Introduction to Hamiltonian dynamics in economics

Abstract

Economics during the fifties and sixties was marked by a substantial resurgence of interest in the theory of capital. While the advances during this period were very impressive, there was also an uneveness in the development of the subject. One-good models were studied in detail, as were many-good models of production-maximal growth and many-good models of consumption-optimal growth for the special case in which there is no social impatience. When treating heterogeneous capital, the literatures on decentralized or descriptive growth and consumptionoptimal growth with positive time discounting were dominated by special cases and examples. Reliance on examples and special cases proved to have some unfortunate consequences. The Battle of the Two Cambridges, ostensibly an argument over approaches to modeling distribution and accumulation, often seemed to focus on the robustness (or lack of robustness) of certain “fundamental” properties of the one-sector model and other worked-out examples when extended to more general heterogeneous-capital models. Furthermore, in large part because growth theory appeared to be an enterprise based only on proliferating special cases, the attention of the young able minds in the profession turned elsewhere, for example, to theat least seemingly-more evenly-developed general equilibrium tradition. This is a shame. Intertemporal allocation and its relationship with the wealth of societies is one of the most important problems in our discipline. Growth models are natural vehicles for the study of what is called “temporary equilibrium.” Dynamic models of multi-asset accumulation provide the theoretically most satisfactory environment for modeling the macroeconomics of income determination, employment, and inflation. The papers in this volume can be thought of as attempts at providing some unification of the theory of heterogeneous capital. The major