History of general equilibrium theory

Adam Smith: The Wealth of Nations, 1776

􀂾 many heterogeneous individuals with diverging interests

􀂾 many voluntary but uncoordinated actions (trades)

􀂾 results in a balanced situation (invisible hand)

􀂾 this state is optimal (today this corresponds to the 1. fundamental theorem of welfare economics)

Leon Walras, 1874 (more than 100 years later!)

􀂾 discovers general equilibrium theory

􀂾 consumers (households) and producers (firms)

􀂾 households endowed with initial wealth (labour)

􀂾 firms described by their production possibilities

􀂾 equilibrium described by a vector of market clearing prices

􀂾 only relative prices matter, one of them can be normalized to 1 (numeraire)

􀂾 Walras' law

􀂾 stability of equilibrium

Edgeworth, 1881

􀂾 discovers the relationship between general negotiation concept and the market.

􀂾 2 individuals with initial endowments can perform arbitrary transactions (barter).

􀂾 results in a set of remaining allocations, called contract curve

􀂾 equilibrium is an element of this set

􀂾 the core of an economy

􀂾 if the number of individuals goes to infinity, the core converges to

equilibrium.

Pareto (1909)

􀂾 formulates general concept of efficiency of an allocation (Pareto optimal allocation)

􀂾 recognized (without proof) that for appropriate initial endowments the market mechanism can single out a given efficient allocation (today this is called the 2. fundamental theorem of welfare economics).

Existence and uniqueness of equilibria starts with German language literature - they could show existence for some special cases and recognized that existence is not as easy to solve as Walras thought (by counting variables):

􀂾 Cassel, 1924

􀂾 Zeuthen, 1932

􀂾 Neisser, 1932

􀂾 von Stackelberg, 1933

􀂾 Schlesinger, 1934

Interaction with game theory which was invented at this time:

􀂾 v.Neumann, 1937, was the first to discover the importance of fixed point

theorems for equilibrium existence theorems

􀂾 v.Neumann & Morgenstern, 1944, proved existence of equilibria for

two person 0-sum games

Formal proof of existence

􀂾 Wald, 1934, 1951

􀂾 McKenzie, 1954 & Arrow und Debreu, 1954, simplified and generalized of the results of Abraham Wald by using the fixed point theorems; present general equilibrium theory model in its current formulation.

􀂾 Debreu, 1959, complete systematic treatment of the basic model, presents further generalizations

Core-equivalence (generalisation of Edgeworth theory to large economies)

􀂾 Debreu, Scarf, 1963

􀂾 Aumann, 1964

􀂾 Hildenbrand, 1970, 1974

Countless modern subfields of economics based on the general equilibrium model:

􀂾 dynamics and growth

􀂾 rationing

􀂾 overlapping generation, modern macro

􀂾 modern finanse

…