Asset Retirement with Infinitely Repeated Alternative Replacements: Harvest Age and Species Choice in Forestry
Bibliographic record
Abstract
At what age should productive assets be retired? How should replacements be chosen when they differ in their uncertain ability to generate future incomes? As a particular version of that problem, we study the tree harvesting decision with two possible replacement species whose values as timber are stochastic and whose growth functions are deterministic. In the single-rotation (Wicksell) problem starting with a bare piece of land (an empty shop), it is optimal to choose and plant one species immediately if its current value is sufficiently high relative to that of the other species (the alternative equipment). However, if the species are insufficiently price-differentiated, it is preferable to leave the land vacant (the shop empty) despite the opportunity cost of doing so. In the repeated version of the problem, it is never optimal to leave the land bare provided the cost of replacement is null. Furthermore, the optimal harvest (tree retirement) age not only depends on the price and current productivity of the trees in place but also on the price and productivity of the other species, because it may replace the current one. The harvest age reaches a peak at some critical threshold of the relative price that signals the necessity to switch to the alternative species; indeed this is when the opportunity cost of choosing one alternative replacement over the other is the highest. The land value (and also the value of the firm) is similar to an American option with free boundary, infinite expiry period, and endogenous payoff. The paper highlights the opportunity cost of alternative replacement options, and the central role of their volatility in both asset-retirement and replacement-choice decisions. All results are derived analytically; a numerical treatment by the penalty method completes the resolution.
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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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".