Slide 1Forests - characteristicsEconomic AnalysisGrowth Function (logistic) output (Q) = wood input (X) = time (waiting)MP and AP - definitionsGrowth: output as a function of timeSlide 7Rotation length - definitionSlide 9Optimal rotation varies by owner categoryRotation based on physical product only – two choicesEconomic efficiency criteriaKey economic insight: net benefits are maximized whereAGEC/FNR 406 LECTURE 29 30-year old Loblolly Pine plantationForests - characteristics1. Renewable2. Interactive3. Common, private, or public property4. Benefits include: Private goods Public goodsEconomic AnalysisSame principles as fishery:Efficiency achieved where MC = MB IF…property rights are structured to allow markets to capture ALL costs & benefits (including social) This assumption is rarely met.TR = P * QQ determined from growth functionPrice determined by market for some outputsGrowth Function (logistic)output (Q) = wood input (X) = time (waiting)0100020003000400050001 3 5 7 9 11 13 15Years (10's), Xcubic feet, QMP and AP - definitionsMarginal Product (MP) periodic annual increment (PAI)marginal change in volume = Q/XAverage Product (AP) mean annual increment (MAI)total volume/total input = Q/X(If managing for perpetual physical volume only, then find maximum MAI)Growth: output as a function of timeAge Volume (Q) PAI (MP) MAI (AP) 10 0 0 0.00 20 75 7.5 3.75 30 200 12.5 6.67 40 750 55 18.75 50 1400 65 28.00 60 2100 70 35.00 70 2550 45 36.43 80 2900 35 36.25 90 3200 30 35.56 100 3450 25 34.50 110 3650 20 33.18 120 3800 15 31.67 130 3900 10 30.00 140 3950 5 28.21 150 3975 2.5 26.50 160 3975 0 24.840204060801 3 5 7 9 11 13 15Years (x10)Volume (cu ft)PAI (MP)MAI (AP)Rotation length - definitionPeriod of time a given area of timber (stand or individual tree) is held, i.e. time between planting or natural regeneration, and harvestingSequence of timber rotations (Rt) from given tract of landTime lineHarvest R1Harvest & plantHarvest & plantHarvest & plantPlant R2R1R2RnPlant R1Plant R3Harvest R2Optimal rotation varies by owner categoryHouseholds - utility maximizersForest products firms - profit maximizersPublic - multiple uses, utility maximizersSingle age/species stand vs. multiage, multispecies stand – very different analysis required.Rotation based on physical product only – two choices1. Choose rotation length to maximize volume over one rotation: optimal length where Q is at maximum2. Choose rotation to maximize volume in perpetuity:optimal length is where MAI is at its maximum (see Table11.2 in text,referred to as culmination of MAI)Economic efficiency criteria1. Static efficiencyMaximize net benefits of one optimal rotation2. Dynamic efficiency Maximize net benefits from continuous series of rotations, where the net benefits from future rotations are discounted back to present value terms.Key economic insight:net benefits are maximized whereNB is maximized, i.e.where TB - TC is greatest where MC = MB (same thing!)Economic criteria:maximize net benefit (static)maximize present value of NB