Leon Walras (1834–1910)

Abstract

After having studied this chapter, the reader should be able to:

FormalPara Learning Objectives

After having studied this chapter, the reader should be able to:

• Understand the basic principles of General Equilibrium analysis.

• Analyse the key assumptions of General Equilibrium models.

• Describe the role of the ‘auctioneer’.

• Name the key players in the economy.

• Analyse the key points of the neoclassical theoretical system.

• Present briefly Leon Walras’s contribution to Economics.

FormalPara Summary

Léon Walras is considered as one of the pioneers of the Neoclassical School of Economics. According to his theory, the economy is composed of different actors: (a) producers, (b) consumers and (c) entrepreneurs, and economic equilibrium results from the simultaneous interaction between them in the market. Market exchange relations are developed by the various agents as a result of the pursuit of their individual interests. Through Mathematics, Walras attempted to answer the question of whether it would be possible to discover the prices that would make all the individual markets in the economy achieve General Equilibrium, and he found that such a discovery is indeed possible, but under certain conditions. Therefore, Walras showed in his General Equilibrium model that the various actors in the economy can reach a market equilibrium – under certain conditions – by pursuing their individual interests. Therefore, he is considered the founder of the General Equilibrium theory, which bears his name, that is also known as Walrasian Equilibrium. Lastly, Walras’s and other neoclassical economists’ work has led to a theory demonstrating that the market is self-regulating and results in optimal resource allocations.

4.1 Introduction

Léon Walras was born in France in 1834 and, along with Carl Menger and Stanley Jevons with whom he came to similar conclusions although they did not work together, is considered one of the pioneering economists of the so-called Neoclassical School.¹ His work is very important because he is the ‘father’ of the modern Neoclassical General Equilibrium theory,² which dominates Microeconomic Analysis and also certain fields of Macroeconomic Analysis with microeconomic foundations.

His father, Auguste Walras, was an amateur economist of his time, and it was he who encouraged the young Léon to take up the study of Economics. In fact, he believed that Economics would be transformed into Mathematics, and it is he who provided young Walras with a highly regarded library of Economics books to study.³ Léon Walras twice failed to gain admission to the famous Ecole Polytechnique, that is, the Polytechnical School of Paris, because of inadequate preparation in Mathematics.⁴ He eventually studied Engineering, but at the Ecole des Mines in Paris,⁵ until his interest was attracted to Social Sciences and Economics, under the constant encouragement of his⁶ father.

Among other professions, such as author of literary books, he was for a short time a journalist, and in 1865, he co-founded a cooperative bank which he ran. Between 1866 and 1868, he also published a monthly magazine, Le Travail, which was mainly devoted to the cooperative movement. During this period, Walras gave public lectures on social issues.⁷ The activities of the cooperative bank were terminated in 1868, whereupon he started working for a private bank until 1870,⁸ at the same time that, thanks to an important acquaintance with an influential politician,⁹ he occupied the chair of Political Economy at the University of Lausanne. There, he remained engaged in research and teaching Economics until 1892 when he retired at the age of 58. Unfortunately, he was not an inspiring teacher,¹⁰ and perhaps for this reason, he had no loyal students, combined with his frequent mental exhaustion and irritability.¹¹

His life was unconventional for the time, with children in and out of marriage, one of whom died in infancy, two marriages, the first of which ended with the death of his wife and with unprecedented financial problems that caused him to experience very difficult years. Thus, in addition to his research and teaching at the university, he was forced to write for newspapers and to work as a consultant for an insurance company.¹² His second marriage was a happy one, and he inherited some considerable money that helped him to pay off the debts he had incurred from the publication of his work and the dissemination of its¹³ results.

Léon Walras is considered the founding figure of the Neoclassical School of Lausanne, while his successor in the chair of Political Economy and the successor of his work was Vilfredo Pareto. Walras’s innovative ideas on how prices are determined, transactions are conducted and General Equilibrium is achieved were published in 1874 in his work entitled Éléments d’ Économie Politique Pure.¹⁴ The ideas of both Walras and the other pioneers of the ‘marginal revolution’, Menger and Jevons, were incorporated into mainstream economic theory several decades after their formulation and gradually formed the core of what is now called ‘Neoclassical Economics’.¹⁵

As regards the relatively late integration of Walras’s work into Economic, this may have been due to the fact that Walras was French and, moreover, that he belonged to the area of so-called utopian socialism.¹⁶ His work shows that he identified himself as a ‘scientific socialist’ and this may be indicated by the fact that he was an advocate of nationalisation of land and natural monopolies and supported the reliable operation of the capital market by the state. At the same time, his Political Philosophy was a mixture between liberalism and state interventionism that favoured moderate reforms in socio-economic matters,¹⁷ while arguing that Economics has nothing to do with economic policy¹⁸ making.

