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