A Companion to the History of Economic Thought - Chapter 18 pdf

18.1.2 Walras’s mature comprehensive model COMPETITION Walras was the first economist to construct a complete general equilibrium model, the mature comprehensive model set forth in the se

C H A P T E R E I G H T E E N Early General Equilibrium Economics: Walras, Pareto, and Cassel

Donald A Walker

18.1 LÉON WALRAS

18.1.1 Background Walras, the founder of the modern theory of general economic equilibrium, was born on December 16, 1834 in Evreux, France, and christened Marie Esprit Léon Despite his lack of formal credentials in economics, he obtained an appointment

at the Academy (subsequently University) of Lausanne in 1870, and remained there for his entire career He retired in 1892, and died on January 5, 1910 in Clarens, Switzerland (for biographical information, see Jaffé, 1935: for biblio-graphical information, see Walker, 1987; A and L Walras, 1987– )

18.1.2 Walras’s mature comprehensive model

COMPETITION

Walras was the first economist to construct a complete general equilibrium model,

the mature comprehensive model set forth in the second edition of the Eléments

(1889) It is called “comprehensive” because it encompasses exchange, production, consumption, capital formation, and money; and “mature” to differentiate it from the models in the first and fourth editions In that model, Walras not only

expressed the belief that all economic phenomena are interrelated, which had been done by many economists before him, he also specified their interrelations, studied their disequilibrium behavior, and described their conditions of equilibrium One of Walras’s fundamental methodological convictions was that the assump-tions of a theory must be drawn very carefully from empirical reality (1896b, p 10), and one of his principal objectives as an economic theorist was to understand the behavior of the markets that functioned in the economy of his time His study

of empirical reality convinced him that “free competition in regard to exchange is the almost universal regime” (Walras, 1965, vol 2, letter 999, pp 434–5), “practiced

on all markets with more or less precision and therefore with less or more frictions” (Walras, 1895, p 630), and so he drew the assumption of a purely competitive economy from the real economy That is why he constructed a general equilib-rium model of a freely competitive economy; not, as has been suggested ( Jaffé, 1977), in order to design a utopia whose conditions necessitated the operation of that type of system The specific type of real market from which he drew some characteristics was a freely competitive organized market, like a stock exchange

or a wholesale market for an agricultural commodity (Walras, 1988, §41, pp 70–

1, cited because this is a variorum edition, with section numbers that enable the reader to find the passage in the 1954 English translation) In such markets, prices are determined by the forces of supply and demand without collusion and are changed by buyers and sellers in the same direction as the sign of the market excess demand (1988, §42, pp 71–2), which is what Walras meant by the term “free competition.” That feature, he contended, was also sufficiently true of unorganized competitive markets that the workings of free competition and its consequences can be attributed to them also (1988, §41, pp 70–1) Regarding competition, he had

“as a first step, reduced that mechanism to its essential elements.” Subsequent steps should be taken, he argued, to create a progressively more realistic model, namely one infused with additional empirically derived conditions: “it is appropriate to introduce into [my] model one by one all the complications that reality presents” (1894, p 624) Thus his general equilibrium model, he declared, was “not only the idea but the image” (1896a, pp 469–70) of the real economy of his time

MARGINAL UTILITY THEORY

Another of the fundamental building blocks of Walras’s general equilibrium model

is his idea of marginal utility and the maximization of total utility by each parti-cipant Those concepts provided a motive for economic behavior and a condition

of equilibrium, elements that were essential for the functioning of his model of general equilibrium Instead of confining the marginal utility theory to the inves-tigation of consumption and of simple exchange, Walras went far beyond the work of its other initiators by using it to analyze the behavior in multiple markets

of a variety of participants undertaking different economic functions In his model

of consumer behavior (1988, §74, p 107; §75, p 111; §80, p 116), Walras assumed that the utility a consumer derives from any commodity is independent of the amount he or she consumes of other commodities, that utility is cardinally meas-urable, and that each individual’s demand for a commodity is, in principle, a function of the prices of all commodities A consumer efficiently maximizes total

utility by buying the quantity of each commodity that makes the utility received from the expenditure of a unit of money on it equal for every commodity pur-chased Likewise, in Walras’s models, professional traders and wholesale and retail merchants add to their holdings of each commodity, or sell out of their stocks of commodities, until they hold the batch of commodities that maximizes their utility Entrepreneurs and capitalists strive to maximize utility by maximizing their profit and interest incomes respectively (1988, §188, p 284)

