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Economics of Forest Resources Ashir Mehta Source : Field, Barry (2001) : Natural Resource Economics : An Introduction, Chapter 12, McGraw Hill.

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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)

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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) (MSY) (max. av. Yield) (Max. wood)

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biology of tree harvest Qty. of wood (cu.ft) Age in years

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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, over 1000 yrs, yield = 1000 x 27.7 = cu.ft. as against 100 yr. cycle yield = 1000 x 20.9 = 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).

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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 t 2t 40t years

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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.

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Optimal rotation period Let, V 0 : monetary value of wood if harvested this year V 1 : monetary value of wood if harvest delayed one year ∆V = V 1 – V 0 : 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]

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Optimal rotation period If forest is harvested this year, proceeds will be, (V 0 – C) + S i.e. sum of net benefits and selling price of land. If harvest delayed until next year, PV will reflect added growth,V 0 + ∆V and revenue from selling land next year. Discounting both gives, V 0 + ∆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 : (V 0 + ∆V) – C + S > (V 0 – C) + S 1 + r [benefits of waiting & harvesting next year] [benefits of harvesting this year]

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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, (V 0 + ∆V) – C + S = (V 0 – C) + S 1 + r is the condition when to harvest the forest. The last expression can be reduced to : ∆V = (V 0 – C)r + Sr and r = ∆V S + (V 0 – C)

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optimal rotation period $ (V 0 – C)r + Sr (MB of harvest) ∆V (MC of harvest) Sr (V 0 =C) t* Time (no. of years)

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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 (V 0 – 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 (V 0 – 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, V 0 & S though not necessarily in same proportion – interaction of Mb & MC curves may shift to right or left

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