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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.

Scope of Application

  • 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.

  • 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.

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.

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.

Abstract Reasoning

  1. Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
  2. 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.
  3. Check operation and conditions.

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.

Relationships to Other Abstractions

Local relationship map for Faustmann's formulaParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Faustmann's formulaDOMAINPrime abstraction: Discounting (Present Value) — is a kind ofDiscounting(Present Value)PRIME

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

Neighborhood in Abstraction Space

Faustmann's formula sits in a sparse region of the domain-specific corpus (82nd 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