| Preface | p. 1 |
| Some Growth Models | p. 3 |
| A General Growth Model | p. 4 |
| The Harrod Model | p. 6 |
| The Domar Model | p. 7 |
| The Solow-Swan Model | p. 8 |
| The Frankel Model | p. 10 |
| Some Conclusions | p. 11 |
| The Ramsey Model | p. 13 |
| The Model | p. 13 |
| The Assumptions | p. 15 |
| Feasible Paths | p. 16 |
| Existence of Optimal Paths | p. 16 |
| Properties of the Optimal Paths | p. 19 |
| Value Function - Bellman Equation - Optimal Policy | p. 21 |
| Some Properties of the Value Function | p. 22 |
| Bellman Equation | p. 25 |
| Optimal Policy | p. 29 |
| Dynamic Properties of the Optimal Path | p. 31 |
| Mangasarian Lemma | p. 32 |
| On the Continuity of the Value Function and of the Optimal Policy with respect to the Discount Factor and the initial Capital Stock | p. 34 |
| An Aggregated Optimal Growth Model with a Convex-Concave Production Function | p. 37 |
| The Model | p. 38 |
| The Assumptions | p. 39 |
| Feasible Paths | p. 39 |
| Existence of Optimal Paths | p. 40 |
| Properties of the Optimal Paths | p. 40 |
| Value Function - Bellman Equation - Optimal Policy | p. 41 |
| Some Properties of the Value Function | p. 41 |
| Bellman Equation | p. 42 |
| Optimal Correspondence | p. 43 |
| On the Differentiability of the Value Function | p. 45 |
| Dynamic Properties of the Optimal Paths | p. 49 |
| On the Mangasarian Lemma | p. 60 |
| Multisector Optimal Growth Models With Bounded From Below Returns | p. 63 |
| The General Case | p. 66 |
| Existence of an optimal solution | p. 67 |
| Value Function and Optimal Correspondence | p. 69 |
| Properties of Optimal Paths | p. 77 |
| On the Continuity of the Value Function and of the Optimal Correspondence with respect to ([beta], x[subscript 0]) | p. 78 |
| The Case with Concave Return Function and Convex Technology | p. 80 |
| The One Dimension Case | p. 84 |
| Examples | p. 86 |
| Example 1 (The Ramsey Model) | p. 86 |
| Example 2 | p. 87 |
| Example 3: A Consumption-Savings Problem | p. 89 |
| Example 4: A Two-Sector Model | p. 92 |
| Example 5: A Human Capital Model | p. 94 |
| Example 5: Learning by Doing Model | p. 96 |
| Optimal Growth Models With Unbounded From Below Returns | p. 101 |
| The Model | p. 102 |
| Existence of Optimal Solutions | p. 103 |
| Value Function | p. 105 |
| Optimal Policy - Properties of Optimal Paths | p. 113 |
| Examples | p. 115 |
| Example 1 | p. 115 |
| Example 2: The AK model | p. 118 |
| Optimal Growth and Competitive Equilibrium | p. 121 |
| The Model | p. 121 |
| Optimal Growth Models Without Discounting | p. 131 |
| The Model | p. 132 |
| Good programmes | p. 132 |
| Optimal Programmes | p. 137 |
| Value Function - Bellman Equation | p. 141 |
| Turnpike in Optimal Growth Models with Convex Technology | p. 149 |
| The Visit Lemmas | p. 150 |
| The Neighborhood Turnpike | p. 155 |
| Turnpike Theorems | p. 159 |
| Remarks | p. 162 |
| Cycles and Chaos in Optimal Growth Models | p. 165 |
| Two-Sector Models | p. 165 |
| The model | p. 165 |
| Examples | p. 167 |
| Optimal interior stationary state | p. 168 |
| Difficulties | p. 170 |
| Existence of periodic orbits | p. 171 |
| Optimal chaos | p. 173 |
| Two definitions of complicated dynamics | p. 173 |
| "Rationalizability" of a map | p. 175 |
| Appendix | p. 177 |
| Appendix | p. 181 |
| Metric Spaces and Normed Spaces | p. 181 |
| Distances and Metric Spaces | p. 181 |
| Topology on Metric Spaces | p. 182 |
| Compact Spaces, Compact Sets | p. 185 |
| Normed Spaces | p. 185 |
| Product Topology | p. 186 |
| Concave Functions | p. 187 |
| Subdifferentiability, Differentiability of Concave Functions | p. 188 |
| Negative Matrix | p. 189 |
| The Implicit Functions Theorem | p. 190 |
| Correspondences, The Maximum Theorem | p. 190 |
| Examples | p. 191 |
| Bibliography | p. 193 |
| Index | p. 199 |
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