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Tables of Contents for Optimal Control Theory and Static Optimization in Economics
Chapter/Section Title
Page #
Page Count
Preface
ix
Static optimization
1
73
Unconstrained optimization, concave and convex functions
1
19
Optimization under equality constraints: the method of Lagrange
20
23
Comparative statics
43
9
Optimization under inequality constraints: nonlinear programming
52
15
Economic applications of nonlinear programming
67
3
The special case of linear programming
70
4
Appendix
74
5
Exercises
79
266
Ordinary differential equations
87
30
Introduction
87
1
Definitions and fundamental results
88
3
First-order differential equations
91
4
Systems of linear FODE with constant coefficients
95
5
Systems of two nonlinear FODE
100
17
Appendix
111
2
Exercises
113
4
Introduction to dynamic optimization
117
10
Optimal borrowing
118
1
Fiscal policy
119
1
Suboptimal consumption path
120
1
Discounting and depreciation in continuous-time models
121
6
Exercises
124
3
The maximum principle
127
42
A simple control problem
127
2
Derivation of the maximum principle in discrete time
129
4
Numerical solution of an optimal control problem in continuous time
133
4
Phase diagram analysis of optimal control problems
137
14
Economic interpretation of the maximum principle
151
10
Necessity and sufficiency of the maximum principle
161
8
Exercises
165
4
The calculus of variations and dynamic programming
169
18
The calculus of variations
169
4
Dynamic programming: Discrete-time, finite-horizon problems
173
9
Dynamic programming in continuous time
182
5
Exercises
184
3
The general constrained control problem
187
34
The set of admissible controls
187
3
Integral constraints
190
2
The maximum principle with equality constraints only
192
6
The maximum principle with inequality constraints
198
12
Necessity and sufficiency theorems: The case with inequality and equality constraints
210
8
Concluding notes
218
3
Exercises
218
3
Endpoint constraints and transversality conditions
221
42
Free-endpoint problems
222
4
Problems with free endpoint and a scrap value function
226
3
Lower bound constraints on endpoint
229
6
Problems with lower bound constraints on endpoint and a scrap value function
235
5
Free-terminal-time problems without a scrap value function
240
7
Other transversality conditions
247
1
A general Formula for transversality conditions
248
3
Sufficiency theorems
251
2
A summary table of common transversality conditions
253
1
Control parameters
253
10
Exercises
259
4
Discontinuities in the optimal controls
263
22
A classical bang-bang example
263
4
The beekeeper's problem
267
7
One-sector optimal growth with reserves
274
3
Highest consumption path
277
4
Concluding comments
281
4
Exercises
282
3
Infinite-horizon problems
285
22
Optimality criteria
285
2
Necessary conditions
287
1
Sufficient conditions
288
1
Autonomous problems
289
5
Steady states in autonomous infinite-horizon problems
294
4
Further properties of autonomous infinite-horizon problems
298
9
Exercises
304
3
Three special topics
307
38
Problems with two-state variables
307
3
Trade in capital goods: jumps in the state variables
310
22
Constraints on the state variables
332
13
Exercises
342
3
Bibliography
345
6
Index
351