Resource capital theory and ecosystem economics: developing nonrenewable habitats with heterogeneous quality.

I. Introduction

Public concern for the interdependence of economic actions and ecosystem reactions has matured to raise ecosystem management and sustainability to the forefront of public policy. For example, federal land agencies and the U.S. Environmental Protection Agency have adopted "ecosystem management" as their primary approach, affecting hundreds of millions of acres of public land and regulations toward industrial use of private land.

This environmental concern motivates a spectrum of models to identify environmental allocation rules, e.g., for pollution control or preservation of wild habitats [11; 24; 28; 31]. Some recent works merge models of an economy with those of ecosystems. Notably, Crocker and Tschirhart's [9] framework permits policy analysts to trace the effects of human intervention through both the ecosystem and the economy and to identify, in principle, which ecosystem resources may be efficiently degraded and which can be efficiently maintained.

While many, if not most, of these studies use the principles of capital theory following Arrow [2] or Dorfman [10], the literature on ecosystem economic issues has not re-examined the well developed insights from standard theories for natural resource capital, particularly the nonrenewable resource models following Hotelling [14] and the renewable resource models following Clark and Munro [7].(1) Swallow [25] developed a dynamic model that merges renewable and nonrenewable resource theories and explores tradeoffs between interdependent renewable and nonrenewable resources, stability of nonrenewable resource development, and sustainability of renewable resource harvests. However, that model omitted resource heterogeneity that complicates many of Crocker and Tschirhart's [9] policy conflicts over the ecological implications of economic decisions or, conversely, conflicts over the economic implications of ecological interdependencies among heterogeneous resources.

This paper extends resource capital theories to develop an understanding of allocation rules for the efficient development of ecological resources. The analysis cautions economists on the use of some of the most fundamental and intuitive principles of resource economic theory. For example, the principle of extracting "least-cost ores first" commonly guides resource economic studies, such as wetland development [24; 18], but, in an ecosystem-economic setting, "least-cost first" assumptions may mislead policy evaluations. That is, both economic and ecosystem dynamics affect economic efficiency. Resource economic theory may mislead if applied within an ecological vacuum.

To aid exposition, the model is motivated by the ecologic-economic implications of development of coastal, estuarine wetlands that provide or protect habitat for renewable fishery resources. Coastal development causes up to 90% of losses of estuarine wetland acreage with additional indirect impacts on estuarine productivity. Since up to 90% of commercial fishery landings derive from estuarine-dependent species, coastal development may substantially impact renewable resource production [17; 29]. Even when developers minimize impacts, coastal development may still permanently alter the role of coastal lands in the estuarine ecosystem. To the extent that landuse changes irreversibly alter the ecosystem, one may view wetland development as development of a nonrenewable resource [3; 11; 15].(2)

More generally, the model applies where a nonrenewable resource, when left in situ, leaves intact critical habitat contributions for a renewable resource. Unlike Swallow [25], this model directly addresses the implications of heterogeneous quality of the nonrenewable resource "ore."(3) For example, coastal developers may value estuarine wetlands differently due to their geographic location relative to urban demand centers or due to physical features, such as quality factors affecting agricultural productivity [18; 24]. Concomitantly, the model here examines heterogeneous resource quality from the perspective of the renewable resource sector, since different ecological types of estuarine wetlands might contribute differently to fishery productivity. Thus, judgments of the "ore grade" may differ, depending on whether the judge works within the renewable or the nonrenewable resource sectors.

The paper begins with a three-state, three-control problem, attempting an intuitive analysis. Section two presents the multi-state model and develops allocation rules based on rates of return to natural capital. Following Spence and Starrett [22] the analysis capitalizes on intuitive "most rapid approach paths" to establish general insights within a model structure that adapts well for policy application.(4) Results, for example, develop a more general criteria to judge non-renewable resource grade. Section three alters the specification to add some ecological details that, in turn, reveal a bias that economists may create by overlooking Crocker and Tschirhart's [9] advice to fully incorporate ecology. Section four summarizes an empirical example and section five discusses implications for public policy.

II. A Dynamic Model of Interdependent Stocks

The analysis follows from capital theory, assuming, for ease of exposition, that a benevolent "resource manager" internalizes ecosystem interactions among natural resource stocks and attempts to maximize the present value of social benefits received from resource use. This study's objective is to examine the implications of heterogeneous quality of the nonrenewable resource (wetlands) when it contributes to production of renewable (ecological) resource goods (fish). That objective requires a basic model where the stock of nonrenewable resources, E, is split into at least two blocks, one of high grade, [E.sup.H], and one of low grade, [E.sup.L].

The Basic Model

The designation of "high" and "low" nonrenewable resource grades comes from the perspective of the extractive sector, or nonrenewable wetland developers. Following the structure of non-renewable resource models [12; 16; 27], within each block extractive rents decline continuously with cumulative extraction: block [E.sup.i] obtains marginal rents, from development of the marginal unit, given by [C.sup.i]([E.sup.i]), with [C.sup.H]([E.sup.H]) [greater than] [C.sup.L]([E.sup.L]) and [Mathematical Expression Omitted]. With initial stocks [Mathematical Expression Omitted] and [Mathematical Expression Omitted], assume development of the last unit of [E.sup.H] is at least as profitable as development of the first unit of [E.sup.L], so [Mathematical Expression Omitted].(5) Producers of nonrenewable resource goods prefer to develop higher grades, particularly [E.sup.H], first. Developers view ore grades within the aggregated stock, E = ([E.sup.H], [E.sup.L]), to decline continuously in quality (perhaps with one discrete jump). One issue in this paper concerns the ecosystem-economic conditions under which one may harmlessly model development decisions based on a generic index E for the nonrenewable stocks, such that development benefits may be condensed to C(E) as follows

C(E) = [C.sup.H] ([E.sup.H]), if E = ([E.sup.H], [E.sup.L]) [greater than] 0

= [C.sup.L]([E.sup.L]), if E = (0, [E.sup.L]).

This assumption or simplification is not implemented in the present analysis.

Here, wetland development benefits depend on the marginal rent functions times the number of acres or "ore units" ([d.sup.i]) developed from stock [E.sup.i] at any time: [C.sup.i]([E.sup.i])[d.sup.i]. For example, this development model represents a coastal economy with a finite stock of developable wetlands, while other locations provide a large supply of a perfect substitute, so marginal rents decline as local development proceeds.(6) Variation in rents could derive from a continuum of change either in the "wetness" of undeveloped wetlands or in their proximity to extant facilities, like tourist centers [4; 5].

