2364. Stationary-through-immigration Populations: Optimization beyond Pivot Points
Invited abstract in session TA-4: Optimality Conditions and Optimal Control, stream Continuous and Global Optimization.
Thursday, 8:45-10:15Room: H6
Authors (first author is the speaker)
| 1. | Andreas Novak
|
| Business Decisions and Analytics, University of Vienna | |
| 2. | Thomas Fent
|
| Vienna Institute of Demography | |
| 3. | Stefan Wrzaczek
|
| Economic Frontiers, Institute for Applied Systems Analysis (IIASA) | |
| 4. | Gustav Feichtinger
|
| Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology |
Abstract
Starting point are stationary-through-immigration (SI) populations (Espenshade, Bouvier, and Arthur 1982), which are achieved by replenishing stable but shrinking populations with a constant influx of migrants. As a first step the optimal entry age maximising the support ratio in order to identify a new decisive threshold of demographic change is calculated.
We derive analytical conditions under which two local maxima of the support ratio exist. As demographic change progresses, a level is reached at which the global maximum jumps from the local maximum at higher ages to the local maximum at lower ages. We interpret this as the pivot point separating two regimes of demographic change. This threshold marks a significant change in population dynamics and we can quantify at any time whether this threshold has already been surpassed.
In a next step the model is extended to an age-structured OC-problem where the dynamics of the population is governed by the McKendrick von Foerster equation including a jump at a certain age due to immigration which acts as control variable.
Keywords
- Optimal Control
- Dynamical Systems
Status: accepted
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