all economic problems are determinate and determinable. As he put it, "in nature there is no indeterminateness. If we say that a problem is not determinate, then a well-constructed theory must indicate that there was occasion to take into account certain circumstances which were neglected."

With respect to the determinateness of economic problems, the proof produced by Walras and Pareto can surely not be considered as definitive. The Walrasian concept of tâtonnements—"gropings"—cannot stand up under a rigorous examination since it does not lead to a unique equilibrium position. As the Italian mathematician Gaetano Scorza has shown in a famous polemic with Pareto, there may be more than one equilibrium price even in the case of an exchange of only two quantities between two groups of buyers and sellers. In the case of a larger number of commodities the problem becomes still more complicated. There may be an infinite number of systems of equilibrium prices.

In this connection very difficult problems arise, which in the Paretian analysis are treated with the help of the theory of "closed and open cycles." Aside from an additive constant which determines the unity of measure, an unequivocal correspondence between the quantities of goods combined in the indifference curves and the utilities enjoyed by each individual exists in two cases: (1) when the cycle is closed, that is, when the order of consumption is indifferent, and the pleasure resulting from the incremental consumption of each commodity depends only on the quantity of that commodity; (2) when the pleasure is different, depending on the order of consumption, that is, when the cycle is open. There remains excluded the case of closed cycles when the basic utilities are functions of more than one variable.

Unfortunately, this ingenious theory was met with silence by the contemporary critique. For further penetration into this mysterious realm, the Paretian theory of open and closed cycles does not suffice. A distinction of this type does not adequately exhaust the profundity of the problem. If one has to accept the consensus auctorum, it is convenient to take equal account of divergence of opinion. Moreover, the paths should be laid out along which a choice must be made among the infinite number of systems providing solutions and the infinite number of constants and arbitrary integration functions which can be adapted to economic reality. This could be done with the help of certain criteria which satisfy the integrability conditions from the point of view of economic reality. With the form of the basic functions known, one can choose one of the infinite number of positions covered by the functions. In the third place, it seems necessary to abandon certain absolute references if the functions or arbitrary constants are to be determined in advance on the basis of economic reality. This does not mean that one should proceed in accordance with partial equilibrium theory—where the form of the curves is ingeniously presupposed—but, on the contrary, that attention be given to some indisputable empirical truths, the distribution of income, for example; or that an inductive criterion, uncertain as it is, be adopted consisting of the system of prices as it existed a moment before; or that a relationship be established with the concrete mechanism of price-level determination as controlled by the monetary authorities. The ultimate goal, remote as it may seem, consists of the transformation of problems posed in terms of differential equations into simple algebraic problems.

Whatever the future development of these investigations may be, they will have to resume the basic themes of Pareto's thought. The participants in this dialogue will all stand in the same light, as it were. The public of today, the literary economists, and the exponents of the various partial-equilibrium theories do not have the slightest idea of this dialogue about an issue on which the future of scientific economics depends.

The importance of pure hypotheses has been pointed out in the preceding paragraphs. When these are rigorously defined—as Pareto wanted them to be—and when the integration of the differential equations and the determination of arbitrary constants and functions have finally taken place, the economist of later times will truly be in a position where he can advance to the exploration of the future. He will attain this position when the material for his constructions has become coherent—under the same conditions as those which have enabled the modern scientist to determine thousands of years in advance the movements of the stars and the eclipses on the basis of the law of gravitation. Compared with literary economics and the theories of partial equilibrium—based, to the present, on a series of artifices and on a world of conventions and subterfuges—Pareto's work has broken the path which leads to the proper appreciation of the problem.

IV

The study of the interrelation between demand (or supply), price, and income is equally remarkable among Pareto's relatively secondary contributions. This well-known study takes its origin from the Walrasian system of equations of general equilibrium, and centers around the search for the sign of a double series of partial derivatives. These partial derivatives bring into a precise relationship the small variations of the demand (or of the supply) of different goods, small variations of the income of the exchanger, and small variations of different prices.

