Dynamic Optimization and Mathematical Economics

1. Front Matter

   Pages i-x

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2. Control Theory in Economic Systems

   1. Front Matter

      Pages 1-3

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   2. Asset Pricing in an Economy with Production: A “Selective” Survey of Recent Work on Asset-Pricing Models

      • William A. Brock

      Pages 5-29

   3. Alternative Long-Run Goals and the Theory of the Firm: Why Profit Maximization May Be a Better Assumption Than You Think

      • Hayne E. Leland

      Pages 31-50

   4. Mathematical Optimization and Economic Behavior

      • Sheldon S. L. Chang

      Pages 51-69

   5. Performance Improvement of Uncertain Macroeconomic Systems

      • George Leitmann, Henry Y. Wan Jr.

      Pages 71-88

   6. Stochastic Games, Oligopoly Theory, and Competitive Resource Allocation

      • Martin Shubik, Matthew J. Sobel

      Pages 89-100

3. Dynamical Theory of the Economics of Extractive Natural Resources

   1. Front Matter

      Pages 101-104

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   2. Optimal Pricing, Use, and Exploration of Uncertain Natural Resource Stocks

      • Kenneth J. Arrow, Sheldon S. L. Chang

      Pages 105-116

   3. Restricted Access to Common-Property Fishery Resources: A Game-Theoretic Analysis

      • Colin W. Clark

      Pages 117-132

   4. Cartel and Oligopoly Pricing of Nonreplenishable Natural Resources

      • Tracy R. Lewis, Richard Schmalensee

      Pages 133-156

   5. Optimum Extraction of an Exhaustible Resource: A Mathematical Analysis

      • Pan-Tai Liu

      Pages 157-168

   6. Royalties and the Extraction Rate of an Exhaustible Resource

      • Jon G. Sutinen

      Pages 169-178

4. Large-Scale Systems and Decentralized Control

   1. Front Matter

      Pages 179-181

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   2. Dynamics and Control of a System Composed of a Large Number of Similar Subsystems

      • Masanao Aoki

      Pages 183-203

   3. Hierarchical Decisionmaking under Uncertainty

      • Tamer Başar

      Pages 205-221

   4. A Game-Theoretic Approach to Bureaucratic Behavior

      • Dagobert L. Brito, Michael D. Intriligator

      Pages 223-236

   5. Optimal Stabilization Policies for Decentralized Macroeconomic Systems with Conflicting Targets

      • Hajime Myoken

      Pages 237-251

   6. A Minimum Principle for Decentralized Stochastic Control Problems

      • Pravin Varaiya, Jean Walrand

      Pages 253-266

5. Back Matter

   Pages 267-269

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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.

• asset pricing
• calculus
• conflict
• dynamics
• growth
• mathematical economics
• modeling
• optimal control
• optimization
• research
• sets
• stabilization
• time

• Mathematics Department, University of Rhode Island, Kingston, USA

  Pan-Tai Liu

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