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Homework #9 Due Thursday Quiz #4 Thursday Group Outline Due Thursday Exam #4 – Dec. 1 st Group Presentations – Dec. 6 & 8

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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 tons of standing timer. And an annual growth rate of 5,000 tons

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At a price of $100 per ton Clear cutting = $10 million Sustainable Management = $500,000 per year

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Clear cutting r=4% PV = $400,000/ 0.04 =$10mil. r=6% PV = $600,000/ 0.06 =$10mil. Sustainable Management PV = $500,000/0.04=$12.5mil. PV = $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 wood $1 per cubic feet Cost to harvest $0.30 per cubic feet

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

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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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Interdependences Applying single-harvest model may not be so simple Single-harvest model, harvest when marginal benefit of an additional year’s growth = marginal opportunity cost of capital Infinite-planning model, you examine the optimal length of harvest and replanting (“Optimal Rotation”). Length of each period affects the benefits in the next period The opportunity cost of delay is the benefit from the next best alternative (harvesting and replanting).

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All else constant, the optimal rotation in the infinite-planning case is shorter than in the single-harvest case. The marginal cost of delay is higher since there is now an opportunity cost of starting the next cycle later. Thus, the optimal rotation is shorter.

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Opportunity costs are the forgone benefits from the next best alternative Marginal cost of delay is the forgone benefits from harvesting and replanting for the next period. The net benefits in the next period depend on the planting costs and the harvesting cost.

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Occurs when the marginal cost of delay equals the marginal benefit of delay. How do an increase in the following affect the optimal rotation age? Planting costs Harvesting costs Per-unit tax on harvesting

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