Benefits from the renewable resource sector follow an analogous structure. Here the marginal net rent per unit harvested depends on an exogenous price, p, and the average cost of harvest, w(X), depends on the renewable stock ([w.sub.X] [less than] 0, [w.sub.XX] [greater than] 0).(7)

Then social utility equals the present value of net benefits (PVNB), including the value of development from nonrenewable stocks plus the value of harvest from the renewable stock:

PVNB [equivalent to] [integral of] [e.sup.-rt][[C.sup.H]([E.sup.H])[d.sup.H] + [C.sup.L]([E.sup.L])[d.sup.L] + (p - w(X))h]dt between limits [infinity] and 0, (1)

where the [d.sup.i], i = H, L, are the rates of development for each nonrenewable stock, h is the rate of harvest from the renewable stock, r is the social discount rate, and X, h, and the [E.sup.i] and [d.sup.i] depend on time. The resource manager strives to maximize PVNB in (1) by choosing efficient rates of development and harvest subject to productive capacities in each sector and to the ecosystem dynamics, including renewable resource impacts from nonrenewable resource use.

As shown below, the ecosystem-economic dynamics lead the manager to balance the rate of return to holding the nonrenewable stocks in their natural state versus the rate of return to development. As development of each nonrenewable stock proceeds, that stock declines

d[E.sup.i]/dt [equivalent to] [E.sup.i][prime] = -[d.sup.i], i = H, L, (2)

so that the nonrenewable habitat stocks provide less input to the natural rate of growth (or "recruitment") to the renewable population, F. The recruitment function F - the ecological production function - captures the ecosystem effects of developing each ore block; natural stocks of undeveloped ore affect the growth in X, net of harvest, over time:

dX/dt [equivalent to] X[prime] = F(X, [E.sup.H], [E.sup.L]) - h. (3)

The recruitment function is assumed concave in the resource stocks ([F.sub.XX] [less than] 0; [Delta]F/[Delta][E.sup.i] [equivalent to] [F.sub.i] [greater than] 0, i = H, L; also [F.sub.Xi] = [F.sub.iX] [greater than] 0, [F.sub.ij] [less than] 0, for all i = H, L and j = H, L; F(0, [E.sup.H], [E.sup.L]) = F([X.sub.max], [E.sup.H], [E.sup.L]) = 0; F [greater than] 0 requires X [greater than] 0 and [E.sup.i] [greater than] 0 for some i = H, L). (8)

For example, [E.sup.H] could represent shallow, near-shore estuarine (saltwater) wetland acres which are cheaper to develop than deeper estuaries, represented by [E.sup.L]; but within each estuarine type development costs [C.sup.i]([E.sup.i]) rise for each acre developed farther from dry land. Since emergent plants might dominate shallow estuaries and submergent plants might dominate elsewhere [29], each type could provide different inputs for renewable resource production, as represented in (3).

Finally, each sector's capacity to produce constrains the harvest or development rate:(9)

0 [less than or equal to] h [less than or equal to] [h.sub.max]; (4)

[d.sup.H] + [d.sup.L] [less than or equal to] [d.sub.max]; (5a)

0 [less than or equal to] [d.sup.i], i = H, L. (5b)

Here, [h.sub.max] represents the capacity of the fishing fleet while [d.sub.max] represents the capacity of developers. In addition, [d.sub.max] might also depend on the maximum rate at which a regulatory agency can issue permits to develop wetlands. The resource manager's task is to choose the [d.sup.i] and h in order to maximize PVNB (1) while satisfying the stock and ecosystem dynamics in (2) and (3), with non-negative stocks, and control constraints (4) and (5).(10)

Optimal Resource Allocation Rules

The intuition of the resource allocation rules is summarized immediately so that discussion may proceed to how nonrenewable grades and ecosystem concerns affect the optimal pattern of development and affect policy choices. Consistent with natural resource economic theory [7; 14] and capital theory [2], the necessary conditions(11) imply that each resource stock should be managed (harvested or developed) so that the rate of return to the remaining stock becomes equal to the social discount rate. Following Spence and Starrett [22], if the stock of natural capital exceeds the level that just earns the social rate of return, then the optimal strategy is to draw the stock down at the maximum economic (feasible) rate; if the stock is too low to earn the social rate of return, then the optimal strategy is to allow the stock to "recover" at the maximum economic (feasible) rate, so harvest or development of such stocks would be zero optimally. Since development and its ecological effects are irreversible, the nonrenewable stocks cannot "recover" from over exploitation. Thus, the rules for efficient allocation of resource stocks are:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where i = H, L; j = H, L; j /= i; [Z.sub.1] and [Z.sub.2] are Lagrangian shadow values on the upper and lower bounds on harvest rate from (4); and the asterisk (*) on resource stocks indicates the "singular" level of the stock. The singular stocks, [X.sup.*] and [E.sup.i*], are defined as the stocks that set the ratio on the right, in (6) and (7), equal to discount rate r; [X.sup.*] is defined by (6) conditional on E, while [E.sup.i*] is defined by (7) conditional on [E.sup.j] and X. The optimality of the harvest and development rates in (6) and (7) is discussed below. Note, however, that in (7) development of nonrenewable stock i depends on development of nonrenewable stock j.

Rules (6)-(7) rely on rates of return that depend on how marginal changes in the stocks affect the recruitment function F([center dot]), which is the sustainable ecological product. In (6), a marginal increase in breeding stock increases the sustainable harvest at rate [F.sub.X] and lowers the marginal cost of harvest at the rate [w.sub.X]/(p - w) per unit (F); here p - w is the net value of a unit of harvest or, equivalently, the opportunity cost of a marginal investment in X.(12) Then the ratio on the right in (6) is the rate of return to foregoing a marginal unit of renewable resource harvest in order to invest in breeding stock. In (7), the rate of return to preservation of stock [E.sup.i] is the ratio of the value of an increase in sustainable harvest due to preserving a marginal unit of [E.sup.i] over the opportunity cost of preserving that marginal unit; that is, the ratio is the rate of return to foregoing a marginal unit of development in order to hold the investment in nonrenewable inputs for the renewable resource. Note from (7) that the rate of return to preservation includes an adjustment for a delay in achieving the optimal target level of the renewable stock X which may arise from harvest sector constraints (4). Thus the value of preservation is diminished if the renewable stock is already above the current target ([X.sup.*]) since fishing capacity constrains the harvest ([Z.sub.1] [greater than] 0) and slows the approach to the target stock, while the preservation value is increased if the renewable stock X is below the manager's current target so that preservation speeds recovery of X([Z.sub.2] [greater than] 0).

Nonrenewable Resource Grade and the Optimal Pattern of Development

Standard nonrenewable resource theory [12; 16; 27] suggests that development proceeds with [E.sup.H] first. But the rates of return to development, in (7), depend on the economic consequences of its ecosystem impacts. We first review allocation of the renewable stock and then focus on the nonrenewable sector.