Today, it is characteristic that parts of Walras’s work are found in many modern Economics textbooks, while today’s economists are more familiar, even if unaware of it, with Walras’s work than any other well-known economist. Typical of the influence of the concept of General Equilibrium, and of Walras’s wider work in Economics, is the fact that Joseph Schumpeter considers him to be the most important theoretical economist.¹⁹ In contrast, Keynes mentions him in his well-known General Theory only once.²⁰

Walras used Mathematics extensively to analyse economic phenomena and was a proponent of the idea that Economics should make use of the methods and tools of Physics. This is why he finds parallels between physical phenomena (such as friction) and economic phenomena (such as free competition).²¹ For instance, we argued that the market is perfectly competitive, just as in pure Mechanics we assume that machines operate without friction.²² Thus, Walras, through his work, offered a different prism through which to analyse the important role that the competitive market model holds for modern neoclassical Microeconomic Analysis.²³

4.2 The Functioning of the Economy

Although the issue of the interdependency between the various actors in an economy had been studied by earlier economists such as Condorcet and Cournot using Mathematics, no economist had been able to construct a general analytical structure linking the various economic actors in the system. It was, after all, the time when economists admired physicists and began to use Mathematics more widely in Economics. The two most important representatives were the British chemist, meteorologist and author Stanley Jevons, and the other was certainly Léon Walras.²⁴ Meanwhile, in addition to Jevons, Walras considered Ricardo’s theory to be logically and economically flawed and, therefore, unable to contribute in a way that would provide coherence to both the determination of the relative prices of commodities and the distribution of income.²⁵

For the first time, in Walras’s theory, the economy consists of various economic agents participating in the market either as (a) producers, (b) consumers (c) or entrepreneurs, interacting in the market. That is, labour is transformed into (a) products, which are (b) either purchased by entrepreneurs for further use in the production of other products or (c) consumed by final consumers. The latter, having offered their labour to the entrepreneurs, buy the products produced from them, spending the income they have received from them in return for their labour. The pursuit of their individual interests leads the various actors to develop exchange relationships on the market.²⁶

A key objective of Walras’s theory was to analyse and demonstrate how voluntary exchanges between economic actors who are (a) well-informed, (b) aware of their own interests, (c) seeking to maximize their goals, will lead to an efficient and effective mode of production and income distribution.²⁷ Thus, through the General Equilibrium model constructed by Walras, he demonstrated that the agents in the economic system, through the pursuit of their self-interest, can – under certain conditions – reach a market equilibrium and for this contribution, he was the founder of the theory of General Equilibrium, named in his honour ‘Walrasian Equilibrium’.²⁸

Walras, developing his theory after the era of the Classical economists, for the first time presented a theoretical model that took analytical expression and had as its basic starting point the fact that all actors in the economy interact and are fully interdependent.²⁹ In fact, Walras’s theoretical effort to find under which mathematical conditions an economy with interdependent agents could operate efficiently and mutually beneficially had an enormous influence on modern Neoclassical Economics, so much so that a very large part of modern Economics deals with issues of Walrasian General Equilibrium.

4.3 The General Equilibrium

In order to establish, with the help of Mathematics, the General Equilibrium model at a given price level, Walras made the following assumptions, which to this day are dominant in modern Neoclassical Economics:³⁰

• Consumers seek to maximise their utility, while firms seek to maximise their profits.

• The market is competitive, as the number of consumers and producers is so large and they act in an individual way, which does not allow them to influence the price level of the products.

• Firms produce homogeneous products, face the same cost conditions and have similar technological capabilities.

• Economic actors take their decisions with full knowledge of the current product prices.

• Both, inputs and outputs, have a positive price and are not unlimited.

• Consumers’ utility increases with increasing quantity, but at a decreasing rate, and their desire to consume is not subject to satiation.

• The demand for inputs and outputs depends on their price.

• The supply and demand functions in the economy do not experience unexpected jumps, that is, they are practically continuous.

• Each production function of a good corresponds to a specific and unchanging combination of factors of production, as the substitution of production factors is not possible by existing technology.

• There is a good whose price is arbitrarily chosen as a measure of the values of the other goods and factors of production (numéraire).

• Products and factors of production initially have a given distribution.

His analysis took as its starting point an exchange economy and, more specifically, a market in which auctions take place and where everyone has at their disposal some quantity of each good as an initial endowment.³¹ The quantity of goods is given, and each person in the room knows how many units of each good he or she possesses. A central auctioneer, who is responsible for conducting the auctions, is responsible for announcing the relative prices of the goods on a table, based on the price of the arbitrarily chosen unit of the good.

