Leon Walras (1834-1910)
“[A]s far as pure theory is concerned, Walras is in my opinion, the greatest of all
economists. His system of economic equilibrium, uniting … the quality of ‘revolutionary’
creativeness with the quality of classical synthesis, is the only work by an economist that
will stand comparison with the achievements of theoretical physics.” [Schumpeter, 827]
Background:
- French son of a professor, Auguste Walras
- trained as a mining engineer
- worked as a free lance journalist until a paper he presented at a conference got him a
chair in political economy at the law school of the University of Lausanne in 1870
- published Elements of Pure Economics in 1874 (exchange) and 1877 (distribution)
– three? subsequent editions with notable changes
- also published applied economics
- cited his father as his most important influence (rareté) and then Cournot, a fellow
student of his fathers
- steeped in the French tradition (J.B. Say, Quesnay) but discounted English economics
except for Adam Smith
- little direct influence on economic theory until the 1920s
– taught law students
– not translated into English until 1954 (Jaffé)
- did influence Pareto, Wicksell, and Fisher
- independently discovered the marginal utility approach but more important for his
original system of general equilibrium equations and his modern theory of money
Method:
- his ‘point of departure’ is ‘rareté’ (scarcity) along with maximization of satisfaction
– acknowledged his similarity here to Jevons (‘final degree of utility’ and ‘equation of
exchange’) and Menger
- condemned partial analysis - e.g., Cournot, and later, Marshall – which examined the
relation between specific variables while holding others constant
– e.g., price is a function of quantity demanded of the commodity, ceteris paribus
- argued that economic phenomena mutually determined each other
– e.g., analyzed price as a function of all prices and quantities in the economy
simultaneously, not in isolation
Note: development of economics, like other sciences, generally proceeded by isolating
phenomena to examine specific relations and then broadened the scope. Walras,
however, considered all variables simultaneously => no cause and effect
– Walras’s system is the first to analyze all problems in the same formal manner
- successive perfections of his theory through different editions reduced the dependence of
the theory on marginal utility
-> general equilibrium renders marginal utility unnecessary
- argued that pure theory abstracts “ideal-type concepts from reality and then uses these
definitions to deduce a priori theorems and their proofs “ (W, 71)
=> quantitative nature of economics => mathematical analysis
– reduced economic variables and relations to a system of equations
– incorporated rigorous proofs of each step which profoundly affected subsequant
analysis
Utility (will use W’s notation for the most part)
- defined social wealth as all things material or immaterial “that are scarce”, i.e., “useful …
and in limited quantity” (W, 65)
- distinguished between finished products (material) and services (immaterial) wealth
- distinguished two types of finished products: consumer goods (revenue) used only once
and “fixed capital or capital in general” which was “all forms of social wealth which
… serve more than once” (W, 177)
=> land, labour, and capital are all capital with the distinction that land is natural but
not perishable, labour is natural and perishable, and capital proper is producible and
not perishable?
-> services are “the forms of wealth which are consumed immediately” ? [W, 177]
-> services of land, labour, and capital enter production not land, labour, and capital
[=> definite break with the classical conception of production of commodities by means
of commodities]
- defined ‘m’ finished products (exclusive of capital) A, B, C … M and ‘n’ productive
services
T, T’, T’’, …
services of land per unit of time
P, P’, P”. …
services of labour per unit of time
K, K’, K”, …
services of capital per unit of time
– price and quantity of these products and services are determined in the product/services
market whereas the price of capital goods is determined in the capital market which he
analyzes later
- defined ‘rareté’ as the relation between utility and the quantity possessed
- ‘rareté’ diminishes with quantity
- value in exchange is proportional to ‘rareté’
- [‘rareté’ is equivalent to Jevons ‘last degree of utility’ and Menger’s last unit of utility]
- defines utility curves for finished products and services solely as a function of the quantity
of each product or service [Note that this is inconsistent with general equilibrium]
-> r = (q)
=> n + m utility functions
Exchange
Data (Given)
- individuals possess given initial quantities of productive services
= qT, qT’, …, qP, qP’, … qK, qK’, ..
qi  0
- individuals confront given prices
(prices are determined in general equilibrium)
PB, … PN, PT, …, PP, …PK .. ,
- Walras defines good A as the numeraire so that PA = 1
-> all goods are measured in terms of PA
- ‘numeraire’ = standard commodity to express the exchange relations of all commodities
-> n (consumed goods) and m (productive services) prices with one known price (PA = 1)
=> n + m – 1 unknown prices
- Individual demands and offers (supplies) quantities of goods and services at equilibrium
prices
oT, oP, oK, oT’, …..