Renewable Resource Allocation. Conditional on [E.sup.H](t) and [E.sup.L](t) in (6), the resource manager targets the renewable stock at which the resource manager is indifferent between additional investment in X or additional consumption from X; i.e., at [X.sup.*] the marginal net benefit of harvest equals its marginal opportunity cost and investment in X earns the social rate of return, r. The efficient harvest rate, h, promotes the target value for X by allowing the renewable stock to grow at a maximum rate (h = 0) when current stock X is below [X.sup.*] or by drawing the renewable stock down at a maximum rate (h = [h.sub.max]) when the current stock X exceeds [X.sup.*]. When the current stock coincides with [X.sup.*], then the efficient harvest rate, h, is chosen to maintain X at [X.sup.*]; this harvest rate exceeds the instantaneously sustainable rate, F(X, [E.sup.H], [E.sup.L]), if at least one nonrenewable stock continues to decline.(13) These criteria for choosing h represent a "most rapid approach" policy [22], where the target stock, [X.sup.*], is dynamic.

Nonrenewable Resource Allocation. Characterization of efficient development rates ([d.sup.H], [d.sup.L]) relies on understanding (7) and the effects of stock dynamics on the terms in (7). We present implications of (7) intuitively.(14)

In general, the two nonrenewable stocks exhibit different rates of return to preservation. At time t, the manager's objective is maximized by preserving both stocks ([d.sup.H] = [d.sup.L] = 0) if both rates of return to preservation exceed r. However, if preservation earns a rate of return less than r for nonrenewable stock [E.sup.i], then development of that stock may be optimal, depending upon whether development of stock [E.sup.j] is optimal. The present value of resource use is maximized by first developing stocks with the lowest rate of return to preservation (if that rate is below r), since that condition implies the highest rate of social return to development. This allocation rule may counter the traditional intuition, since this rule may not allocate the least cost (highest benefit) ore [E.sup.H] to development first.

Denote the rate of return to the preservation of stock [E.sup.i] by [[Gamma].sup.i](i = H, L); [[Gamma].sup.i] represents the right side of (7). When development is optimal, the efficient choices are summarized, for i /= j, as follows:

(a) develop stock i if [[Gamma].sup.i] [less than] r and [[Gamma].sup.j] [greater than] r, so stock j is preserved ([d.sup.i] = [d.sub.max], [d.sup.j] = 0);

(b) develop stock i if [[Gamma].sup.i] [less than] [[Gamma].sup.j] [less than] r, preserving stock j in order to gain the most from development capacity [d.sub.max] (again [d.sup.i] = [d.sub.max], [d.sup.j] = 0);

(c) develop both stocks i and j if [[Gamma].sup.i] = [[Gamma].sup.j] [less than] r and development capacity is sufficient so that [d.sup.i] [greater than] 0, [d.sup.j] [greater than] 0, [d.sup.i] + [d.sup.j] = [d.sub.max] maintains [[Gamma].sup.i] = [[Gamma].sup.j].

These rules (a)-(c), with (7), ensure that the manager earns the highest social returns to development first, gaining the most net social value from development capacity [d.sub.max].

The anticipated pattern of development, beginning with the highest quality nonrenewable stock [E.sup.H] first, will only be clearly optimal if that stock is low quality as habitat. The quality of the nonrenewable resources as habitat depends on the ecosystem production function, represented here by the recruitment function F. If [F.sub.L]. [greater than] [F.sub.H], then the high quality nonrenewable stock is, in fact, the lowest quality (least productive) habitat resource for the renewable sector; in this case, [[Gamma].sup.H] is clearly smaller than [[Gamma].sup.L], since the marginal net return to preservation (numerator in (7)) is clearly larger for [E.sup.L] while the foregone development benefit for [E.sup.L] (denominator in (7)) is smaller. In that case, the greatest net return to development would derive from developing [E.sup.H] as rapidly as possible while preserving [E.sup.L]. However, if the productivity of [E.sup.H] as, for example, estuarine wetland habitat for fisheries, exceeds the productivity of [E.sup.L]([F.sub.H] [greater than] [F.sub.L]), then the rate of return [[Gamma].sup.H] to preserving [E.sup.H] may exceed the rate of return [[Gamma].sup.L]. In that case, development of stock [E.sup.L], which produces the lowest benefit within the development sector, may be optimal before development of [E.sup.H].

Then, if one is to simplify, harmlessly, the model for development by using a generic index E for quality, it must be the case that ecological conditions order the qualities of [E.sup.H] and [E.sup.L] opposite to their qualities for development, requiring [F.sub.L] [greater than] [F.sub.H]. This case seems unlikely to prevail. For example, drainage of wetlands may access fertile soils to create highly productive fields, but these same soils also make natural wetlands highly productive of unique vegetative habitats or foods for renewable resources, so [F.sub.H] [greater than] [F.sub.L]. Even when [F.sub.H] [greater than] [F.sub.L], development may appear to follow the usual "[E.sup.H] then [E.sup.L]" sequence, but we shall see that some dynamic circumstances may lead development to include an efficient overlap between development of [E.sup.H] and [E.sup.L].

Whether the reverse order of development (with [E.sup.L] first) is optimal depends on the marginal costs of increasing the sustainable harvest through preservation of the two stocks. These marginal costs are represented by

M[C.sup.i] [equivalent to] [C.sup.i]([E.sup.i])/[F.sub.i], i = H, L, (8)

i.e., the foregone development opportunity cost to preserve [F.sub.i] additional units of sustainable harvest. Differences in the net marginal benefits of development may imply that marginal cost M[C.sup.L] is lower than marginal cost M[C.sup.H], even when stock [E.sup.H] is the most productive habitat type. So, development of the high quality stocks first may still be optimal even when [F.sub.H] [greater than] [F.sub.L].

There is no reason to expect that an index of quality in the nonrenewable sector will also be a reliable index of quality for habitats in the renewable sector. The efficiency of developing high quality nonrenewable stocks first depends not only on the marginal net benefits from development but also on the ecological quality of the undeveloped nonrenewable stock. The renewable sector's demand (i.e., the environmentalist's demand) to preserve "critical" or "unique" habitats, despite high values for development, may be consistent with an economic efficiency argument that accounts for the productive value of ecological habitats.

However, an economist could err still if, after identifying which nonrenewable stock is of the highest quality for development from society's view, she goes on to ignore dynamics of the ecological-economic system. To see this point, consider an example: suppose that applied economic research shows that stock [E.sup.i] gives the highest net social return to development, so stock i is efficiently developed first. As development proceeds with [d.sup.i] [greater than] 0, the ecology of the renewable resource will alter the marginal productivity of both habitat stocks: the marginal productivity of the stock under development may rise as that habitat, and the ecological service it offers, becomes scarcer while the other habitat stock (which is being preserved) becomes relatively more critical to sustain the renewable resource (recall [F.sub.ii] [less than] 0, [F.sub.ij] [less than] 0 while d[E.sup.i] [less than] 0). Meanwhile the marginal benefit of further development from [E.sup.i] is declining.

These factors imply that the marginal cost M[C.sup.i] will tend to decrease as development proceeds, and furthermore, marginal cost M[C.sup.j] will also tend to decrease.(15) Moreover, as development of [E.sup.i] proceeds, the rates of return to preservation, [[Gamma].sup.i] and [[Gamma].sup.j], both may rise as the associated marginal cost tends to decrease. Thus, if the preservation of stock [E.sup.j] arises initially because preservation earns a higher rate than r(r [less than] [[Gamma].sup.j]), the incentives for preservation may increase even without development of [E.sup.j].

