View source for Faustmann's formula

{{Short description|Forestry equation}}
'''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 [[Optimal rotation age|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.<ref>{{cite book | author=John Cunningham Wood | author-link = John Cunningham Wood|title=Bertil Ohlin: Critical Assessments | publisher=Routledge | year=1995 | isbn=978-0415074926}}</ref>

: &fnof;(''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:
: <math> 
PV = pf(T) \exp(-rT) \cdot {(1 + \exp(-rT) + \exp(-2rT) + \cdots) } = \frac{pf(T)}{\exp(rT) - 1}.
</math>

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.<ref name=intro>{{cite web
 | title =The Faustmann Model (Part I)
 | work =Introduction to Forestry, Forest Policy, and Economics
 | url =http://foper.unu.edu/course/?page_id=167
 | access-date =2013-06-08
 | archive-url =https://web.archive.org/web/20111229211645/http://foper.unu.edu/course/?page_id=167
 | archive-date =2011-12-29
 | url-status =dead
 }}</ref>

: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.<ref name=intro/>

==See also==
*[[Hotelling's rule]]

== References ==
<references />

==Further reading==
*{{cite journal |authorlink=Jon David Erickson |last1=Erickson |first1=J. D. |last2=Chapman |first2=D. |last3=Fahey |first3=T. J. |first4=M. J. |last4=Christ |year=1999 |title=Nonrenewability in Forest Rotations: Implications for Economic and Ecological Sustainability |journal=Ecological Economics |volume=31 |issue=1 |pages=91–106 |doi=10.1016/S0921-8009(99)00040-3|url=http://ageconsearch.umn.edu/record/127837 |hdl=1813/58253 |hdl-access=free }}
*{{cite journal |first=Yngve |last=Willassen |title=The Stochastic Rotation Problem: A Generalization of Faustmann's Formula to Stochastic Forest Growth |journal=Journal of Economic Dynamics and Control |volume=22 |issue=4 |year=1998 |pages=573–596 |doi=10.1016/S0165-1889(97)00071-7 }}

{{Forestry}}

[[Category:Intertemporal economics]]
[[Category:Mathematical optimization]]
[[Category:Forest management]]
[[Category:Forest modelling]]