Walrasian Philosophy
and Theory of

General Equilibrium

by Kamrouz Ghadimi





In order to simplify an idea as abstract as achieving equilibrium simultaneously within multiple markets, the requisite of mastery in economic science must be present.  This esoteric understanding demands a certain vision that not only satisfies the necessities of the present but also one that foreshadows the conditions of the future.  The science and philosophy behind such thought supercede the borders of simple intellect and dive into the realm of realistic imagination.  Much like neurons within the mind develop webs of signal exchange, the markets within an economy work interdependently with one another.  The realization of the mechanics behind these relationships delineates the essence of Walrasian economics.  Before understanding the economics of Walras’ teachings, it is important to understand his social and biographical background so as to place his ideas and theories in a perspective from which we can derive the basis for his thoughts. 


Biography and Influences 


Leon Walras was born in Evreux, France on December 16, 1834.   His father was Auguste Walras, who was a well-known economist of the 19th century and was close colleagues with Augustin Cournot (from whom the “Cournot Equilibrium” is derived).  Walras was born into a time of ongoing industrialization in France.  In essence, an “industrial revolution was unfolding, particularly in terms of the consequences: the creation and impoverishment of a growing industrial working class in a previously agrarian society” (1). The working class sank to a minimum in working conditions, salary and housing as well as in morality, which then was described as being “unworthy of man kind” (2).  The slums in Paris housed masses of potential workers willing to offer their services for a small payment, as well as fostering an environment for social disorder.

In February of 1848, the social abuses eventually led to what is now known as the “Revolution of 1848” (1).  The revolt meant the end of the reign of Louis-Phillippe, and the beginning of the Second Republic with Louis Bonaparte as president.  On December of 1851, a coup d’etat elevated Louis Bonaparte to his investiture as Emperor Napoleon Bonaparte III (2).  The emperor implemented a practice of social and political reform, with an overlying theme of repression at the forefront. 


In turn, these events contributed to Walras’ upbringing and the evolution of his ideas.  Walras himself writes, “I was thus one of these young men united through the Revolution [of 1848] by heads and hearts in a movement, on which the coup d’etat of December 1851 fell so brutally” (1).  It must be noted, however, that Walras was not a member of any particular political party most aptly due to the “social and political turbulence” (2) of the Revolution of 1848.  In lieu of this complete renewal of society in order to overcome social problems, Walras advocated a gradual change in the organization of society.  This adjustment could, eventually, lead to a more durable result, and as Walras claimed, “and believing, as I do, in humanity, in eternal progress, the causes will be found in the development of human progress” (4).

 Walras’ idea of general equilibrium was not entirely original.  In fact, an early implicit pattern of mutually interdependent relationships underlies the writings of the great classical founders of economics, Adam Smith, David Ricardo, and Jean Baptiste Say (2).  The true influence on Walras’ original idea of multi-equational formulation with regards to general equilibrium, however, was Louis Poinsot’s Elements de Statique (Static Elements) published in 1803.  Poinsot held that “if there are an equal number of unknowns as there are equations, then the unknowns could be solved” (1).  Walras kept a copy of Static Elements with him throughout his life and referred to the reading on many occasions, particularly during the concoction of his main piece, the Elements. 


William Jaffe & Walras’ Philosophical Framework


The leading authority on Leon Walras and Walrasian economics is William Jaffe.  He spent many years during the first half of the 20th century studying Walras’ biography, his theories and most importantly, how his philosophies fit into the framework of his economic views (1).   Prior to Jaffe’s translation of the Elements d’economie politique pure (The Elements of the Pure Political Economy), Walras’ theoretical ideas were not accessible to English-speaking readers and economists.  Walras’ obscurity to the English-speaking economist also spurred from the fact that he emphasized the mathematical method.  In essence, he was speaking in a different language, twice removed (once because it was French and twice because it was mathematics).  Furthermore, Jaffe studied Walras’ life and focused on “the elements if biography that affect a writer’s selection of theoretical problems and his method of handling them” (2). 