But consider an alternative case where [[Gamma].sup.i] and [[Gamma].sup.j] are both below r initially, so the efficiency conditions would permit development of both stocks subject only to the development capacity [d.sub.max]. Then two outcomes are possible, depending on the rate of change in marginal cost M[C.sup.i] relative to the rate of change in M[C.sup.j]. In the first outcome, the rate of return to preserving the stock that is currently under development, [[Gamma].sup.i], may rise quickly enough to become equal to its counterpart [[Gamma].sup.j], such that both remain below the discount rate. Then development rule (c) will apply and the optimal pattern of development would divide development capacity [d.sub.max] between both stocks, since under these conditions the stocks are of equal quality for development as judged from a social efficiency objective.(16) That is, after some time, both stocks may become of equal quality for development, based on the net social returns to development. However, in the second outcome, the rate of return [[Gamma].sup.j] to preserving [E.sup.j] may rise above discount rate r, so that despite the initial indications that [E.sup.j] could be efficiently developed given sufficient capacity, the stock [E.sup.j] is never actually developed since its return to preservation rises above r before its development begins. Thus, if conditions lead to initial development following rule (b) above, the dynamics of the ecological-economic system may move the system to rule (c), under which both stocks are developed some, or to rule (a), under which stock [E.sub.j] would be preserved. Of course, once [[Gamma].sup.i] rises to equal r, its development would cease according to (7) and the remaining nonrenewable stocks would be preserved. Clearly, the ecosystem and economic dynamics do not imply a permanent identification of the "best social grade" or "quality" for development.(17)

Thus, the manager always promotes development of the ore grade which produces the highest present value of marginal social rents. This ore grade will be the grade with low development costs only by chance. Given X = [X.sup.*] (so X satisfies (6) as an equality), an equilibrium occurs when the rates of return to preservation equal or exceed r([[Gamma].sup.i] [greater than or equal to] r, i = H, L).(18) Under these conditions, the resource manager lacks any incentive to reallocate additional renewable stocks toward consumption, while the social incentives promote preservation of the nonrenewable stocks.(19)

Figure 1 illustrates one example of possible stock trajectories in the nonrenewable sector, assuming X = [X.sup.*] (so [Z.sub.1] = [Z.sub.2] = 0); the curves labeled "[[Gamma].sup.i] = r" (i = H, L) define the target stock [E.sup.i*] conditional on [E.sup.j] and [X.sup.*]. Once a trajectory reaches region III [ILLUSTRATION FOR FIGURE 1 OMITTED], the rate of return to preserving both stocks cannot fall below r. Therefore, all points within or bordering region III represent potential equilibria. Trajectories a and d [ILLUSTRATION FOR FIGURE 1 OMITTED] illustrate cases where initial preservation of one stock is temporary and, after some development of the other stock, the rates of return to preservation may become equal and optimal development may exploit both stocks. Trajectories b and c [ILLUSTRATION FOR FIGURE 1 OMITTED] illustrate cases where, given initial stocks, optimal development exploits only one stock, either [E.sup.H] in case b or [E.sup.L] in case c.

Returning to the case of coastal zone management, the optimal policy may be to preserve a stock of each type of estuarine wetland habitat. However, under some conditions [ILLUSTRATION FOR FIGURE 1 OMITTED], exhaustion of one or both stocks may be efficient. For example, a high discount rate would be more likely to exceed the rates of return to preservation.

In a nonlinear model, development of each nonrenewable stock proceeds if the rate of return to preserving the first unit of that stock is below r so that some positive rate of development balances the benefits of development against losses in renewable resource production. Otherwise, the results remain qualitatively similar to those presented here. For example, consider the implications for Figure 1. A model which is nonlinear in the nonrenewable sector produces stock trajectories similar to those in Figure 1 except in quadrant I. For example, trajectories analogous to trajectory d would curve in quadrant I so that the development rate [d.sup.L] is high relative to [d.sup.H]; similarly, trajectories analogous to trajectory a would curve in quadrant I so [d.sup.H] is high relative to [d.sup.L].

III. Ecosystem Economic Role of Developed Habitats

Like earlier models, the preceding model assumes that profits motivate developers to convert nonrenewable (wetland) resources to the highest-valued use. However, in an ecosystem-economic context, this assumption may mislead policy assessments because the ecological role of nonrenewable resources in the developed state affects social value.

For example, consider the case of "pocosin wetlands," which are freshwater wetlands found in the coastal plains of many southern states. Alternative uses of pocosin wetlands include row-crop agriculture and intensive forestry. In North Carolina, for example, scientists report that pocosin wetlands regulate drainage of rainwater in a manner that protects estuarine wetlands from a sudden drop in salinity. Salinity changes can greatly reduce recruitment of young shrimp. Thus, rather than direct loss of fish habitat, it is the loss of the hydrologic functions of pocosin wetlands that affects fisheries.(20) Since agriculture manipulates land more intensively and continuously than does forestry, these developed uses compromise the hydrologic function to different degrees.

These ecosystem concerns may be captured by modifying model (1)-(5) to permit a choice among one of two developed uses. Development of stock [E.sup.i] will return benefits depending upon its allocation to these uses, leading to a simple generalization of PVNB:

[Mathematical Expression Omitted]

where i ranges over H, L and uses u range over A, F (e.g., agriculture, forestry), [C.sup.iu]([E.sup.i]) is the marginal net benefit of developing a unit of [E.sup.i] for use u, and [d.sup.iu] is the rate of development of stock i for use u.(21) Since developed uses, agriculture or forestry, have different impacts, the model must track the stock of developed land, [D.sup.u], of type u(u = A, F), which adds two straightforward state-transition equations, while depletion of nonrenewable stocks now depends on rates of development for both uses, leading to an obvious modification of (2). Of course the ecosystem impacts arise through a modified recruitment function, so

F(X, [E.sup.H], [E.sup.L]) [implies] F(X, [E.sup.H], [E.sup.L], [D.sup.A], [D.sup.F]), (10)

with [F.sub.u] [equivalent to] [Delta]F/[Delta][D.sup.u] [less than] 0; [F.sub.iu] [greater than] 0; i = H, L; u = A, F. The development rates are still non-negative and constrained by capacity of the sector.

Now, however, the rate of return to preserving each stock [E.sup.i] depends upon the ecological effect of the use to which developers convert nonrenewable wetlands:(22)

[[Gamma].sup.iu] [equivalent to] [p - w(X) - [e.sup.rt]([Z.sub.1] - [Z.sub.2])]([F.sub.i] - [F.sub.u])/[C.sup.iu]([E.sup.i]), i = H, L; u = A, F. (11)

In general, the social rate of return to preservation now depends upon the use-dependent marginal cost of maintaining sustainable harvests,

M[C.sup.iu] [equivalent to] [C.sup.iu]/([F.sub.i] - [F.sub.u]); i = H, L; u = A, F. (12)

where the preservation of stock i increases sustainable harvests by [F.sub.i] - [F.sub.u] units, which explicitly captures the ecological (production) effect of preserving a unit of habitat [E.sup.i] that would have been converted to non-natural habitat [D.sup.u]. Note that we assume [F.sub.i] - [F.sub.u] is nonnegative, which was implicit in section II where only one use was considered.

