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Comparative Analysis of Mechanisms of Schumpeterian Evolution

100%
Lipieta A., Malawski A.
Journal of Entrepreneurship, Management and Innovation
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2018
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vol. 14
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issue 1
7-28
EN
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 positions 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 action, 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.
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Od wolności do swobody wyboru – formalizacja idei Sena w modelu Arrowa-Debreu

100%
Mrówka J., Malawski A.
Prakseologia
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2014
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issue 156
157-175
EN
The aim of the paper is to reconstruct the Senian idea of development as a growing range of freedoms in the research program of modelling Schumpeterian evolutionary economics in the dynamical version of the Arrow-Debreu general equilibrium theory. In the context of the Schumpeterian circular flow freedom of choice of consumers and producers is studied in both qualitative and quantitative setting. The static results presented in the form of mathematical theorems are generalized by use of the theory of quasi-semi-dynamical systems, where cumulative extension of economic systems under consideration is preserved over time and models a growing range of freedoms as well as their quality.
3
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The role of imitative mechanisms within the economic evolution

88%
Lipieta A.
Economics and Business Review
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2018
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vol. 4(18)
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issue 4
64-82
EN
In the light of Schumpeter’s pioneering vision of economic evolution the innovations and innovative entrepreneurs play a fundamental role in the economic development. However, imitations and producers-imitators are essential in diffusing and adapting innovations into the economic exchange processes. In this context the aim of the paper is to model and analyse some properties of imitative mechanisms appearing within the economic evolution. Innovative and imitative mechanisms defined in Hurwicz’s conceptual apparatus are analysed in the economy determined by the use of topological tools usually applied in the general equilibrium theory. As a result it is shown that, in the economy under study, imitative mechanisms are the reasons for and the consequences of innovative mechanisms as well as that the innovative and imitative processes can coexist in the framework of the same innovative mechanism. Moreover it is proven that under some assumptions equilibrium in the economic system analysed can be obtained as a consequence of either of an innovative or an imitative mechanism.
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Producers' Optima in Schumpeterian Evolution

63%
Kornafel M., Denkowska A.
Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie
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2017
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issue 10(970)
55-66
EN
The paper presents a production system in the Debreu model of general equilibrium. According to Schumpeter, economic development is possible only on the strength of innovations being introduced. This process provides a sequence of optimal production plans, corresponding to each stage of the innovative evolution. The paper characterises the sequence of optimal plans and provides the conditions for its convergence. Moreover, the limiting production plan is shown to be the producer’s optimum in the final state.
PL
W artykule rozważany jest system produkcji w modelu równowagi ogólnej Debreu. Zgodnie z teorią J. Schumpetera w celu wybicia gospodarki ze stagnacji konieczne jest wprowadzenie innowacji. W ich wyniku otrzymuje się ciągi planów optymalnych, odpowiadających każdemu etapowi wprowadzania innowacji. W pracy scharakteryzowano proces zmiany optymalnych planów produkcji i opisano warunki, przy których zagwarantowana jest ich zbieżność w taki sposób, że stan graniczny realizuje optimum stanu finalnego.
5

Innovative Mechanisms in a Private Ownership Economy with a Financial Market

63%
Ćwięczek I., Lipieta A.
Argumenta Oeconomica Cracoviensia
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2017
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issue 17
7-19
EN
Let a private ownership economy with a financial market be given. In this economy, innovations in Schumpeter’s sense of the term can be modeled by the use of the Arrow and Debreu topological apparatus. This set-up reveals the impact of the relationship between the financial and the real markets in the economy on innovation. The paper distinguishes and models innovations and different types of innovative mechanisms revealed within Schumpeterian evolution. Following Hurwicz’s approach to modeling economic mechanisms, the main results take the form of mathematical theorems interpreted in the language of economics.
PL
W ekonomii z własnością prywatną i rynkiem finansowym innowacje w ujęciu Schumpetera można opisać w topologicznym aparacie pojęciowym Arrowa i Debreu, dzięki czemu uwidacznia się wpływ wzajemnych powiązań między rynkami realnym i finansowym na procesy innowacyjne. Celem artykułu jest modelowanie innowacji i różnych rodzajów mechanizmów innowacyjnych ujawniających się w procesie schumpeterowskiej ewolucji. Zastosowanie hurwiczowskiego aparatu pojęciowego sprawia, że główne rezultaty przybierają postać twierdzeń matematycznych interpretowanych w języku ekonomii.
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