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)

Total vol. of wood (cu.ft.)(2)

Average vol. (cu.ft/age =2/1)

Annual increase in vol.(cu.ft/yr=∆2/∆1)

0 0 0 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 harvestQty. of wood (cu.ft)

2200200018001600140012001000800600400

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 75 1000

0 t 2t 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 periodLet,

• 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 + S1 + 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 > (V0 – C) + S1 + r

[benefits of waiting & harvesting next year] [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 = (V0 – C) + S1 + r

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.

-------------------------------------------