Again, efficient development will only convert nonrenewable resources if their rate of return to preservation falls below the discount rate r. However, the alternative uses now create two possible rates of return to preserving stock i, so development rules (a)-(c) need modification. The most rapid approach path and the maximum principle lead to the rule that efficient development only involves those combinations (i, u) of resource stocks i and developed-uses u such that

[[Gamma].sup.iu] = min{[[Gamma].sup.HA], [[Gamma].sup.HF], [[Gamma].sup.LA], [[Gamma].sup.LF]}, with min{[[Gamma].sup.HA], [[Gamma].sup.HF], [[Gamma].sup.LA], [[Gamma].sup.LF]} [less than] r. (13)

Those i-u combinations that satisfy (13) will produce the highest rate of return to development, since their rate of return to preservation is lowest and below r. If only one i-u combination satisfies (13), then stock i is developed for use u at the maximum rate ([d.sup.iu] = [d.sub.max], [d.sup.jv] = 0 for all u, v when j /= i and all i, j when v /= u).

However, increments in development tend to cause the marginal cost M[C.sup.iu] to decrease, so that the rate of return [[Gamma].sup.iu] tends to rise as development proceeds. This dynamic stock effect may cause [[Gamma].sup.iu] to rise to equal the rate of return [[Gamma].sup.jv] while both are still less than discount rate r.(23) Then optimal resource use may involve development of more than one stock, with developed units allocated between more than one use.

If more than one i-u combination satisfies (13), then development capacity is distributed among them so that, as developers convert natural stocks to developed stocks, the rates of return to those i-u combinations remain equal. For example, if

[[Gamma].sup.HF] = [[Gamma].sup.LA] = min {[[Gamma].sup.HA], [[Gamma].sup.HF], [[Gamma].sup.LA], [[Gamma].sup.LF]} [less than] r,

then development capacity is allocated so that [d.sup.HF] + [d.sup.LA] = [d.sub.max] and so that development maintains the equality across these rates of return.

These results, despite their intuitive appeal, appear to be unrecognized in both the theoretical and applied literature. The results show that optimal development policies may involve more developed-uses than developers would prefer. That is, within an ecosystem economic context, the highest-valued use that developers propose for nonrenewable (wetland) habitats may not be the highest-valued use from a social perspective. Moreover, no single use may be considered "highest-valued" since the ecosystem functions of natural and developed habitats may create circumstances where a given habitat-type (say [E.sup.i]) is best allocated to one use, while another habitat-type is best allocated to another use. Finally, ecosystem-economic dynamics imply that identification of the highest-valued use for a nonrenewable habitat stock may change as development proceeds and rates of return to different stock-use combinations become efficient, including the possibility that one stock may be allocated to more than one developed-use.

IV. A Case Example of Preservation Values

These resource-theoretic insights arise in applied efforts to estimate the value of natural wetlands. This section discusses an example involving agriculture, forestry, pocosin wetlands, and estuarine dependent fish, especially shrimp, in Pamlico Sound on the north portion of North Carolina's coast. The discussion relies on and modifies an applied study by Swallow [26]; that study does not develop the theoretical results above.(24)

In this case, the "grade" or "quality" of wetlands may correlate with geographic location, with more westerly locations being of higher value to developers desiring access to inland transportation networks. Pocosins at these westerly locations may also play a more critical ecological role, since the nearby estuarine wetlands are further from natural pathways for undiluted saltwater which might maintain estuarine salinity in the absence of natural pocosins.(25) For this discussion, both the development sector and the fishery sector view the same (western) wetlands as "high" quality.

This application uses shrimp as the key species since the shrimp fishery dominates Pamlico Sound. Shrimp are characterized by independent generations [32] due to their high fecundity and, in North Carolina, their arrival in the estuary via ocean currents that carry larval shrimp from a world breeding center (Swallow [26] reviews the biological literature). With independent generations, one may estimate rents in the renewable fishery sector using a single-period optimization model [32, 96]. Of course, the stocks of nonrenewable habitats (i.e., pocosin wetlands that buffer estuarine nursery) determine the survival of larval immigrants to Pamlico Sound and, thereby, establish the dynamic link between renewable and nonrenewable sectors. Then the objective function may be simplified:

PVNB = [integral of] [e.sup.-rt][[[Sigma].sub.i][[Sigma].sub.u][C.sup.iu]([E.sup.i])[d .sup.iu] + (p - w(X))[h.sup.*](X)]dt between limits [infinity] and 0 (14)

where [h.sup.*] arises from the single-period optimization model in which X = X([E.sup.H], [E.sup.L], [D.sup.A], [D.sup.F]) at time t, with [E.sup.H] representing westerly pocosins and [E.sup.L] representing easterly pocosins.

Defining a single period as one year, fishery rents were simulated with an optimization model that assumes that shrimp production follows a Cobb-Douglas production function with environmental inputs represented through an index of the shrimp population, denoted [X.sup.fb], and the number of standardized craft-days (boat-days) of fishermen's effort in Pamlico Sound, denoted L. The Pamlico Sound industry is considered a price-taker [30]. For an average year (based on 1978 to 1986 data), production was simulated on a weekly basis, using weekly prices and effort-costs for Pamlico Sound based on exogenous seasonal trends and an index of the national market price for shrimp. The simulation was conducted on the assumption that regulation in Pamlico Sound would establish conditions of efficiently restricted access. This simulation and optimization model estimated the shrimp fishery benefits as the value of profit maximizing harvests using a Cobb-Douglas harvest technology, represented by

(p - w(X))[h.sup.*](X) [equivalent to] [Pi]([X.sup.fb]) [equivalent to] (1 - [Beta])[(pk([X.sup.fb]).sup.[Psi]]).sup.(1/1-[Beta])][([Beta]/[w. sub.L]).sup.([Beta]/1-[Beta]) (15)

where the production function is

h = k[([X.sup.fb]).sup.[Psi]][L.sup.[Beta]]

where k is a constant, [Psi] is the elasticity of shrimp harvest with respect to the population index, [Beta] is the elasticity of harvest with respect to fishermen's labor L, [w.sub.L] is the cost of a unit of labor (cost of a craft-day), and [Pi] represents economic profits.(26) Swallow [26] linked the shrimp index [X.sup.fb] to pocosin wetlands using least squares regressions between [X.sup.fb], estuarine salinity, and data on landuses adjacent to the estuary; using hydrological and ecological data, these regressions established an empirical model for X = X([E.sup.H], [E.sup.L], [D.sup.A], [D.sup.F]).

