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Author: K. Okuguchi
Publisher: Springer Science & Business Media
ISBN: 3642463479
Category : Mathematics
Languages : en
Pages : 111
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Book Description
Ever since A.C.Cournot(1838), economists have been increasingly interested in oligopoly, a state of industry where firms producing homogeneous goods or close substitutes are limited in number. The fewness of firms in oligopoly gives rise to interdependence which they have to take into account in choosing their optimal output or pricing policies in each production period. Since each firm's profit is a function of all firms' outputs in an oligopoly without product differ entiation, each firm in choosing its optimal output in any period has to know beforehand all other rival firms' outputs in the same period. As this is in general impossible, it has to form some kind of expecta tion on other firms' most likely outputs. Cournot thought that in each period each firm assumed that all its rivals' outputs would remain at the same level as in the preceding period. Needless to say, the Cournot assumption is too naive to be realistically supported. However, the Cournot profit maximizing oligopoly model characterized by this assumption has many important and attractive properties from the view point of economic theory and provides a frame of reference for more realistic theories of oligopoly. In Chapters 1-3, we shall be engaged in analyzing the Cournot oligopoly model in greater detail from the viewpoints of existence, stability, uniqueness and quasi-competitive ness of the equilibrium.
Author: K. Okuguchi
Publisher: Springer Science & Business Media
ISBN: 3642463479
Category : Mathematics
Languages : en
Pages : 111
Get Book Here
Book Description
Ever since A.C.Cournot(1838), economists have been increasingly interested in oligopoly, a state of industry where firms producing homogeneous goods or close substitutes are limited in number. The fewness of firms in oligopoly gives rise to interdependence which they have to take into account in choosing their optimal output or pricing policies in each production period. Since each firm's profit is a function of all firms' outputs in an oligopoly without product differ entiation, each firm in choosing its optimal output in any period has to know beforehand all other rival firms' outputs in the same period. As this is in general impossible, it has to form some kind of expecta tion on other firms' most likely outputs. Cournot thought that in each period each firm assumed that all its rivals' outputs would remain at the same level as in the preceding period. Needless to say, the Cournot assumption is too naive to be realistically supported. However, the Cournot profit maximizing oligopoly model characterized by this assumption has many important and attractive properties from the view point of economic theory and provides a frame of reference for more realistic theories of oligopoly. In Chapters 1-3, we shall be engaged in analyzing the Cournot oligopoly model in greater detail from the viewpoints of existence, stability, uniqueness and quasi-competitive ness of the equilibrium.
Author: Koji Okuguchi
Publisher: Springer Science & Business Media
ISBN: 3662026228
Category : Business & Economics
Languages : en
Pages : 177
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Book Description
In this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.
Author: Giancarlo Gandolfo
Publisher: Springer Science & Business Media
ISBN: 9783540627609
Category : Business & Economics
Languages : en
Pages : 712
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Book Description
Treating the mathematical methods used in the economic dynamics, this book shows how they are utilised to build and analyse dynamical models. Accordingly, the focus is on the methods, and every new mathematical technique introduced is followed by its application to select economic models. The mathematical methods coveredc range from elementary linear difference and differential equations and simultaneous systems to the qualitative analysis of non-linear dynamical systems. Stability considerations are stressed throughout, including many advanced topics. Bifurcation and chaos theory are also dealt with. The reader is guided through a step-by-step analysis of each topic, be it a mathematical method or an economic model. The Study Edition also provides the reader with solutions to the numerous exercises.
Author: G Gandolfo
Publisher: Elsevier
ISBN: 0444601228
Category : Technology & Engineering
Languages : en
Pages : 584
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Book Description
Economic Dynamics: Methods and Models aims to give a simple but comprehensive treatment of mathematical methods used in economic dynamics and show how they are utilized to build and to analyze dynamic models. The text also focuses on methods, and every mathematical technique introduced is followed by its application to selected models. The book is divided into three different parts. Part I: Different Equations discusses general principles; first-order, second-order, higher-order equations; simultaneous systems; and their economic applications. Part II: Differential Equations also discusses the same areas as those in Part I, but instead features differential equations, as what the section name suggests. Part III: More Advanced Material covers comparative statistics and the comparative principle; stability of equilibrium and Liapunov's second method; and linear mixed differential and difference equations, as well as its other related topics. The text is recommended for mathematicians and economists who have an idea on advanced mathematics and would like to know more about its applications in economics.
Author: László Á. Kóczy
Publisher: Springer
ISBN: 3319698419
Category : Mathematics
Languages : en
Pages : 320
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Book Description
This book presents a systematic overview on partition function form games: a game form in cooperative game theory to integrate externalities for various applications. Cooperative game theory has been immensely useful to study a wide range of issues, but the standard approaches ignore the side effects of cooperation. Recently interest shifted to problems where externalities play the main roles such as models of cooperation in market competition or the shared use of public resources. Such problems require richer models that can explicitly evaluate the side-effects of cooperation. In partition function form games the value of cooperation depends on the outsiders' actions. A recent surge of interest driven by applications has made results very fragmented. This book offers an accessible, yet comprehensive and systematic study of properties, solutions and applications of partition function games surveying both theoretical results and their applications. It assembles a survey of existing research and smaller original results as well as original interpretations and comparisons. The book is self-contained and accessible for readers with little or no knowledge of cooperative game theory.
