A resource stock may be termed ‘renewable’ if constant periodic removals from it can be indefinitely prolonged. A renewable resource may be further classified as depletable or nondepletable, according to whether or not its productivity is affected by the level of exploitation. Biological resources such as fish, bird and animal populations, forests, grasslands and agricultural soils, provide examples of the depletable type, while surface water resources, solar and geothermal energy may be classified as nondepletable.

Economic Analysis

In spite of the absolute dependence of all economic systems upon renewable resources, no detailed economic analysis of the economics of renewal resources as such was attempted until the mid-20th century. Renewable resources were simply subsumed under the concept of economic rent of land, defined by Ricardo as ‘that portion of the produce of the earth which is paid to the landlord for the use of the original and indestructible powers of the soil’ (Ricardo 1817). But expansion of human populations and technological development throughout the 19th century gradually resulted in the depletion, sometimes to the point of extinction, of once superabundant renewable resource stocks. (A famous example, the passenger pigeon of Eastern North America, once the New World’s most abundant bird species and a resource of economic significance in colonial America, had passed into extinction by 1914.) Such development made it clear that the original powers of the soil were in fact far from indestructible. Popular concern with resource issues led to the ‘conservation movement’ of the early 20th century, resulting in legislation devoted toward the preservation of agricultural, forest and wildlife resources.

Theoretical analysis of the role of renewable resources in economics was hindered by the inevitable temporal dimension of resource exploitation, necessitating the use of dynamic models and the calculus of variations (see Hotelling 1931). Works devoted to verbal analysis of ‘the economics of conservation’, such as those of Ciriacy-Wantrup (1952) and Scott (1955), set the stage for subsequent comprehensive theoretical treatment of resource economics by variational techniques. Finally by the 1970s, a major expansion of public interest in the ‘environment’, and in the ‘limits to growth’ (Meadows et al. 1972), combined with such resource-associated events as the OPEC cartelization of petroleum production and the collapse of major marine fisheries, led the economics profession to take a serious interest in resource and environmental issues – if merely in some instances to defuse the public hysteria. Theoretical developments in constrained dynamic optimization had meanwhile greatly improved the requisite mathematical techniques.

A generalized model of resource exploitation by private or public resource owners may be expressed as follows:

$$ \frac{\mathrm{d}x}{\mathrm{d}t}=G(x)-h(t),\ \ \ t\geqslant 0 $$
(1)
$$ x(0)={x}_0,\ \ \ x(t)\geqslant 0,\ \ \ h(t)\geqslant 0 $$
(2)
$$ \uppi =\uppi \left[x(t),h(t),t\right] $$
(3)
$$ V\left({x}_0\right)=\underset{\left[h(t)\right]}{\max }{\int}_0^{\infty}\alpha (t)\uppi\;\mathrm{d}t $$
(4)

in which x(t) denotes the size (‘state’) of the resource stock at time t, G(x) is the natural rate of replenishment, h(t) is the rate of removals, or ‘harvest’, of the resource, π denotes the net flow of economic benefits at time t and V(x0) is the optimized present value of net benefits, relative to the discount factor

$$ \alpha (t)=\exp \left[-{\int}_0^tr(s)\mathrm{d}s\right] $$
(5)

where r(s) is the instantaneous rate of discount at time s.

The specification G(x) ≡ 0 provides a general exhaustible resource model. A renewable resource model is obtained by allowing G to depend on the resource stock x, with \( G(x)=0 \) for some \( \overline{x}>0\ \ \ \mathrm{and}\ \ \ G(x)>0\ \ \ \mathrm{for}\ \ \ 0<x<\overline{x}. \) For the case of a biological resource stock one would assume that \( G(0)=0: \) a nondepletable resource could be modelled (not very well) by assuming \( G(0)>0. \) For the latter two cases, \( \overline{x} \) represents the natural, or environmental ‘carrying capacity’ for the given stock.

A popular, widely accepted objective of renewable resource management is the so-called ‘maximum sustained yield’ (MSY), characterized simply by the equation

$$ {h}_{\mathrm{MSY}}=\underset{x}{\max }G(x). $$
(6)

According to this principle, any renewable resource stock should be maintained at the level \( x={x}_{\mathrm{MSY}} \) at which its exploitable productivity G(x) is a maximum. Perpetuation of MSY has indeed been considered as the sacred and sole trust of many resource management agencies, seldom with any cognizance of the economic implications of such a policy. Not infrequently the resource industry itself seems to exhibit a preference for some quite different objective.