This empirical model allows us to evaluate the "preservation value," denoted [V.sup.iu], of preserving an acre of pocosin wetlands of type i rather than developing it for use u. Thus, we focus on [V.sup.iu], which is the numerator of the use-dependent rate of return to preservation in (11), using the empirical analog:(27)

[TABULAR DATA FOR TABLE I OMITTED]

[Mathematical Expression Omitted]

Table I lists the annual value [V.sup.iu] of preserving pocosin wetlands when the developed-state would allow forestry (u = F) or agricultural (u = A) uses. The issue at hand, however, is how these values might differ from the naive approach, where an analyst ignores both quality of wetlands and their potential allocation to different uses, implicitly assuming [V.sup.iu] = V, for all i, u. Using Swallow's data and methods, one can derive the common "naive estimate,"(28) ignoring habitat quality of both natural and developed wetlands. The naive estimate, $0.391/acre/yr, differs by up to a factor of nine from the estimated values that recognize the ecosystem-economic dimensions (Table I). Moreover, the naive value may not represent well the value of an "average" acre, differing, for example, by more than a factor of two as compared to the weighted-average preservation value for pocosins developed for agriculture (Table I). In the empirical mathematics, these differences arise due to the ecology-induced, non-linearity in estimating the value of an acre, so the value of an average acre differs from the average value of an acre.

Clearly, these differences are sufficient to affect public policy. For example, current wetland policy in coastal North Carolina is motivated, in large part, by local concerns that agricultural development may substantially diminish productivity of critical fisheries. Current policy nearly prohibits development of any pocosin wetlands, yet it appears that forestry development on some types of wetlands may not lead to a loss in fishery values. Policy-makers' (nearly) absolute ban on wetland development originates from ecological concerns with the impacts of agriculture, yet that policy may well deserve re-evaluation given that some wetlands may play a less valuable ecological role and some developed-uses may generate smaller fishery losses. Applied models that consider the ecosystem effects of quality differences of both the natural wetlands and the wetlands in their developed state will clarify economic differences among development options. In coastal North Carolina, any misguided policy toward wetlands would bear directly on the quality of life for the local, broadly underprivileged rural communities.

V. Conclusions and Implications

This paper shows that ecological interactions among renewable and nonrenewable resources may invalidate commonly accepted, intuitive implications of standard nonrenewable resource theory. Specifically, ecosystem-economic policy is unreliable if based upon assumptions that either developing least cost (highest quality) ores first or allocating those ores to the most profitable use are consistent with optimum social value. Preservation of "highest quality" habitat or restriction of "most damaging" developed-uses depends on marginal costs and rates of return in social value for each class of the nonrenewable resource. An empirical example involves irreversible development of nonrenewable wetlands important to renewable fisheries. Empirical results show analysts may misjudge the social value of wetlands, by substantial margins (factors over eight), if wetland quality or the developed-state landuse is ignored.

The scope of the implications extends to national policy concerning economic use of natural ecosystem resources. Recent studies have considered the market implications of wetland policy [24] and welfare effects of those policies [23] as well as the budgetary costs to achieve target acreages for wetland restoration [18]. Yet these studies could not consistently associate wetland values with quality differentials or with anticipated developed-state landuses; rather, the studies follow assumptions based on standard capital theory for natural resources. Without a fuller assessment of ecosystem effects, the guidance that such empirical economic analyses offer must be viewed cautiously, at least. The issue is not trivial since government policy to alter landowners' incentives toward wetlands may involve millions of acres [24] and the cost of achieving federal targets for some wetland preservation programs may exceed one billion and approach two billion dollars [18].

Empirical policy models may be able to take advantage of this theory, even with currently available economic and ecological data. For example, Stavins' [23; 24] model is rich enough to allow variation in wetland values across geographic and temporal dimensions. These dimensions could be used, with an understanding of the ecosystem-economic dynamics, to simulate changes in wetland values that might occur as acres of various quality are developed.

The implications of ecological interactions among natural resources also challenge the fundamental approach by which government regulates uses of these resources. Regulations often require developers to offer proposals concerning specific resources, such as a wetland site, and specific uses, such as agriculture or forestry. For example, as part of an application for a wetland development permit under section 404 of the Clean Water Act, an economic analysis may be included in an "environmental impact statement" which, in concept, could determine whether the proposed development meets a benefit-cost test. While the permit review may assess some alternatives, the review usually restricts attention to alternative "levels" of the proposed development. The developer's proposal drives the regulatory process, so that the developers' perspective tends to drive the identification of "quality" resources (sites) to develop and "most beneficial uses" to permit. The ecosystem interactions modeled here show a need to evaluate development proposals not only for the economic choice of uses for specific resources but also for the economic choice of resources (or sites) to be developed. Current regulatory reviews are deficient, unable to address completely the ecosystem-economic implications of natural heterogeneity.

For example, the review process could call for other entrepreneurs to propose developing the site for alternative uses, as well as calling for proposals to develop alternative sites for the proposed use. Furthermore, such a call for proposals, while still based in regulation rather than market incentives [1], may create a more efficient means by which the system could account for the dynamic evolution of resource values, because the entrepreneurs who respond would do so based on the current-period net values for development of alternative grades.

Still, these implications add to economists' concerns regarding the efficiency of bureaucratic approaches to controlling resource uses [1]. For example, a sufficiently rich set of incentives, that recognizes wetland quality and developed-state impacts, may relieve some bureaucratic costs of reviewing developers' proposals so comprehensively. The simulation approach of Stavins [23; 24] could be readily adaptable, using intuition from an ecosystem-economic theory, to determine such a set of incentives for practical wetland policy.

Policy toward wetland development is but one example of where ecological interactions may confound the intuition from capital theory. Indeed, the Stavins and Jaffe [24] model of wetland development has inspired a cost assessment for policy toward global warming [19]. Thus, a capital theory for heterogeneous ecological resources may improve the scope of a wetland development model, which then may improve cost assessments of global warming policy. For another example, one may review analyses of the oil industry's Trans-Alaska Pipeline, from the mid-1970s, to see evidence that alternative uses for shipping ports (e.g., oil tanker's potential toxic impacts versus more benign fishing fleets) and alternative routes for the pipeline (e.g., a Trans-Canada route) offered potential divergences between the interests of the oil development sector, the renewable resource sectors, and the social value of environmental impacts [6, especially 116-122]. A more complete capital theory for ecological-economic interactions may have better informed the pipeline-policy issues.

One final example deserves elaboration. Consider the additional development of energy resources in the far north where development may damage habitat that is important to renewable resources, such as Arctic caribou, from which native communities traditionally harvest food. In Alaska, oil companies commonly argue that impacts affect a small percentage ([less than] 2%) of Arctic tundra. Economists may quickly argue that quantity, not percentage, is the relevant basis of impact, while ecologists note that not only quantity but also "which units" of tundra is also relevant. Meanwhile, native communities suggest that additional development may alter their subsistence lifestyle to a differing degree than past development. Both quantity and "which units" are elements of a complete economic analysis, as is the dynamics of cumulative conversions of productive nonrenewable habitats. Economists most consider ecological heterogeneity (i) whenever it implies that the quality of a nonrenewable resource for a developed use is positively correlated with its quality in production of renewable ecological services or (ii) whenever it implies that the most profitable developed-use is positively correlated with the degree of ecological impact.