EQUILIBRIUM IN THE MATURE COMPREHENSIVE MODEL

Walras studied the existence, uniqueness, and stability of general equilibrium in his model He thought that he had proved that an equilibrium exists in it because

he had described it with as many equations as there are unknowns (for example,

1988, §205, pp 306–7) He then undertook a comparative static analysis in order

to analyze how the solutions to the equations are affected by arbitrarily postu-lated or exogenously induced changes of their parameters, such as preferences, the quantity of money, and the quantity of a commodity held by the participants Walras’s proof was not valid, however, because he did not take account of the effect of disequilibrium processes on phenomena that are parameters in the equations, and because he did not establish that the solutions to the equations are economically admissible, as will be explained at the end of this essay Nevertheless, his examination of the question went far beyond the analyses of other nineteenth-century economists, inasmuch as he dealt with a model of general rather than particular equilibrium His study of uniqueness was limited to the consideration

of isolated markets and a multi-market model of pure exchange, and his conclusion that “generally” multiple equilibria do not occur in the latter case was a statement rather than a proof (1988, §156, pp 242–3)

DISEQUILIBRIUM BEHAVIOR IN REALITY AND IN THE MODEL

The basis of Walras’s theoretical work on stability was his conception of the real economy as always undergoing processes of change (1988; §322, pp 579–80) The disequilibrium adjustments, Walras maintained, continually move the real economy toward a position of general equilibrium He called them the process of

“tatonnement,” a word that means “reiterated hesitant groping movements to find something.” Walras set himself the task of modeling that behavior (Walras,

1965, vol 2, letter 927, p 364) Presenting his initial results in the years 1874–7,

he thus became the first economist to study the stability of a general equilibrium model (1895, p 630)

On every market day in the model, transactions of any particular commodity occur only at the price at which the supply and demand quantities are equal Walras knew that was not true in many real markets, but believed that it was a

“hypothesis that no scientific mind will hesitate to concede to the theoretician” (1895, p 630) After attainment of that price, the market day in his model is nevertheless in disequilibrium if the price and the average cost of production of the commodity are not equal, or if the participants are affected by the prices subsequently determined in other markets The aspect of the model’s tatonnement that takes place with respect to new quantities manufactured is the progressive

diminution of the difference between price and average cost of the product as a result of the changes of the price in the output market and of the prices of inputs The rate of output in each industry is changed in the same direction as the sign of that difference The aspect that takes place with respect to sales of each commod-ity is the progressive diminution of the difference between the quantcommod-ity supplied and the quantity demanded The price is changed in each market in the same direction as the sign of the excess demand quantity “The system of new quant-ities manufactured and new prices is closer to equilibrium than the previous one, and it is necessary only to continue the tatonnement in order to approach it more and more closely” (Walras, 1889, p 241) In equilibrium, “prices are those

at which the quantities demanded and supplied of each service or product are equal, and for which, moreover, the price of each product is equal to its average cost of production” (1988, p 13) The mutually determined sets of prices, average costs, and quantities supplied and demanded are harmonious and fulfill the plans of all the participants in the model

THE ENTREPRENEUR

Walras believed that entrepreneurs undertake essential functions in the real eco-nomy and therefore accorded them a role of crucial importance in the dynamic behavior of the mature comprehensive model (Walras, 1965, vol 2, letter 800,

p 212) Entrepreneurs lead it to equilibrium Walras portrayed them as relating input and output markets by buying labor, land services, capital-goods services, and raw and semi-finished goods, combining them to produce consumer com-modities or capital goods, and selling them (1988, §189, pp 287–8) One connection between input and output markets is established by the entrepreneur through the circumstance that the average cost of production is determined on the input side of the market and is an important part of the price charged on the output side Entrepreneurs make a profit, which is their remuneration, as long as aver-age cost is less than price and a loss in the opposite case They adjust production from one disequilibrium rate to another, thereby altering average cost and price until they become equal Profit is then zero and a state of equilibrium obtains (1988, §189, pp 194–7) Another connection between input and output markets established by the entrepreneur is that they pay incomes to the owners of the economic resources that they hire and those incomes are spent by their recipients

on consumer commodities and capital goods (1988, §§185–6, pp 281–2)

