The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Transversality Condition

  • Robert A. Becker
Reference work entry


The transversality condition for an infinite horizon dynamic optimization problem is the boundary condition determining a solution to the problem’s first-order conditions together with the initial condition. The transversality condition requires the present value of the state variables to converge to zero as the planning horizon recedes towards infinity. The first-order and transversality conditions are sufficient to identify an optimum in a concave optimization problem. Given an optimal path, the necessity of the transversality condition reflects the impossibility of finding an alternative feasible path for which each state variable deviates from the optimum at each time and increases discounted utility.


Arbitrage Asset pricing models Bubbles Capital accumulation programmes Competitive equilibrium Depreciation Euler equations Infinite horizons Optimal growth paths Ramsey model Transversality condition 
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  1. Becker, R.A., and J.H. Boyd. 1997. Capital theory, equilibrium analysis, and recursive utility. Malden: Blackwell Publishers.Google Scholar
  2. Benveniste, L.M., and J.A. Schienkman. 1982. Duality theory for dynamic optimization models of economics: The continuous time case. Journal of Economic Theory 27: 1–19.CrossRefGoogle Scholar
  3. Gray, J.A. and S.W. Salant 1983. Transversality conditions in infinite horizon models. Working paper, Washington State University.Google Scholar
  4. 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
  5. LeRoy, S.F. 2004. Rational exuberance. Journal of Economic Literature 41: 783–804.CrossRefGoogle Scholar
  6. Malinvaud, E. 1953. Capital accumulation and efficient allocation of resources. Econometrica 21: 233–268.CrossRefGoogle Scholar
  7. Michel, P. 1982. On the transversality condition in infinite horizon optimal problems. Econometrica 50: 975–986.CrossRefGoogle Scholar
  8. Mirman, L.J., and I. Zilcha. 1975. Optimal growth under uncertainty. Journal of Economic Theory 11: 329–339.CrossRefGoogle Scholar
  9. Weitzman, M.L. 1973. Duality theory for infinite horizon convex models. Management Science 19: 783–789.CrossRefGoogle Scholar
  10. Weitzman, M.L. 2003. Income, wealth, and the maximum principle. Cambridge, MA: Harvard University Press.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Robert A. Becker
    • 1
  1. 1.