History of Economics


8th Lausanne school Part I




1st Introduction

2nd The most important representatives

3rd The Walras's system of equations

4th the Walrasian auctioneer

5th Assumptions about the utility

6th The system of indifference curves

7th The budget equilibrium

8th Present goods and future goods

9th Leisure utility versus consumer utility



1st Introduction


In a similar way to the Vienna school, the Lausanne school takes up the basic ideas of classicism but corrects them in certain points.


Thus, the value problem is also at the focus of the Lausanne school. The value of a good represents the long-term price of a good. It is asked on what determinants it depends, which value a good acquires and to what factors the difference in long-term prices must be attributed. 


A second fact is of equal importance: even among the representatives of the Lausanne school, the concept of value refers always to value relations and not, as with Karl Marx, to absolute values. 


It is not about determining the absolute value of a good, but only the relations that exist between the individual long-term prices. It is the price relations that determine which goods and in which quantities are produced actually. 


The Vienna school differed from classical teaching mainly in the way that it did not see itself as an objective value theory, which attributes the value of a good to the costs incurred in its production. Rather, it assumed that the utility is caused by a good is ultimately determining its value.


Contrary to this, the Lausanne school focuses more on the overall economic aspect, while classicism was focused more on the individual market.


A macroeconomic view of the economic problems can already be found among the physiocrats. Francois Quesnay, the founder of physiocratism, who lived from 1694 to 1774 and was the personal physician of the French King Louis XV, published a paper on a 'Tableau Economique' in 1758. Here, the cyclical relationships of the flows of goods between the individual sectors of the economy have already been outlined.


This tradition was now incorporated into the Lausanne school, in which particularly Walras attempted to capture the overall economic situation in a simultaneous system of equations.



2nd The most important representatives


Among the most important representatives of the Lausanne school are Leon Walras and Vilfredo Pareto. But also Enrico Barone, Gustav Cassel and Francis Ysidro Edgeworth have dealt with the subject of the Lausanne school, although they do not belong to the Lausanne school in the strict sense.


León Walras, a Swiss economist who lived from 1834 to 1910, is considered to be the founder and main representative of the Lausanne school.


As his major works are considered:


Eléments d'économie pure (1874)

Théorie de la monnaie (1886)

Études d'économie politique appliquée (1898)


In contrast to the English neoclassical tradition of partial analysis, Walras focuses on the mathematical determination of a total equilibrium in the form of systems of equations. He strives to prove a static equilibrium.


Money merely fulfils the role of a numeraire; it alone determines the amount of the price level, but not the price ratios.


The formation of prices is done by a fictitious auctioneer, the price changes until supply and demand match.


Vilfredo Pareto, an Italian economist who lived from 1848 to 1929, is alongside Walras one of the main representatives of the Lausanne school. He is also considered to be the founder of modern welfare theory.


His major works include:

Les nouvelles théories économiques (1892)

Cours d'économie politique (1896)

Economie mathématique (1911)


Among the most important contributions of Pareto is the 'Law of Income Distribution', according to which the personal income distribution can be represented by a function nx = by-α, its logarithm represents a straight line with the gradient angle α. Pareto assumed that this parameter is relatively constant in the course of time.


In his welfare-theoretical work, Pareto emphasized that the utility could only be determined ordinally and was therefore neither cardinally nor interpersonally comparable.


According to the Pareto criterion named after him, an increase in welfare can be determined if at least one person experiences an increase in utility without that a single other person experiences a loss in utility. Utility units are illustrated by Pareto in the so-called indifference curves.


Although Enrico Barone is an Italian economist in the tradition of the Cambridge school, he lived from 1859 to 1924, he is nevertheless associated with the Lausanne school, since he attempted to integrate the theory of marginal productivity into the Walras system.


His industry cost function is also well known, in which the average costs of the individual providers are drawn on the abscissa ordered by their amount. This results in a staircase-shaped total cost curve.


He is convinced that an efficient calculation of prices is also possible in a state planned economy.


Gustav Cassel (1866 - 1945)

Swedish economist, but in the tradition of Walras's teachings.


Among his major work are:

Grundrisse einer elementaren Preislehre (1899)

Theoretische Sozialökonomie (1918)

Money and Foreign Exchange after 1914 (1922)


Cassel's main concern was to represent Walras's system of equations in a simplifying way. He developed a price theory that was based solely on the "principle of scarcity".

Within foreign trade theory he developed the theory of purchasing power parities.


Francis Ysidro Edgeworth (1845 - 1924)

An Irish-English neo-classicist, who subjects the neo-classics to mathematical analysis and here he already contributes approaches to collective indifference curves.


Among his major works are:

The Hedonical Calculus (1879)

Mathematical Psychics (1881)

The Law of Error (1887)


The demand structure is represented in indifference curves, and equilibrium values are determined in the Edgeworth box by combining two market participants.

Within the framework of the theory of tariffs, social indifference curves are used to determine an optimal tariff rate.



3rd The Walras's system of equations


In contrast to the English tradition of neoclassical partial analysis, Leon Walras and with him the Lausanne school strove for the mathematical determination of a total equilibrium in the form of a simultaneous system of equations. The most important problem variables are the prices of the individual goods. If we start from x goods, then it is also necessary to determine the x equilibrium prices.


This determination takes place within the framework of a simultaneous system of equations. As is well known, the determination of x unknowns requires exactly x independent equations. Now we can, of course, determine a demand equation for each good, which indicates how the demand for this good depends on the prices.


Therefore, we actually do have x equations at our disposal. However, one equation results from the other equations. If we want to determine, for example, the consumer demand for five goods and we define the demand relationship for four goods, then the demand for the fifth good can be determined from the remainder that results from the disposable total income and the demand for the remaining goods. For example, if we spend 85% of income on the first four goods, then the demand for the fifth good is just 15%.


Thus, we only have x-1 independent equations for x prices of goods. This means that with our simultaneous system of equations we can only determine the price relations, but not the absolute prices. In other words: the demand structure and the technical production coefficients determine solely the price relations, and these reflect the respective scarcity relations.


If one also wants to determine also the absolute prices, another equation is required. This equation refers to the required quantity of money, the unit of account (the numeraire), and determines how many monetary units are required at a certain total turnover and at an assumed velocity of circulation of money. 


From this follows by implication that in the Walras's system the money and its circulating amount has no influence on the price relations and thus on the allocation of resources, thus it is allocation-neutral. 


Walras assumes that prices on a stock exchange are set by an auctioneer. In a first step, a random price (e.g. the price of the previous day) is called out and price changes are suggested until supply and demand correspond.


In contrast to the demand equations in the microeconomic models of the neoclassical economics, the demand for a good depends not only on the price of this good, but also explicitly on all other prices of goods. For one thing, this reflects the fact that between individual goods there can be substitution relationships and complementary relationships.


If two products can be exchanged for each other, the substitution ratio is determined by the relationship between the prices of the two products. If the price of a substitution good decreases, it is worthwhile to ask for more of the other good even if the price of this other good remains constant. 


The same applies (mutatis mutandis) to relations between complementary goods. If, for example, the price of a complementary good rises, then it means that more must be spent on the total package of both complementary goods. Consequently, the demand for complementary goods whose price has (in a first step) remained constant will also decrease usually.


Naturally, in a certain relationship all goods are in a competitive relationship with each other. All goods compete for the given income; if there is more demand for one good, then there must be less demand for the other goods at the same total income.


However, this Walras equation system initially only permits the determination of equilibrium prices; it is a purely static theory that says nothing about whether in reality there is actually a tendency towards a perfect equilibrium on all markets, i.e. whether there is a renewed tendency towards equilibrium from any state of imbalance that can be triggered by any change in data.


The traditional statements of the dynamic theory generally refer to individual markets. Already here - as the cobweb system has shown - it can only be expected under certain conditions that market forces will converge towards the new equilibrium price. Even then, if we could prove for each individual market that an approximation to the equilibrium prices is taking place, the question of a tendency towards a total equilibrium would still not be decided.


It could indeed be that the market successfully reduces the imbalance where an imbalance initially occurs, but that it is precisely these equilibrium movements that would create new imbalances in other markets as a result of the manifold substitution relationships and complementary relationships. Another set of further restrictive assumptions is required to prove that these mutual imbalance movements show the character of dampening oscillations.


Thus, it was not until much later, especially in 1936, that A. Wald attempted to elaborate the exact conditions under which it was possible to speak of a tendency towards equilibrium from a macroeconomic perspective. 


4th the Walrasian auctioneer


We will now deal in more detail with the auctioneer that was assumed by Walras. Walras is not assuming that in reality such auctioneers are at work on all markets. Rather, this fiction is intended to show how the action of the invisible hand, as Adam Smith postulated, becomes effective. However, on stock exchanges, an auctioneer indeed ensures that supply and demand are brought together.


We must assume that the auctioneer knows supply and demand, but that supply and demand diverge initially. Let us assume, for example, that demand would exceed supply at an initial price that is arbitrarily set by the auctioneer.


Since we can assume that in the event of a price increase some demanders might leave and at the same time some suppliers will increase their supply, the auctioneer will propose a slightly higher price in such a situation, with the result that the demand surplus will be reduced by both the reduced demand and the increased supply.


If the auctioneer continues with further price increases in this way, then a state is reached eventually where an equilibrium is just reached, and the market is cleared.


However, there is quite a risk here that a further price increase could replace the previous demand surplus with a supply surplus. In the context of the cobweb system it was shown that it depends on the ratio between the price elasticities of supply and demand, whether in this way an equilibrium can be achieved at all. However, this risk can be reduced considerably if the auctioneer implements price changes in very small steps.


In reality, price changes are mostly not triggered by such an auctioneer. Nevertheless, equilibrium processes take place here as well. If we have a demand surplus, which means that the demanders run the risk of coming away empty-handed, they are the ones who propose a higher price in order to obtain the goods.


Naturally, also in this case the supplier can take the initiative with the prise rise and raise prices on his own accord. In this case, the suppliers assume that because of the scarcity of these goods, the demanders will accept the higher price.


Conversely, in the event of a supply surplus, it is in the interest of the supplier to propose lower prices in order not to be left sitting on the goods.