Optimal Population and Sustainable Growth Under Environmental Constraints
Bibliographic record
Abstract
This paper develops a dynamic optimal growth model that integrates population dynamics, economic activity, and environmental constraints to investigate sustainable long-run development. The model incorporates capital accumulation, consumption, pollution abatement, and a demographic equation where population growth responds negatively to pollution. A critical environmental threshold is imposed, beyond which population growth collapses. Calibrations with plausible parameter values indicate that the sustainable steady state supports a global population of approximately 3–5 billion people, a level consistent with high per capita consumption and stable environmental conditions. The optimal policy involves devoting about one-third of output to pollution abatement, which is sufficient to stabilize pollution below the safe threshold without excessive economic costs. At this equilibrium, the economy achieves high consumption per person, stable capital, and environmental balance, while avoiding overshooting and collapse scenarios. The results highlight the trade-off between economies of scale and environmental limits: larger populations can stimulate production and innovation but risk unsustainable pollution levels, whereas smaller populations allow higher per-capita welfare within ecological boundaries. The findings suggest that sustainable development requires actively managing population dynamics and abatement policies to ensure both ecological integrity and long-term economic prosperity.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.008 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".