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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) 0000 108088 202001012 3040013.320 407201832 50136027.264 60 (MSY)166027.7 (max. av. Yield)30 70184026.318 80196024.512 90204022.78 1002090 (Max. wood)20.95 1102090190 120209017.40 140209014.90

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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

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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, 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).

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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 25 75 1000 0 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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