The theory of competitive equilibrium is a natural starting point for most economists—whether they approach a partial, general, applied or theoretical market problem. The basic ideas were formulated in the eighteenth century by Adam Smith, and refined and mathematically reformulated by Léon Walras and Gustav Cassel. Mathematicians Abraham Wald and Gérard Debreu brought the theory in contact with modern mathematics and could show that a general equilibrium of non-negative prices and quantities could exist under seemingly reasonable axiomatic assumptions of convexity of preferences and production techniques.
General equilibrium theory is based on an analysis of the differential equations dz/dt=g(z), with z = a vector of excess demands, and dp/dt = f(p) having an equilibrium if (g(z), f(p)=0 or ≤0) and (z,p≥0). The derivation of f(p) and g(z) from preferences and production possibilities of all the numerous agents was an impressive effort by twentieth-century economists and mathematicians.
There are three key issues in general competitive equilibrium theory:
Much of the elegance of general equilibrium theory (GET) was achieved at considerable expense in terms of axiomatic simplifications. Indivisibilities and other causes of increasing returns are not compatible with the theory, and interdependencies between producers or consumers can generate positive feedback loops that destroy the stability of the equilibrium states.
These problems are to a great extent the result of the formulation of GET as a static and space-free construct. Debreu’s “trick”—which was...
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