Advertisement

Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System

  • Tapan Mitra
  • Kazuo Nishimura
Chapter

Abstract

The theory of optimal intertemporal allocation has been developed primarily for the case in which the objective function of the planner or representative agent can be written as \(U(c1, c2\ldots) \equiv {{{\sum}^\infty}_{t=1}} {{\delta}^{t-1}}w(c_{t})\) where c t represents consumption at date t, w the period felicity function, and \(\delta\,\,\epsilon\) (o,1) a discount factor, representing the time preference of the agent.

Keywords

Utility Function Euler Equation Discount Factor Characteristic Root Optimal Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abel, A. B. (1990), “Asset Prices under Habit Formation and Catching up with the Joneses,” American Economic Review Papers and Proceedings, 80, 38–42.Google Scholar
  2. Amir, R. (1996), “Sensitivity Analysis of Multisector Optimal Economic Dynamics,” Journal of Mathematical Economics, 25, 123–141.CrossRefGoogle Scholar
  3. Amir, R., Mirman, L. J. and W. R. Perkins (1991), “One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics,” International Economic Review, 32, 625–792.CrossRefGoogle Scholar
  4. Araujo, A. (1991), “The Once but not Twice Differentiability of the Policy Functions,” Econometrica, 59, 1381–1393.CrossRefGoogle Scholar
  5. Araujo, A. and J. A. Scheinkman (1977), “Smoothness, Comparative Dynamics, and the Turnpike Property,” Econometrica, 45, 601-620.CrossRefGoogle Scholar
  6. Becker, R. and J. Boyd (1997), Capital Theory, Equilibrium Analysis, and Recursive Utility, Basil Blackwell: Oxford.Google Scholar
  7. Benhabib, J. and K. Nishimura (1985), “Competitive Equilibrium Cycles,” Journal of Economic Theory, 35, 284–306.CrossRefGoogle Scholar
  8. Bernheim, B. D. and D. Ray (1987), “Economic Growth with Intergenerational Altruism,” Review of Economic Studies, 54, 227–243.CrossRefGoogle Scholar
  9. Boyer, M. (1978), “A Habit Forming Optimal Growth Model,” International Economic Review, 19, 585–609.CrossRefGoogle Scholar
  10. Clark, C. W. (1976), ”A Delayed-Recruitment Model of Population Dynamics, with an Application to Baleen Whale Populations,” Journal of Mathematical Biology, 3, 381–391.CrossRefGoogle Scholar
  11. Chakravarty, S. and A. S. Manne (1968), “Optimal Growth when the Instantaneous Utility Function Depends upon the Rate of Change of Consumption,” American Economic Review, 58, 1351–1354.Google Scholar
  12. Dasgupta, P. (1974), “On Some Problems Arising from Professor Rawls’ Conception of Distributive Justice,” Theory and Decision, 4, 325–344.CrossRefGoogle Scholar
  13. Deaton, A. (1992), Consumption, Oxford University Press.Google Scholar
  14. Franks, J. (1979), Manifolds of C r Mappings and Applications to Differentiable Dynamical Systems, in Studies in Analysis, ed. by Rota, G.-C., New York: Academic Press, 271–290.Google Scholar
  15. Gale, D. (1967), “On Optimal Development in a Multi-Sector Economy,” Review of Economic Studies, 34, 1–18.CrossRefGoogle Scholar
  16. Hautus, M. L. J. and T. S. Bolis (1979), “A Recursive Real Sequence,” American Mathematical Monthly̌, 86, 865–866.Google Scholar
  17. Heal, G. M. and H. E. Ryder (1973), “Optimal Growth with Intertemporally Dependent Preferences,” Review of Economic Studies, 40, 1–31.CrossRefGoogle Scholar
  18. Irwin, M. C. (1970), “On the Stable Manifold Theorem,” Bulletin of the London Mathematical Society, 2, 196–198.CrossRefGoogle Scholar
  19. Iwai, K. (1972), “Optimal Economic Growth and Stationary Ordinal Utility: A Fisherian Approach,” Journal of Economic Theory, 5, 121–151.CrossRefGoogle Scholar
  20. Kohlberg, E. (1976), “A Model of Economic Growth with Altrusim Between Generations,” Journal of Economic Theory, 13, 1–13.CrossRefGoogle Scholar
  21. Koopmans, T. C. (1960), “Stationary Ordinal Utility and Impatience,” Econometrica, 28, 287–309.CrossRefGoogle Scholar
  22. Koopmans, T. C., Diamond, P. A. and R. E. Williamson (1964), “Stationary Ordinal Utility and Time Perspective,” Econometrica, 32, 82–100.CrossRefGoogle Scholar
  23. Lane, J. and Mitra, T. (1981), “On Nash Equilibrium Programs of Capital Accumulation under Altruistic Preferences,” International Economic Review, 22, 309–331.CrossRefGoogle Scholar
  24. Mitra, T. and K. Nishimura (2001), Cyclical and Chaotic Optimal Paths in a Model with Intertemporal Complementarity, mimeo, Cornell University.Google Scholar
  25. Mitra, T. and K. Nishimura (2003), Simple Dynamics in a Model of Habit Formation, mimeo, Cornell University.Google Scholar
  26. Montrucchio, L. (1998), “Thompson Metric, Contraction Property and Differentiability of Policy Functions,” Journal of Economic Behavior and Organization, 33, 449–466.CrossRefGoogle Scholar
  27. Parker, F. D. (1964), “Inverses of Vandermonde Matrices,” American Mathematical Monthly, 71, 410–411.CrossRefGoogle Scholar
  28. Rosenlicht, M. (1986), Introduction to Analysis, Dover: New York.Google Scholar
  29. Ross, S. M. (1983), Introduction to Stochastic Dynamic Programming, Academic Press: New York.Google Scholar
  30. Samuelson, P. A. (1971), “Turnpike Theorems even though Tastes are Intertemporally Dependent,” Western Economic Journal, 9, 21–26.Google Scholar
  31. Santos, M. S. (1991), “Smoothness of the Policy Function in Discrete-Time Economic Models,” Econometrica, 59, 1365–1382.CrossRefGoogle Scholar
  32. Scheinkman, J. A. (1976), “On Optimal Steady States of n-Sector Growth Models when Utility is Discounted,” Journal of Economic Theory, 12, 11–20.CrossRefGoogle Scholar
  33. Sundaresan, S. M. (1989), “Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth,” Review of Financial Studies, 2, 73–89.CrossRefGoogle Scholar
  34. Topkis, D. (1968), “Minimizing a Submodular Function on a Lattice,” Operations Research, 26, 305–321.CrossRefGoogle Scholar
  35. Topkis, D. (1998), Supermodularity and Complementarity, Princeton University Press.Google Scholar
  36. Wan, H. Y. (1970), “Optimal Savings Programs under Intertemporally Dependent Preferences,” International Economic Review, 11, 521–547.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of EconomicsCornell UniversityIthacaUSA
  2. 2.Institute of Economic ResearchKyoto UniversityKyotoJapan

Personalised recommendations