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Homework #9 Due Wednesday Quiz #4 Wednesday Group Outline Due Wednesday Exam #4 – Nov. 28th Group Presentations – Dec. 3 & 5

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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?

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Imagine you own a stand of trees with 100,000 cubic feet of standing timer. And an annual growth rate of 5,000 cubic feet.

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At a price of $100 per cubic foot Clear cutting Net Benefit = $10 million Sustainable Management = $500,000 per year

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Clear cutting r=4% PVNB = $400,000/ 0.04 =$10mil. r=6% PVNB = $600,000/ 0.06 =$10mil. Sustainable Management PVNB = $500,000/0.04=$12.5mil. PVNB = $500,000/0.06=$8.33mil.

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Timber Characteristics Output and capital good Time from investment (planting) to recovery of investment (harvesting) is long, 25 year or greater Growth of a tree Measured in volume Biologists can track the growth of a tree Small initial volume Experiences considerable growth early on But growth rate declines as it gets older

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Copyright © 2009 Pearson Addison- Wesley. All rights reserved. 13-8

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Weather Soil Insects, diseases Tree types Care Forest fires Air pollution

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Trees 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.

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Tree grows at rate shown in above figure Cost to plant is $1,000 Price of pulp wood $1 per cubic feet Cost to harvest $0.30 per cubic feet

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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.

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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.

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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.

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When undiscounted Opportunity cost = 0 When discounted r>0 implies there is an opportunity cost

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Harvesting 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.

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A 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.

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Environmental Value – the value generated from increased biodiversity, reduced climate change, and existence of the tree.

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Benefits Materials for housing, paper, wood products Fuel Cleanse the air (CO 2 to O 2 ) Mitigates climate change Provides shelter and habitat for wildlife Increased biodiversity Maintain the watersheds that supply drinking water

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