Forest resources are a good starting point for analyzing the economics of renewable resources.  Biological resources are self-reproducing, and the basic principle of renewable resource management is to maximize the net present value of the resource subject to its reproductive behavior.

We begin by modeling a stand of trees or forest as a capital asset producing marketable timber. Although we omit the values of all other uses here, we could conceivably factor these into the model as additional benefit streams or externalities associated with timber harvest.

The marketable volume of a stand depends on tree species, site class (height of dominant trees at some standard age), stand age and density, prior site management (pesticide treatments, thinnings to maintain efficient stocking levels), and type of product the lumber will be used for. Growth in marketable volume and stand value typically slow as stands get older. In effect, time is the production input. The optimal time of harvest is where the rate of growth in stand value declines to the rate of discount.  Note that forest management also involves substantial risk costs--fire, insect damage, disease, etc. which we will ignore for the moment--so that longer harvest cycles are implicitly riskier than shorter cycles.

Review Teitenberg's single-rotation model, summarized below.  Volume is a simple (cubic) function of stand age or time:

Foresters recommend harvesting when so-called "mean annual increment" (MAI=stand volume/age) is maximized.  This forestry term is a misnomer, since it really represents average rather than marginal growth per year.   Note that this harvest recommendation is based only on the biology of the resource.  It is not likely to be economically efficient, since it has no economic component: it ignores timber prices, planting and harvesting costs and discounting.

The maximum MAI occurs when MAI equals the marginal growth increment or "annual incremental growth" (AIG), i.e. the extra growth per year.  Mathematically, this is the time derivative of the growth function:

The economically optimal growth strategy becomes apparent when we calculate the annual percent growth, which is AIG/volume.  Treating the stand as a financial asset, we would let it grow as long as its percent rate of growth exceeds the rate of discount.  Once this rate of growth falls to the rate of discount, we harvest the stand.  The graph below shows annual percent growth declining to 2% at a stand age of 68 years.  As this graph suggests, higher rates of discount imply earlier optimal harvests.

In this simple single-rotation case, the optimal harvest time is where dV/dt = r.  Since any site prepration and planting costs are paid up-front, they have no influence on the optimal timing of the harvest (although they do help determine whether commercial forestry is economically viable or not.)  Net revenue per cubic foot is constant (doesn't vary with stand volume), so a change in price or harvest costs shifts the entire net profit schedule up or down, but doesn't influence the rate of growth in net benefits, and thus doesn't influence the optimal timing of harvests.

Since harvested forestland regenerates naturally or may be replanted, the single-rotation model can be expanded to include the opportunity costs of delaying harvests from subsequent rotations. The multi-rotation model implies shorter harvest intervals. An increase in planting costs reduces the opportunity costs of delaying subsequent rotations, and increases optimal rotation period. An increase in harvesting costs or a decrease in price also extends the optimal rotation period.

Formally, if commercial forestry is profitable so that replanting is justified, and if prices and costs are assumed to remain constant through time, we would expect to see harvesting and replanting every T years, providing the landowner a perpetual stream of discounted returns from a sequence of harvests, with present value PV*, where

Here we calculated PV and PV* for different values of t = T when r = 0.025.  In the single-rotation case, optimal harvest is at T = 61 years; in the multi-rotation case, the optimal harvest interval is T = 54 years.

Since mature forests provide important environmental benefits, a severance tax per cubic foot might be imposed to delay harvests. The single-rotation model indicates that such a tax will have no influence on the timing of the harvest. The multi-rotation model indicates such a tax will delay harvests. If the amenity benefits associated with mature forests are sufficiently large, it may be socially optimal to keep the stand as a wilderness area. Some species, notably Douglas fir in the Pacific Northwest, actually require forest fires to reproduce. Logging interests argue that if old-growth forests aren't harvested, they will simply be lost to fire, disease or insects instead; closing these areas eliminates timber industry jobs and hurts rural economies. The extensive habitat requirements of the Northern spotted owl make the jobs-versus-preservation controversy in the Pacific Northwest even more difficult to resolve.

Forests provide numerous benefits: besides generating marketable forest products, they absorb CO₂, a principal "greenhouse" gas (Actually the recent buildup of atmospheric CO₂ is probably due more to combustion of coal and petroleum than to reductions in global plant biomass); they improve watershed quality; they provide wildlife habitat and support biodiversity; and they support wilderness recreation. Most forest land in the US is privately owned, and presumably managed to maximize private returns (from timber harvests or recreation) to the owner. Commercial harvests often generate significant environmental externalities, however. There is intense controversy over US public forests, reflecting conflicting interests of loggers and environmentalists. The US Forest Service has tried to promote "multiple-use forestry" on public forest lands, but is perpetually embroiled in conflicts over incompatible uses.