CAPITAL FORMATION

Walras’s treatment of savings and investment (1988, §§241–2, pp 357–63) reveals yet another way in which entrepreneurs connect different economic sectors and markets The incomes paid to owners of economic resources by entrepreneurs are partially saved by the recipients in their role as members of households, in which connection Walras formulated the first macroeconomic savings function He developed a model of processes by which capitalists transfer their money savings

to entrepreneurs through purchasing stocks and bonds (1988, §269, pp 434–6), and explored those processes in studies of credit markets (1898, pp 307–36) Walras showed how the capital goods that the entrepreneurs produce are priced and

employed in the most profitable uses He likewise constructed a model of the determination of the rate of net income generated by the use of capital goods, and of the determination of the market and equilibrium rates of interest (1988,

§§231–71, pp 345–436)

WELFARE ECONOMICS

Walras enunciated the principle of consumer sovereignty and modeled the way in which it operates to determine the set of commodities that are produced The entre-preneur transmits the desires of consumers to the production side of the market, thus allocating resources so that the set of commodities produced is in accordance with the structure of consumer demands and hence reflects consumer preferences and purchasing power (1988, §188, pp 283–4) On the basis of that analysis, Walras developed a thesis that became a central issue in the study of welfare economics, namely that free competition tends to generate a maximum of well-being for society (1988, §221, p 334; §264, p 424) The maximum is a relative one, because it depends upon the distribution of income and wealth and the dynamic characteristics of the model that result in it moving toward a particular set of equilibrium values He emphasized that the maximum results from actions by economic agents to maxim-ize utility, the establishment of a set of prices that equalmaxim-izes supply and demand, the sovereignty of the consumer, and the other features of a competitive economy that he put into his model The theory makes clear that “the mechanism of free com-petition leads precisely to the solution by tatonnement of this system of equations; from which it follows that the mechanism creates maximum satisfaction” (Walras,

1965, vol 2, letter 928, pp 364–5; and see Walras, 1988, §264, p 424)

18.1.3 The written pledges sketch The problem for Walras’s exposition is that the equations that he wrote out have parameters that are actually endogenous variables in the tatonnement process in his model He explained that production and exchange occur in disequilibrium

in the mature comprehensive model, varying as prices change during the course

of the adjustment of the markets toward their equilibrium set of variables (see, for example, 1889, pp 235, 238, 294; 1988, §§209–12, pp 315–19, §258, pp 399– 401) The phenomena that change as a result include the asset holdings of the participants, which alter as a function of the variations in hiring, production and sales that occur as entrepreneurs adjust levels of output in order to maximize profits; and they include the amounts of each type of capital good, which vary in accordance with changes in the amount and composition of investment, which

in turn varies with changes of the prices, costs, and incomes of capital goods, and with the rate of interest and changing levels of saving Other variables that are affected are the incomes of the participants Since consumer demand func-tions depend on both asset holdings and income, they also change during the tatonnement Consequently, the equations that Walras presented as relating to the mature model of general equilibrium do not in fact describe it Their solu-tions – prices, rates of employment of resources, incomes, outputs, and quantities traded – are not the values toward which the model actually converges

In 1899 and in the fourth edition of the Eléments (1900), Walras tried to design

a virtual model that would eliminate this problem, thus abandoning his objective and method of trying to construct a realistic model A virtual model is one in which no economic activities occur in disequilibrium, except for the quotation of prices and the manifestation of the associated desired supply and demand quan-tities In that way he hoped that the parameters of his equations would represent conditions that are truly constant during the equilibrating process of his model

