This compact and original exposition of optimal control theory and applications is designed for graduate and advanced undergraduate students in economics. It presents a new elementary yet rigorous proof of the maximum principle and a new way of applying the principle that will enable students to solve any one-dimensional problem routinely. Its unified framework illuminates many famous economic examples and models.

This work also emphasizes the connection between optimal control theory and the classical themes of capital theory. It offers a fresh approach to fundamental questions such as: What is income? How should it be measured? What is its relation to wealth?

The book will be valuable to students who want to formulate and solve dynamic allocation problems. It will also be of interest to any economist who wants to understand results of the latest research on the relationship between comprehensive income accounting and wealth or welfare.

  Introduction                                                       1

Part I. Introduction to the Maximum Principle
  1 The Calculus of Variations and the Stationary Rate of Return on Capital  13
  2 The Prototype-Economic Control Problem                            30
  3 The Maximum Principle in One Dimension                            66
  4 Applications of the Maximum Principle in One Dimension           111

Part II. Comprehensive Accounting and the Maximum Principle
  5 Optimal Multisector Growth and Dynamic Competitive Equilibrium  185
  6 The Pure Theory of Perfectly Complete National Income Accounting  238
  7 The Stochastic Wealth and Income Version of the Maximum Principle  295


  References                                                        329
  Index                                                             337