The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Transversality Conditions and Dynamic Economic Behaviour

  • Takashi Kamihigashi
Reference work entry


Transversality conditions are optimality conditions often used along with Euler equations to characterize the optimal paths of dynamic economic models. This article illustrates the role of transversality conditions in characterizing optimal paths as well as in ruling out economic phenomena such as asset bubbles and hyperdeflations in infinite-horizon models.


Bubbles Calculus of variations Dynamic models Dynamic optimization Euler equations Hyperdeflation Infinite horizons Optimality Overlapping generations models Ponzi games Ramsey model Transversality condition Transversality conditions and dynamic economic behaviour 

JEL Classifications

C61 E1 
This is a preview of subscription content, log in to check access.


  1. Benveniste, L.M., and J.A. Scheinkman. 1982. Duality theory for dynamic optimization models of economics: The continuous time case. Journal of Economic Theory 27: 1–19.CrossRefGoogle Scholar
  2. Blanchard, O.J., and S. Fischer. 1989. Lectures on macroeconomics. Cambridge, MA: MIT Press.Google Scholar
  3. Bolza, O. 1904. Lectures on the calculus of variations. Chicago: University of Chicago Press.Google Scholar
  4. Brock, W.A. 1974. Money and growth: The case of long run perfect foresight. International Economic Review 15: 750–777.CrossRefGoogle Scholar
  5. Hahn, F.H. 1987. Hahn problem. In The new Palgrave: A dictionary of economics, ed. J. Eatwell, M. Milgate, and P. Newman, vol. 2. London: Macmillan.Google Scholar
  6. Hestenes, M.R. 1966. Calculus of variations and optimal control theory. New York: Wiley.Google Scholar
  7. Kamihigashi, T. 1998. Uniqueness of asset prices in an exchange economy with unbounded utility. Economic Theory 12: 103–122.CrossRefGoogle Scholar
  8. Kamihigashi, T. 2001. Necessity of transversality conditions for infinite horizon problems. Econometrica 69: 995–1012.CrossRefGoogle Scholar
  9. Kamihigashi, T. 2002. A simple proof of the necessity of the transversality condition. Economic Theory 20: 427–433.CrossRefGoogle Scholar
  10. Kamihigashi, T. 2003. Necessity of transversality conditions for stochastic problems. Journal of Economic Theory 109: 140–149.CrossRefGoogle Scholar
  11. Kamihigashi, T. 2005. Necessity of the transversality condition for stochastic models with bounded or CRRA utility. Journal of Economic Dynamics and Control 29: 1313–1329.CrossRefGoogle Scholar
  12. Kneser, A. 1900. Lehrbuch der Variationsrechnung. Braunschweig: F. Vieweg und Sohn.Google Scholar
  13. Lucas, R.E. Jr. 1978. Asset prices in an exchange economy. Econometrica 46: 1429–1445.CrossRefGoogle Scholar
  14. Mangasarian, O.L. 1966. Sufficient conditions for the optimal control of nonlinear systems. SIAM Journal of Control 4: 139–152.CrossRefGoogle Scholar
  15. Michele, P. 1982. On the transversality condition in infinite-horizon problems. Econometrica 50: 975–985.CrossRefGoogle Scholar
  16. Montrucchio, L., and F. Privileggi. 2001. On fragility of bubbles in equilibrium asset pricing models of Lucas-type. Journal of Economic Theory 101: 158–188.CrossRefGoogle Scholar
  17. Obstfeld, M., and K. Rogoff. 1986. Ruling out divergent speculative bubbles. Journal of Monetary Economics 17: 349–362.CrossRefGoogle Scholar
  18. Stokey, N., and R.E. Lucas Jr. 1989. Recursive methods in economic dynamics. Cambridge, MA: Harvard University Press.Google Scholar
  19. Weitzman, M.L. 1973. Duality theory for infinite horizon convex models. Management Science 19: 783–789.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Takashi Kamihigashi
    • 1
  1. 1.