Author: Ronald Shone
Publisher: Cambridge University Press
ISBN: 9780521017039
Category : Business & Economics
Languages : en
Pages : 730
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Book Description
This is the substantially revised and restructured second edition of Ron Shone's successful advanced textbook Economic Dynamics. The book provides detailed coverage of dynamics and phase diagrams, including: quantitative and qualitative dynamic systems, continuous and discrete dynamics, linear and non-linear systems and single equation and systems of equations. It illustrates dynamic systems using Mathematica, Maple V and spreadsheets. It provides a thorough introduction to phase diagrams and their economic application and explains the nature of saddle path solutions. The second edition contains a new chapter on oligopoly and an extended treatment of stability of discrete dynamic systems and the solving of first-order difference equations. Detailed routines on the use of Mathematica and Maple are now contained in the body of the text, which now includes advice on the use of Excel and additional examples and exercises throughout. Supporting website contains solutions manual and learning tools.
Author: Pierre von Mouche
Publisher: Springer
ISBN: 3319292544
Category : Business & Economics
Languages : en
Pages : 298
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Book Description
This state-of-the-art collection of papers on the theory of Cournotian competition focuses on two main subjects: oligopolistic Cournot competition and contests. The contributors present various applications of the Cournotian Equilibrium Theory, addressing topics such as equilibrium existence and uniqueness, equilibrium structure, dynamic processes, coalitional behavior and welfare. Special emphasis is placed on the aggregative nature of the games that are relevant to such theory. This contributed volume was written to celebrate the 80th birthday of Prof. Koji Okuguchi, a pioneer in oligopoly theory.
Author: James Friedman
Publisher: CUP Archive
ISBN: 9780521282444
Category : Business & Economics
Languages : en
Pages : 262
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Book Description
James Friedman provides a thorough survey of oligopoly theory using numerical examples and careful verbal explanations to make the ideas clear and accessible. While the earlier ideas of Cournot, Hotelling, and Chamberlin are presented, the larger part of the book is devoted to the modern work on oligopoly that has resulted from the application of dynamic techniques and game theory to this area of economics. The book begins with static oligopoly theory. Cournot's model and its more recent elaborations are covered in the first substantive chapter. Then the Chamberlinian analysis of product differentiation, spatial competition, and characteristics space is set out. The subsequent chapters on modern work deal with reaction functions, advertising, oligopoly with capital, entry, and oligopoly using noncooperative game theory. A large bibliography is provided.
Author: Yoshikazu Sawaragi
Publisher: Springer Science & Business Media
ISBN: 3642466095
Category : Business & Economics
Languages : en
Pages : 467
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Book Description
In the past, technological as well as economic forces dominated the evolution of industrial structures: these factors have been treated extensively in numerous studies. However, another major factor which has begun to have a decisive influ ence on the performance of the chemical industry is technological risk and public and environmental health considerations, in particular those related to toxic and hazardous substances used in industrial production processes. The issues of con trolling process risk, waste streams, and potential environmental consequences of accidental or routine release of hazardous chemicals are rapidly gaining in impor tance vis CI vis narrow economic considerations, and are increasingly reflected in national and international legislation. In the context of several ongoing R&D projects aiming at the development of a new generation of tools for "intelligent" decision support, two related problem areas that have been identified are: (i) Structuring the industry or plant for the minimum cost of production as well as least risk - e.g., toxicity of chemicals involved. In this multi-criteria framework, we seek to resolve the conflict between industrial structure or plant design established by economic considerations and the one shaped by environmental concerns. This can be formulated as a design problem for nor mal production conditions. In section 3.1. and 3.2. an approach on how to deal with this problem at the industry and plant level is discussed.
Author: David Batten
Publisher: Springer Science & Business Media
ISBN: 3662025221
Category : Business & Economics
Languages : en
Pages : 389
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Book Description
Since the beginning of the fifties, the ruling paradigm in the discipline of economics has been that of a competitive general equilibrium. Associated dynamic analyses have therefore been preoccupied with the stability of this equilibrium state, corresponding simply to studies of comparative statics. The need to permeate the boundaries of this paradigm in order to open up new pathways for genuine dynamic analysis is now pressing. The contributions contained in this volume spring from this very ambition. A growing circle of economists have recently been inspired by two distinct but complementary sources: (i) the pathbreaking work of Joseph Schumpeter, and (ii) recent contributions to physics, chemistry and theoretical biology. It turns out that problems which are firmly rooted in the economic discipline, such as innovation, technological change, business cycles and economic development, contain many clear parallels with phenomena from the natural sciences such as the slaving principle, adiabatic elimination and self-organization. In such dynamic worlds, adjustment processes and adaptive behaviour are modelled with the aid of the mathematical theory of nonlinear dynamical systems. The dynamics is defined for a much wider set of conditions or states than simply a set of competitive equilibria. A common objective is to study and classify ways in which the qualitative properties of each system change as the parameters describing the system vary.
