| Abstract: |
| We use Ekeland`s variational principle together with Pontryagin`s maximum
principle to solve an optimal spatiotemporal economic growth model with a
state constraint (no-negative capital stock) where capital law of motion
follows a diffusion equation. We obtain the set
of necessary optimal conditions for the solution to meet the state
constraints for all time and locations. The maximum principle allows to
reduce the infinite-horizon optimal control problem into a finite-horizon
one ultimately leading to prove the uniqueness of the optimal solution with
positive capital, and non-existence of the optimal solution
with eventually strictly positive capital when the time
discount rate is too large or too small. |
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