At the time of Pareto, everything in this field was still to be accomplished. Although his work left a notable mark, much remains to be done. In any event, Pareto pointed out the direction into which, according to his own prediction, "the economists must move if they aim at the true progress of science." The road laid out by Pareto in 1892, four years before the publication of the Cours, was again taken by Slutzky in 1915, and later on has been widely travelled by English and American economists. These applied his method to a number of practical problems, including the statistical derivation of collective demand and supply. Unfortunately there were neglected in their work certain basic objections which can be raised from a heuristic point of view. The theory of the partial derivatives of incomes and prices has for all practical purposes remained at the stage of cogitationes privatae. The knowledge of it has, however, spread more widely than is true of the matters discussed in the preceding paragraph, since it has become more widely known in the form of special theories of income and substitution effects and of the multidirectional character of demand and supply.

We shall limit ourselves to a single observation. The theory of partial derivatives concentrates on movements around a point. It would seem desirable to arrive at a complete solution, represented by finite rather than by point variations. This is a problem in dynamics—also studied by Pareto as will be seen shortly.

V

In the Walrasian fortress with its complex of exchanges, consumption, savings, investments, and mutually dependent production, there is one element which was destined to provoke the most profound discord with Pareto's speculation. This is the production function, represented by coefficients of production which are axiomatically assumed as constant. These functions have no roots because they assume empirically known data—but, on the other hand, these data must be considered unknown, especially since the dynamic succession can only be explained in this manner. The difference between theory and reality is not considerable, however, since the dynamic succession—in the case of the assumption of an uniformly progressive society—is hardly pronounced. But, in a clearly dynamic situation, the coefficients of production cannot figure among the given data. The idea of passive coefficients of production is untenable in every respect whenever they constitute active agents in the production function. The theory of variable coefficients of production constitutes perhaps Pareto's greatest merit in the field of the representation of the equilibrium of production.

The distinction between constant and variable coefficients of production is fundamental for two reasons.

First, from the point of view of political economy: Pareto was the first who demonstrated that the coefficients have the same value under competition and under state socialism. This was done in 1894, fourteen years before the publication of Enrico Barone's famous essay on this subject. Walras, on the other hand, considered the coefficients of production as determined in a manner designed to realize minimum cost. In contrast therewith, Pareto proposes to examine how they should be determined in order to obtain the maximum of utility for society, and he studies the relation between the two types of coefficients. The state should adopt this value as coefficient of production, regardless of a subsequent redistribution of the goods turned out. When it is desired to guarantee the workers a certain income irrespective of their productive contribution, it is preferable to grant them directly a certain amount of goods, or a certain amount of money taken from other citizens, and thus leave undisturbed the coefficients of production which assure maximum utility at least cost.

We shall not enter into a detailed critique of Pareto's formulation of the problem. Objections may be based on the fact that the prices, by which the coefficients of pro duction are multiplied in order to obtain the costs, cannot be considered as constants. The unknowns of the equations of instantaneous exchange undergo variations in conjunction with the modification of the distribution of goods or money brought about by the public authority. We want to state, nevertheless, that Pareto has posed a true problem of pure economics such as crude observation cannot solve. At the time of Pareto's article, mathematical economics was barely born. Even if his study impresses us as imperfect, as much from the mathematical as from the economic point of view, it nevertheless constitutes one of the very first objective studies. One does not know whether to think more highly of the un-ruffled calmness of his research, of the mathematical preparation, or of the admirable scientific intuition.

There exists, however, a second reason for the fundamental importance of the distinction between fixed and variable coefficients of production. The coefficients of production which are placed under the sign of the integral representing cost of production, are not independent of the limits of the integrals themselves. This is always true in the case of monopoly, and it is true also in the case of competition, but only for one of the numerous firms in existence—unless the whole question of minimum cost is restricted to the moment when all enterprises attain the equilibrium position, considering only small variations around a point.

These observations confirm the conclusion that it is necessary to solve a system of equations which are not only differential but integro-differential as well as related to the time interval. However, even if the variable coefficients of production are considered from this point of view, the movements occur again around the equilibrium point.

VI

Pareto, like Walras, worked primarily in the realm of statics. He barely touched upon the question of how to elaborate a theoretical apparatus which would approach as closely as possible the concrete phenomena, that is, the question of rational dependencies of the dynamic variety. Pareto recognized this himself: "Enormously much remains to be done in this direction."

Although the present sketch must necessarily be brief, a few references are in order to that part of Pareto's work which contains the equations of dynamic equilibrium.

