Franco Donzelli Maria Teresa Trentinaglia Department of Environmental

Franco Donzelli, Maria Teresa Trentinaglia Department of Environmental Science and Policy Università degli Studi di Milano franco. donzelli@unimi. it Walras’s Theories of Exchange and Production Equilibrium in the 1870 s and Beyond ASSA 2019 Atlanta History of Economics Society Pure Mind, Applied Vision, and Social Conscience: Revisiting the Economics of Léon Walras Hilton Atlanta – 203 / 12: 30 – 14: 15 p. m. Saturday, January 5, 2019

The evolution of Walras’s ideas: 1870 -1902 n Léon Walras: 1834 -1910 n Active scientific life as founder and developer of GET: 1870 -1902 n Incessant revisions of Walras’s theoretical system over 30 years n Four editions of the Éléments d’économie politique pure during Walras’s life: n ¨ 1 st edition 1874 -77 ¨ 2 nd edition 1889 ¨ 3 rd edition 1896 ¨ 4 th edition 1900 5 th posthumous edition (édition définitive) in 1926 (last corrections made by Walras in 1902) Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 2

The causes of Walras’s intellectual restlessness 1 n By the Winter 1871 -72, after ten years of efforts, Walras is eventually able to develop a reasonably complete system of thought. n This system of thought is outlined in a series of Notes, called Geneva Notes in the following, written in preparation of ten lectures to be given in Geneva at the beginning of 1872. n The Geneva Notes anticipate a number of features of what will become Walras’s general equilibrium theory in the following years. n Yet, they inherit a number of concepts and constructs from previous economists and schools of thought: from Walras’s father Auguste and Augustin Cournot, but also from J. B. Say, from the economists of the Classical English School, and especially from J. S. Mill. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 3

The causes of Walras’s intellectual restlessness 2 n What is altogether missing is the idea of individual optimization and equilibrium as an array of compatible optimizing plans. n In the Fall 1872, with the fundamental help of the professor of mechanics Paul Piccard, Walras discovers how to link individual demand behavior and utility maximization in the context of a twocommodity economy. n After that, Walras strives to revise his system of thought in the light of his 1872 discovery of the potential role to be played by the assumption of individual optimizing behavior in the construction of a general theory of economic equilibrium. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 4

The causes of Walras’s intellectual restlessness 3 n This attempt is made at first during Walras’s highly creative period 1872 -1877. n But a number of difficulties immediately arise here. n The old ideas prove to be more pervasive and resilient than expected. n Moreover, they are often hardly compatible with the new approach. n The peculiar way in which Walras learns how to make use of the optimization assumption strongly restrains its possible applications. n The penetration of the new equilibrium conception into the four “big problems” of economics (exchange, production, capitalization, money) is highly heterogeneous. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 5

The causes of Walras’s intellectual restlessness 4 n The field of exchange, where the new approach is born, is that where the penetration of the new ideas is more immediate (1873 -74) and pervasive. n Yet, also here the old ideas keep their firm grip, conditioning both the generalization of theory to the multi-commodity case and the analysis of the equilibration process. n Much more difficult proves to be the application of the new approach to the field of production (1875 -76), where the persistence of the old ideas, often of classical origin and incompatible with the optimization assumption, is stronger. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 6

The causes of Walras’s intellectual restlessness 5 n Special difficulties arise as regards the analysis of capitalization, where the penetration of the new approach (1876 -77) is even more restricted. n Finally, the application of the optimization assumption to the field of money is almost inexistent in the 1872 -77 period. n So, even if by 1877 the construction of Walras’s general equilibrium theory is almost complete, theory itself lacks coherence and suffers from the effects of its heterogeneous sources of inspiration. n For the rest of his life, over the period 1878 -1902, Walras will try to extend the grasp of the new approach to all the fields of inquiry, getting rid of the old ideas and removing the inconsistencies wherever possible. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 7

An outline of the paper n In this paper we critically review Walras’s theories of exchange and production equilibrium. n While focusing attention on the period 1871 -77, we also reconstruct the evolution of Walras’s ideas over the following quarter of a century, up to 1902. n First, we summarize theoretical system put forward by Walras in his Geneva Notes of Winter 1871 -72. n Secondly, we analyze the way in which the optimization assumption and the new equilibrium conception enter Walras’s system of thought in the Fall 1872. n Finally, we examine Walras’s post-1872 models of exchange and production equilibrium, stressing their shortcomings due to the survival of old ideas in the new optimizing framework. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 8

Walras’s theoretical system in the Geneva Notes 1 n As far as the exchange equilibrium model is concerned, in the Geneva Notes of Winter 1871 -72, one can find: ¨ a well-defined model of demand-supply equilibrium in a twocommodity economy, with empirically given individual and aggregate demand functions; ¨ an extensive discussion of the arbitrage process (inspired by Cournot) leading to the establishment of a consistent price system in a multicommodity economy, satisfying Walras’s “general equilibrium” condition; ¨ the use of such a consistent price system to express the demand for a consumer good as a function of all commodity prices; ¨ the analysis (traceable to J. S. Mill) of an equilibration process in ‘real’ time of a commodity market, operating through price changes, leading the market to a stationary price equilibrium (“prix stationnaire”). Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 9

