Optimal Control Problems Related to the Robinson-Solow-Srinivasan Model

This book is about the study of optimal control problems related to the Robinson–Solow–Srinivasan (RSS) model,introduced in the 1960s by economists Joan Robinson,Robert Solow,and Thirukodikaval Nilakanta Srinivasan. Two large general classes of optimal control problems are presented,with a turnpike theory developed and the existence of solutions to the corresponding infinite horizon optimal control problems established. The stability of the turnpike phenomenon is analyzed for both classes of problems.

Format: Paperback / softback
Length: 348 pages
Publication date: 09 August 2022
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the study of classes of optimal control problems that arise in the realm of economic growth theory, closely linked to the Robinson-Solow-Srinivasan (RSS) model. Introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan, the RSS model has since gained significant attention in the field of economic dynamics. This book presents two broad categories of optimal control problems, encompassing the RSS model as a specific instance. Within these categories, a turnpike theory is developed, providing insights into the existence of solutions for infinite horizon optimal control problems.

The book is organized into nine chapters, with Chapter 1 exploring turnpike properties for various optimal control problems, including those associated with the RSS model. Chapters 2 to 6 delve into the study of infinite horizon optimal control problems with nonautonomous optimality criteria. These problems involve nonconcave utility functions, which determine the optimality criterion. Notably, the RSS model falls within this class as a particular case. Chapter 3 focuses on analyzing the stability of the turnpike phenomenon for the one-dimensional nonautonomous concave RSS model. The subsequent chapter examines a class of autonomous nonconcave optimal control problems, a subclass of the problems discussed in Chapter 2. Here, the equivalence of the turnpike property and the asymptotic turnpike property is established, along with the stability of the turnpike phenomenon.

Turnpike conditions and their implications for nonautonomous problems are further explored in Chapter 4. The book concludes with Chapter 5, which examines the stability of the turnpike phenomenon for autonomous nonconcave optimal control problems.

In summary, this book offers a comprehensive exploration of optimal control problems related to the RSS model, presenting two broad classes of problems and developing a turnpike theory to establish the existence of solutions for infinite horizon optimal control problems. The theoretical insights and practical applications of these findings make it an invaluable resource for scholars and researchers in economics and related fields.

Weight: 551g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811622540
Edition number: 1st ed. 2021