1. Storable, Renewable Resources: Forests
Chapter 12
Storable, Renewable Resources: Forests

2. Objectives Discuss the biology of forest growth.
Present the difference between the biological decision rule for forest management and the profit maximization rule.
Illustrate the calculation of the present value of net benefits from timber harvesting.
Discuss the sources of inefficiency in forest management.
Discuss global externalities that encourage over harvesting.
Present a history of U.S. forest policy.
Present economic strategies for dealing with global inefficiencies

3. Introduction In many parts of the world, wood is an important fuel
Paper products are derived from wood fiber
Trees cleanse the air by absorbing carbon dioxide and adding oxygen
Provide sanctuary for wildlife and help in maintaining in watersheds
About one-third of the land in the U.S. is covered with forests.
Less than 4% of Pakistan’s land is covered with forests
Trees mature very slowly, manager must decide not only how to maximize yields on a given amount of land but also when to harvest and whether to replant

4. Introduction Some important terms generally used
Reforestation (including plantations)
Afforestation (the conversion of unforested land to forest)
Natural expansion of forests

5. Introduction
Current forestry practices may be violating both the sustainability and efficiency criteria
Sustainability refers to harvesting no more than would be replaced by growth; sustainable harvest would preserve the interests of future generations by assuring that the volume of remaining timber was not declining over time. This is consistent with the environmental sustainability criterion discussed in Chapter 5, but is stronger than needed to satisfy the weak sustainability criterion.
Conceivably, the weak sustainability criterion could be satisfied even if the volume of wood were declining over time by providing a compensating amount of some commodity or service they value even more.

6. Characterizing Forest Harvesting Decisions
Special Attributes of the Timber Resource
Timber is both an output and a capital good.
The harvest decision involves how much timber to harvest, how often to harvest it and whether to replant after harvesting.
Standing trees are a capital asset. Tree growth increases the harvestable volume and standing trees provide watershed protection and wildlife habitat.
Forest managers will decide between harvesting today and waiting to harvest.

7. The Biological Dimension
Tree growth is conventionally measured on a volume basis, typically cubic feet, on a particular site. This measurement is taken of the stems, exclusive of bark and limbs
Young trees will grow tall quickly, but volume growth is slow. Medium aged trees increase in volume quite rapidly while mature trees grow very slowly and eventually stop growing or reverse growth.
Growth will also be affected by weather, soil fertility, disease, forest fires, etc.

8. Model of Tree Growth in a Stand of Douglas Fir
V = a + bt + ct2 + dt3
V = Volume
t = age and
a, b, c, d are parameters

9. The Economics of Forest Harvesting
Let us assume that there is a forest plot, where a forestry business is being planned.
The plan is to plant trees only once, and when trees are harvested, there shall be no replanting of trees. The forest land would be left as it is after the harvesting of trees.
The price of timber remains fixed in all years (say, P=$1 per cuft).
Planting costs are incurred only in the initial year 0 (say, CP=$1,000 per tree).
Harvesting costs are incurred at the time o year of harvesting (say, CH=$0.30 per cuft).
There are no other costs.

10. The 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.
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.
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.

11. The Economics of Forest Harvesting
The objective is to choose t (the year of harvesting), so as to maximize the NPV, i.e., the present value of total net benefits from Vt (the volume of timber available from the tree in that year).
where,
P : the price received per unit of harvested volume
V(t) : the volume of timber harvested at age t
CH : the per-unit cost of harvesting the timber
t : the age of the timber, and
CP : the fixed cost of planting
The expression ((P – Ch) Vt )is called the stumpage value, which is the net value of timber in the tree. And, (P – Ch) is called the net price of timber

12. The Economics of Forest Harvesting
A rational decision-maker compares the marginal benefit of waiting a year more with the marginal cost of waiting a year more. You can also look at this problem as a trade-off between two choices
(i) Harvest now, sell the timber, and invest sales proceeds for a year or
(ii) Wait for the tree to grow one more year and then harvest.

13. Economic Harvesting Decision: Douglas Fir
Look at the NPV column of the above table:
If your r = 0%, when should you harvest? In year 135.
If your r = 1%, when should you harvest? In year 100.
If your r = 2%, when should you harvest? In year 68.
If your r = 4%, when should you harvest? In year 40. Probably, you won’t replant. Costs of replanting would exceed the benefits

14. The Economics of Forest Harvesting
The optimal harvest time occurs where the rate of return from letting the stand grow over the last increment of age should be equal to the market rate of return. (see Appendix, Chapter 12)

15. The Economics of Forest Harvesting
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.
High discount rates and high replanting costs could make replanting prohibitively expensive.
The results show that harvesting period shortens with increase in r. Increase in impatience leads to early harvesting. For highly impatient people (r = 4% in this example), trees grow too slow for forestry business to become profitable.