He thought that he could achieve the virtual property by assuming that suppliers

of resources and other commodities do not produce disequilibrium amounts but, instead, make written pledges to provide the commodities Walras stated that they vary the amounts offered as a function of a series of suggested prices until the set is found at which the desired supply and demand of every commodity become simultaneously equal in every market Only then are other economic activities allowed to take place (1900, pp VIII, 215, 224, 260, 298, 302; 1988, pp 5–7, §§207, 213–14, 251, 273, 274; pp 309, 323, 377, 441, 447) The written pledges construction, however, is an incomplete sketch, notably because would-be demanders of consumption goods do not make pledges and so have no means of expressing their desires (Walker, 1996, pp 372–95) Of course, Walras asserted that there is a tatonnement and that equilibrium is found, but those were just unsupported statements, not a consequence of his assumptions, not an outcome

of the structure of the sketch and the behavior of its participants Furthermore, he did not carry out his plan (1900, p VIII; 1988, pp 5, 7) to convert into written pledges markets all the older sub-models that are supposed to play a role in the

1899 design – sub-models dating from his mature period of theorizing but that he

left unchanged in the fourth edition of the Eléments He therefore presented

disequilibrium production and exchange as occurring in some markets but not in others, a situation contradicted by his equation system, which allows only for virtual behavior Thus Walras did not construct a general equilibrium model

in his last phase of theorizing Neither the written pledges sketch alone, nor it and the collection of sub-models associated with it, contain a pricing process or any other economic activities It does not constitute a functioning system and therefore has no dynamic path and no equilibrium

Nevertheless, by 1889 Walras had a fully formed conception of the interrelat-edness of economic phenomena and well-constructed sub-models of the import-ant parts of a competitive economic system The vitality of those contributions to economic theory was manifested by the strength of their influence on Vilfredo Pareto, to whose ideas we now turn

18.2 VILFREDO PARETO

18.2.1 Background Vilfredo Pareto’s ideas are presented in this essay because he was, after Walras, the second most important economist in the early development of the theory of general equilibrium Pareto was born on July 15, 1848 and christened

Federico-Vilfredo-Damaso In the early 1880s he became interested in the applica-tion of mathematics to economic theory and policy formulaapplica-tion Because of that approach (Walras, 1965, vol 2, letter 1126, n 3, pp 553–4), and recommendations

by Maffeo Pantaleoni and Walras, he was offered the position that Walras had held at the University of Lausanne and began his duties there in 1893 In the

economic realm, he published his most important contributions in the Cours

d’économie politique (1896/1897), Manuale d’economia politica (1906, 1909), and

“Economie mathématique” (1911) After 1905, Pareto concentrated upon sociology

He retired in 1911, but continued making contributions to social science (see Pareto, 1963–2001) He died on August 19, 1923 (for biographical and bibliographical information, see Busino, 1987; Kirman, 1987)

18.2.2 The general equilibrium model Walras’s mathematical method and his conception of a multi-market competitive economy, of its equilibrating processes, and of general equilibrium, were extremely important in Pareto’s economic reasoning (Walras, 1965, vol 3, letter

1489, p 154) He used Walras’s mathematical form of expression of supply and demand, and regarded literary discussions of them as being useless and foolish (Pareto, 1909, ch III, §181, p 220) Pareto improved Walras’s mature comprehen-sive model in some respects, and developed his own original theories He agreed with Walras that the scope of pure economic theory is limited to facts and relationships regarding which free will does not play a part He believed that the methods of positive science should be used in the study of all aspects of eco-nomics and of human behavior generally Like Walras, he thought that the assumptions of a theory should be realistic (1916/1963, pp 28–30) Inferences from them, he argued, should be evaluated by empirical studies, because “theories, their principles, their implications, are altogether subordinate to facts and possess

no other criterion of truth than their capacity for picturing them” (1916/1963,

p 30) He also espoused the method of successive approximations of theory to the real economy, by which he meant the progressive introduction into a model

of empirically derived considerations so as ultimately to achieve a high degree

of realistic detail (1896/1897, vol 1, pp 16–17; vol 2, pp 15, 78)

