<P> Research building on the Arrow--Debreu--McKenzie model has revealed some problems with the model . The Sonnenschein--Mantel--Debreu results show that, essentially, any restrictions on the shape of excess demand functions are stringent . Some think this implies that the Arrow--Debreu model lacks empirical content . At any rate, Arrow--Debreu--McKenzie equilibria cannot be expected to be unique, or stable . </P> <P> A model organized around the tâtonnement process has been said to be a model of a centrally planned economy, not a decentralized market economy . Some research has tried to develop general equilibrium models with other processes . In particular, some economists have developed models in which agents can trade at out - of - equilibrium prices and such trades can affect the equilibria to which the economy tends . Particularly noteworthy are the Hahn process, the Edgeworth process and the Fisher process . </P> <P> The data determining Arrow - Debreu equilibria include initial endowments of capital goods . If production and trade occur out of equilibrium, these endowments will be changed further complicating the picture . </P> <P> In a real economy, however, trading, as well as production and consumption, goes on out of equilibrium . It follows that, in the course of convergence to equilibrium (assuming that occurs), endowments change . In turn this changes the set of equilibria . Put more succinctly, the set of equilibria is path dependent...(This path dependence) makes the calculation of equilibria corresponding to the initial state of the system essentially irrelevant . What matters is the equilibrium that the economy will reach from given initial endowments, not the equilibrium that it would have been in, given initial endowments, had prices happened to be just right </P>

Who has used numeraire in general equilibrium analysis