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Basics of Forest Economics
J. Keith GillessDean & Professor of Forest Economics
6/12/17
COLLEGE OF
Natural ResourcesUNIVERSITY OF CALIFORNIA, BERKELEY
Alternative Systems
• Even-Aged: Managing forests composed of stands of trees in which the age of the trees is relatively uniform – harvesting usually by clearcutting
• Uneven-Aged: Managing forests where three or more age classes are present in all stands – harvesting usually by single-tree selection
Even-Aged Forest Landscape(Note spatial pattern)
Uneven-Aged Forest Stand(Note structural diversity)
Uneven-Aged Forest Stand(Note species diversity)
Decision Making Tools
• Financial Analysis• Linear Programming• Integer Programming• Dynamic Programming• Simulation Modeling
Key Economic Decisions InUneven-Aged Forest Management
• Cutting cycle (how long between entry)• Diameter distribution (Inverse “J”)• Operational costs for roads/harvest setup• Regeneration
Key Economic Decisions InEven-Aged Forest Management
• Rotation (how long to grow)• Planting density• Thinnings (timing and intensity)• How much land to clearcut at different
points in time
Key Constraints InForest Management
• Resource:Land, seedlings, labor, budget
• Environmental:Minimum amounts of habitat Maximum sediment loads
• Economic:Minimum harvest or revenue flows
Linear Programming• General approach for modeling problems that
can be expressed as the maximization or minimization of a linear function of a set of decision variables, subject to a set of linear constraints on those variables
• Applications:o Harvest schedulingo Personnel managemento Project Management
Example: “Poet’s Problem”• Records indicate that managing red pine earns
$90/ha/yr, compared to $120 for hardwoods• Owns 40 ha of red pine and 50 ha of hardwoods• Managing red pine takes 2 days/ha/yr,
compared to 3 days for hardwoods• Doesn’t want to work more than 180 days per
year managing forest (needs time to write)• Wants to maximize return from managing forest
Mathematical Formulation• Objective
Maximize annual revenue• Decision VariablesX1 = ha of red pine to manageX2 = ha of northern hardwoods to manage
• ConstraintsLaborLand
Linear Programming Model
0,200300
000,40200100300
:subject to5.1min
21
2
1
21
21
21
³££
³+³+
+=
XXXX
XXXX
XXZ
Graphical Solution
D
C
B A
X2
X1 0
20
30
40 0
50 0 0
60 0 0 0 10
10
20
30
40
50
0
21 120907600 XXZ +==
21 120903600 XXZ +==
21 120901800 XXZ +==
Spreadsheet Model
12345678910111213141516
A B C D E F GPOET PROBLEM
Red pine HardwoodsManaged area 40 33.333333
(ha) (ha) ResourcesTotal available
Red pine land 1 40 <= 40 (ha)Hardwoods land 1 33 <= 50 (ha)
Poet's time 2 3 180 <= 180 (d/y)Total
Returns 90 120 7,600 Max($/ha/y) ($/ha/y) ($/y)
Key FormulasCell Formula Copied toD6 =SUMPRODUCT(B6:C6,B$3:C$3) D6:D8D10 =SUMPRODUCT(B10:C10,B$3:C$3)
Resources required
Objective function
Integer Programming Models
• Useful when some decision variables are binary, i.e., yes or no
• Applications in forestry:o Design of road networkso Allocation of capital to indivisible projectso Modeling adjacency rules
Dynamic Programming
• Useful for problems where multistage decisions are linked temporally or physically
• Examples:o Thinning decisionso How to buck a tree into logso How to rip or cross cut a board
Example: Thinning Timing & Intensity
30 m3
E
150 m3 5
180 m3 5 220 m3
5
240 m3 5
250 m3 0 5
0 0
0
10 m3
0 0 000
20 m3 000
40 m3
20 m3
40 m3 50 m3
30 m3
A
B C D
F G H L
M
Initial stand
Stage 1 (first thinning)
Stage 2 (second thinning)
Stage 3 (Final harvest)
Solution Algorithm
• Starting at the “end” of the network, decide what would be the best thing to do given the “state” of the system from that point forward
• Recursive equation:
)](*),([max)(* 1 jVjiriV tjt ++=
Dynamic Programming (Crosscut Saws)
Simulation Modeling
• Useful when “optimality” is difficult to define but you can quantify the relationships between key variables
• Allows for experimentation with a system that would be too costly or risky, to do in the real world
• Less threatening to decision makers
Applications of Simulation Modeling in Forestry
• Population modeling:o Survival analysis (for endangered species)o Predator/Preyo Fisheries
• Watershed management• Fire behavior & suppression
Interdisciplinary Isn’t Rocket Science – It’s Harder:
Biologists vs. Economists
Biologist’s Perspective
• From a purely biological perspective culmination of mean annual increment (MAI) maximizes the total production from the stand
MAI = Volume per unit area/age• MAI increases, then decreases with age• This is NOT what economists would
almost ever recommend
Economist’s Perspective
• In the absence of significant price differentials for quality, the economic rotation is ALWAYS shorter than the biological rotation
• This follows from the logistic growth curve over time for trees and discounting
• It is further reduced by considering that delaying harvest delays ALL FUTURE HARVESTS (Faustmann)
Complicating Factors
• Harvesting system costs have fixed and variable components
• The price of wood is highly stochastic• Quality differentials may be important in
some species• Social acceptance varies for even-aged
and uneven-aged forestry• Aesthetic value of forest generally
positively correlated with age
Complicating Factors (con’t)
• Biodiversity value depends on landscape considerations, not particular stands
• Economic agent may be an integrated forest owner/wood processor – capital costs may need to be serviced on mill investment
• Risk factors (fire, disease, regulatory)• Result ~ Most industrial forests are now
owned by third parties in NA & the EU
Sources of Inefficiency
• Externalities (+/-) are ubiquitous & few mechanisms have been internalizedo E.g., sediment, cumulative impacts
• Incentives are often “perverse”oConcessionaires contracts are often too short
to benefit from conservationo Tax & titling structures often encourage
deforestation• Transboundary problems are common
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