It is true that Pareto's dynamic equations offer only a broad outline. The values of various economic quantities are considered at the time t1 and then brought into a relationship with the corresponding values at time t0, the intervening period being very short. The diversity between the two values rests entirely upon the predetermined variation of the coefficients of production. There is implied the assumption of certain innovations, or changes, attributable to outside forces, in the equilibrium of tastes and obstacles. Walras himself had formulated this hypothesis, ascribing the existence of uniformly progressive societies to the variation of the coefficients of production. But Walras had only affirmed that there would be re-equilibrating tendencies as long as the economic quantities had not reached previously established levels. If Pareto's theory would have been restricted in this manner, it would have been rather inconsequential. In the last analysis it would have been reduced to a new form of scholasticism connected with the formulation of certain hypotheses concerning the teleology of the coefficients of production. In effect, the system would not have been dynamic but only static or quasistatic at best, since it would simply contain an explanation of what happens during the time interval. New savings, new capital accumulations, new interest payments, and new production would all have been taken into account, with time considered in physical rather than in dynamic terms. But the essential difficulty would have been passed over with the help of a hypothetical instead of a rational "bridge."

The integration, over time, of the differential equations would simply have been a hypothetical integration, in other words, a science of the possible and virtual, based on certain hypothetical movements arising from the outside.

The real problem, on the other hand, would call for the removal of the indeterminateness which arises from exogenous factors, for the exploration of the roots of these factors. Sooner or later, all problems of pure economics run in this direction. If this decisive turning point is missed, the platform "time" has no significance at all.

In the first paragraph of this study we have come across the problem whether it is possible, by means of a theoretical construction of sociological character, to formulate a theory of these exogenous factors. It was Pareto's idea to develop such a theory through experimentation. He adopted a method of reasoning which had been characteristic of the greatest scientists of his time, for example, of Vito Volterra, who had stated the problem in these terms:

Begin with the formulation of concepts which lend themselves to measurement. Then measure. Then deduce laws. Return from these to the assumptions, and deduce, with the help of analysis, a science, ideal in character but rigorously logical. Compare it with reality. Reject or transform the basic assumptions which you have used, if there are contradictions between the results of the calculation and the real world. Arrive in this manner at the discovery of new facts and analogies. Then deduce, from the present status, what has happened in the past and what will happen in the future. This is a summary, as brief as possible, of the birth and evolution of a science mathematical in character.

In substance, the "bridge" over time must be constructed with the help of inductive knowledge. To Pareto, merely hypothetical knowledge has no value, and he brings the experimental part into the foreground of the science. "We do not know," he said, "the rational laws of movement of the planets, due probably to an infinite number of causes which only God can know. But we do know that it approximates an elliptical movement." One can approach the economic phenomena over time in a similar fashion. They, too, are extraordinarily complex, so much so that at a certain point nobody can have precise knowledge of them. That is why it is necessary to have recourse to empirical expressions which help to reveal approximative stability in time and space.

VII

We shall now briefly review Pareto's practical researches. Having discovered the law of income distribution, and having sharply delineated various types of interpolation, he did much to advance the experimental part of economics.

Pareto's theory of income distribution is a contribution of such momentous importance that its author, had he left nothing else behind, could claim rank among the most outstanding masters of human thought. The curve of "total receipts," as Pareto calls it, virtually is in the nature of an a priori axiom. An abundance of data confirm it. "When exceptions emerge in the future (as they surely will do sooner or later), investigations must be undertaken to search for the special cause responsible for the deviation of the new phenomena from a form which so many facts have proved to be the normal one." If Pareto's law can be considered as pertaining to inductive, quantitative economics, his theoretical results indicate, however, that the mechanism of income distribution forms one of the most important properties of the economic system vis-à-vis the budget constraint.

The second contribution is less widely known, although Pareto had devoted much work to this question. He does not just construct a method of interpolation but of interpolations which are adapted to distinctly different types of oscillations. With the help of a principle similar to Alembert' s, the oscillations are distinguished in accordance with the tangents drawn to the curves. In a way, this theory is a forerunner of the modern statistical theories of the decomposition of historical series, containing, as it does, their limitations and imperfections. The arbitrary element in the establishment of different points of discontinuity can in part be avoided by the use of a single mathematical criterion, tempered either by a priori reasoning aiming at the rational determination of the necessity of maxima and minima and of the length of the various periods, or by unsophisticated historical investigations of the type of Thorp's Business Annals.