services offered (oi > 0) or demanded (oi < 0)
dA, dB, …
finished goods demanded
Equilibrium conditions for the individual:
1) Maximum Satisfaction:
- marginal utilities of goods and services are proportional to their prices
A(dA) = T(qT – oT)/PT = P(qP – oP)/PP = …
[MUA = MUB/PB = … = MUN/PN = MUT/PT = …
(PA = 1 => MUA/PA = MUA)]
-> n + m – 1 equations
2) Budget Balance =>
Revenues = Expenditures
oTpT + oPPP + oKPK + oT’PT’ + …. = dA + …. + dN
-> m + n equations to for m + n unknowns: oT, oP, oK, oT’, ….. PB, … PN
Express the individual’s offer functions for services and demand functions for
commodities in terms of the above prices but now assumed fixed and known to the
individual
oT = fT (PT, PP, ….. PB, …. , PN)
oP = fp (PT, PP, ….. PB, …. , PN)
etc.
dB = fB (PT, PP, ….. PB, …. , PN)
etc.
Demand for A can be derived from other equations (Walras’s Law)
Note: unlike previous authors, the demand function for a commodity is a relationship
between the quantity of a commodity and all prices when the individual’s income [budget]
and tastes [utility function] is constant
Entrepreneur
General equilibrium in the market is defined by four equations
Define
OT = oT ;
DA = dA;
FT = fT;
i.e. market offer = sum of individual offers; market demand = sum of individual
demand; function = sum of individual function
1.
quantities of productive services supplied are functions of the prices
OT = FT (PT, PP, … PB, … PN)
-> n equations for quantities of productive services
2.
quantities of finished goods demanded are functions of prices
DB = FB (PT, PP, … PA, … PN)
-> m equations but only m – 1 are independent
(DA = OTPT + OPPP + … +DBPB + … + DNPN)?
3.
Quantity of Services Employed = Quantity offered
aTDA + bT’’DB + …
= OT
-> n equations
4.
Cost of Production = Prices
Walras assumed in first three additions fixed coefficients of production
aT, aK, aP, aT’, …
bT, bK, ….
which enter into production of one unit of each of the products, A, B, C, etc.
Walras assumed fixed coefficients for simplicity although he thought that they were
variable. In the appendix to the third edition (1896) and in subsequent editions, he
introduced variable proportions
aTPT + aPPP + …
=1
for a total of m equations
- there was no discussion of the cost conditions of the entrepreneur
=> a total of 2m + 2n – 1 equations (DA is independent) for 2m + 2n – 1 unknowns:
Quantities of production services offered (n) and finished goods demanded (m) and
Prices of production services (n) and finished goods (m – 1 since PA = 1)
=> general equilibrium
The solution is simultaneous so that given prices for individual decisions is not a problem
per se.
The simultaneous solution also eliminated cause/effect explanations
COMPETITION
-
The solution holds for perfect competition and perfect equilibrium (i.e., -all variables
are simultaneously determined)
-
Walras thought that the variables fluctuated around these ideal solutions in reality
-
He also proposed an ideal explanation of the path to equilibrium (unlike other
economists)
He imagined a market where an auctioneer called out prices and individuals submitted
their quantities offered and demanded on slips of paper. If Qo  Qd, another price was
called until a price was reached where Qo = Qd. The movement to equilibrium thus
occurred in approximations (‘tatonnements’) through the mechanism of changing
prices.
[This explanation doesn’t explain how general equilibrium occurs in reality since if even
one price is not optimal, the change in that price will change Qo and Qd for that
commodity. This will change individual budgets and the equilibrium for other goods]
-
The entrepeneur combines services and raw materials in production but does not make
any profit in equilibrium [similar to 0 economic profit].
CAPITAL THEORY
-
The valuation of capital (resources) takes place in the capital market
Capital goods are desired for the income they yield
-
In part II, Walras defined the interest rate (i) as the ratio of perpetual net income (R)
to capital value (PK) (ignoring depreciation)
i = R/PK
[Walras is able to solve this equation since he assumes a stationary state (i.e., no change in
capital). Otherwise capital value would be unknown as well as i)