A Synergetic Reformulation of General Equilibrium Theory

Abstract

In the Wealth of Nations, Adam Smith introduced the metaphor of an invisible hand, which alluded to market equilibration. Leon Walras and later Gustav Cassel conjectured the existence of a general equilibrium. Their ``proofs'' were based on counting variables and equations, concluding that a general equilibrium of all markets exists. In the 1930s, Abraham Wald proved the existence of a general equilibrium in Cassel's model. Later, Gerard Debreu proved the existence of a generalized Walrasian equilibrium. Mathematical economists tried in vain to prove the uniqueness and stability of General Equilibrium Theory (GET). Its lack of realism is obvious. Walras acknowledged that GET is metaphysical because it lacks the dimensions of time and space and is thus pre-institutional and lacks trading processes. Mathematicians such as Donald Saari later introduced a dynamic version of GET, while some mathematical economists incorporated space in a dynamic GET. However, a realistic spatial version of GET requires a theory with multiple time scales. This implies that the dynamic processes relevant in markets for goods are too fast for the slow processes of institutional change and network dynamics. We thus reformulate GET as a synergetic theory of fast and slow processes of equilibration and phase transitions.