Forest Economics VI

Forest Economics VI - Forest Economics Peter Berck 2008...

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Click to edit Master subtitle style Forest Economics © Peter Berck 2008
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When to cut? n How much old timber to hold? n Costs of not profit max policies ¡ Like don’t cut till CMAI (top of growth curve) ¡ Like hold onto oldgrowth for a while n Next: the basic optimizing model
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Simple Forest Planning n Type of Site, j n Many “birthdays” ¡ First is –M. n hj(t,s) ¡ t is calendar time ¡ s is birthday of stand ¡ h is acres harvested n Dj(t-s) is volume per acre n Warning: See article to get > and >= correct. n Advantage: no explicit need for stock, x.
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Problem cont… n v(t) is cut at t n n Max present value ¡ of P times V n s.t. biology n v(t+1) & v(t) non declining flow n t-s > CMAI or h = 0
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Biology n Initial Acres = Cut over all time ¡ Aj(s) = h t>s Hj(t,s) n Cut acres regrow and are recut ¡ l s Hj(t,s) = l a Hj(a,t) n Cut at t from all birtHdays (s<=t) is wHat is reborn at t and tHerefore cut in times a>t. This is Johnson and Scheurman, Model II.
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x n x is what is left standing ¡ x(time, birthday) ¡ xj(z,s) = Aj(s) - ¨ t<Z hj(t,s) n For stands born before time zero s< 0 ¡ xj(z,s) = l t<s hj(s,t) - l a<z hj(a,s) n For stands born s>0. first sum is total acreage in stand regenerated in time s n Second sum is amount cut in times prior to z from stands regenerated at time s.
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Expanded Objective Function n Let E(s,t) be value of wildlife, etc n ¡ l j ± s>-M xj(s,t) Ej(s,t) n Max present value of Y(t).
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More meaning to the model n Types of sites, j ¡ different species ¡ site classes ¡ critical locations n near streams n visual buffers n More Constraints ¡ Don’t cut type j ¡ Keep N% of forest at age, t-s, > 100 n constraint on w n More treatments ¡ commercial thin ¡ pre-commercial
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Biology n Could use stand table. ¡ McArdle Bruce Meyer tables for doug fir
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Forest Economics VI - Forest Economics Peter Berck 2008...

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