THE THEORY OF DEMAND

Pareto’s theory of consumer demand is a central pillar of his model of general equilibrium He may have thought that it is not impossible, in principle, to measure utility objectively (see Kirman, 1987, p 805), but he nevertheless observed that no one has “been able to succeed in demonstrating that pleasure can be measured, that it is a quantity, nor above all to discover how one could go about measuring it” (Pareto, 1909, appendix, §137, p 661) He therefore made the important inno-vations of assuming that utility is ordinally measurable, the consumer being able

to specify that he prefers one batch of commodities to another or is indifferent

to them (1909, ch III, §52, pp 168–9), and of showing that his demand function can nevertheless be derived Pareto also assumed that the utilities of different commodities are not independent Some commodities are substitutes for each

other, he noted, and others are complements (1909, ch IV, §§12–14, pp 253–56) Using calculus, Pareto then formulated a theory of consumer demand based on the Walrasian assumptions that the consumer wants to maximize his utility and knows how to do so, and that the quantity he demands of a commodity is a function of the prices of all consumer commodities, given his income and prefer-ences (1896/1897, vol 1, p 35) Pareto also affirmed Walras’s conclusion that the consumer achieves maximum utility by purchasing the amounts of any two commodities for which the ratio of their marginal utilities is equal to the ratio of their prices, although Pareto expressed that condition in the way appropriate for

an ordinal indifference analysis (1909, appendix, §24, p 559) Pareto’s reformula-tion of Walras’s model of consumer behavior was adopted by many continental economists and was developed into the modern theory of consumer demand

THE EXISTENCE, UNIQUENESS, AND STABILITY OF EQUILIBRIUM

Like Walras, Pareto used a set of simultaneous equations in an effort to describe the characteristics of his model of general equilibration and equilibrium of a competitive economy, with the difference that he constructed a completely disaggregated version in which there is an equation for each consumer, for each resource supplier, and for each seller of output (1896/1897, vol 1, pp 44–61) Pareto believed that the dynamized version of his model was highly realistic (1897, p 492) He asserted that equilibrium exists in his model because the number of independent equations equals the number of unknowns (1896/1897, vol 1, pp 26, 44–6, 61), and then discussed how the economy moves toward it

In this connection, Pareto had studied Walras’s attempts to show that his mature comprehensive model is stable and he naturally took its dynamics as his starting point – naturally, because that model, with all of its irrevocable disequilibrium processes and phenomena, is the one presented in the edition of

the Eléments that Pareto studied in the 1890s Pareto believed that the freely

competitive tatonnement process featured in that model accurately described the disequilibrium behavior of the real market system With respect to exchange,

he contended that “Walras has shown that the bargaining that takes place in free competition is the means of solving the equations of exchange by repeated attempts” (1896/1897, vol 1, pp 24–5) “Mr Edgeworth has objected that that

is only one means” by which markets move toward equilibrium “He is right,”

Pareto declared, “but the way indicated by Mr Walras is truly the one that de-scribes the largest proportion” of markets (1896/1897, vol 1, p 25) With respect

to production, he argued that Walras’s idea of tatonnement in that aspect of economic activity should also be adopted, and for the same reason, namely that

it was an accurate description of what happened in the real economy: “Mr Walras has shown that the competition of entrepreneurs and traders is a means of solv-ing the equations of the equilibrium of production through successive attempts This idea, in general, seems very fruitful for economic science” (1896/1897, vol 1,

pp 45–6) Pareto therefore used Walras’s mature concept of tatonnement in his formulations of competitive economic adjustments in the 1890s, and he did not at any time pay any attention to the written pledges sketch He made a minor addition to the analysis of what he called multiple equilibria by arguing that

consumers might choose consumption patterns that lead them to the equilibrium that is best for them (1909, ch III, §§128–9, pp 197–8)

THE ENTREPRENEUR

Pareto followed Walras in arguing that speculators transmit price signals to the production side of the economy by buying or selling in response to price changes, and that they facilitate the process of transforming savings into new capital goods (Walras, 1880, pp 370, 379; Pareto, 1896/1897, vol 2, pp 242–5) “The social function of speculators, insofar as they do not act directly on prices, is to solve the equations of economic equilibrium in the best and promptest manner poss-ible” (Pareto, 1896/1897, vol 2, p 245) For the case of free competition, Pareto adopted Walras’s theory of the entrepreneur, agreeing that their actions would lead to an equilibrium in which economic profits are zero He extended the analysis of how entrepreneurs behave in the phase of disequilibrium, however,

in two major ways First, they make errors in their production decisions:

It is necessary to produce commodities during a certain period of time – sometimes

a very long time – before they are consumed In order for there to be a perfect adaptation of production to consumption it would be necessary: 1° that consumer

predicted It is impossible to do these two things with precision (1909, ch IX, §76,

p 530)

The entrepreneurs try to correct their errors by changing production levels during the equilibrating phase of the economy Secondly, entrepreneurs keep changing their profit goals, thereby repeatedly modifying the path taken to equilibrium, and as a result the equilibrium values of the variables change (1909,

ch V, §11, p 289; §§74–5, p 331) Thus, according to Pareto, path dependency results from disequilibrium transactions and disequilibrium production not only because they change the total amount of commodities and their distribution dur-ing the equilibratdur-ing process – causes of path-dependency in Walras’s model – but also because of errors and revisions of expectations and plans on the part of the entrepreneurs (1896/1897, vol 1, pp 18–19)

Pareto also examined the behavior of firms in markets in which there is a lack

of adequate competition In that event, he noted, there is no tendency to reduce the profits made by an entrepreneur to zero That gave rise to his analysis of a monopolistic entrepreneur who is able to restrict output and thereby to charge a price for his product that is greater than its average cost, which he would not be able to do if he were in a competitive industry (Pareto, 1896/1897, vol 1, pp 62–

9, passim) Like most economists, Pareto argued that private monopolies are

obstacles to an optimum allocation of resources and to efficient rates of their use

“It is easy to see that in all cases the monopolist’s profit is obtained only by harm-ing others” (1896/1897, vol 1, p 69)

Entrepreneurs are the central agents in Pareto’s theory of production He argued that some entrepreneurs choose a technology with variable coefficients of production and other choose one with fixed coefficients He included both types

in his theory of marginal productivity, thus producing a sophisticated version (1896/1897, vol 2, pp 84–90)

WELFARE ECONOMICS

Pareto supported the thesis that free competition generates a relative maximum

of welfare for a society, and he sharpened the definition of that situation by stating that the “members of a group enjoy, in a certain state of the economy, a

maximum of utility when a small change is agreeable to some, disagreeable

to others” (1909, ch VI, §33, p 354); in other words, when it is impossible to make anyone better off without making someone worse off Pareto also developed propositions about the welfare aspects of production and consumption of consumer commodities that were similar to Walras’s theorem on the maximum utility of new capital goods (Walras, 1889, pp 301– 7; 1988, pp 417–25) As a result of these formulations, Pareto became the first theorist to demonstrate, subject to various conditions, that a state of maximum efficiency can be achieved

by an economy of the type that Walras described in his model Pareto’s formulation became the foundation of the “new welfare economics,” which is the modern study of maximum efficiency and well-being In recognition of his contribution, the optimum condition that he identified is known as a Pareto optimum Pareto’s analysis of economic efficiency was powerful and general because he took account of the conditions for maximum efficiency in markets for all types of com-modities, and in exchange, production, consumption, and capital formation One of his notable contributions in this regard was to distinguish between the conditions for maximizing individual welfare and the conditions for maximizing the welfare

of society as a whole He showed that earlier economists sometimes erroneously assumed that because an individual can reach a higher level of well-being when he acts alone, all individuals can do so when they act simultaneously In particular, he noted that if national income is constant, one person may be able to increase his welfare by acquiring more income, but all individuals obviously cannot do so Those who believe that the distribution of income should be changed have not been pleased with Pareto’s law regarding it He developed an equation that he believed describes the general aspects of the distribution of income in many different economies and times, showed the goodness of fit of the equation to the data for some economies, and concluded that the “distribution of income is not the effect of chance” (1897, p 315) He argued that there are underlying laws of production and of the use of economic resources that cause the distribution

of income to take that general form, thereby casting doubt on the possibility of altering the distribution of income by government policies Even if it were true, however, that the functional distribution of income is largely unchangeable, Pareto should not be understood as implying that the personal distribution of income cannot be affected by taxes and transfer payments

18.2.3 General socioeconomic equilibrium

Pareto’s sociology was not an abandonment of economic analysis, but an attempt

to provide a broad perspective which would enable a better comprehension of