There were three major aspects in which Jaffe thought that biography is valuable for the history of science.  First, he adopted the controversial position that “knowledge of the intellectual characteristics of a scientist [was] necessary to understand the meaning of his work” (1).  Second, he believed that biography helped explain the genesis of ideas in that “the genesis of an original analytical contribution is idiosyncratic and…this genesis cannot be adequately understood without reference to the peculiarities of the mind of the originator of the novelty” (1).  Finally, Jaffe maintained that biography illuminates the process of accepting a theory.  In due course, Jaffe assessed the main points of Walras’ life, focusing further on his philosophical approach and from this study, shedding light on Walras’ abstract, yet discernible, economic views. 


Walras was an avid follower of his father, Auguste.  Both Auguste and Leon Walras felt that reason was “an indispensable prerequisite for programs of viable political and economic reform” (4).  As early as 1831, in his work entitled Of the Nature of Wealth and the Origin of Value, Auguste Walras had hinted at the possibility of “creating a mathematical economic science” (2). Jaffe sketched Walras’ overall conception of economics in a three-tier methodology.  Walras referred to this as the “triple point of view of the True [which led him to contribute to economic theory], the Useful [which stimulated him to investigate problems in applied economics], and the Just [which motivated his concern with social economics and morality]” (2).

 Walras’ study of social economics, in particular, did not solely discuss the welfare ramifications of trying to achieve different objectives but also evaluated the objectives themselves and created new goals.  Walras produced many special studies, treating subjects such as “communism, individualism, socialism, liberalism, and utilitarianism” (1).  The social activity referred to by Walras, was differentiated into, on the one hand, relations between persons on an economic basis, and, on the other hand, relations between persons on a moral basis (2).  Both points of view, however, were seen as inseparably forming the “social perspective” (1).  The economic relations between men were, according to Walras, based on the natural fact that “man’s wants always surpass his own abilities to fulfill them” (4).  The only way to satisfy these needs was to specialize in a certain occupation and to create and exchange a surplus of goods with others in society.  Economic relations were, therefore, based on the division of labor in which all men were in contact with each other as specialized workers.  In this respect, “the division of labor was the condition of human destiny in society, in which individualistic situations were excluded – either languish in isolation or prosper in, and through, society” (2).  


Despite the fact that Walras’ ideologies reflect the same basic theory of the specialization of labor which Adam Smith hails in The Wealth of Nations, the ideas of the two economists vary in the sense that Walras felt that Smith’s justification for the value of labor was incorrect.  Walras remarked the following:

Whether labor is all or part of social wealth is beside the point.  In either case, why is labor worth anything? Why is it exchangeable? That is the question before us.  Adam Smith neither asked nor answered it.  Surely, if labor has value and is exchangeable, it is because it is both useful and limited in quantity, that is to say because it is scarce.  Value therefore comes from scarcity.  If there are things other than labor that are scarce, they will also have value and be exchangeable.  So the theory which traces the origin of value to labor is a theory that is completely devoid of meaning rather than too narrow, entirely gratuitous rather than merely deficient (2).

In essence, Walras claims that labor (and any other good that fits this condition of scarcity) is not valuable as a result of the products it can produce but rather it has value due to its “limit in quantity”.


The Essence of General Equilibrium Analysis


As most economists know, the idea of value is delineated by price and price is a reflection of free market equilibrium.  Prior to Walras, economists attempted to piece together various markets in what is known as “partial equilibrium analysis”.  The issue that was addressed was that economies consist of thousands or even millions of distinct but interrelated markets in a constant state of flux.  In due course, how does a harmonious general equilibrium of all markets come to be?  Moreover, will the “disequilibria of forces disrupt the neat harmony of the partial equilibrium model” (1)?  Walras affirmed that “competitive capitalism would be able to generate a set of general equilibrium prices by which all markets could be cleared simultaneously” (3). He claimed that within the general equilibrium framework, the demand and supply schedules in each market (in a total of X amount of markets) will be functions of their own price and the prices of all other commodities in the economy.  These interrelationships are due to the substitute and complimentary relationships amongst various products.  As formulated by Walras, the general equilibrium system will consist of X equations and X unknowns.  Walras, however, went on to elucidate the fact that the value of purchases must equal the value of sales, later on referred to as Walras’s Identity (3). Insofar as , “there must be one commodity singled out as a numeraire, and the system can then be solved for a consistent set of equilibrium prices” (3), general equilibrium analysis now consisted of X-1 unknowns and unknown equations.  The numeraire, or standard, dictated the absolute prices and the other market prices adjusted relative to the initial shift in absolute prices (e.g. the supply of the stock of gold drops therefore the absolute price of gold increases, followed by a series of leftward/upward supply shifts in other markets).  Walras’ main point suggested that general equilibrium does exist and the economy will return to a new equilibrium if the initial equilibrium in disturbed (4).   