The solution of the optimization problem of equation (4) is characterized by the following necessary conditions:

$$ {\uppi}_h=\lambda (t) $$
(7)
$$ {G}_x+\frac{\uppi_x}{\uppi_h}=r(t)-\frac{\lambda (t)}{\lambda (t)} $$
(8)

where λ(t) denotes the current ‘shadow price’ (formerly, user cost) of the resource stock, equal to the marginal value of the resources stock x(t), and where subscripts designate partial derivatives and overdot the time derivative.

If π does not depend explicitly on time t, and if r(t) = r is constant, equation (8) possesses an equilibrium solution \( x={x}^{\ast } \) determined by

$$ {G}_x+{\uppi}_x/{\uppi}_h=r $$
(9)
$$ h=G(x). $$
(10)

Equation (9) is recognizable as the standard marginal productivity rule of optimal capital accumulation, in which marginal productivity Gx is equated to the discount rate r. The correction term πx/πh arises from the fact that x and G(x) are specified in physical units, rather than as asset and flow values, respectively (see Clark 1976, ch. 3).

In the event that \( {\uppi}_x\equiv 0 \) (costs and benefits independent of stock level x) and \( r=0 \), equation (9) becomes \( {G}_x=0, \) namely \( x={x}_{\mathrm{MSY}}, \) the MSY solution. In general, under the reasonable assumptions that \( {G}_{xx}<0 \) and \( {\uppi}_x>0,{\uppi}_h>0, \) we see from equation (9) that (i) discounting tends to decrease x*, whereas (ii) the dependence of π on x tends to increase x*, relative to the MSY solution. The numerical significance of these effects can only be assessed by estimating model parameters for particular cases.

The Effects of Discounting

A theme that runs through much of the conservation literature pertains to the effect of discounting, or time-preference, on the conservation of resource stocks. Pigou, for example, says that

There is widespread agreement that the state should protect the interests of the future in some degree against the effects of irrational discounting, and of our preference for ourselves over our descendants. The whole movement for ‘conservation’ in the United States is based upon this conviction. (Pigou 1920, p. 29, as quoted by Scott, 1955).

This raises the question of whether the social rate of time preference differs, or ought to differ, from the market rate.

For the case of renewable resources, equation (9) suggests that the effect of discounting will be large when Gx is small. Since Gx represents marginal growth rate of the resource stock, we conclude that discounting will be especially important for resource stocks having low growth rates (although the effect of πx/πh must also be considered).

Biological resources exhibit a wide range of growth rates. Some species, called ‘r-selected’ by ecologists, are highly fecund: populations consisting of numerous small individuals expand rapidly to take advantage of environmental opportunities. At the opposite end of the growth spectrum are large, slow growing ‘K-selected’ species, which are also often highly valued and easily exploited by modern techniques. The latter type, which includes whales and other marine mammals, forests, desert grazing lands, and the like, are particularly subject to severe over-exploitation, both under common-property conditions of exploitation and under private profit maximization by firms employing market rates of discount.

User Conflicts

The paradigm, assumed above, of an isolated renewable resource stock exploited by a sole owner is seriously unrealistic for most actual renewable resource industries. Imperfection of ownership rights, multiple uses and users, and a wide variety of externalities, are the rule rather than the exception in fisheries, forestry, wildlife, water resources, and such like.

Most commercial fisheries, for example, are still exploited under common-property conditions, although the introduction of 200-mile fishing zones in the late 1970s has at least placed the majority of marine fishery resources under national jurisdiction. Wildlife, water, and recreational resources are often also utilized as common-property resources. The historical trend, however, is towards progressive allocation of resource-use rights to individuals, if not via outright sole ownership than vai user permits, quotas and fees. As a general rule, the delineation of resource sub-allocations can be expected to increase along with the economic importance of the resource, but the process is inevitably confounded by political and legislative components.

Over-exploitation of renewable resource stocks and over-expansion of harvest capacity are frequent occurrences in resource industries utilizing non-owned, or commonly owned resources. In the absence of property rights, each exploiter tends to ignore the effects that his own removals will have on the total resource stock and its future production. Thus in a common-property resource industry, the rate of harvest will increase (unless restricted by regulation) to a level at which the marginal exploiter receives zero net revenue:

$$ {\uppi}_h=0. $$
(11)

The industry thus behaves as if the shadow price λ of the resource were zero [see equation (7)]. By imposing a removals tax \( \uptau =\uplambda \) per unit of harvested resource, the management authority (should one exist) can in principle force the competitive exploiting industry to utilize the socially optimal rate of exploitation. Resource rents then accrue to the management authority, rather than being dissipated through over-exploitation or over-capacity.

Renewable resource industries impose a variety of externalities upon other resource users. Logging of forests may affect surface water retention and flow. Public demand for parks and wilderness areas may lead to conflicts with resource industries such as forestry, agriculture and hydroelectric power. Pesticides employed to protect forests or crops may damage fish and wildlife populations.

