Tõnu Puu Books

Focusing on the evolution of nonlinear economic dynamics, this book builds on earlier editions, enhancing its content for economics students. It integrates mathematical foundations such as ordinary differential equations and iterated maps, making it a comprehensive textbook. The revised edition includes new chapters on partial differential equations and bifurcation theory, reflecting advancements in the field. The author aims to provide up-to-date analyses, addressing the rapid development in nonlinear dynamics over the past decade.

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.

Business cycle theory has been one of the fastest growing fields in modern nonlinear economic dynamics. The book is centered around models of multiplier-accelerator type, emerging from Samuelson's seminal work, later developed into nonlinear formats by Hicks and Goodwin. These models left open ends, as the tools then available did not permit more systematic analysis. The present situation is different, due to the emergence of new methods also focusing global analysis. The focus on classical, causal or recursive models implies a deviation from current main stream business cycle theory, based on „rational expectations“, which in view of the possibility of mathematical chaos becomes untenable. This book is a rejoinder to Puu and Sushko, Oligopoly Dynamics - Models and Tools , (Springer 2002).

Focusing on mathematical models in economics, this work emphasizes non-linear dynamics, drawing inspiration from models developed between 1920 and 1950. It begins with an introduction tailored for mathematicians and modelers, then compiles a collection of specific functions useful for global dynamic modeling. Additionally, it presents twelve outlined research agendas, or "research stubs," that offer avenues for further exploration. This resource is particularly beneficial for young scientists seeking to apply their mathematical and computational skills in economic contexts.

The book explores key concepts in spatial economics, emphasizing plant location, market area theories, and spatial competition. It delves into land use, specialization, trade, and transportation network layouts, utilizing Beckmann's continuous flow model as a focal point. The text prioritizes structural stability over optimality and introduces necessary mathematical tools in an intuitive manner, enhanced by rich computer graphics. The new edition expands on spatial competition and oligopoly theory, particularly addressing Hotelling's case with elastic demand to clarify previous paradoxes.

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.

The book studies oligopoly situations by using dynamic tools Includes supplementary material: sn. pub/extras

Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.

A sample of Professor Tönu Puus contributions to economic theory, ranging from seminal results on investment criteria under imperfect capital markets, via rules for optimal resource extraction when the grade of the ore is heterogeneous, to modern nonlinear dynamics as applied to well-known economic fields such as business cycle analysis and oligopoly theory. Puus thinking on cultural economics and his views on the methodology of economic science shine through every paper in this volume.

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).