Walras’s theoretical system in the Geneva Notes 2 n As far as the production equilibrium model is concerned, one can find therein: ¨ a statement of the equilibrium condition in the market for a produced consumer good, identified by the equality of selling price and unit cost (a condition once again traceable to J. S. Mill); ¨ the characterization of the entrepreneurs as the agents who combine productive services to obtain products (an idea inspired by J. -B. Say), and who, at a state of production equilibrium, make neither gains nor losses; ¨ a graphical analysis of an equilibration process in ‘real’ time (again drawn from J. S. Mill), functioning through quantity changes in the market for a produced commodity, brought about by the entrepreneurs who react to incentives represented by gains or losses in the production processes they control; ¨ such equilibration process is shown to drive the market to an equilibrium state where price equals unit cost and the quantity produced is stationary. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 10

Walras’s discovery of optimization in the Fall 1972 n In the Fall 1872, with the help of Paul Piccard, Walras learns how to derive individual demand (and supply) functions from the solution of constrained utility maximization problems. n Such derivation is obtained in a two-commodity, pure-exchange economy, where competitive consumers-traders exchange consumer goods at uniform rates of exchange (uniform relative prices). n Walras immediately applies the new optimizing approach to his theory of exchange equilibrium, which is almost completely revised by 1874. n In the wake of Walras, we distinguish between theory of equilibrium determination (with the associated “solution mathématique” or “théorique” or “scientifique”) and theory of equilibrium establishment (with the associated “solution empirique” or “pratique”). Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 11

Exchange equilibrium models: equilibrium determination n As regards the post-1872 theory of the determination of exchange equilibrium, the fundamental difference with respect to the pre-1872 theory is the following: n now individual, hence aggregate, demand functions are no longer taken as “empirically given”, but derived from the solution of constrained utility maximization problems. n Yet, apart from this remarkable difference, the structure of theory remains the same as before. n By finding the roots of the system of market-clearing ordinary algebraic equations, one obtains the “solution mathématique” of the exchange equilibrium problem. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 12

Exchange equilibrium models: equilibrium establishment 1 n According to Walras, such a solution must be supplemented by another kind of solution, the “solution empirique”. n Such “solution empirique” is reached by the market “par tâtonnement”, through a process of price changes governed, as in the Geneva Notes, by a law traceable to J. S. Mill, the “law of supply and demand”. n Walras however wants the “solution empirique” to be identical with the “solution mathématique”. n A necessary condition for such coincidence of the two “solutions” is that the time-invariance of the data be preserved during the equilibration process. n Yet, as a result of the new behavioral assumption concerning the consumers-traders, who are now supposed to behave as competitive optimizing agents, new and more serious difficulties crop up here: Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 13

Exchange equilibrium models: equilibrium establishment 2 n Differently from the Geneva Notes, in the post-1872 exchange models: ¨ competitive consumers-traders can no longer take care of price changes, which must therefore be explained by relying on a different super-individual mechanism; ¨ the out-of-equilibrium behavior of the consumers-traders becomes now an issue that must be separately tackled, since the available theory of optimizing behavior is unable, by itself, to explain out-ofequilibrium actions (as distinguished from plans of action); ¨ whenever the change in the data is endogenously produced, the assumption of time-invariance of the data is ill-founded, as in such a case theorist cannot simply assume away something that is endogenously determined. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 14

Exchange equilibrium models: equilibrium establishment 3 n As to the assumption of time-invariance of the data, Walras states: “C'est le droit du théoricien de supposer les éléments des prix invariables durant le temps qu'il emploi à formuler la loi d'établissement des prix d'équilibre. ” n But in the mid-1870 s he overlooks that trading itself is bound to change the data, via the reallocation of the endowments among consumerstraders, so that his data-invariance assumption is ill-founded. n All the same, Walras takes it for granted (“certain”) that the equilibration process will converge to a “stationary” equilibrium. n Yet, a curious paradox arises here: the equilibrium eventually arrived at must be stationary, to give the equilibration process a realistic flavor, in the wake of the classical tradition of the English School. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 15

Exchange equilibrium models: equilibrium establishment 4 n Yet, since “les éléments des prix sont essentiellement variables”, a stationary equilibrium is after all utterly unrealistic. n Since the data change instant by instant, and the plans are similarly instantaneous, a notion of ‘instantaneous equilibrium’ would fit the new optimizing approach better than the notion of stationary equilibrium, inherited from the classical school. n After Bertrand’s criticism (1883), in 1885 Walras explicitly introduces a no-trade-out-of-equilibrium assumption which turns the tâtonnement process in exchange into a purely virtual process in ‘logical’ time, taking just one instant of ‘real’ time to carry its effects through. n At the same time, Walras seems to perceive that optimizing behavior, ‘instantaneous equilibrium’, and virtual equilibration process are strictly associated. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 16

