Un teorema sobre la relación entre la estabilidad hicksiana y la verdadera estabilidad dinámica

Abstract

A well known theorem –due to Metzler- asserts that if the matrix of a dynamic system is stable for all possible positive speeds of adjustment, then the Hicks conditions for perfect stability will be verified. In general, the converse theorem does not hold. The following proposition is shown to be true. If in a system of n commodities and m consumers and the budget constraint is operative for every individual consumer and the commodities can be classified in three groups (relative prices remaining always constant for each of them), then the Hicksian perfect stability conditions –for all positive speeds of reaction- are sufficient for the system's asymptotic local stability, independently of the speeds of adjustment.