Chapter

Optimal Control Theory 631

20.1 The Nature of Optimal Control 631

Illustration: A Simple Macroeconomic Model 632

Ponlryagin s Maximum Principle 633

20.2 Alternative Terminal Conditions 639

Fixed Terminal Point 639 Horizontal Terminal Line 639 Truncated Vertical Terminal Line 639 Truncated Horizontal Terminal (due 640 Exercise 202 643 203 Autonomous Problems 644

20.4 Economic Applications 645

¬°dfetime Utility Maximization 645 Exhaustible Resource 647 Exercise 2Q,4 649

20.5 Infinite Time Horizon 649

Neoclassical Optimal Growth Model 649 The Current- Value llamiltonian 65 / Cons one ting a Phase Diagram 652 Analyzing the Phase Diagram 653

20.6 Limitations of Dynamic Analysis 654

The CreekAlphabet 655 Mathematical Symbols 656 A Short Reading List 659 Answers to Selected Exercises 662 Index 677

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