Price, scarcity rent, and a modified <i>r</i> per cent rule for non‐renewable resources
Bibliographic record
Abstract
Since Hotelling's seminal paper on the optimal depletion of exhaustible resources, much has been published; yet confusion remains about whether scarcity rent and price increase or decrease as a resource is depleted when costs tend to rise with depletion. We show that Hotelling's fundamental results of rising scarcity rent and price paths are sustained and that the path of scarcity rent converges on the r per cent rule, provided the objective function is concave. Predictions of non‐monotonic or declining scarcity rent paths are due to implicit assumptions that lead to a non‐concave objective function. We identify the sources of these non‐concavities. JEL Classification: Q30, D90, C60 Prix, rente de rareté et une règle modifiée du r‐pourcent pour les ressources non renouvelables. Malgré la volumineuse littérature spécialisée qui a fleuri depuis qu'Hotelling a écrit son mémoire fondateur sur l'épuisement optimal des ressources renouvelables, une grande confusion règne toujours quand il faut établir si la rente de rareté et le prix augmentent ou chutent à proportion que la ressource s'épuise quand les coûts tendent à croître avec l'épuisement. Ce mémoire montre que les résultats fondamentaux obtenus par Hotelling quant aux sentiers de croissance de la rente de rareté et du prix tiennent toujours, et que le sentier de croissance de la rente de rareté converge vers la règle du r‐pourcent pourvu que la fonction objective soit concave. Les prédictions de sentiers de croissance non monotone ou de déclin de la rente de rareté présentées dans la littérature spécialisée sont attribuables à des postulats implicites qui engendrent une fonction objective non concave. Les auteurs identifient les sources de ces non‐concavités.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".