16. The Economics of Forest Harvesting
What would happen to harvesting period if planting costs were $1,500, instead of $1,000?
Nothing because planting cost is a fixed cost and therefore has no effect on choice of harvesting period. However, a large increase in planting cost can make forestry business unprofitable, if the net sales revenue from timber is not sufficient to cover the initial plantation cost.
What would happen if harvesting cost increased, say from $0.30 to $0.40 per cuft?
Because this cost is also fixed independent of choice of harvesting period, it does not affect the harvesting period. Show in the graph that the curve shifts proportionately up or down with a change in harvesting cost. Once more, a very large increase in harvesting cost can make replanting unprofitable.

17. The Economics of Forest Harvesting
A tax levied on each cubic foot of wood harvested would simply raise the marginal cost of harvesting by the amount of the tax.
This type of tax simply increases cost of harvesting independent of when it is harvested. To have any effect the tax has to be graduated over years: the more you prolong harvesting, the less should be the incidence of tax.
Allow a one-time jump in price; assume that this new higher price will now remain fixed for the remaining years. What would happen to harvesting period then?
Once again, for similar reasons there shall be no effect.
Instead of a fixed price for all years, now allow price to rise over time. What would this knowledge do to harvesting period?
The price change now will matter; waiting will now become more beneficial, as one can get a higher price for the same timber. This is likely to prolong harvesting period. The higher prices in future offset the losses in time value of future receipts.

18. Summary of the one-time (basic) model
The rule is to choose the year when the NPV is maximum.
When planting costs are fixed, maximization of NPV is equivalent to choosing the year when the stumpage value is the maximum.
When interest rate increases, harvesting period shortens.
Too high an interest rate can make forestry business unprofitable (not worth doing).
Changes in planting costs, harvesting costs, severance tax on harvesting, or a discrete or one-time change in timber price does not change harvesting period; but, these factors can change the overall profitability of forestry business.
A trend of timber price rising over time will prolong harvesting period.

19. Optimum rotation model or infinite-horizon model
The above basic model allowed only one time planting and harvesting of trees, leaving the land unutilized after harvesting
We now allow for an infinite number of rotations of replanting and harvesting. It is important to keep in mind that we are looking at one tree in the model; what is true for optimum rotation of one tree would be true for all trees in the given forest site, assuming all trees are of the same species.

20. Optimum rotation model or infinite-horizon model
The objective is to choose the rotation period, t; that is, to choose the age of tree when a planted tree would be harvested and at the land vacated another tree plant would be replanted and let grow for the same number of years of age before harvesting.

21. Optimum rotation model or infinite-horizon model
Suppose the solution for optimum rotation is 10 years. Assume you have 100 acres of forest plot to plant trees. Given 10-year rotation period, you shall divide your forest plot into 10 equal areas, i.e., 10 plots of 10 acres each.
The initial planting of trees would then be staggered over first 10 years; one 10-acre plot shall be planted one year, another plot the second year, the third plot the third year and so on.
In the first 10 years all 10 plots would have been planted, but then the very first plot would be ready to harvest at the end of the 10th year, the second plot in the 11 th year.
Every plot after harvest shall be replanted. In this fashion, the forestry business shall yield a sustainable (equal) quantity of timber every year.

22. Optimum rotation model or infinite-horizon model
The infinite-planning model is different from the single- harvest model in that it recognizes the interdependencies between periods.
Decisions to delay harvests impose costs on the next harvest period. For this case, the opportunity cost of delaying the next rotation must be outweighed by the gain in tree growth.
All else constant, the optimal rotation (the time between planting and harvesting that crop) 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.

23. Comparing basic model with infinite horizon model
When interest rate changes, the result is the same as the one-time model.
When plantation cost rises, harvesting period is likely to be prolonged. Since it is going to cost more to replant, why not wait a little longer to get a better return from trees already planted. This result is different from the one-time model.
When harvesting cost is likely to rise in future, the optimal rotation period would be lengthened
Since increased harvesting costs in the infinite-horizon model lengthen the optimal rotation period, a per-unit tax on harvested timber would also lengthen the optimal rotation period in this model.
Introducing relative prices for timber that rise at a constant rate in The infinite-horizon model causes the optimal rotation period to increase relative to the fixed-price case

24. Considering multiple uses of timber
We were focusing on only one use of forest – timber, in which the benefit of letting trees grow is the growth in their stumpage value of timber.
If trees as they grow also render benefits of better recreational opportunities, better habitat for wildlife, and better stabilization of watersheds, etc., then the present value of these benefits need to be added to the right hand side when we choose the optimal harvesting period t, to maximize NPV.
Because multiple uses add to the benefits of letting trees grow, the optimum harvesting time is likely to prolong. Theoretically it is possible that if non-timber benefits of trees are very high, relative to their timber value, it could be considered optimal to preserve (rather than harvest) forest or to leave it as wilderness forever.

25. Sustainable Forestry
Profit-maximizing decisions may not be efficient due to externalities.
Efficiency and sustainable forestry are not necessarily compatible.
Practices aimed at sustainable forestry that is also economically sustainable had led to a focus on rapidly growing trees and plantation forestry.
Plantation forestry is controversial.

26. Source of Inefficiencies
Handout given in class