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Arts, Sciences, and Economics
This book deals with the economic aspects of changing attitudes in arts and sciences. The effects of the public good character of culture, along with the very long production period and lifetime for its products, are emphasized, since both contribute to the failure of normal market solutions. Embodiment of ideas and the consequences of modern reproduction technology for protection of property rights are closely examined. The evolution within arts and sciences, which often seems to return to previously scrapped ideals, is illustrated by detailed case studies, in which the importance of changing tastes, rather than progress proper, is emphasized. The author attempts an understanding for this using Darwinian evolution in combination with modern mathematical complexity theory, expressed in terms accessible to the general reader. The second edition is extended and updated especially as regards the illustration material.
Disequilibrium Economics
This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author’s over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve “research stubs” – outlined research agendas that have not yet been fully worked on – are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.
Business Cycle Dynamics
Business cycle theory has been one of the fastest growing fields in modern nonlinear economic dynamics. This book presents new mathematical methods for global analysis which have not previously been available in this easily accessible form. In addition it contains a presentation of full analyses of several models left open in the 1950s when the tools then available did not permit more systematic analysis.
Arts, Sciences, and Economics
This book deals with the economic aspects of changing attitudes in arts and sciences. The effects of the public good character of culture, along with the very long production period and lifetime for its products, are emphasized, since both contribute to the failure of normal market solutions. Embodiment of ideas, and the consequences of modern reproduction technology for protection of property rights are closely examined.
Oligopoly
The book focuses classical oligopoly theory as developed in 1840-1940. By the end of this period oligopoly came under the spell of game theory in its probabilistic equilibrium format. Work by Cournot, von Stackelberg, Palander, and Hotelling, causal and dynamic in essence, but ignored, is reconsidered in the light of modern dynamics using topology and numerics. As particular features, von Stackelberg leadership is included in the dynamic Cournot model, the Hotelling problem is solved with elastic demand, thus skipping the absurd idea of quadratic transportation costs. Further, it is shown that the celebrated destabilisation of Cournot equilibrium under increased competition is due to mistakenly assuming constant returns, and that the whole idea of rational expectations is untenable in dynamic oligopoly. Early original ideas in oligopoly theory, such as coexistence and multiplicity of attractors are focused again after many undeserved decades of oblivion.
Mathematical Location and Land Use Theory
The author presents economic phenomena in the continuous 2-dimensional geographical space with particular focus on the emergence of spatial structures. This text starts out from the classical models of the space economy, associated with such names as: von Thünen, Launhardt, Weber, Christaller and Lösch. The theories are stated in terms of precise mathematical models, and are generalized by the use of results from modern topology. The mathematical tools needed - variational calculus, vector analysis, and differential equation theory - are stage by stage developed in the context of applications, and the reasoning is supported by a lavish supply of elaborate computer graphics, making even topics considered tough intuitively digestable. The reader will therefore not only acquire an understanding for the importance of including geographical space in economic models, but he will also learn to handle the mathematical tools needed for working with such models.
Oligopoly Dynamics
This book has its focus on the dynamics of oligopoly games. Several contributions show how easily the unique Nash equilibria in some most traditional oligopoly models may lose stability, giving way to complex phenomena, such as periodic/chaotic processes, and to multi stability of coexistent attractors. The bifurcations producing these phenomena are studied by means of recently accumulated global methods, based on the use of critical curves. These tools are explained in a separate methodological chapter. The book also contains some historical background of the present theory. In this way the book becomes suitable also as an advanced text for industrial organisation courses. The various models presented in the book focus both classical Cournot types, and Hotelling`s "ice cream vendor" problems, including location choice. The author list comprises some of the most prolific contributors to current dynamic oligopoly modelling.
Nonlinear Economic Dynamics
This book was first pUblished in 1989 as volume 336 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and it reappeared in a 2nd edition as a Springer monograph in 1991. After considerable revisions it appeared in a 3rd edition in 1993. The origin, still visible in the 3rd edition, was the joint work of the author with Professor Martin J. Beckmann, documented in two co-authored mono graphs "Spatial Economics" (North-Holland 1985), and "Spatial Structures" (Springer-Verlag 1990). Essential dynamics had, however, been almost com pletely lacking in these works, and the urge to focus the dynamic issues was great. To fill this particular gap was the aim of the previous editions, and so the spatial aspect provided core and focus. In the present edition a substantial quantity of spatial issues have been removed: All those that were dynamic only in the sense that structures were characterized which were structurally stable, or robust in a changing world. The removed material has meanwhile been published as a separate mono graph under the title "Mathematical Location and Land Use Theory" (Springer-Verlag 1996).
