Abstract
Hamiltonian dynamics arises not only in economic optimization problems but also in descriptive economic models in which there is perfect foresight about asset prices. Hamiltonian dynamics applies in discrete time as well as in continuous time. In discrete time, the system of differential equations is replaced by a closely related system of difference equations. The theory accommodates differential correspondences or difference correspondences, which naturally arise in economics. The Hamiltonian approach through the Hamiltonian function has proved remarkably successful in establishing sufficient conditions for the saddle-point property and related stability questions in a class of optimal economic growth models.
This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume
This is a preview of subscription content, log in via an institution to check access.
Bibliography
Brock, W.A., and J.A. Scheinkman. 1976. Global asymptotic stability of optimal economic systems with applications to the theory of economic growth. In Cass and Shell (1976a).
Cass, D., and K. Shell. 1976a. The Hamiltonian approach to dynamic economics. New York: Academic Press. [Reprinted from the Journal of Economic Theory 12, February 1976, Symposium: ‘Hamiltonian dynamics in economics’.]
Cass, D., and K. Shell. 1976b. The structure and stability of competitive dynamical systems. In Cass and Shell (1976a).
Magill, M.J.P. 1970. On a general economic theory of motion. Berlin: Springer-Verlag.
McKenzie, L.W. 1968. Accumulation programs of maximum utility and the von Neumann facet. In Value, capital and growth, ed. J.N. Wolfe. Edinburgh: Edinburgh University Press.
Pontryagin, L.S., G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mischenko. 1962. The mathematical theory of optimal processes. New York: Interscience.
Rockafellar, R.T. 1976. Saddlepoints of Hamiltonian systems in convex Lagrange problems having nonzero discount rate. In Cass and Shell (1976a).
Samuelson, P.A., and R.M. Solow. 1956. A complete model involving heterogeneous capital goods. Quarterly Journal of Economics 70: 537–562.
Shell, K., ed. 1967. Essays on the theory of optimal economic growth. Cambridge, MA: MIT Press.
Shell, K. 1969. Applications of Pontryagin’s maximum principle to economics. In Mathematical systems theory and economics, ed. H.W. Kuhn and G.P. Szegö, vol. 1. Berlin: Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2008 The Author(s)
About this entry
Cite this entry
Shell, K. (2008). Hamiltonians. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_1166-2
Download citation
DOI: https://doi.org/10.1057/978-1-349-95121-5_1166-2
Received:
Accepted:
Published:
Publisher Name: Palgrave Macmillan, London
Online ISBN: 978-1-349-95121-5
eBook Packages: Springer Reference Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences
Publish with us
Chapter history
-
Latest
Hamiltonians- Published:
- 15 March 2017
DOI: https://doi.org/10.1057/978-1-349-95121-5_1166-2
-
Original
Hamiltonians- Published:
- 26 November 2016
DOI: https://doi.org/10.1057/978-1-349-95121-5_1166-1