Faustmann's formula¶

The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.

Version: v1 · 2026-09-28 · History
Domain-specific #: 9419
Domain group: Social Sciences
Origin domain: Economics & Finance
Subdomain: Forest Economics → Economics & Finance

Core Idea¶

Faustmann's formula is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.

Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. It was derived by the German forester Martin Faustmann in 1849. The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.

ƒ(T) is the stock of timber at time T. p the price of timber and is constant. which implies that the value of the forest at time T is pf(T).

For Faustmann's formula, the abstraction is narrower than the article's general subject matter: a positive case must preserve The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in mathematics, logic, and statistics, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — The optimal time to cut is when the time rate of change of its value is equal to the interest rate modified by land rent.
Constitutive relation — It was derived by the German forester Martin Faustmann in 1849.
Operating condition — The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.
Recognition evidence — Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation.
Admissible variation — which implies that the value of the forest at time T is pf(T).
Characteristic consequence — PV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}.
Failure boundary — The optimal time to cut the forest is when the time rate of change of its value is equal to interest on the value of the forest plus the interest on the value of the land.

What It Is Not¶

Not the whole field of mathematics, logic, and statistics. The node requires the specific identity stated by The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.
Not an over-broad reading. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation.
Not an over-broad reading. which implies that the value of the forest at time T is pf(T).
Not an over-broad reading. PV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}.
Not automatically Heckscher–Ohlin Model. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Faustmann's formula applies literally inside mathematics, logic, and statistics wherever the source-defined carrier and relation can be established. Its documented habitats include:

Documented setting. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation.
Documented setting. which implies that the value of the forest at time T is pf(T).
Documented setting. PV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}.
Documented setting. The optimal time to cut the forest is when the time rate of change of its value is equal to interest on the value of the forest plus the interest on the value of the land.
Documented setting. The optimal time to cut is when the time rate of change of its value is equal to the interest rate modified by land rent.
Documented setting. It was derived by the German forester Martin Faustmann in 1849.

Outside mathematics, logic, and statistics, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Theory or should be marked as analogy.

Clarity¶

A clear use of Faustmann's formula names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. The strongest recognition evidence in the frozen account is: Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Faustmann's formula compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—it was derived by the German forester Martin Faustmann in 1849.—and the practical consequence—pV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
State the relation. Use the source-grounded identity: The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.
Check operation and conditions. The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860.
Demand recognition evidence. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation.
Test variation. Change an implementation or setting while preserving which implies that the value of the forest at time T is pf(T).
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Theory.

Knowledge Transfer¶

Within the home domain. Knowledge about Faustmann's formula transfers literally when a new case preserves the same carrier type, relation, and recognition test. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. which implies that the value of the forest at time T is pf(T).

Beyond the home domain. No canonical parent is asserted for Faustmann's formula. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860; recognition evidence → Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation

Applied / In Practice¶

which implies that the value of the forest at time T is pf(T). The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → the applied context; invariant → The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860; boundary → the case exits the class when faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation

Structural Tensions¶

T1 — Stable identity versus admissible variation. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. which implies that the value of the forest at time T is pf(T). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. PV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. The optimal time to cut the forest is when the time rate of change of its value is equal to interest on the value of the forest plus the interest on the value of the land. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The optimal time to cut is when the time rate of change of its value is equal to the interest rate modified by land rent. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Faustmann's formula literally, co-instantiate Theory, or only resemble it?

T6 — Autonomy versus reduction. It was derived by the German forester Martin Faustmann in 1849. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Faustmann's formula distinguish that the broader parent Theory leaves together?

Structural–Framed Character¶

Faustmann's formula is structural-leaning. Its structural side is the repeatable organization summarized by The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. Its framed side is the mathematics, logic, and statistics vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Theory. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: The optimal time to cut is when the time rate of change of its value is equal to the interest rate modified by land rent. It was derived by the German forester Martin Faustmann in 1849. It further constrains recognition and variation through: The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation.

What is domain-bound. mathematics, logic, and statistics supplies the operative entities, technical vocabulary, warrants, and exceptions that make Faustmann's formula literal. Its documented scope includes the condition that Faustmann's formula, or the Faustmann model, gives the present value of the income stream for forest rotation. Another bounded application condition is that which implies that the value of the forest at time T is pf(T). These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—which implies that the value of the forest at time T is pf(T).—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Discounting (Present Value).

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Faustmann's formula. The reviewed identity is: The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Faustmann's formula Domain-specific

Parents (1) — more general patterns this builds on

Faustmann's formula is a kind of Discounting (Present Value) Prime

Faustmann's formula is explicitly the present value of a forest's income stream, i.e., a discounted-cash-flow present-value calculation.

Hierarchy paths (5) — routes to 3 parentless roots

Faustmann's formula → Discounting (Present Value) → Commensurability

Show alternative paths (4)

Neighborhood in Abstraction Space¶

Faustmann's formula sits in a sparse region of the domain-specific corpus (82^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Theory. The parent omits the specialist differentia. Tell: Can the case establish The rotation problem, deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the Faustmann-Ohlin theorem, although other German foresters were aware of the correct solution in 1860?
Heckscher–Ohlin Model. A general-equilibrium trade model in which countries sharing production technologies but differing in relative factor endowments tend to export goods intensive in relatively abundant factors and import goods intensive in relatively scarce factors. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Sherman–Morrison Formula. The Sherman–Morrison formula gives the exact inverse of an invertible matrix after a rank-one outer-product update, provided one scalar denominator is nonzero. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Solow–Swan Model. The neoclassical growth model whose diminishing-returns structure drives each economy to a parameter-pinned steady state, yielding conditional convergence — economies sharing fundamentals close their gaps at a rate set by the capital share, while saving raises the level of income but not the long-run growth rate. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Faustmann's formula remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside mathematics, logic, and statistics lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Theory?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Faustmann%27s_formula (revision 1195765705).
Preserved source candidate: http://foper.unu.edu/course/?page_id=167
Preserved source candidate: https://web.archive.org/web/20111229211645/http://foper.unu.edu/course/?page_id=167
Preserved source candidate: http://ageconsearch.umn.edu/record/127837

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.