Optimal harvesting under annuity and compound interest laws: economic-ecological trade-offs in a logistic growth model

TEXT START: The relationship between investment policy associated with species growth profile is essential in seeking the most appropriate strategy for a policymaker.

The Dissection

The paper converts ecological extraction into a closed optimal-control problem. A species stock follows a one-dimensional logistic curve, harvesting is linear, financial returns follow either annuity or compound interest, and a policymaker selects the mathematically optimal path.

Its real operation is narrower than its language suggests: it makes sustainability legible as a revenue-and-equilibrium calculation. Political enforcement, ownership, ecological complexity, distribution, and institutional breakdown disappear behind Pontryagin’s Maximum Principle. The result is a conditional extraction map, not a general theory of sustainable governance.

The Core Fallacy

The central error is confusing mathematical solvability with real-world governability.

The reported result—annuity being preferable for low-growth species at low interest rates, compounding for faster-growing species—holds only inside the imposed model. It does not establish that either law produces sustainable outcomes outside a fixed logistic environment. “Optimal” means optimal for the chosen objective and assumptions, not optimal for an ecosystem, a society, or a collapsing economic order.

Under the Discontinuity Thesis, the paper also treats the policymaker, interest regime, and revenue objective as stable background conditions. P1–P3 attack precisely that stability. Once AI concentrates productive capacity and control in Sovereign hands, ecological assets become objects of ownership and extraction. The relevant question is no longer merely which discount law maximizes net revenue, but who controls the resource, who can enforce the policy, and whether the population remains economically necessary. This paper does not address those mechanisms.

Hidden Assumptions

• Logistic growth adequately represents the species and its carrying capacity.
• Growth rates, interest rates, prices, and accumulation laws remain stable and exogenous.
• Linear harvesting captures the actual technology and does not create nonlinear depletion or collapse thresholds.
• The policymaker can observe, enforce, and implement the calculated strategy.
• Maximizing net revenue is an acceptable proxy for welfare and sustainability.
• A steady-state equilibrium is ecologically meaningful and reachable.
• Biodiversity, ecosystem interdependence, climate shocks, illegal extraction, ownership conflict, and distributional effects are secondary or irrelevant.
• The surrounding economic institutions survive long enough for the interest-law comparison to matter.

None of these assumptions is harmless. Together they manufacture a clean world in which the planner’s objective is coherent, the resource is measurable, and extraction remains administratively controllable.

Social Function

Classification: partial truth wrapped in prestige signaling and ideological anesthetic.

The paper may provide a legitimate local result for a narrowly specified model. But its technical vocabulary gives a contested political choice—the rate and manner of extracting living resources—the appearance of neutral optimization. It relocates the hard questions from power, enforcement, ownership, and ecological irreversibility into the safer machinery of capital theory.

This is not useless mathematics. It is just incapable of carrying the policy burden implied by its framing. For a Sovereign controlling ecological capital, the model may be a small pricing or extraction instrument. For everyone else, it offers no protection against the concentration of that capital or the collapse of productive participation.

The Verdict

A competent local optimization exercise mistaken for a systemic answer. It identifies which financial convention wins inside a sanitized logistic fishbowl; it does not prove sustainability, resilience, or durable governance. Under the Discontinuity Thesis, this is not a counterforce to economic obsolescence. It is a narrow tool for managing the carcass—useful to whoever owns the resource, irrelevant to the population that no longer controls production.