Chiang Elements Of Dynamic Optimization Pdf File

Alpha Chung-i Chiang (born 1927) is an American mathematical economist, Professor Emeritus of Economics at the University of Connecticut, and author of perhaps the most well known mathematical economics textbook; Fundamental Methods of Mathematical Economics.^{[1][2][3][4][5]}

Problem, we have to change the constrained dynamic optimization problem into a uncon-strained problem, and the consequent function is known as the Hamiltonian function denoted as H, H(t;y;u; ) = F(t;y;u) + (t)f(t;y;u) (2) where (t) is known as the costate variable. It’s interpretation is not unlike the multiplier.

Chiang's undergraduate studies at St. John's University, Shanghai led to a BA in 1946, and his postgraduates studies at the University of Colorado an MA in 1948 and at Columbia University a PhD in 1954.^[6]

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He taught at Denison University in Ohio from 1954 to 1964, serving as Chairman of the Department of Economics in the last three years there. Then he joined the University of Connecticut as Professor of Economics in 1964. He taught for 28 years at the University of Connecticut—becoming in 1992 Professor Emeritus of Economics. He also held Visiting Professorships at New Asia College (Hong Kong), Cornell University, Lingnan College (Hong Kong), and Helsinki School of Economics and Business Administration.

Married to Emily Chiang, he has a son Darryl, and a daughter Tracey. His wide extracurricular interests include ballroom dancing, Chinese opera, Chinese painting/calligraphy, photography, and piano. A piano-music composition of his is featured in Tammy Lum's CD 'Ballades & Ballads' (2015).

Selected publications[edit]

• Chiang, A. C., (1967). Fundamental methods of mathematical economics. McGraw-Hill, New York. (Now (2005) in 4th Edition with Wainwright, Kevin)
• Chiang, A. C. (1992). Elements of dynamic optimization. McGraw-Hill, New York. Now, published by Waveland Press Inc., Illinois.

References[edit]

1. ^McGraw Hill: Meet the authors: Fundamental Methods of Mathematical Economics, 4/e - Alpha C. Chiang, University of Connecticut, Kevin Wainwright, British Columbia Institute of Technology(Accessed Jan 2015)
2. ^Talbott, Clint (2011) In Shanghai, CU beckoned future economist, Colorado Arts and Sciences Magazine, University of Colorado (Accessed Jan 2015)
3. ^Bello, I. (1970). 'Book Review: Fundamental Methods of Mathematical Economics'. Econometrica. 38 (5): 787–788. JSTOR1912217.
4. ^Rothenberg, T. J. (1968). 'Book Review: Fundamental Methods of Mathematical Economics'. American Economic Review. 58 (5): 1421–1422. JSTOR1814064.
5. ^(1984). Fundamental methods of mathematical economics Alpha C. Chiang. 3rd ed. New York: McGraw-Hill, 1984. 788 pp. ISBN0-07-010813-7. Journal of Macroeconomics. 6.
6. ^Who’s Who in Economics: A Biographical Dictionary of Major Economists 1900–1994. MIT Press.

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. “This book is immensely valuable, especially for students coming to this material for the first time. Professor Chiang has a singular talent for clear exposition of complex mathematical concepts.

This text is simply the best introduction to dynamic optimization I have ever seen.” — John McDermott, University of South Carolina“Chiang has done it again.” — Henry Thompson, Auburn University“A brilliant, highly readable book. Bringing together tractable dynamics and a rich array of applications, it covers in depth some major analytical developments in dynamic macroeconomics. Dynamic macroeconomics in the 1990s was about introducing various kinds of market imperfections and heterogeneity in the models available before. This book teaches, in a comprehensive and understandable way, how to use and formulate these models. Chiang makes it insightful and natural for the reader, using the tools he has laid out, to go on to attack substantive and original research in dynamic macroeconomics.

Invaluable for teachers and students alike.” — Zuhair Al-Fakhouri, Wayne State University“This is the most understandable text I have come across on topics of optimization. The author discusses the formal elements of problems in an informal way to facilitate an easy grasp of the crucial points. I have learned and re-learned control theory from this book better than any other text.” — Abdul Qayum, Portland State University. The Nature of Dynamic OptimizationSalient Features of Dynamic Optimization Problems / Variable Endpoints and Transversality Conditions / The Objective Functional / Alternative Approaches to Dynamic OptimizationPart II. THE CALCULUS OF VARIATIONS2. The Fundamental Problem of the Calculus of VariationsThe Euler Equation / Some Special Cases / Two Generalizations of the Euler Equation / Dynamic Optimization of a Monopolist / Trading Off Inflation and Unemployment3. Transversality Conditions for Variable-Endpoint ProblemsThe General Transversality Condition / Specialized Transversality Conditions / Three Generalizations / The Optimal Adjustment of Labor Demand4.

Second-Order ConditionsThe Concavity/Convexity Sufficient Condition / The Legendre Necessary Condition / First and Second Variations5. Infinite Planning HorizonMethodological Issues of Infinite Horizon / The Optimal Investment Path of a Firm / The Optimal Social Saving Behavior / Phase-Diagram Analysis / The Concavity/Convexity Sufficient Condition Again6.

Constrained ProblemsFour Basic Types of Constraints / Some Economic Applications Reformulated / The Economics of Exhaustible ResourcesPart III. OPTIMAL CONTROL THEORY7. Optimal Control: The Maximum PrincipleThe Simplest Problem of Optimal Control / The Maximum Principle / The Rationale of the Maximum Principle / Alternative Terminal Conditions / The Calculus of Variations and Optimal Control Theory Compared / The Political Business Cycle / Energy Use and Environmental Quality8.

More on Optimal ControlAn Economic Interpretation of the Maximum Principle / The Current-Value Hamiltonian / Sufficient Conditions / Problems with Several State and Control Variables / Antipollution Policy9. Infinite-Horizon ProblemsTransversality Conditions / Some Counterexamples Reexamined / The Neoclassical Theory of Optimal Growth / Exogenous and Endogenous Technological Progress10. Optimal Control with ConstraintsConstraints Involving Control Variables / The Dynamics of a Revenue-Maximizing Firm / State-Space Constraints / Economic Examples of State-Space Constraints / Limitations of Dynamic OptimizationAnswers to Selected Exercise Problems. Constitution of india by j n pandey pdf.