Outline:

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 n_{x}_{ = 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.