Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems

Abstract

We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problems under the overtaking criterion, as well as the conditions under which such a limit is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of the one-sector growth model to examine the impacts of discounting on optimal paths.

References in corpus (1)

• Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems

Cited by in corpus (3)

• Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems
• Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems
• The "Eating up Assumption", Transversality Conditions, and Steady States for Discrete Time Infinite Horizon Problems