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.
KeywordsArbitrage Asset pricing models Bubbles Capital accumulation programmes Competitive equilibrium Depreciation Euler equations Infinite horizons Optimal growth paths Ramsey model Transversality condition
JEL ClassificationsD4 D10
- Becker, R.A., and J.H. Boyd. 1997. Capital theory, equilibrium analysis, and recursive utility. Malden: Blackwell Publishers.Google Scholar
- Gray, J.A. and S.W. Salant 1983. Transversality conditions in infinite horizon models. Working paper, Washington State University.Google Scholar
- Weitzman, M.L. 2003. Income, wealth, and the maximum principle. Cambridge, MA: Harvard University Press.Google Scholar