Cass / Shell The Hamiltonian Approach to Dynamic Economics

1. Auflage 2014
ISBN: 978-1-4832-6685-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 212 Seiten, Web PDF

The Hamiltonian Approach to Dynamic Economics focuses on the application of the Hamiltonian approach to dynamic economics and attempts to provide some unification of the theory of heterogeneous capital. Emphasis is placed on the stability of long-run steady-state equilibrium in models of heterogeneous capital accumulation. Generalizations of the Samuelson-Scheinkman approach are also given. Moreover, conditions are sought on the geometry of the Hamiltonian function (that is, on static technology) that suffice to preserve under (not necessarily small) perturbation the basic properties of the Hamiltonian dynamical system. Comprised of eight essays, this book begins with an introduction to Hamiltonian dynamics in economics, followed by a discussion on optimal steady states of n-sector growth models when utility is discounted. Optimal growth and decentralized or descriptive growth models in both continuous and discrete time are treated as applications of Hamiltonian dynamics. Theproblem of optimal growth with zero discounting is considered, with emphasis on a steepness condition on the Hamiltonian function. The general problem of decentralized growth with instantaneously adjusted expectations about price changes is also analyzed, along with the global asymptotic stability of optimal control systems with applications to the theory of economic growth. This monograph will be of value to mathematicians and economists.

Autoren/Hrsg.

Cass, David

Shell, Karl

Inhaltsverzeichnis

1;Front Cover;1
2;The Hamiltonian Approach to Dynamic Economics;4
3;Copyright Page;5
4;Table of Contents;6
5;Acknowledgments;8
6;About the Authors;10
7;ESSAY I.
Introduction to Hamiltonian Dynamics in Economics;12
7.1;REFERENCES;20
8;ESSAY II.
On Optimal Steady States of n-Sector Growth Models when Utility is Discounted;22
8.1;I. THE VISIT LEMMA, CONTINUITY, AND LOCAL PROPERTIES OF OPTIMAL STEADY
STATES;23
8.2;II. THE CONTINUITY OF THE STABLE
MANIFOLD;30
8.3;III. THE INSENSITIVITY OF THE GLOBAL TURNPIKE RESULT;39
8.4;REFERENCES;40
9;ESSAY III. The Structure and Stability of Competitive
Dynamical Systems;42
9.1;1. INTRODUCTION AND SUMMARY;42
9.2;2. THE GENERAL MODEL;45
9.3;3. STABILITY OF THE OPTIMAL GROWTH MODEL;59
9.4;4. STABILITY OF THE DESCRIPTIVE GROWTH MODEL WITH MARXIAN
SAVING–INVESTMENT BEHAVIOR;73
9.5;ACKNOWLEDGMENTS;79
9.6;REFERENCES;80
10;ESSAY IV. Saddle Points of Hamiltonian Systems in Convex Lagrange
Problems Having a Nonzero Discount Rate;82
10.1;1. INTRODUCTION;82
10.2;2. LOCAL BEHAVIOR AND OPTIMALITY;89
10.3;3. REDUCTION FROM THE LOCAL TO THE GLOBAL CASE;96
10.4;4. GLOBAL RESULTS;100
10.5;5. RESULTS FOR THE INTERVAL (— oo, 0];112
10.6;6. SOME COMPLEMENTARY RESULTS;119
10.7;REFERENCES;124
11;ESSAY V. Existence of Solutions to Hamiltonian Dynamical
Systems of Optimal Growth;125
11.1;1. INTRODUCTION;125
11.2;2. SUFFICIENT CONDITIONS FOR EXISTENCE;127
11.3;3. CONSEQUENCES OF THE EXISTENCE CONDITIONS: A PRIORI BOUNDS;129
11.4;4. EXISTENCE PROOF;134
11.5;APPENDIX: THE CONTINUATION PRINCIPLE;136
11.6;ACKNOWLEDGMENTS;140
11.7;REFERENCES;140
12;ESSAY VI. A Characterization of the Normalized Restricted Profit Function;142
12.1;1. INTRODUCTION;142
12.2;2. DUALITY THEOREMS;145
12.3;3. HESSIAN MATRIX IDENTITIES;159
12.4;4. CONCLUDING REMARKS;164
12.5;APPENDIX;165
12.6;ACKNOWLEDGMENTS;172
12.7;REFERENCES;172
13;ESSAY VII. Global Asymptotic Stability of Optimal Control Systems with Applications to the Theory of Economic Growth;175
13.1;1;175
13.2;2. A FIRST RESULT ON G.A.S.;183
13.3;3. A General Result on Convergence of Bounded Trajectories;186
13.4;4. A MORE GENERAL RESULT;192
13.5;5. SUGGESTIONS FOR FUTURE RESEARCH;197
13.6;REFERENCES;199
14;ESSAY VIII. A Growth Property in Concave-Convex Hamiltonian Systems;202
14.1;REFERENCES;206
15;Index;208