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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In the present study, a recursive algorithm for generating the equations of motion of serial chains that undergo spatial motion is presented. The method is based on treating each rigid body as a collection of constrained particles. Then, the force and moment equations are used to generate the rigid body equations of motion in terms of the Cartesian coordinates of the dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotation matrices. For the open loop case, the equations of motion are generated recursively along the serial chains. Closed loop systems are transformed to open loop systems by cutting suitable kinematic joints and introducing cut-joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
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Ekonomiści wyjaśniając zjawiska gospodarcze często odwołują się do pojęcia mechanizmu. W rezultacie, ważnym narzędziem badawczym ekonomii są modele mechanizmów. Celem artykułu jest analiza tego, czym są tego rodzaju modele, a także, jaki status epistemologiczny posiadają budowane na ich bazie stwierdzenia teoretyczne. Kwestie te omawiane są przy wykorzystaniu wybranych koncepcji filozofii nauki, w tym filozofii ekonomii. Artykuł odwołuje się też do historii ekonomii, gdy wskazuje na przyczyny popularności mechanicystycznych wyjaśnień w tej nauce. Rozważania metodologiczne zawarte w tekście ilustrowane są odniesieniami do dwóch modeli ekonomicznych – modelu segregacji rasowej T. Schellinga (1978) i modelu wyprzedaży H. Variana (1980). Jedną z podstawowych konkluzji artykułu jest konstatacja, iż prawa ekonomiczne formułowane na bazie modeli mechanizmów mają status jedynie przekonań o świecie (beliefs), a nie stwierdzeń o istnieniu uniwersalnych regularności. Ponadto, przekonania te są tym bardziej wiarygodne, im struktura modelu cechuje się większym stopniem izomorfizmu z tą istniejącą w rzeczywistości.
EN
Economists often refer to mechanisms in explaining economic phenomena. Therefore, models of mechanisms play an Important role in economics. The goal of the paper is to investigate of what kind of entities such models are and what is the epistemological status of theoretical claims built upon them. These issues are analyzed from the perspective provided by the general philosophy of sciences, including philosophical studies on economics. The paper refers also to the history of economics while accounting for the popularity of mechanistic explanations in this particular science. Methodological studies here presented are illustrated by references to the chessboard model by T. Schelling (1978) and a model a sales by H. Varian (1980). The paper concludes that theoretical claims built upon models have the status of beliefs rather than claims about universal regularities. Moreover, the closer the structure of such a model to the structure of its target, the more credible such a model is.
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This paper presents a generalized approach to the mechanisms of oxidation, hydrogenation and nitriding of metals under ion irradiation with reactive particles at elevated temperatures. Experimental results on the plasma oxidation of bilayered Y/Zr films, the plasma hydrogenation of Mg films and the ion beam (1.2 keV N2+) nitriding of stainless steel are presented and discussed. We make special emphasis on the analysis of surface effects and their role in the initiation of mixing of bilayered films, the ingress of reactive species in the bulk and the restructuring of the surface layers. It is suggested that primary processes driving reactive atoms from the surface into the bulk are surface instabilities induced by thermal and ballistic surface atom relocations under reactive adsorption and ion irradiation, respectively. The diffusion of adatoms and vacancies, at temperature when they become mobile, provide the means to relax the surface energy. It is recognized that the stabilizing effect of surface adatom diffusion is significant at temperatures below 300–350°C. As the temperature increases, the role of surface adatom diffusion decreases and processes in the bulk become dominant. The atoms of subsurface monolayers occupy energetically favorable sites on the surface, and result in reduced surface energy.
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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In this paper, recursive dynamic formulation for the dynamic simulation of multibody systems are presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. Closed-chain system is transformed to open-chain by cutting suitable kinematic joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
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