Faustmann's formula

Faustmann's formula   (Redirected from Faustman–Ohlin theorem) Jump to navigation Jump to search 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.[1] 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) r is the discount rate and is also constant.

The Faustmann formula is as follows: {displaystyle PV=pf(T)exp(-rT)cdot {(1+exp(-rT)+exp(-2rT)+cdots )}={frac {pf(T)}{exp(rT)-1}}.} From this formula two theorems are interpreted: 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.[2] 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.[2] See also Hotelling's rule References ^ John Cunningham Wood (1995). Bertil Ohlin: Critical Assessments. Routledge. ISBN 978-0415074926. ^ Jump up to: a b "The Faustmann Model (Part I)". Introduction to Forestry, Forest Policy, and Economics. Archived from the original on 2011-12-29. Retrieved 2013-06-08. Further reading Erickson, J. D.; Chapman, D.; Fahey, T. J.; Christ, M. J. (1999). "Nonrenewability in Forest Rotations: Implications for Economic and Ecological Sustainability". Ecological Economics. 31 (1): 91–106. doi:10.1016/S0921-8009(99)00040-3. Willassen, Yngve (1998). "The Stochastic Rotation Problem: A Generalization of Faustmann's Formula to Stochastic Forest Growth". Journal of Economic Dynamics and Control. 22 (4): 573–596. doi:10.1016/S0165-1889(97)00071-7. hide vte Forestry IndexForest areasMinistriesResearch institutesCollegesJournalsArbor Day Types Agroforestry dehesaAnalog forestryBamboo forestryClose to nature forestryCommunity forestryEcoforestryEnergy forestryMycoforestryPermaforestryPlantation forestrySocial forestrySustainable forestryUrban forestry Ecology and management ArboricultureControlled burnDendrologyEcological thinningEven-aged managementFire ecologyForest informaticsIPMinventorygovernancelawold-growthpathologyprotectionrestorationsecondarytransitionForest certification ATFSCFSFSCPEFCSFISmartWoodWoodland Carbon CodeForestation afforestationreforestationGrowth and yield modellingHorticulture GM treesi-Tree urbanSilvicultureSustainable managementTree allometrybreedingTree measurement crowngirthheightvolume Environmental topics Acid rainCarbon sequestrationClearcuttingDeforestationEcosystem servicesForest diebackForest fragmentationHigh gradingIllegal logging Timber mafiaInvasive species wildingREDDShifting cultivation chitemeneslash-and-burnslash-and-charsvedjebrukTimber recyclingWildfire Industries CoppicingForest farmingForest gardeningLoggingManufacturing lumberplywoodpulp and papersawmillingProducts biocharbiomasscharcoalnon-timberpalm oilrayonrubbertanbarkRail transportTree farm Christmas treesWood engineeredfuelmahoganyspruce-pine-firteakWoodworking Occupations ForesterArboristBuckerChoker setterEcologistFellerFirefighter handcrewhotshotlookoutsmokejumperRiver driverTruck driverLog scalerLumberjackRangerResin tapperRubber tapperShingle weaverTimber cruiserTree planterWood process engineer WikiProject Category Outline Categories: Intertemporal economicsMathematical optimizationForest managementForest modelling