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Existence and uniqueness of the producers’ optimal adjustment trajectory in a Debreu-type economy

100%
Lipieta A.
Mathematical Economics
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2015
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issue 11(18)
55-68
EN
The aim of this paper is the analysis of adjustment processes in a Debreu-type economy. The reasons taken into account, e.g. incentives, cooperation of economic agents under full access to information, the way of sending messages described formally, are the basis for defining adjustment trajectories. Some reasons, such as introducing new legal requirements or implementing new profitable technologies formulated in mathematical language, can contribute to the transformation of the production sector and induce an appropriate way of adjusting the producers’ plans of action. This survey relies on an examination of the relationships between quantities of goods and quantities of the productive factors used to produce them. As a result, the optimal producers’ trajectories, due to the criterion of cost minimization, are defined. The paper also contains some remarks on the uniqueness of the trajectories under study.
2
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The private ownership economy with a reduced consumption sphere as an economic mechanism

100%
Lipieta A.
Mathematical Economics
|
2013
|
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

Procesy dostosowawcze na rynku z przeliczalną liczbą agentów i towarów

100%
Lipieta A.
Przegląd Statystyczny
|
2017
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vol. 64
|
issue 3
249-264
4
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The role of imitative mechanisms within the economic evolution

100%
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.
5
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Comparative Analysis of Mechanisms of Schumpeterian Evolution

63%
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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