An important long-term externality resulting from the alteration or destruction of natural habitats by resource industries is the progressive loss of genetic material, which may ultimately limit the diversity of domestic crops and animals, and reduce the supply of naturally derived pharmaceutical and industrial compounds (Oldfield 1984).

Most externalities of his kind increase in economic importance with the intensity of resource exploitation. Consequently the socially optimal exploitation policy will often involve less intensive exploitation than would be practised by private resource owners. Much of the rationale for the establishment of government management authorities doubtlessly stems from these considerations. The fact that the external costs of resource exploitation are often much longer lasting than the internal benefits adds to the need for timely government regulation.

Resource Management

Numerous management agencies have been established to regulate the exploitation of renewable resources such as water supplies, marine and freshwater fish stocks, wildlife populations and forests. Such agencies face many difficulties, including particularly the allocation of a limited supply in the presence of excessive demand, enforcement of regulations, and the problem of dealing with major uncertainties regarding resource inventories, ecosystem dynamics and environmental factors. It is also becoming increasingly recognized that the traditional resource management objective of maximum sustained yield is often not adequate to deal with resource conflicts, multiple uses and externalities of resource use.

Both fiscal and quantitative instruments are frequently employed by resource management agencies. Fees and taxes levied on resource users reduce excess demand for the resource, while collecting resource rent for the public purse. In many localities where resource-based industries dominate the economy, such charges can constitute a major component of state revenue, although a dominant resource industry may have sufficient political influence to prevent the full capture of rents by government.

The degree to which resource taxes can be used in practice as proxies for shadow prices is severely limited by the complexity and uncertainty of both biological and economic systems. Consequently direct regulation is the usual rule, at least for resource industries based on publicly owned resource stocks. Regulation may ultimately pertain to almost every aspect of exploitation, including time, place, amount and methods of harvest, as well as details of species, size, sex etc. permitted to be taken.

It might of course be argued that the need for such complex systems of regulation would be obtained if ownership were to be transferred entirely to private hands, but this may be neither feasible nor desirable in cases where resource stocks are not readily appropriated, or where significant externalities must be controlled. But it is certainly true that regulations can have perverse economic consequences. An example common by the 1970s was the tendency to regulate commercial fisheries by means of total annual catch quotas. Such non-allocated quotas force individual fishermen into a competitive ‘scramble’ wherein each attempts to catch as many fish as possible prior to the closure of the fishery. The consequences include unnecessary expansion of fishing capacity in terms of number, size and horsepower of vessels, reduction in the quality of fish and highly uneven rates of delivery of fish to processors and markets.

A potential method for overcoming these problems is the use of allocated quotas: if such quotas are transferable, the price of quotas will play a similar role to a tax on catches. Quota allocations are also of potential value for the regulation of other resources such as water resources and public grazing lands. Monitoring and enforcement are of course essential to the success of any allocated quota system. The quotas must also be flexible, to allow for natural fluctuations in resource abundance.

Fluctuations and Uncertainties

Renewable resource industries face significant uncertainties regarding both supply and demand. Unpredictable environmental fluctuations can have large-scale effects on the production and availability of renewable resource stocks, which can in some cases have nationwide or worldwide economic consequences. Unexpected decreases in resource abundance become especially serious when exploitation has reached high levels, with industries or even entire segments of the economy dependent upon the resource. While developed nations may possess institutions to mollify the worst effects of such natural fluctuations, the less developed nations often face economic disaster in times of drought, flood, insect or crop pathogen plagues, or fishery collapses.

Temporary periods of low resource availability can be extremely unpleasant in themselves. But they can also result in severe over-exploitation as the dependent industry continues to harvest the resource in desperation. In extreme cases ultimate recovery may become impossible owing to irreversible destruction of breeding stocks, or of soil productivity. The more infrequent are the bad years, the more likely ultimate disaster may become, as communities grow to rely upon the resource and discount the possibility of a decline.

Resource managers face many kinds of uncertainty beyond that pertaining to the scope and timing of natural fluctuations (Mangel 1985). The long-term response of depletable resource stocks to exploitation is often difficult if not impossible to predict quantitatively. Even current inventories of resource stocks such as marine populations may be highly uncertain – current estimates of whale stocks in the Antarctic, for example, range over two orders of magnitude. Discerning trends from such inaccurate data often borders on the impossible, but improving the accuracy of the data base is often unacceptably expensive.

In response to such gross levels of uncertainty the risk-averse public resource manager tends to prefer a conservative exploitation policy which minimizes the probability of depletion.

The exploiting industry, however, often takes the opposite view, preferring certain current revenues to uncertain future benefits. Since uncertainty increases with the planning horizon, an additional bias towards depletion of renewable resource stocks is observed.

See Also