Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.

"Mathematical Optimization and Economic Analysis" is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demonstrate each technique’s advantages and applicability as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy. Key Features include: - A detailed presentation of both single-objective and multiobjective optimization; - An in-depth exposition of various applied optimization problems; - Implementation of optimization tools to improve the accuracy of various economic models; - Extensive resources suggested for further reading. This book is intended for graduate and postgraduate students studying quantitative economics, as well as economics researchers and applied mathematicians. Requirements include a basic knowledge of calculus and linear algebra, and a familiarity with economic modeling.

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.

Our objectives may be briefly stated. They are two. First, we have sought to provide a compact and digestible exposition of some sub-branches of mathematics which are of interest to economists but which are underplayed in mathematical texts and dispersed in the journal literature. Second, we have sought to demonstrate the usefulness of the mathematics by providing a systematic account of modern neoclassical economics, that is, of those parts of economics from which jointness in production has been excluded. The book is introductory not in the sense that it can be read by any high-school graduate but in the sense that it provides some of the mathematics needed to appreciate modern general-equilibrium economic theory. It is aimed primarily at first-year graduate students and final-year honors students in economics who have studied mathematics at the university level for two years and who, in particular, have mastered a full-year course in analysis and calculus. The book is the outcome of a long correspondence punctuated by periodic visits by Kimura to the University of New South Wales. Without those visits we would never have finished. They were made possible by generous grants from the Leverhulme Foundation, Nagoya City University, and the University of New South Wales. Equally indispensible were the expert advice and generous encouragement of our friends Martin Beckmann, Takashi Negishi, Ryuzo Sato, and Yasuo Uekawa.

As an outgrowth of the advancement in modern control theory during the past 20 years, dynamic modeling and analysis of economic systems has become an important subject in the study of economic theory. Recent developments in dynamic utility, economic planning, and profit optimiza tion, for example, have been greatly influenced by results in optimal control, stabilization, estimation, optimization under conflicts, multi criteria optimization, control of large-scale systems, etc. The great success that has been achieved so far in utilizing modern control theory in economic systems should be attributed to the effort of control theorists as well as economists. Collaboration between the two groups of researchers has proven to be most successful in many instances; nevertheless, the gap between them has existed for some time. Whereas a control theorist frequently sets up a mathematically feasible model to obtain results that permit economic interpretations, an economist is concerned more with the fidelity of the model in representing a real world problem, and results that are obtained (through possibly less mathematical analysis) are due largely to economic insight. The papers appearing in this volume are divided into three parts. In Part I there are five papers on the application of control theory to economic planning. Part II contains five papers on exploration, exploita tion, and pricing of extractive natural resources. Finally, in Part III, some recent advances in large-scale systems and decentralized control appear.

Mathematics of Computing -- Miscellaneous.

This book investigates the interaction of effective goods demand with the wage-price spiral, and the impact of monetary policy on financial and the real markets from a Keynesian perspective. Endogenous business fluctuations are studied in the context of long-run distributive cycles in an advanced, rigorously formulated and quantitative setup. The material is developed by way of self-contained chapters on three levels of generality, an advanced textbook level, a research-oriented applied level and on a third level that shows how the interaction of real with financial markets has to be modelled from a truly integrative Keynesian perspective. Monetary Macrodynamics shows that the balanced growth path of a capitalist economy is unlikely to be attracting and that the cumulative forces that surround it are controlled in the large by changes in the behavioural factors that drive the wage-price spiral and the financial markets. Such behavioural changes can in fact be observed in actual economies in the interaction of demand-driven business fluctuations with supply-driven wage and price dynamics as they originate from the conflict over income distribution between capital and labour. The book is a detailed critique of US mainstream macroeconomics and uses rigorous dynamic macro-models of a descriptive and applicable nature. It will be of particular relevance to postgraduate students and researchers interested in disequilibrium processes, real wage feedback channels, financial markets and portfolio choice, financial accelerator mechanisms and monetary policy.

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.

Multinomial Probit

The Export—Import Bank: An Economic Analysis provides a critical analysis of the export financing issue and the Eximbank's performance in fulfilling its congressional mandate. The analysis is based on extensive interviews with Eximbank officials and on numerous internal documents in addition to published materials. This book is composed of 11 chapters that reflect the three perspectives on Eximbank's performance. First, an analysis of the need for such financing is presented in conjunction with an assessment of the competitiveness of U.S. programs compared with those provided by other nations. Second, Eximbank performance is evaluated in terms of the cost of its programs, their potential welfare impacts, and the likely impact on U.S. exports. Third, an evaluation is provided of the Eximbank's decision making and its methodology for evaluating the impact of its direct credit program. Recommendations are made concerning U.S. export financing objectives, strategies for achieving those objectives, and Eximbank administrative procedures. This work also provides an economic analysis of Eximbank financing and includes a case study of Eximbank decision making in the granting of a $200 million aircraft credit to Ansett Airlines of Australia. This book will prove useful to those who are interested in international trade and finance, as well as those concerned more broadly with government intervention in markets.