Then, each person, based on the announced prices, states his intentions about which part of the goods he intends to sell and his intentions about the above products he intends to buy and records them on a piece of paper. The auctioneer, Walras argued, would collect these papers, and after ascertaining which goods’ prices were causing an excess demand and which were causing an excess supply, he would announce new increased prices for the first class of goods and new decreased prices for the second class of goods, respectively.

Individuals will restate their intentions as to the quantities of goods they are willing to demand or offer at the new prices, the auctioneer will reassemble the cards to determine where there is excess demand and excess supply, and this auction process (tâtonnement in French and trial-and-error in English) will continue until the price at which demand equals supply is found for each good. At these prices, the famous Walrasian Equilibrium is reached, and before these prices are discovered, individuals are not allowed to buy or sell goods.³²

Using the above assumptions, Walras showed, using systems of linear interdependent equations, that there can be prices that lead to equilibrium markets, that is ensure equality between aggregate demand and aggregate supply.³³ Moreover, as far as the General Equilibrium is concerned, it does not imply the absence of excess demand on the part of consumers or excess supply on the part of sellers. In some markets, supply may exceed demand or vice versa. What equals zero will be the sum of the values of excess demand and excess supply, which means that under this condition, Walras’s law can hold even when all individual markets are out of equilibrium.³⁴ Thus, for Walras, the imbalance between supply and demand will be settled if the price of the good changes, while causing spillover effects in other markets in the system.

But at the same time, there is another issue. In order to show that the wishes of the individual agents lead to mutually beneficial transactions, we need to show that there exist prices which make this possible. To this end, price analysis is central to General Equilibrium theory, since prices are the parameters on the basis of which individual choices are made. This establishes a set of relationships between the prices and the quantities exchanged in relation to inputs and outputs. Indeed, this set of relationships is in a state of General Equilibrium when prices and quantities are such that all actors maximise their³⁵ objectives.

More precisely, an economy is in a state of General Equilibrium when there is a set of prices for which: (a) in every market supply equals demand, (b) every agent in the economy is able to buy and sell exactly what he/she planned to buy and sell, (c) all firms and consumers can exchange exactly the quantities of goods that maximize their profits and utility, respectively.³⁶

In order to arrive at this result, we need to know the number of consumers, the number of firms, the initial stocks of resources, consumer preferences and the available production technologies. All the rest of the process is left free to the maximising behaviour of the economy and the competitive market³⁷ mechanism. In practice, however, two key elements are needed to achieve this balance. The first, as we have already seen, is the specific role of the auctioneer. The second is the equally specific role of firms.

Walras, in his analytical model, considered that in an equilibrium position, the profit of firms is zero, because of competition between them. Thus, in practice, in the Walrasian General Equilibrium approach, only one class of agents maximises its objectives, and that is the consumers. The entrepreneurs, like the auctioneer, simply coordinate and organise, taking prices and production technologies as given. Thus, the existence of profit is a sign of disequilibrium, so the entrepreneur reacts by increasing the scale of production when there is a profit and, correspondingly, reducing it when there is a loss.³⁸ In other words, in a state of equilibrium, entrepreneurs have neither profits nor losses.³⁹ That is, for Walras, a firm is in equilibrium when its profit becomes zero due to competition between firms.⁴⁰

In this context, Walras tried to answer, with the help of Mathematics, the question whether it is possible to discover those prices that will lead all markets in an economy to General Equilibrium and found that this is indeed possible, but under the conditions: (a) that purchases and sales will be hidden until the central auctioneer manages to ‘discover’ General Equilibrium and (b) that firms make zero profits in General Equilibrium.

As we have seen, Walras constructed a system of simultaneous interdependent equations to describe the interaction between consumers and entrepreneurs. There are as many markets as there are goods, including their factors of production and services, and for each market, three equations are defined: one for demand, one for supply and one for equilibrium. However, a necessary but not sufficient condition for such a system to have a solution is that the number of unknowns equals the number of equations, a condition that has created several problems. One of these is, for example, that such a system is not always guaranteed to have a unique solution, since it may be either impossible or have infinite solutions, or even if there is a unique solution, we do not know whether it has economic significance (e.g. a negative value or quantity). The problem in question took almost a century to be addressed by neoclassical economists⁴¹ with the famous Arrow-Debreu (1954) model which showed that under certain restrictive conditions there can be a unique solution in the General Equilibrium of the market.⁴²