This paper strives to contribute three points to the mainstream user of economic theories of renewable and nonrenewable resources: (i) ecosystem interactions suggest defining the quality of resource grades from a social perspective, rather than from the developer's perspective; (ii) ecosystem interactions suggest identifying "best-use" for each grade from the social perspective as well; and (iii) the concepts of quality and "best use" may be dynamic, not depending upon any physiographic index of quality, but rather depending on the contemporaneous contribution to renewable ecosystem goods in both the natural and the developed states. This last point, on the implications of dynamics, is especially challenging for policy analysts since their identification of resource grades and of best uses for each grade may require re-evaluation on a continual basis. All these points may be as simple and intuitive as the insights from standard theories of independent renewable or nonrenewable resources [7; 12; 14], but this intuition remains absent in otherwise rigorous policy assessment models [18; 24] affecting millions (or billions) of acres and billions of dollars. As government increasingly addresses ecosystem-economic issues, economic intuition requires adaptation if policy assessments are to promote efficiency through regulation or market incentives.

1. Notable extensions for nonrenewable resources include Schulze [21], Swierzbinski and Mendelsohn [27], Hartwick [12], and Heal [13]. Similar extensions for renewable resources include Clark, Clarke, and Munro [8], Tahvonen [28], van der Ploeg and Withagen [31], Wilen [32].

2. Even if ecological functions may be simulated or partially rehabilitated, most likely some ecosystem functions are inadequately understood, thereby limiting design of minimum-impact development methods or the technology for environmental rehabilitation [9], or, if a feasible rehabilitation/protection technology exists, it may be economically prohibitive, in the spirit of Krutilla [15].

3. Swallow's [25] nonrenewable resource rents depend on the stock of remaining ore [16; 27], but that analysis does not question the intuition of extracting "least cost first" [12] or consider the effect of "ore" quality from the ecosystem perspective.

4. The model is linear in controls, consistent with highly successful policy frameworks, like Stavins and Jaffe [24] and Parks and Kramer [18]. A review of how traditional renewable and nonrenewable resource literature relates directly to this model is available from the authors upon request. The present focus is on the economics of ecosystem management.

5. This assumption will highlight some ecosystem-economic results because it eliminates the need to discuss whether those results are driven by Hartwick's [12] "more complicated" cost function where the extraction costs of one deposit of ore may rise to that of another deposit of ore. Hartwick's social planner may optimally extract from two deposits simultaneously, but the planner still extracts the least-cost (highest grade) units first. Since a (social) opportunity cost of extraction from each stock may rise relative to another stock, the effective social extraction-cost function will generate the possibility of efficient extraction from two ores with different private extraction costs, even though Hartwick's more-complicated private cost function is excluded.

6. This model implies that a close substitute for E is readily available at a high but constant "backstop" extraction cost [13] or that the price of extracted ore rises more slowly than do marginal extraction costs, where the backstop cost provides an upper bound on price. Swallow's [25] model indicates modifications needed if development benefits are nonlinear in [d.sup.i]. Swierzbinski and Mendelsohn [27] confirm that the remaining stock indexes extraction costs [21], as [C.sup.i]([E.sup.i]) suggests here.

7. Subscripts on functions denote partial differentiation of the parent function with respect to the subscript variable.

8. These assumptions imply the implicit function [X.sub.max] = [X.sub.max]([E.sup.H], [E.sup.L]), with [X.sub.max](0,0) [greater than or equal to] 0, [Delta][X.sub.max]/[Delta][E.sup.i] [greater than] 0. If [X.sub.max](0, 0) = 0, then F(X, 0, 0) [less than or equal to] 0 as X [greater than or equal to] 0. The alternative, with [X.sub.max](0, 0) [greater than] 0, is left for the reader to analyze and implies F(X, 0, 0) [greater than] 0.

9. These constraints also keep the mathematics intuitive, following Spence and Starrett [22], without affecting the main results. The maximum rates remain consistent with malleable capital of fixed availability [8]. A model with nonlinearity in controls [25] determines maximum rates through declining marginal net returns, but it adds little of interest to the ecosystem-economic issues here.

The discussion assumes [Mathematical Expression Omitted] where [X.sub.MSY] maximizes F given the initial nonrenewable stocks. This assumption avoids the aberrant case where fishing capacity alone is insufficient to draw down a supra-optimal fish stock.

10. Let [Mathematical Expression Omitted] be the nonrenewable stock below which profitable opportunities in the nonrenewable sector no longer exist (i.e., [C.sup.L](E) = 0 for [Mathematical Expression Omitted]) and let [X.sub.[infinity]] be the renewable stock below which harvesting ceases (p- w([X.sub.[infinity]]) = 0; [7]). A model in strict agreement with Heal [13] would assume [Mathematical Expression Omitted] is zero. The present model allows the nonrenewable stock to include units whose development costs exceed that of the abundant perfect substitute. In the discussion, only [Mathematical Expression Omitted] is positive, and [Mathematical Expression Omitted], an assumption which allows a convenient theoretical analysis without affecting the key results. However, some applications might involve [Mathematical Expression Omitted], necessitating changes in detail (drawing on Hartwick [12]).

11. Mathematical details are in an Appendix, available upon request.

12. These terms yield a solution for [X.sup.*] (see section II) that is structurally similar to that in Clark and Munro [7] for constant E and in Swallow [25] for an undifferentiated nonrenewable stock E.

13. If [E.sup.i][prime] [less than] 0, then d[X.sup.*]/dt [less than] 0 so that an efficient h, [h.sup.*], must equal F + [absolute value of d[X.sup.*]/dt], following Swallow [25]. For example, d[X.sup.*]/dt = -([Delta][X.sup.*]/[Delta][E.sup.i])[d.sup.i] if only [d.sup.i] [greater than] 0.

14. A technical presentation is available in an Appendix from the author.

15. The direct effects of development are measured by [Mathematical Expression Omitted], where k = i, j and [Mathematical Expression Omitted]. However, development causes a feedback through the ecology of the renewable resource, since development diminishes the marginal return to holding X. Including this indirect feedback, [Mathematical Expression Omitted], where the additional term causes an indeterminate sign on [Delta]M[C.sup.k]/[Delta][E.sup.i], since [F.sub.ki] [less than] 0 but [F.sub.kX] [greater than] 0 (and [Delta]X/[Delta][E.sup.i] [greater than or equal to] 0 since additional habitat leads to higher recruitment at time t). Then the direct effect decreases M[C.sup.k]([Delta]M[C.sup.k]/[Delta][E.sup.i][where]x [greater than] 0 with d[E.sup.i] [less than] 0 during development) while the ecological feedback may offset this tendency. Since [p - w(X) - ([Z.sub.1] - [Z.sub.2])[e.sup.rt]] is common to [[Gamma].sup.i] and [[Gamma].sup.j], comparison of [Delta]M[C.sup.i]/[Delta][E.sup.i] and [Delta]M[C.sup.j]/[Delta][E.sup.i] determines whether [[Gamma].sup.i] = [[Gamma].sup.j] occurs before [[Gamma].sup.i] reaches r ([Delta][[Gamma].sup.k]/[Delta][E.sup.i] = -[w.sub.x]/[[Delta]M[C.sup.k]/[Delta][E.sup.i]]). The discussion assumes that [Delta]M[C.sup.k]/[Delta][E.sup.i] [greater than] 0 for k = H, L and i = H, L.

