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Author | Avinash K. Dixit | |

ISBN-10 | 0198772106 | |

Release | 1990 | |

Pages | 188 | |

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Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and reviews functions defined by solutions of optimization problems. Recently revised and expanded, the second edition will be a valuable resource for upper level undergraduate and graduate students. |

Author | Avinash K. Dixit | |

ISBN-10 | 0198772114 | |

Release | 1990 | |

Pages | 188 | |

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Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and reviews functions defined by solutions of optimization problems. Recently revised and expanded by the author, the second edition of this popular student text will be a valuable resource for upper level undergraduate and graduate students. |

Author | Michael D. Intriligator | |

ISBN-10 | 9780898715118 | |

Release | 2002-01-01 | |

Pages | 508 | |

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A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics. |

Author | Daniel Léonard | |

ISBN-10 | 0521337461 | |

Release | 1992-01-31 | |

Pages | 353 | |

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Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor. Economic intuition is emphasized, examples and problem sets covering a wide range of applications in economics are provided, theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with the simple formulations and progressing to advanced topics. Optimal control theory is introduced directly, without recourse to the calculus of variations, and the connection with the latter and with dynamic programming is explained in a separate chapter. Also, the book draws the parallel between optimal control theory and static optimization. No previous knowledge of differential equations is required. |

Author | Bruce D. Craven | |

ISBN-10 | 9780387242804 | |

Release | 2006-03-30 | |

Pages | 161 | |

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Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book. |

Author | Morton I. Kamien | |

ISBN-10 | 9780486310282 | |

Release | 2013-04-17 | |

Pages | 400 | |

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Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition. |

Author | Alpha C. Chiang | |

ISBN-10 | 9781478608349 | |

Release | 1999-12-22 | |

Pages | 327 | |

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In this text, Dr. Chiang introduces students to the most important methods of dynamic optimization used in economics. The classical calculus of variations, optimal control theory, and dynamic programming in its discrete form are explained in the usual Chiang fashion, with patience and thoroughness. The economic examples, selected from both classical and recent literature, serve not only to illustrate applications of the mathematical methods, but also to provide a useful glimpse of the development of thinking in several areas of economics. |

Author | Gordon Mills | |

ISBN-10 | 0415313163 | |

Release | 2003 | |

Pages | 195 | |

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One of the fundamental economic problems is one of making the best use of limited resources. As a result, mathematical optimisation methods play a crucial role in economic theory. Covering the use of such methods in applied and policy contexts, this book deals not only with the main techniques (linear programming, nonlinear optimisation and dynamic programming), but also emphasizes the art of model-building and discusses fields such as optimisation over time. |

Author | Rangarajan K. Sundaram | |

ISBN-10 | 9780521497190 | |

Release | 1996-06-13 | |

Pages | 357 | |

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Divided into three separate parts, this book introduces students to optimization theory and its use in economics and allied disciplines. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained. |

Author | Yasuo Murata | |

ISBN-10 | 9781483271293 | |

Release | 2014-05-10 | |

Pages | 438 | |

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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. |

Author | Monique Florenzano | |

ISBN-10 | 9783642565229 | |

Release | 2012-12-06 | |

Pages | 154 | |

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This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study. |

Author | Michael Ralph Caputo | |

ISBN-10 | 0521603684 | |

Release | 2005-01-17 | |

Pages | 579 | |

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Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type. |

Author | Mukul Majumdar | |

ISBN-10 | 9783662040607 | |

Release | 2013-06-29 | |

Pages | 454 | |

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This collection of essays brings together some articles on dynamic optimization models that exhibit chaotic behavior. Chapters 3, 4, 5, 6, 7, and 9 appeared in a Symposium on Chaotic Dynamical Systems in Economic Theory (Volume 4, Number 5, 1994). Also, Chapters 10,11, and 12 appeared in the Journal of Economic The ory. We would like to thank the authors, and Academic Press for permission to reprint. We are grateful to Professor C.D. Aliprantis for suggesting the idea of a book structured around the Economic Theory Symposium, and without the support and patience of Dr. Mueller this project could not have been completed. We would like to thank Ms. Amy Gowan who cheerfully per formed the arduous task of typing the manuscript. Thanks are also due to Xiao Qing Yu, Tridip Ray and Malabika Majumdar for their help at various stages in the preparation of the manuscript. For a course on dynamic optimization addressed to students with a good background in economic theory and real analysis, one can assign Chapter 2 as a partial introduction to the basic tech niques. Chapters 3 and 4 can be assigned to provide examples of simple optmization models generating complicated behavior. |

Author | P. S. Dasgupta | |

ISBN-10 | 0521297613 | |

Release | 1979 | |

Pages | 516 | |

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A presentation of the economic principles relating to the use and management of natural resources, including analysis of optimal use policies. |

Author | Angel de la Fuente | |

ISBN-10 | 0521585295 | |

Release | 2000-01-28 | |

Pages | 835 | |

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A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics. |

Author | Thomas A. Weber | |

ISBN-10 | 0262015730 | |

Release | 2011 | |

Pages | 360 | |

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This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models. |

Author | Dean Corbae | |

ISBN-10 | 9781400833085 | |

Release | 2009-02-17 | |

Pages | 688 | |

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory |