Transcript Slide 1

Economics of Forest Resources
Ashir Mehta
Source : Field, Barry (2001) : Natural Resource Economics : An Introduction, Chapter 12, McGraw Hill.
issues
• When to cut a tree
• obj. : max. sust. value of timber harvest
• Assumptions:
(a) 1000 acres (b) replant upon harvest
immediately (c) timber harvest small relative
to total market (P)
biology of tree harvest
Age of trees (yrs)
(1)
0
Total vol. of wood (cu.ft.)
(2)
0
Average vol.
(cu.ft/age =2/1)
0
Annual increase in vol.
(cu.ft/yr=∆2/∆1)
0
10
80
8
8
20
200
10
12
30
400
13.3
20
40
720
18
32
50
1360
27.2
64
60 (MSY)
1660
27.7 (max. av. Yield)
30
70
1840
26.3
18
80
1960
24.5
12
90
2040
22.7
8
100
2090 (Max. wood)
20.9
5
110
2090
19
0
120
2090
17.4
0
140
2090
14.9
0
biology of tree harvest
Qty. of wood (cu.ft)
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
10 20 30 40 50 60 70 80 90 100 110 120 130 140
Age in years
Harvest decision options :
• Max. amt. of wood = 100 years, 2090 cu. ft. – but long wait. Better to have a
smaller harvest but earlier in time.
• Cut at 60 years – average yield highest, 27.7. over 1000 yrs, yield = 1000 x
27.7 = 27000 cu.ft. as against 100 yr. cycle yield = 1000 x 20.9 = 20900 cu.ft.
• Thus, 60 yrs = maximum sustained yield
• But – is this the harvest age that maximizes net benefits of forest to society?
• Cutting at 50 yrs gives less would but is available sooner.
• Thus, there is a trade off : solution depends on values society places on time
as well as on value of wood.
• Since trees are replanted as soon as cut each time : what is the optimal
timber harvest rotation? i.e. optimal rotation period (ORP).
Optimal rotation path (period) for 1000 acres = 40 yrs – typical acre is harvested
every 40 yrs. Thus, 25 acres each yr, (1000/40), so that over 40 yrs 1000 acres are
replanted.
Qty of wood
25
0
t
2t
75
1000
40t
years
Socially optimal value of rotation period, t
• should we cut the trees and send them to the market
this year or should we wait to do it next year.
• Early years – low growth,
=> benefits of cutting < waiting
• Later years – low growth,
=> benefits of waiting < cutting
• In-between – tip-off
=> benefit of cutting today = waiting
=> right time to harvest.
Optimal rotation period
Let,
•
•
•
•
V0 : monetary value of wood if harvested this year
V1 : monetary value of wood if harvest delayed one year
∆V = V1 – V0 : value of 1-yr growth increment
C : harvest cost – monetary costs of felling and marketing
the trees
• r : discount rate
• S : present value of all future net benefits when forest is
harvested with the optimal rotation period [price at
which land is sold after clearing – buyer will replant and
harvest forever at ORP = S]
Optimal rotation period
• If forest is harvested this year, proceeds will be, (V0 – C) + S i.e. sum
of net benefits and selling price of land.
• If harvest delayed until next year, PV will reflect added growth,V0 +
∆V and revenue from selling land next year. Discounting both gives,
V0 + ∆V – C + S
1+r
• When forest is young and ∆V is relatively large (because of rapid
growth of young trees), the following inequality will hold :
(V0 + ∆V) – C + S
1+r
>
[benefits of waiting & harvesting next year]
(V0 – C) + S
[benefits of harvesting this year]
Optimal rotation period
• As the forest grows older, ∆V will eventually decline and the
net proceeds of harvesting this year will eventually become
equal to those of waiting until next year. Thus,
(V0 + ∆V) – C + S
1+r
=
(V0 – C) + S
is the condition when to harvest the forest.
The last expression can be reduced to :
∆V = (V0 – C)r + Sr
and
r=
∆V
S + (V0 – C)
optimal rotation period
$
(V0 – C)r + Sr (MB of harvest)
∆V (MC of harvest)
Sr
(V0=C)
t*
Time (no. of years)
factors affecting efficient rotation
• Harvesting costs :
thro externalities (social costs – flooding, soil erosion OR closure of
nearby logging mill so necessary to ship logs further distance) – will
shift the (V0 – C)r + Sr fn. downwards, C appears as a minus OR will
shift the ∆V fn. upwards with increased cost. This lengthens the
ORP to later years.
• Interest rate :
fall in r will shift the (V0 – C)r + Sr fn. downwards, r appears as a
plus - lengthens the ORP to later years. If r = 0, no returns on alt.
invt. assets – eff. to let forest grow until natural gr. rate falls to 0.
• Price of timber :
higher timber price - outcome ambiguous - increase in ∆V, V0 & S
though not necessarily in same proportion – interaction of Mb &
MC curves may shift to right or left.
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