In conclusion, thanks to Walras’s work, one has the opportunity to reflect both on the complexity of all the economic interdependencies and transactions that take place and on the difficulty of achieving the Walrasian General Equilibrium in a real economy in order to solve problems such as unemployment or economic fluctuations and crises.⁴³

4.4 The Theoretical Legacy of Walras

There are several key features of the neoclassical theoretical system that prevailed in economic thought and are present in Walras’s⁴⁴ work. Thus, a first key to such point is the abandonment of economic development and other socio-economic aggregates. In their place, emphasis was put on the allocation of the limited resources between alternative uses, and especially the analysis of the conditions that ensure optimal such allocation. As Samuelson⁴⁵ informed us, at the heart of all economic problems is now the maximisation of a mathematical function under constraints, for example, the maximisation of utility under a budget constraint.

A second feature that has to do with the ‘methodology’ is that of using the calculus of variations to search for the conditions under which the optimal solution is chosen.⁴⁶ Thus, there is the concept and the dominance of ‘marginal utility’⁴⁷ in terms of the calculus of variations, that is ‘extra utility’, seen as a measured quantity, that an ‘extra unit’ of a good provides.⁴⁸

A third characteristic element that runs through the analysis of neoclassical economists and Walras’s work is the acceptance of the utilitarian approach as a pillar of the neoclassical synthesis, the best-known representative of which is Bentham. The adoption of this approach means that man is no longer by his ‘nature’, for example a merchant as in Smith, but a subject who acts according to the principle of maximum utility, that is directs his actions towards increasing the pleasures from the use of goods,⁴⁹ since nature has placed mankind under the dominion of pain and pleasure.⁵⁰

This leads us to a fourth element which implies the replacement of the ‘objective’ theory of value with a ‘subjective’ theory of value derived from the utility of the object. Thus, an object now has value only if a subject⁵¹ desires it, as opposed for instance to the labour theory of value, where its value exists independently of individual choice and is due to the labour expended to produce it. Therefore, labour is no longer seen as the intrinsic, quantitative characteristic of commodities.⁵²

A fifth element that is pervasive in Walras’s work as a neoclassical economist has to do with the individualistic status of all actors in the economy and the maximisation of the interests of individual actors maximising their own individual interest. Thus, we have, for example, the individual as consumer, as producer, as entrepreneur and the ‘minimal’ possible social actors, such as households and firms, eliminating the total economy and the large social classes. That is, it does not require or imply any social concept or theory. Consequently, the individual or agent is considered to be sufficiently representative of the whole society. The neoclassical approach does just that. It applies the principle of the ‘substitution’ of the individual⁵³ for society, since society is seen as an abstract theoretical concept and it is considered meaningless to speak of the interest of society without understanding the interest of the individual.⁵⁴

Finally, a sixth and last basic element related to the previous one in the work of Walras, as one of the main representatives of the neoclassical school, is the attempt to transform Economics into Physics, with strict laws in Physics and theorems in Mathematics which are, in Platonic terms, absolute, objective, indestructible and eternal. Thus, we must remove social relations from the field of Economics in order to establish the universal validity of their ‘laws’.⁵⁵ Thus, Walras, redesigned Economics on the lines of the Natural Sciences, while being hostile to those who resisted the process of its transformation into a Mathematical Science.⁵⁶

In conclusion, through the neoclassical approach, Microeconomic Theory emerged as a theory of individual choice, as opposed to the Classical approach of Macroeconomic Theory as a theory of aggregate, social quantities.⁵⁷ Of course, both approaches share a love of the laissez-faire free market. However, in the classical school, this was focused on aggregate accumulation, while in the neoclassical school, it is oriented towards individual maximisation. Consequently, a theory emerged through the work of Walras, as well as other neoclassical economists, which argued that the market is ‘self-regulating’, leading to the optimal allocation of resources for the agents within it.⁵⁸

The next turning point in the dominance of the Neoclassical School in Economics was the work of Keynes, who refocused on the laws of the total economy and questioned the ‘automatic’ tendency of a market economy to return to equilibrium, thus creating a new Keynesian theory of macroeconomics.

Key Takeaways

• The economy is composed of a variety of market participants.

• Economic activity arises from the interaction of all market participants.

• Market participants pursue their own interests in exchange relations.

• Under certain conditions, an equilibrium can be achieved in the market.

• Markets are ‘self-regulated’ to distribute resources efficiently.

Revision Questions

• How would you define ‘Neoclassical Economics’?

• What are the key players in the economy?

• What are the main assumptions behind General Equilibrium analysis?

• What is the ‘auctioneer’s’ role?

• When does a firm experience zero profits in the economy?

• Does the General Equilibrium problem have a solution?

• What is Walras’s main contribution to Economics?