However, changes in the renewable stock could also affect the dynamics here. For example, M[C.sup.k] rises and [[Gamma].sup.k] tends to fall if X decreases tends to fall if X decreases ([Mathematical Expression Omitted] with dX [less than] 0 and recalling [Delta][[Gamma].sup.k]/[Delta]X = -[w.sub.X]/[[Delta]M[C.sup.k]/[Delta]X] [greater than] 0). These factors affect whether development, once begun, is efficiently continued without interruption, a question addressed previously by Swallow [25] for undifferentiated E.

16. Capacity would be divided to maintain [[Gamma].sup.i] = [[Gamma].sup.j] with [d.sup.i] + [d.sup.j] = [d.sub.max], for i /= j. If these conditions cannot be met simultaneously, then development would cycle between the two stocks, alternating which stock is developed (instantaneously) at the maximum rate.

17. The case where ecology causes [F.sub.H] [greater than] [F.sub.L] sometimes and [F.sub.L] [greater than] [F.sub.H] sometimes is a hybrid of the cases discussed here.

18. If X [greater than] [X.sup.*] initially, then preservation of one or both nonrenewable stocks may be optimal initially while harvest draws down the renewable stock. However, this initial preservation policy may be temporary for one or both nonrenewable stocks since one expects the value of a marginal unit of sustainable harvest (the numerator of each [[Gamma].sup.i], i = H, L) to decline as the renewable stock declines, so that renewable harvests may cause [[Gamma].sup.i] to fall below r. Also note that the optimality conditions for the constrained Hamiltonian of this problem imply p - w(X) [greater than or equal to] [e.sup.rt][Z.sub.1] since the adjoint variable on X must be non-negative (a math Appendix is available upon request).

19. The equilibrium may he unstable if one or both of the opportunity costs of development remains strictly positive. Swallow [25] discusses this point further in a model with [F.sub.H] = [F.sub.L] and a general, Hotelling-type nonrenewable resource sector.

20. See the review and references in Swallow [26].

21. Conceptually, developers may sell units for one use at a premium over the other use (e.g., [C.sup.iA] - [C.sup.iF] = k [greater than] 0), so that marginal development costs would be equivalent and [Delta][C.sup.iA]/[Delta][E.sup.i] = [Delta][C.sup.iF]/[Delta][E.sup.i]. For example, initial development of wetlands for either agriculture or forestry may involve clearing existing vegetation and installing a set of primary drainage canals.

22. The allocation rules in the renewable resource sector rely on an equation analogous to (6) but using (10). The harvest rate is determined as in the earlier model.

23. Recall [F.sub.ii] [less than] 0, [F.sub.uu] [greater than] 0, so [F.sub.i] - [F.sub.u] will increase as development proceeds. Since [Mathematical Expression Omitted], the effect of development is to decrease M[C.sup.iu] (since [E.sup.i][prime] [less than] 0). Similar effects occur for the other marginal costs (with [F.sub.ij] [less than] 0), so these may also decrease. Therefore, the dynamic effects imply that development of any stock for any use may cause all rates of return to preservation, the [Gamma]s, to increase.

24. Historically, developers have converted pocosin wetlands to agricultural uses, but recently developers have proposed forestry uses. Richardson and Gibbons [20] report the largest change in private-sector ownership of pocosin wetlands since about 1978 is a massive transfer from agricultural firms to forestry firms. Estuarine-dependent species comprise over 90% of U.S. fish harvests; shrimp comprise over 25% of total harvest from coastal North Carolina where over 140 estuarine-dependent species are harvested.

25. Pocosins cover much of the Pamilico-Albemarle Peninsula, which forms Pamlico Sound estuary behind North Carolina's barrier islands. Inlets through these islands allow ocean water to regulate salinity in the eastern portion of the estuary, but the western portion may be 50 or more miles from open ocean and be sensitive to influx of freshwater.

26. The Cobb-Douglas formulation involved 0 [less than] [Psi] [less than] 1 and 0 [less than] [Beta] [less than] 1. Swallow's [26] estimation imposed a restriction that [Psi] + [Beta] = 1, which an F-test failed to reject. [X.sup.fb] was the index measured for each year of data, while L and h were weekly data on effort and harvest. Then (15) is the sum of profits over the weeks in the season.

This empirical formulation departs from the theoretical model since it does not imply linearity in the harvest rate. However, generalizing the fishing sector to allow for nonlinearity adds to the mathematics in the earlier sections without altering the main conclusions.

27. The independent generations model allows us to dispense with the constraints on the harvest rate, since these are satisfied by the single-period optimization model. Therefore, [Z.sub.1] = [Z.sub.2] = 0 in (11) and the remaining terms in (16) correspond to the numerator in (11) with (15), specifically corresponding to [p - w(X)]([F.sub.i] - [F.sub.u]).

28. In Swallow's [26] analysis, [X.sup.fb] is a function of salinity ([X.sup.fb] = [g.sub.1] (SAL)), while salinity (SAL) is a function of landuses, SAL = [g.sup.2]([E.sup.H], [E.sup.L], [D.sup.A], [D.sup.F]). The landuses include the proportion of land in pocosins (WETLAND) of each type (WETLAND and WETLAND x SESHORE, where the latter represents an interaction with a dummy variable, SESHORE, with SESHORE = 1 for easterly wetlands when i = L and SESHORE = 0 for westerly wetlands when i = H) and the proportion of land in developed uses (AGRIC and FOREST, for u = A and u = F). Then, empirically, SAL = [g.sub.2](WETLAND, WETLAND x SESHORE, AGRIC, FOREST).

To obtain the "naive" estimate, the pivotal "salinity (SAL) regression" in Swallow [26] is changed to SAL = [g[prime].sub.2] (WETLAND) as follows

[Mathematical Expression Omitted]

where s.e. is in parentheses, DYRnn is dummy variable for year 19nn, RAIN10 measures recent rainfall, SESHORE accounts for proximity of sample-sites to ocean inlets (see n. 25), and WETLAND is the proportion of land, near the salinity-sampling site, that remains as pocosin wetlands. Note that the interaction variable, WETLAND x SESHORE, and the landuse variables, AGRIC and FOREST, are omitted in this naive specification.

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