Time inconsistency in the calculus of variations
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Fri, 06/02/2009 16:30 |
Professor Ivar Ekeland (University of British Columbia) |
Colloquia  |
L2 |
| In classical economic theory, one discounts future gains or losses at a constant rate: one pound in t years is worth exp(-rt) pounds today. There are now very good reasons to consider non-constant discount rates. This gives rise to a problem of time-inconsistency: a policy which is optimal today will no longer be optimal tomorrow. The concept of optimality then no longer is useful. We introduce instead a concept of equilibrium solution, and characterize it by a non-local variant of the Hamilton-Jacobi equation. We then solve the classical Ramsey model of endogenous growth in this framework, using the central manifold theorem | |||