VIII

Let us return to the topic considered in Section VI. Nobody can say for sure what the content of the treatise on economic dynamics would have been, which Pareto mentioned so often in his correspondence as well as in public statements, and in which the exogenous factors were to be systematically related to the representation of the equations of dynamic equilibrium.

It may be that Pareto's grandiose construction was stopped by the lack of statistical material of the type which is becoming available only now and to whose collection he gave such a powerful impetus. It surely is true that the hypothetical "bridge" for dynamic work is better marked today than it was at the time of Pareto. This is due to the gradual introduction, during the past 25 years, of the Bergsonian concept of evolution, as well as to the investigations of variables and strategic relations through time.

In the light of these investigations, the Paretian method of dynamic abstraction lacks acuity. This criticism does not detract from the honor and recognition which are due to the most illustrious exponent of the Italian school. He considers dynamic abstraction as a mere problem of averages. Today, however, dynamic abstraction has become more specific. The emphasis has become more concrete and more general as well, as witnessed by investigations into the "order of infinitesimals" or by statistical calculations of strategic variables, as done, for example, by J. M. Clark. These studies are still tentative, because, in this realm, the phase of fragmentary equilibria, or, at most, of particular equilibria, has barely been reached. At the moment, these are highly artificial, but they promise more than a merely generic formulation à la Moore. There is agreement that a synthesis must be worked out at the end, and that one or more links must be forged to connect the dynamic partial equilibria obtained from slices of space with economic time. Valuable tools, which can become a lasting component of the alphabet of dynamics, have been made available, at the very first, by Pantaleoni with his dynamic theory of instrumental, complementary, substitute, and joint relations among families of goods and economic agents, then by Keynes and other well-known authors, such as Haberler, with the dynamic theories based on the principle of acceleration and the multiplier.

IX

In the preceding paragraphs we have tried to cast light on the most remarkable parts of Pareto's work. But, side by side with these, there are others which perhaps impressed their author as still more important, at least in view of the length of time which it took to develop them. Nevertheless, these parts do not enable us to separate neatly the Walrasian and Paretian formulations of the problem and to establish the original character of the latter. We have in mind the arrangement of the theory of general equilibrium and the theory of the maximum total utility of a collective entity.

The relationship between the Walrasian and Paretian positions is very close. Pareto's system of equations is divided into two parts, and so is that of Walras. The first part treats of instantaneous exchange, with a complex of given data which in the second part—relating to capital accumulation and production—figure as many unknowns. Walras has the same immense conception. Both have pushed the search for equilibrium positions to the maximum of generality. Pareto's synthesis is more complete, however, since monopoly and exchange are considered as one special case of the general theory; since the mathematical argument can be applied equally to societies based on individualism or on socialism; and since the Paretian language utilizes simultaneously a variety of forms of expressions: utility, indifference curves, and index functions. Such a wealth of vistas and of new perspectives, added to the gigantic analytical design, constitutes a grandiose spectacle, fascinating to followers and opponents alike. We do not intend here to pass judgment on Pareto's exposition. We only wish to refer in passing to the fact that Pareto eliminated psychological analysis from economics, by rejecting such concepts as the final degree of utility, rarity, and ophelimity, the comer stones of hedonistic economics, and by retaining only the pure and simple fact registered by indifference curves which are derived from experience and which Pareto presents as an authentic discovery. In our opinion, however, all this is less decisive from the scientific point of view than Pareto believed. In any event—and this applies equally to the theory of "obstacles" which technology puts in the way of various transformations or which result, for each individual, from the attitude adopted by his partners—this approach does not raise intrinsically new problems. To Pareto, the theory of indifference curves was destined to enlarge the world of theory. He repeatedly found oc casion to recommend their application and never tired in his efforts at their improvement.

