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The Hamiltonian Approach to Dynamic Economics

Editor

Listed:
  • Cass, David
  • Shell, Karl

Abstract

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.

Suggested Citation

  • Cass, David & Shell, Karl (ed.), 1976. "The Hamiltonian Approach to Dynamic Economics," Elsevier Monographs, Elsevier, edition 1, number 9780121636500.
    • Handle: RePEc:eee:monogr:9780121636500
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    Citations

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    Cited by:

    1. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    2. Brock,W.A., 2000. "Some mathematical tools for analysing complex-nonlinear systems," Working papers 20, Wisconsin Madison - Social Systems.
    3. Russell, Thomas, 2004. "Investing capital rentals to sustain periodic motion in classical mechanics by John Hartwick," Japan and the World Economy, Elsevier, vol. 16(3), pages 359-362, August.
    4. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    5. Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
    6. Tahvonen, Olli, 1995. "Net national emissions, CO2 taxation and the role of forestry," Resource and Energy Economics, Elsevier, vol. 17(4), pages 307-315, December.
    7. J H P Paelinck, 1979. "Interactive Groups with Related Limited Efficiency," Environment and Planning A, , vol. 11(10), pages 1179-1187, October.
    8. Olli Tahvonen, 1991. "On the dynamics of renewable resource harvesting and pollution control," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 1(1), pages 97-117, March.
    9. Wolff, Reiner, 1997. "Saddle-point dynamics in non-autonomous models of multisector growth with variable returns to scale," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 267-282, April.

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