Contents
Preface
Part 1 Elementary Dynamical Systems and Prevalent Economic Models
Chapter 1 Standard Growth Models
1.1 Introduction
1.2 Notation and Elementary Structure of the Model
1.3 Discrete-time Aggregative Growth Model
1.4 Ramsey-Cass-Koopmans Growth Model
1.5 OLG Model and Agreeability
1.6 The Continuous-time Cass-Koopmans Model
1.7 Appendix: Two-period Case
Chapter 2 Fundamental Theory of Dynamical Systems
2.1 Introduction
2.2 Fundamental Theory of Mathematical Analysis
2.3 Discrete Dynamical Systems: Difference Equations
2.4 Discrete-time Optimization Problem
2.5 Continuous-time Dynamical Systems
2.6 Dynamic Optimization Problem
2.7 Appendix
Part 2 General Mathematical Theory and Discrete-time Dynamic Systems
Chapter 3 Metric Spaces, Normed Vector Spaces and Hilbert Spaces
3.1 Introduction
3.2 Metric Space
3.3 Compactness and Completeness
3.4 Connectedness and Arcwise-connectedness
3.5 Normed Vector Space, Banach Space, and Hilbert Space
Chapter 4 Euclidean Space
4.1 Introduction
4.2 Vector Space and Linear Mapping
4.3 Matrix and Linear Mapping
4.4 Topological Structure
4.5 Differential
4.6 Nonnegative Square Matrix and Linear Model
Chapter 5 Static Optimization and Dynamic Programming
5.1 Introduction
5.2 Unconstrained Optimization
5.3 Constrained Optimization
5.4 Dynamic Programming
Chapter 6 The Logical Connection of Optimality Concepts
6.1 Introduction
6.2 General Framework
6.3 Agreeability and Optimality Concepts
6.4 Agreeability and Potential Maximality
Chapter 7 The Discrete-time Model with Many Capital Goods
7.1 Introduction
7.2 The Discrete-time Dynamic Economic Model
7.3 Necessary Conditions for Agreeability and Optimality
7.4 Quasi-Stationary Economic Model
7.5 Linear Dynamic Model with Product Innovation
Part 3 Continuous-time Dynamic Economic Systems
Chapter 8 Dynamical Systems and Ordinary Differential Equations
8.1 Introduction
8.2 Flows and Dynamical Systems
8.3 Autonomous Ordinary Differential Equations
8.4 Non-autonomous Ordinary Differential Equations
Chapter 9 Dynamic Optimization
9.1 Introduction
9.2 Optimal Control and Maximum Principle
9.3 Dynamic Optimization and Calculus of Variations
9.4 Isoperimetric Problem
Chapter 10 Continuous-time Model with Many Capital Goods
10.1 Introduction
10.2 Continuous-time Dynamic Economic Model
10.3 Optimal Growth Paths and Agreeable Paths (1)
10.4 Optimal Growth Paths and Agreeable Paths (2)
10.5 Appendix: A Proof of the Existence of the Modified Golden-Rule Paths
Chapter 11 Endogenous Growth Models
11.1 Introduction
11.2 Human Capital and Endogenous Growth
11.3 Innovation, Human Capital, and Growth
11.4 Quality-Ladder and Endogenous Growth
Chapter 12 Renewable Resource Problem
12.1 Introduction
12.2 Formulation of the Model
12.3 The Renewable Resource Problem without Production
12.4 The Renewable Resource Problem with Production
Part 4 Existence Problem and Some Other Topics
Chapter 13 Measure and Integration
13.1 Introduction
13.2 Measures
13.3 A Sequence of Functions and Convergence
13.4 Measurable Functions
13.5 Integration
13.6 Stochastic Dynamic Programming
Chapter 14 Existence Problem
14.1 Introduction
14.2 Existence Problem in a Continuous-time Model
14.3 Existence Problem in Discrete-time Models
14.4 Existence of Agreeable Paths
14.5 Appendix: Upper Semicontinuity
Chapter 15 Concluding Remarks and Future Research
15.1 Chaos Theory
15.2 Main Topics of the Endogeneous Growth Theory
Bibliography