Framework behind the General Theory of Equilibrium *


                General equilibrium refers to the idea that divergent interests of consumers and producers can be harmonized not only for single markets, but also for all markets simultaneously (3).  Walras’ primary work, the Elements, created a scenario for general equilibrium, a scenario that was perfected throughout his following three editions.  The quintessential nature of the Elements was, and continues to be, a theory of social wealth (1).  His classification of social wealth divided durable goods, or capital, from non-durable goods, or income.  Capital included land, personal faculties and capital goods proper, which could be used more than once in its purpose (2).  Income, in turn, could only be used once, after which it no longer existed.  According to Jaffe, Walras referred to each successive use of capital as a “service”, which was passed to the category of income due to it non-durable nature.  The fundamental necessity of money was injected into the scenario by separating it into two categories due to its mixed nature of durability and non-durability.  As cash holdings in circulation, for instance, money was considered a capital good, but for money as savings, it was considered a form of income (2).  


  Jolink describes the following categorization of social wealth, as presented by Walras.  This categorization distinguishes thirteen elements, which serve to elucidate the development of the modeling of exchange.  These elements are:


      In the category of ‘capital’

1.        land capital

2.        personal capital

3.        capital goods proper

(Note: 1-3 yield consumers’ services)

4.        land capital

5.        personal capital

6.        capital goods proper

(Note: 4-6 yield producers’ services)

7.        new capital goods

8.        cash holdings of consumers

9.        cash holdings of producers


In the category of ‘income’

10.     consumers’ goods (including consumers’ services)

11.     raw materials (including producers’ services)

12.     new income goods

13.     money savings


Walras admits that his production of several theories utilizing the thirteen elements is a bit abstract, “but when they are progressively absorbed in one another by a process of systematic synthesis, they take us right into the midst of reality” (1). Therefore, the theoretical structure presented in the Elements “consisted of a progressively expanding world into which an increasing number of variables were injected” (4).  Jaffe translated Walras’ ideas into the Exchange model, the Production model, the more advanced Capital Formation model and the Money model.

In the Exchange model, only item 10 of social wealth (the elements of consumer goods) was employed to delineate the workings of free competition in the exchange of two or more commodities in the commodity market.  In the market, “suppliers and demanders” of consumers’ goods meet, and exchange the commodities on the basis of the utility the product will provide them.  According to Walras, one would have to impose 2 conditions on the exchange model in order to ensure the outcome of an optimal situation.  These conditions are:

I.                     The rate of exchange of two commodities would apply to all traders (in the particular market). Thus, there is only one price for each commodity (2).

II.                   The rate of exchange of two commodities is proportional to the rate of exchange of these commodities separately to a third commodity (2). 


The Exchange model was then extended to include items 1-6, 10, 11, and 12, excluding new capital goods and money (2).  This new model was referred to as the Production model, which examined the mechanism of free competition in two separate markets.  The production of the commodities, which will be traded in the Exchange model, the producers and entrepreneurs required producer services and raw materials (1).  The owners of the capital, yielding these services in a second market -- the services market -- offered these particular services.  The raw materials in the market are absorbed in the productive services that entered into the production of these raw materials.  With this in mind, landowners, workers and capitalists offered land-services, labor-services, and capital services, respectively (2).  In return, these capital-owners demand consumers’ goods in the commodity market and consumers’ services in the services market  (See Fig.1). 

The Production model, fundamentally, became a determination of the prices of consumers’ goods and services as well as raw materials and productive services by means of a “theory of exchange in which production takes place but is not explained” (1).  In this respect, the particular behavior of the consumers (e.g. the traders within the Exchange model) remained the same.  The producers and entrepreneurs, conversely, were mainly guided by their “profit or loss” position rather than by judgments based on utility (1). The Production model, though maintaining the prerequisite conditions of I and II, prescribed a third condition within the overall framework:


III.                 The selling prices of the commodities are equal to the costs of the services and raw materials used to produce the commodities (2). In other words, total revenue equals total costs, with profits equaling zero.

