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.
The paper extends the research program of modeling the Schumpeterian vision of innovative development in the framework of the Arrow-Debreu theory of general equilibrium. To study changes in the production 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 evolution in the conceptual apparatus of Hurwicz’s theory of economic mechanisms.
The paper is aimed at expanding our previous studies into two new directions. First, we establish the conditions sufficient for improving positons of various groups of agents such as producers, innovators, consumers, etc., under the price or qualitative mechanism regime. Second, to compare mechanisms of Schumpeterian evolution, we respect the logic of this process which is determined by innovative, as well as adaptive, equilibrium changes in the evolving economy under consideration. Consequently, we formulate two diﬀerent criteria in our comparative analysis based, on the one hand, on the index of the distance between two innovative extensions of the given economic system and, on the other hand, on the increase in wealth of the given set of agents.
The motivations of innovators, and the reason for which innovations are adopted into the producers’ and consumers’ plans of acton, are also precisely explained in the paper. The results of our theoretical research can be useful in economic analyses, among others, in the case of the lack of the sufficient access to statistical 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 axiomatic deductive system of mathematical theorems interpreted in the language of economics.
Keywords: Schumpeterian evolution, mechanisms, designing mechanisms, Debreu economy