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

• Author: Swallow, Stephen K.

1. 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.

2. 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]...