A general equilibrium market will then include both consumption and production of consumers’ goods.

Figure 1 (which is borrowed from Jolink), directs the flow of services offered towards the services market and continues either directly to the consumers or to the creation of the commodities.  The flow of the commodities, in turn, is directed towards the commodity market, ultimately being offered to the consumers


By adding new capital goods (item 7) and money savings (item 13), Walras “extended the Production model into what is now referred to as the Capital Formation model” (2).  This model examined the mechanism of free competition taking into account capital formation and credit, thereby extending the analysis to the explanation of the prices of capital goods proper (2).  This new model relates the prices of the capital goods proper to the income they generated for their services.  Walras deducted for depreciation costs and obtained the net income, the ratio of which to the capital goods proper, may be considered as the rate of return on the investment, or the “rate of net income” (2).  In this model, Walras injected the notion that producers could produce either consumers’ goods or new capital goods proper and that consumers could buy either consumers’ goods and services or the new capital goods proper.  Walras was the first to suggest the idea of credit in that the latter of the two newly introduced ideas were bought through shares.  These shares would secure future income for the consumer to which they attributed a present utility.  Ultimately, a third market was introduced, one where capital proper was traded (see Figure 2).

Figure 8 (also borrowed from Jolink) displays the flow of services and commodities.  The capital-services offered on the services market are demanded either for final consumption (consumers’ services demanded), the production of commodities (productive services demanded) or new capital goods (offered in the capital market in forms of shares).  The produced commodities are therefore offered on the commodity market either as raw materials or final consumers’ goods (commodities demanded).  According to Walras, the former will enter into the production of new capital goods whereas the latter will leave the system  (2).


Given this expanded model, Walras added one more condition:

IV.                 The ratio of net income of the capital-service to the price of the capital good is equal for all capital goods.  (In other words, there is only one rate of net income) (1)

The Money model followed the introduction of the Capital Formation model and provided the last two elements of social wealth, items 8 (cash holdings of consumers) and item 9 (cash holdings of producers) (2).  This final ingredient completed Walras’ mechanism for exchange.  His view was that stocks of consumers’ goods or raw materials and final commodities could be kept “in kind or in money” (2).  This methodology allowed for the integration of cash holdings of consumers (item 8) and the cash holdings of producers (item 9) into the model.  The stocks were referred to as “circulating capital” and, as Jaffe indicates, reflected in the Walrasian model a certain amount of “services of availability” (versus the services of use that the other models portrayed).  A unique feature of the Money model was that final consumption goods could be added to the capital stock, as well (2).  *


A discussion of Statics versus Dynamics


 According to Jolink, “the four models observe, describe and explain the mechanism of free competition in the exchange of social wealth during a certain period (2).  Jolink goes on to indicate, however, that this does not imply that the mechanism could not be considered as being dynamic.  In actuality, the system itself operates in such a manner that the “basic input data” (e.g. the initial quantities of capital and income and the preference of the consumers) will change or will create an impetus that will procure the technical circumstances of production to change (2).  Walras himself addressed this question and indicated that once the analysis included several periods, “the market will continually meet different circumstances” (1).  Walras did indeed address the topic of the “variation of prices in a progressive economy”, formulated in a law with the same name (2).   In this context, he claims:

"Pure economics, as I have formulated it…defines in this manner…that there are two natural types of social wealth:1.the land and 2.the personal faculties of man; in addition, it defines that the value of the second does not necessarily change whereas the value of the first rises necessarily in a progressive society which goes through the transition of a regime of hunting and fishing to the pastoral, agricultural, industrial and commercial regimes.” (2)


He stated, however, that such a solution could be arrived at “in an economy in normal operation which has only to maintain itself in an equilibrium state” (1).  Walras recognized that “in a society that has just been economically disrupted by a war, a revolution, or a crisis” (2), the attainment of equilibrium would not be anticipated. 

