A Globally and Universally Stable Quantity Adjustment Process

Abstract

The question whether the Walrasian equilibrium is stable, is difficult to answer. Although for a number of special cases the Walrasian tatonnement process as formulated in Samuelson (1941) has been shown to be globally stable, see Theorem 3.11.2, and, generically, the price adjustment process of Chapter 10 is globally and universally stable, it is not clear whether these price adjustment processes are the right model of price adjustment processes taking place in the real world. For example, even if the Walrasian tatonnement process converges to a Walrasian equilibrium, convergence may take too much time and does not take place, a point of view considered in Blad (1978). Obviously, the same remark is true for the price adjustment process of Chapter 10. Therefore, it is well possible that, at least in the short run, a Walrasian equilibrium price system is not reached and therefore trade has to take place at a non-Walrasian equilibrium price system. Clearly, there are several other reasons why trade may take place at a non-Walrasian equilibrium price system. Even if the Walrasian equilibrium is stable with respect to some price adjustment process, and even if convergence takes place fast enough, then government intervention, for instance minimum wages or price indexation, might result in a non-Walrasian equilibrium price system at which trade has to take place. In the models of the political economic system as described in Part III such interventions are the generic case. Similarly, as the results in Madden (1983), Silvestre (1988), and Bénassy (1993) indicate, a non-Walrasian equilibrium price system may result as the outcome of a game played between consumers and firms or the outcome of a game played between workers and shareholders.