Inefficiencies: Even efficient private management decisions fail to consider macro-scale environmental issues (biodiversity, global warming, etc.). In some LDC's, extreme poverty motivates rapid deforestation: concern for immediate survival implies near-infinite rates of discount. Forests in many LDC's are common property resources: individual users have no incentive to conserve these resources for others. Land pressures may induce squatters to seize these lands and clear them for farming. "Slash and burn" farming in tropical rainforests quickly exhausts forest soil nutrients. LDC governments often face strong incentives to cash in public forest resources for needed foreign exchange or international debt payments. Government officials may be bribed to sell off logging rights for far less than their actual values, and artificially low stumpage costs motivate excessively rapid depletion of forest resources.

57% of all forest land in the US is owned by individuals; 15% is owned by forest products companies; 28% is publicly owned. One third of all privately-owned parcels are 100 acres or less. Most private forest holdings are too small to support necessary scale economies in stand management or harvesting, so these parcels are typically neglected until owners can find more profitable uses for the land and clear it. Both in the US and abroad, agricultural price supports create additional incentives to clear forest land for cropping. International trade in forest products is limited by trade restrictions and incompatible grading standards.

Publicly owned forests in the US aren't necessarily managed much better. The National Forests were originally controlled by the Interior Dept., but the US Forest Service under Gifford Pinchot was transferred to the USDA in 1905. Pinchot developed the USFS's official "sustainable multiple use" philosophy. However the USFS continues to approve below-cost sales of timber to politically powerful logging companies (costs of government-provided timber management and logging roads exceed sales revenues). Clear-cuts may be economical for logging companies, but are visually offensive and often cause soil erosion and turbidity in streams.

Non-profit environmental groups have developed several strategies for protecting environmentally important forests.

In debt-for-nature swaps, non-profit environmental groups buy up LDC foreign debt in secondary bond markets, and forgive that debt if LDC governments guarantee protection of their forest resources. Countries may establish extractive reserves such as Brazil's rubber tree reserves, and bar development of them. Treaties allowing countries to patent and license commercial use of genetic materials derived from their forest resources should also improve forest conservation incentives. Conservation easements can be purchased from private landowners: the owner retains possession of the land under a restricted-use title. Tietenberg discusses a grandiose plan for a global conservation easement program.

Appendix: Some Basics of Forestry

Depending on prior management and species, forest stands may be even-aged or mixed-age; and single-species or mixed-species. Different species have different shade tolerances dictating natural successions of species: many conifers and pioneering hardwoods (birch, aspen) are eventually out-competed for crown space by oaks, maples and beeches and other more shade-tolerant species. Most hardwoods can regenerate from stump sprouts; softwoods can't.

Delaware's forests naturally tend to mixtures of pines, red and white oaks, red maple and gum. On the coastal plain, loblolly pine is the principal commercial species, used for paper and lumber; pure pine stands require planting, periodic release thinnings and suppression of hardwoods. Most of the hardwood volume has little economic value. Delaware does export some high-grade oak and paulownia from the piedmont. Most non-industrial forest parcels in Delaware are unmanaged, over-stocked, slow-growing and unhealthy. Aggregate loblolly pine volume is declining; hardwood volumes are more stable. Between 1974 and 1984, Delaware experienced a net loss of only 1.2% of its farmland because cropland conversions to development were largely offset by forest conversions to cropland: deciduous forest acreage declined 3.6%, mixed deciduous/coniferous forest acreage declined 7.1%, and coniferous forest acreage declined 15.4%.

Foresters gauge stocking levels via basal area (aggregate surface area of stumps, estimated with a prism), stems/acre, average diameter and degree of crown closure (see figure). Most species should have a minimum of 40 percent of length in live crown, 1 to 2 feet/inch DBH spacing between trees. Sites indices gauge the height of (never-suppressed) dominant trees at a standard age (50 or 100 years), and indicate site quality. Trees can be aged using an increment borer; heights and volumes and basal areas estimated using Biltmore stick.

Marketable volume as a percent of total volume depends on type of product. Pulpwood harvests use most of the total biomass. Stands begin generating marketable volume fairly early. Rotations typically occur at 20-40 year intervals. Sawtimber harvests use less of the total biomass, since the logs must meet larger minimum length and diameter standards. Stands may not generate any marketable volume in the first 20 years. Sawtimber rotations require longer time intervals. Veneer logs and other specialty products usually represent very little of the total biomass; top-quality trees may be selectively harvested, with other trees left standing, although repeated "high-grading" leaves only weaker trees to regenerate, and results in low-quality forests. Foresters use various log-rule formulas to estimate marketable yields from raw logs.