The Hamiltonian Approach to Dynamic Economics

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.

Acknowledgments

About the Authors

Essay I. Introduction to Hamiltonian Dynamics in Economics

Essay II. On Optimal Steady States of N-Sector Growth Models when Utility Is Discounted

Essay III. The Structure and Stability of Competitive Dynamical Systems

Essay IV. Saddle Points of Hamiltonian Systems in Convex Lagrange Problems Having a Nonzero Discount Rate

Essay V. Existence of Solutions to Hamiltonian Dynamical Systems of Optimal Growth

Essay VI. A Characterization of the Normalized Restricted Profit Function

Essay VII. Global A Symptotic Stability of Optimal Control Systems with Applications to the Theory of Economic Growth

Essay VIII. A Growth Property in Concave-Convex Hamiltonian Systems

Index