In the same line of reason, Walras divided his analysis into three phases, known as the tatonnement phase, the static phase and dynamic phase (1).  In the first phrase, he examined the exchange process prior to equilibrium, in which prices tended towards this equilibrium (tatonnement means “groping” in French). The second phase focused on the effective establishment of equilibrium, whereas the third phase analyzed the change in data and the deviations from the initial equilibrium.  Consequently, Walras established his “Law of the Establishment of Equilibrium Prices” (1), specifying that equilibrium is actually achieved only when conditions I-IV are attained (2).  From the third phase, Walras then established the “Law of the Variation of Prices”, in which he investigated the increase and decrease of prices with respect to the causes of fluctuation (2).  The two laws together formulated “Walras’ Law of Supply and Demand”.  Walras’ proof of this composite law employs “analytical mathematics as a means of abstract reasoning, for the purpose of providing theoretical solution to the problem of the determination of equilibrium prices” (1).   His proof, though in agreement with the “practical state of affairs” (1), is not the end all, be all of general equilibrium analysis.  He himself asserts, within his writing of the Elements, “it should be recalled…that what we have in mind throughout this volume is not to pose and solve the problem in question as if it were a real problem in a given concrete situation, but solely to formulate scientifically the nature of the problem which actually arises in the market where it is solved empirically” (1).  Indeed, Walras based his empirical analysis on the Paris Stock Exchange (2).  Although Walras concluded that “the conformity of the tatonnement-process with an actual movement of prices at the Stock Exchange could indeed be found” (2), Jaffe maintains that, “Walras failed in his attempt to show that the real market system solves his equations by the tatonnement-process” (1). 


Laissez-faire and Free Competition under the Walrasian School


                According to Walras, “laissez-faire was the act of allowing free competition to exist and thus guaranteeing the optimal conditions for abundant and proportional production.”  He presented an active approach to laissez-faire and felt that many specific instances of competition deviated from the ideal situation presented in his theory of pure economics (1).

 The principle of free competition, from which Walras built his fundamental argument upon, rested on three cornerstones.  The first suggested that the individual have an optimal understanding of his or her utility as was manifested within their individual demand of commodities and services (2).  Secondly, producers could enter or withdraw from any productive branch, thus inducing profits to move to zero (2).  The third cornerstone implied that the “State should not only organize and maintain the proper conditions, but should also remedy the consequences of the deviations from free competition” (2). 


Final Comments


                Jaffe suggested that “despite the fact that Walras’ general equilibrium approach was incorporated in British and American economics, it is noteworthy to indicate that this incorporation was not a result of direct reference to his work by most economists, but a consequence of a study of the Walrasian economics of such writers as H.L. Moore, Irving Fisher, Henry Schultz, and J.R. Hicks” (4).  Walras’ Elements, as Jaffe adds, served as the “fundamental source of inspiration for economists such as Sir John Hicks and Joseph Schumpeter” (2). In fact, Schumpeter declared “ as far as pure theory was concerned, Walras [was] in [his] opinion the greatest of all economists” (2).  Barone praised his general equilibrium system in numerous publishings, calling it the “most general, most comprehensive and most harmonious” theory that had yet appeared (2). Conversely, there were those economists, amongst them being Janos Kornai and Michio Morishima, who felt that “at best [the Elements] were an unfortunate anachronism and at worst a diabolical influence that had led modern economics woefully astray” (5).   Irrespective of the type of reaction that Walras’ views have received, the thought provoking nature of his teachings have left a lasting impression on economic thought. 


Works Cited


(1) Jaffe, William. Essays on Walras. Cambridge University Press: Cambridge.  1983.


(2) Jolink, Albert.  The Evolutionist economics of Leon Walras. Routledge Publishing, New York.1996. 


(3) Gregory, Paul R., Stuart, Robert C. .Comparative Economic Systems.  Houghton Mifflin Publishing:

 Boston.  1980.


(4) Jaffe, William. Journal of economics. “Leon Walras: An Economic Adviser Manque”. v85 (340),  pp.810-823. December 1975.


(5) Morishima, Michio. Walras’ economics: a Pure Theory of Capital and Money.  Cambridge University Press:  Cambridge, England.  1977. 


* The ‘Framework’ has been adopted mainly from Jolink, with addendums by Jaffe (1) as well as Jaffe (4).

* Aside: My discussion of Walras’ framework neglected the incorporation of mathematics in the spirit of clarity and an uncomplicated explanation of the economics behind his ideas.  With emphasis, however, Walras has been credited for his in depth incorporation of mathematics within the study of general equilibrium analysis.










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