Agnieszka Lipieta, Ph. D. , Cracow University of Economics, Faculty of Finance and Law, Department of Mathematcs, Rakowicka 27, 31 - 510 Cracow, Poland, email: alipieta@uek. krakow,pl.
Andrzej Malawski, Professor, Cracow University of Economics, Faculty of Finance and Law, Department of Mathematcs, Rakowicka 27, 31 - 510 Cracow, Poland. He passed away in 2016.

Abstract

The paper extends the research program of modeling the Schumpeterian vision of innovatve development in the framework of the Arrow-Debreu theory of general equilibrium. To study changes in the producton sector, as well as in the whole economy, the concept of extension of the systems under study is introduced. It enables us to model the mechanisms of Schumpeterian evoluton in the conceptual apparatus of Hurwicz’s theory of economic mechanisms.

The paper is aimed at expanding our previous studies into two new directons. First, we establish the conditons sufcient for improving positons of various groups of agents such as producers, innovators, consumers, etc., under the price or qualitatve mechanism regime. Second, to compare mechanisms of Schumpeterian evoluton, we respect the logic of this process which is determined by innovatve, as well as adaptve, equilibrium changes in the evolving economy under consideraton. Consequently, we formulate two different criteria in our comparatve analysis based, on the one hand, on the index of the distance between two innovatve extensions of the given economic system and, on the other hand, on the increase in wealth of the given set of agents.

The motvatons of innovators, and the reason for which innovatons are adopted into the producers’ and consumers’ plans of acton, are also precisely explained in the paper. The results of our theoretcal research can be useful in economic analyses, among others, in the case of the lack of the sufcient access to statstcal data.

Due to both the formal conceptual apparatus of the general equilibrium theory and Hurwicz’s approach to the problem of designing economic mechanisms, the paper takes the form of an axiomatc deductve system of mathematcal theorems interpreted in the language of economics.

Keywords: Schumpeterian evoluton, mechanisms, designing mechanisms, Debreu economy