Production equilibrium models: equilibrium determination 1 n In fact, in 1885 he openly speaks for the first time of a “general equilibrium” ruling “à un moment donné”. n Yet such perception is only confined to the exchange model. n In fact, the penetration of the optimizing perspective is more limited in the post-1872 production models, developed in the years 1875 -77. n These models are populated by two broad categories of agents: consumers-owners and entrepreneurs. n Only consumers-owners are supposed to behave as competitive optimizing (namely, utility maximizing) agents. n On the contrary, exactly as in the Geneva Notes, in the wake of the classical English School, entrepreneurs are modeled as selfinterested, but not optimizing, agents. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 17

Production equilibrium models: equilibrium determination 2 n They are supposed to react to the existence of gains or losses in the production processes they control by changing the quantities of the products they produce. n Walras assumes that there exists a uniquely defined single-output, fixedcoefficient technology. n A hint at the possible variability of production coefficients, to be determined by solving a unit cost minimization problem, can be found in Walras’s 1876 -77 writings. n Yet, in the mid-1870 s, in spite of the help provided by the mathematician Hermann Amstein, Walras is unable to solve the cost-minimization problem. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 18

Production equilibrium models: equilibrium determination 3 n The issue, set aside for about twenty years, will be taken up again in the mid-1890 s, when, with Pareto’s and Barone’s help, it will be briefly dealt with in the 3 rd (1896) and then in the 4 th edition of the Éléments (1900). n But the analytical core of Walras’s theory of production will never be affected by such afterthoughts. n The equilibrium condition characteristic of Walras’s production model is that the price of a produced consumer good be equal to its unit cost of production, which is supposed to be independent of the level of output (given input prices). n But this condition, dating back to the Geneva Notes, is basically the same as the condition specified by J. S. Mill for the class of commodities which can be produced in unlimited amounts without increase in cost. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 19

Production equilibrium models: equilibrium establishment 1 n Also in this case, the “mathematical solution” must be supplemented by an “empirical solution”, coinciding with the former, supposedly achieved by the market via a tâtonnement process. n Yet here the design of the tâtonnement construct proves even more difficult than in the exchange model. n Such further difficulties are chiefly due to two reasons. n First, the problem of the invariance of the data during the equilibration process, which until 1899 is supposed to take place in ‘real’ time, is more complicated than in the exchange model since here production involves the physical transformation of inputs into outputs. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 20

Production equilibrium models: equilibrium establishment 2 n Secondly, there is also the problem of the coexistence in the production model of two categories of agents, consumers-owners and entrepreneurs, whose behavior abides by different rules. n Due to these difficulties, in the production model put forward in the mid 1870 s, and kept basically unchanged until 1899, not only the convergence, but the very viability of the equilibration process, leading to a stationary equilibrium in ‘real’ time, rests on shaky foundations. n This is the reason why Walras is eventually led to abandon all hope of constructing a tâtonnement process involving observable production activities taking place in ‘real’ time. n Walras makes such a sharp turn by adopting the so-called “hypothèse des bons”, at first in 1899 and then in the 4 th ed. of the Éléments (1900). Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 21

Production equilibrium models: equilibrium establishment 3 n By means of this assumption, not only the trading and consumption activities, already virtualized since 1885, but also all the production activities are no longer allowed to take place out of equilibrium. n The entire tâtonnement process becomes a purely virtual process taking place in a sort of ‘logical’ time, disconnected from the ‘real’ time over which the economy evolves. n When so conceived, the tâtonnement process takes just one instant of ‘real’ time to carry all its effects through. n The notion of stationary equilibrium, inherited from the classical English school, is dropped in favor of a notion of instantaneous equilibrium, the only one which proves to be in line with the new optimizing approach. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 22

Conclusions 1 n In the Fall 1872, Walras discovers that the assumption of optimizing behavior can play a key role in theory of economic equilibrium. n Since optimizing individual choices were not contemplated in Walras’s preexisting theoretical system, as summarized in the Geneva Notes drafted in Winter 1871 -72, Walras’s 1872 discovery brings about a remarkable change in his theoretical perspective. n Walras tries to apply the new ideas to all the main fields of economic inquiry, starting from theory of exchange. n Yet, a number of pre-existing ideas, often scarcely compatible with the new approach, prove hard to eradicate and tend to persist in the new setting. n Hence, the penetration of the new approach is relatively slow and fragmentary, particularly in the field of production. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 23

Conclusions 2 n Here the analysis of the supply side of the product market is still largely affected by the survival of ideas traceable to the approach of J. S. Mill and the classical economists. n Such a mixture of old and new assumptions and conceptions is responsible for a number of inconsistencies, marring Walras’s analysis. n In particular, Walras’s original analysis of an equilibration process taking place in ‘real’ time, with the associated notion of stationary equilibrium, is hardly consistent with the new notion of equilibrium as an array of optimally chosen and compatible plans of action. n For this reason it is eventually abandoned by Walras, in favor of a notion of ‘instantaneous equilibrium’, supported by a virtual equilibration process taking place in ‘logical’ time. Franco Donzelli Walras's Theories of Exchange and Production Equilibrium in the 1870 s 24