Lecture 2

Upcoming in ClassHomework #9 Due Wednesday

Quiz #4 Wednesday

Group Outline Due Wednesday

Exam #4 Nov. 28th

Group Presentations Dec. 3 & 51Forests (p.327-339)What is the optimal policy for cutting trees?

What is the optimal harvest age for a stand of trees?

What is the optimal rotation age for a stand of trees?2A stand of treesImagine you own a stand of trees with 100,000 cubic feet of standing timer.

And an annual growth rate of 5,000 cubic feet.

3Sustainable Management vs. Clear CuttingAt a price of $100 per cubic footClear cutting Net Benefit = $10 millionSustainable Management = $500,000 per year

4Sustainable Management vs. Clear CuttingClear cuttingr=4%PVNB = $400,000/ 0.04 =$10mil.r=6%PVNB = $600,000/ 0.06 =$10mil.

Sustainable ManagementPVNB = $500,000/0.04=$12.5mil.PVNB = $500,000/0.06=$8.33mil.5What is the optimal harvest age?Timber CharacteristicsOutput and capital goodTime from investment (planting) to recovery of investment (harvesting) is long, 25 year or greaterGrowth of a treeMeasured in volumeBiologists can track the growth of a treeSmall initial volumeExperiences considerable growth early onBut growth rate declines as it gets older

Output is salable, capital left standing provides increased benefit in the future because the tree grows.2 yr. vs. 8 yr.

7Copyright 2009 Pearson Addison-Wesley. All rights reserved.13-8Model of Tree Growth in a Stand of Douglas Fir

8Hypothetical follow the shape suggested by the biologist. We can use this to determine the efficient age to harvest the trees.

Things that affect growthWeatherSoilInsects, diseasesTree typesCareForest firesAir pollution

9Value of a TreeTrees have two kinds of value. Stumpage value - the sales of timber or other products. In theory the stumpage value of a timber tree equals the value of lumber that can be sawed out, minus the costs of harvest, transport, and conversion to lumber.

10Consider the following growth modelTree grows at rate shown in above figureCost to plant is $1,000Price of pulp wood $1 per cubic feetCost to harvest $0.30 per cubic feet

11The Economics of Forest Harvesting Benefits are measured using the potential volume of wood given the growth rate and the price of the lumber. The annual incremental growth represents the marginal growth.

Planting costs are immediate and thus are not discounted while harvesting costs are discounted because they are paid in the future.12Compare benefits and costs. Benefits you can use the wood as fuel. The larger the tree the more volume it has and the more fuel it provides. Two costs-planting cost (not discounted), harvest cost (discounted b/c paid in future)Timber Revenues and Costs Over Time

Value of timber= price X volume/(1+r)tCost= planting + harvest X volume/(1+r)t

Net benefit = value-cost

13The Economics of Forest Harvesting The optimal time to harvest from a profit maximization perspective would be the age that maximizes the present value of net benefits from the wood.14Compare benefits and costs. Benefits you can use the wood as fuel. The larger the tree the more volume it has and the more fuel it provides. Two costs-planting cost (not discounted), harvest cost (discounted b/c paid in future)

When should the stand be harvested?Net benefits are calculated by subtracting the present value of costs from the value of the timber at harvest age.

The discount rate will affect the harvest decision. 15Compare benefits and costs. Benefits you can use the wood as fuel. The larger the tree the more volume it has and the more fuel it provides. Two costs-planting cost (not discounted), harvest cost (discounted b/c paid in future)

16Age increasesVolume increases

Calculate PVNB for 4 scenarios of discount ratesAs discount rate increases the value in the future decreases

Net benefits in scenario 1 max in the last yearScenario 2 is earlyScenario 3 is earlier stillScenario 4 is super early at 40 years. AND the NB are negativeDiscountings Importance in Harvesting TreesWhen undiscountedOpportunity cost = 0When discountedr>0 implies there is an opportunity costUndiscounted implies it pays to leave the money invested in the tree because theres no other opportunity or alternative to using that money.

r>0 implies other uses for land and money invested in the treesHarvesting costs are discounted and are proportional to the amount of timber harvested.

The net benefit of a unit of wood harvested at any age is the price of the wood minus the marginal cost of that unit.

A tax levied on each cubic foot of wood harvested would simply raise the marginal cost of harvesting by the amount of the tax.

Harvesting costs affect on the Optimal Age of Harvest18Benefits are constantly increasing MINUSPlanting cost represent a fixed cost, and Harvest cost which is proportional to the amount of timber

Tax is just going to shift up the cost curve, increasing the optimal age to harvest.Three Main ResultsA higher discount rate implies a shorter harvest period.

Increasing the planting cost or harvest cost will not affect the optimal harvest age.

With a high discount rate, replanting may not be efficient.19Optimum Harvest Period with Discounting

20Additional Values of a TreeEnvironmental Value the value generated from increased biodiversity, reduced climate change, and existence of the tree.

21Benefits of a Forest Excludable?BenefitsMaterials for housing, paper, wood productsFuelCleanse the air (CO2 to O2)Mitigates climate change Provides shelter and habitat for wildlifeIncreased biodiversityMaintain the watersheds that supply drinking waterPositive externalities means you harvest sooner.

http://www.arborday.org/trees/benefits.cfm