In connection with the deduction of the law of demand, he considered as real progress the passing from independent utilities—as formulated already by Dupuit, Gossen, Jevons, Menger, Launhardt, and Pantaleoni—to complementary utilities—as they can be found also in the Walrasian equations—and from there to the indifference series, to the choices among goods, visualized in pairs, and to choices considered as effects of resistances. From choices he deduced not only the law of demand but all conditions of economic equilibrium. This procedure was considered by Pareto as a great advance because it dispensed with the need for knowing whether utility is measurable and for examining total utilities and their partial derivatives. From an analytical point of view, the procedure was entirely new. However, the assumption of known choices is a hypothesis equivalent to the assumption that utility is known. In the theory based on choices, the projections of the indifference curves are considered as known. The other theory, on the other hand, assumes that the pleasure surface is known. In reality, very little is gained in precision, since the empirical knowledge assumed in the two cases remains nearly the same. For this reason the distinction is not as interesting on the practical as on the conceptual level. But, even in the latter realm, the definitions of equilibrium remain identical; only two different ways are selected. Instead of a relation between the intensities of wants there is one between the partial derivatives of the ordinate expressing the equation of choices. The equivalence of the two procedures is sufficiently demonstrated also by the fact that Edgeworth had arrived at the equation of indifference curves by taking knowledge of the pleasure surface as a point of departure. Remaining always on the same conceptual level, there is no obstacle to the formulation of the problem in still other terms, for example, with the help of marginal rates of substitution—as was done by Hicks, using a concept implied by Walras as well as Pareto—or with the help of other concepts such as the Walrasian "transformed utilities" and those which can be derived from certain properties of the determinants. All this does not involve a new idea—unless the new speculation receives a decisive experimental content.

In expressing these thoughts, we do in no way intend to regard the new orientations as rationally unjustified or illegitimate. They illustrate the aptitude of Paretian thought to express the same problem in different formulations. Nobody has had on hand a similar wealth of formulations.

What is the most important conclusion which can be derived from the theory of general equilibrium? In an approximative manner, it was already known in the light of the theory of partial equilibria that a competitive order entails the maximum of total utility for society. Walras had expressed this thought in a general manner, but only in the language of utilities. This procedure could not fail to raise suspicion, operating, as it did, with non-homogeneous quantities. This breach in the Walrasian edifice was repaired in a general manner by Pareto, who multiplied the variations of total ophelimity—pertaining to each individual—by certain coefficients with the view of rendering them homogeneous. In economic equilibrium, the variations of the quantities of goods are multiplied by prices. These products correspond to the relations between the derivative of total utility and marginal utility. In the sociological equilibrium, the Paretian procedure is even more daring. The coefficients in question are determined in the light of an objective goal, such as the prosperity of the collective entity.

Pareto then went on to demonstrate that the problem of the maximum is a problem of production, not of distribution. The variation of a coefficient of production will bring forth increases or reductions of utility for different individuals. When the sum of the increments exceeds the sum of the decrements, it is possible to transfer from the individuals who receive increments such a quantity of goods as is required for the reduction of the decrements to zero, and still have an excess of increments. Society, considered as a whole, thus receives a benefit. In this manner, the search for the value of the coefficient of production guarantees production in such quantities as, if properly redistributed, will assure for each individual maximum utility, expressed as the algebraic sum of the positive and negative utilities.

We do not intend to discuss here whether this procedure is entirely legitimate. Reference has been made to the polemic between Scorza and Pareto, which is of relevance in the present context. Scorza had estimated that the derivatives of total utilities cannot all be positive or negative unless special restrictions prevailed. But even in this case the procedure is not complete, since Pareto's maximum condition can equally be applied to monopoly and imperfect competition. In any event, however, Pareto deserves credit for having arrived, on a road which never was used before, at a new formula, which expresses, imperfectly but in scientific terms, a concept which until his time was discussed only in metaphysics.

X

Pareto belonged to those thinkers who are unable to resign themselves to a single direction in their scientific work. Incessantly he related his own central concepts to a whole world of special studies, covering the vast realm of applied economics. He aimed at the fundamental revision of current principles, traditional concepts, and generally accepted interpretations, with the help of daring speculations which to this day deserve close attention. This applies to the theories of circulation in Pareto's writings, to the theory of international trade, and to the inexhaustible historical documentation with which he enriched and supported his theoretical demonstrations. One cannot with advantage neglect his caustic critique of the political and economic regime of his own country as illustrated by the chronicles published by him in the Giornale degli economisti and in a number of political dailies. In this critique he is inspired by the principle requiring that all economic activities, public and private, be appraised in the light of experimental logic, abstracting from all idealistic and spiritual premises. In this respect one could correctly speak of a Paretism, that is, of a new pedagogy, a new doctrine of politico-economic education, applied to all interventions of the government in the economic sphere.