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1

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.

2

The private ownership economy with a reduced consumption sphere as an economic mechanism

100%

Lipieta A.

Mathematical Economics

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2013

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issue 9 (16)

39-54

EN

Let Ep be a Debreu private ownership economy in which every consumption set is contained in the proper subspace V of the commodity – price space . Two kinds of economic mechanisms, in the sense of Hurwicz, are designed. The goals of the design are, either the modified to the subspace V, producers’ and consumers’ optimal plans (plans maximizing appropriately profits or preferences on the budget sets) which form the state of equilibrium, or the modified to the subspace V production sets. In the presented economic mechanisms, the producers’ maximal profits do not decrease, and also the consumers’ preferences and the budget sets remain unchanged.

3

Producers’ Adjustment Trajectories Resulting in Equilibrium in the Economy with Linear Consumption Sets

88%

Lipieta A.

Central European Journal of Economic Modelling and Econometrics

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2015

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issue 4

4

The economy with production and consumption systems changing in time

63%

Lipieta A.

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2012

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vol. 59

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issue 3

233-245

EN

Assume that, in a private ownership Debreu economy Ep, among all the commodities there are at least two whose quantities, employed by consumers in all their plans of action, are proportional. This property leads producers change their production plans to satisfy the consumers’ requirements. The producers’ adjustment process, caused by the special form of consumers’ plans, is modeled. As the result, the economy E_p with dynamical production and consumption systems is defined. The commodity – price space of economy E_p is the space of continuous functions defined on time interval [0,1] with values in the commodity – price space of economy Ep.

PL

Załóżmy, że w ekonomii Ep Debreu z własnością prywatną, istnieją przynajmniej dwa towary, których ilości we wszystkich planach konsumpcji są proporcjonalne. Ta zależność powoduje, że producenci zmieniają swoje plany produkcji, tak aby dopasować je do wymagań konsumentów. W artykule analizowany jest proces dostosowawczy producentów, spowodowany przez wspomnianą własność zbiorów konsumpcji. W rezultacie zdefiniowano ekonomię E_p, ze zmieniającymi się w czasie systemami produkcji i konsumpcji, której przestrzeń towarów i cen jest przestrzenią funkcji ciągłych określonych na przedziale czasu [0,1], o wartościach w przestrzeni towarów i cen początkowej ekonomii Ep.

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4 Lipieta A.

1 Malawski A.

Comparative Analysis of Mechanisms of Schumpeterian Evolution

The private ownership economy with a reduced consumption sphere as an economic mechanism

Producers’ Adjustment Trajectories Resulting in Equilibrium in the Economy with Linear Consumption Sets

The economy with production and consumption systems changing in time