QUALITATIVE ANALYSIS, DETERMINACY AND STABILITY.

Recent mathematical research has led to the formulation of many theorems of great interest to the economist. They permit him to judge a priori if it is possible to derive meaningful propositions of comparative statics from the system of relationships that characterize a given static model; it is not necessary for him to derive the reduced form nor to render explicit the dynamic model. The purpose of the paper is: to clarify the premises and the methodological implications of such research; to enlarge on the most significant results from the point of view of the construction of economic models; to demonstrate how the two classes of qualitatively stable models combine among themselves and to demonstrate how their intersection contains models of a causal type. The theory of qualitatively determinate systems permits the substitution (as cost of the qualitative determination) of a certain loss (though minimum and calculated) in terms of the complexity of the model for a certain loss in terms of empirical relevance. This loss may be measured by the number of the non-zero elements in the augmented matrix of the system of equations that characterize the model.