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ForestSlides - Forest Resources Introduction Forest Growth...

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12/10/2010 1 Forest Resources Introduction Forest Growth and the Harvesting Problem Supply from Private Forests Determination of rent and land use decision Comparative dynamics of the harvesting decision Total Timber supply. Public Policy Toward Forests Forest supply from U.S.F.S. forests; Managing for conservation using easements Benefits from standing forest services. Deforestation Trends and processes Deforestation and commercial logging, insecure ownership
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12/10/2010 2 Forest growth Time (age) T Cu. ft. per acre Volume F(T) Growth rate Growth rate = slope of F(T) dT T dF ) (
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12/10/2010 3
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12/10/2010 4 Simple Forest Harvesting Problem 1. Notation and Assumptions T age of forest. F(T) volume per acre. dT T dF ) ( annual growth per acre per year. P price per unit for uncut timber (assumed constant over time) r interest rate (assumed constant over time). Assume: Forest will be harvested only once, and not replanted.
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12/10/2010 5 2. Harvest Rule for Single Harvest Marginal benefit of waiting an additional year before harvesting is MB W (T) = P dT T dF ) ( Marginal cost of waiting an additional year is MC w (T) = rPF(T) . Profit maximizing forest owner harvests at age when MB w (T 1 ) = MC w (T 1 ) . Result: P dT T dF ) ( 1 = rPF(T 1 ) , or dT T dF ) ( 1 = rF(T 1 ) Restatement of harvest age condition: Harvest when ) ( ) ( 1 1 T F dT T dF = r , (% growth rate = interest rate.)
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12/10/2010 6 Time (age) T Cu. ft. per acre MB w (marginal benefit of waiting) = MC w ( marginal cost of waiting) = rF r = interest rate Price of timber = 1 Simple harvest problem: harvest once, no replanting T 1 dT T dF ) (
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12/10/2010 7 Average Annual Timber Supply (per acre) Time (age) T Cu. ft. per acre Volume F(T) T 0 T m Average annual supply with harvests at T 0 is F(T 0 )/T 0 (Slope of line ab) a b F(T 0 ) Largest average annual supply (maximum sustainable yield) occurs at T m , with yield MSY = F(T m )/T m (Slope of line am) F(T m ) m
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12/10/2010 8 Harvesting and Replanting 3. Optimal Harvest Rule with Replanting and Re-harvesting R (land rent) is opportunity cost of using an acre of land, $ per acre per year. Marginal cost of waiting an additional year to harvest now has two parts: MC w (T) = rPF(T) + R . (Marginal benefit of waiting is same as before.) Profit maximizing forest owner harvests chooses T * to satisfy: P dT T dF *) ( = rPF(T*) + R , or dT T dF *) ( = rF(T*) + R/P (F.1)
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12/10/2010 9 Time (age) T Cu. ft. per acre MB w = MC w = rF + R/P r = interest rate Price of timber = 1 General problem: harvesting and replanting T 1 rF T * dT T dF ) ( *
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12/10/2010 10 4. The Land Use Decision and Determinants of R (land rent) Notation: Subscripts ‘ f ’ and ‘ a’ land uses, "forestry" and "alternative". The return an acre of land can earn these two uses is denoted R f and R a . The owner will: allocate the acre of land to forestry if R f R a allocate the acre to alternative use if R f < R a . The resulting rent will be R = max(R f , R a ) .
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12/10/2010 11 5. What determines R f ? (4 steps) 1. Harvesting the forest once at age T* yields the net present value: N = * ) 1 ( *) ( T r T PF - C .
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This note was uploaded on 12/26/2011 for the course ECON 122 taught by Professor Staff during the Fall '08 term at UCSB.

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ForestSlides - Forest Resources Introduction Forest Growth...

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