The role of technological change

We develop an optimal growth model that includes several important new features. First, technological change is endogenously related to the growth of “knowledge.” Investment may be directed either towards physical capital or knowledge (or both). Knowledge becomes an effective substitute for scarce resources by increasing the technical efficiency of resource utilization both for consumption and in capital. Nevertheless, a finite quantity resource must be embodied in capital and a finite flow is required for depreciation. Thus, there is an upper limit to technical efficiency and economic growth is thus ultimately limited by the availability of renewable resources. For a simple aggregate production function it is shown that technical efficiency never approaches unity on an optimal path.     

Decentralized regulation of a common property renewable resource industry with irreversible investment

The effectiveness of output controls for rationalizing a common property renewable resource has been called into question by the theoretical work of J. R. Gould [Economica, Nov., 383–402 (1972)]. A proper examination of this question requires an intertemporal analysis, one that takes into account that asymmetries between persistent factors of production (“immaleable capital”) and factors that are instantaneously consumed (“labor” or ldharvest effort”). We present here a nonlinear intertemporal model of a renewable resource industry, under conditions of irreversible capital investment, and undertake to analyze its dynamics, both at open access and under centralized optimal management. We then examine the theoretical possibility of decentralized regulation by Pigouvian taxes, and reconsider the proposition of Gould.     

Control theory applied to natural and environmental resources an exposition

Four control theory models of natural and environmental resource use, drawn from the existing literature, are developed in a manner to emphasize their technical and decentralized interpretive similarity. Renewable, nonrenewable, and amenity resource use are treated as closely related problems of optimal (biological, earth material, ecological, or environmental) capital allocation over time. Thus nonrenewable resources, and the problem of exhaustion, are just limiting (zero growth) cases of renewable resources, and the problem of species extinction. Just as exhaustion can be optimal, extinction can be optimal. Waste recycling is treated as part of the problem of optimal regeneration of “sclean” environmental capital; wilderness use as a problem of managing the regeneration of ecological capital.     

The optimal use of non-renewable resources: The theory of extraction

The traditional theory of exhaustion is revised to allow for long run capital mobility. This model is extended to include the impact of cumulative environmental damages on the optimal path of resource use. Models and optimal markets are then analyzed for cases where minerals are available over a continuum of quality and where recycling ameliorates inevitable exhaustion of non-renewable resources. Finally, the impact of technological change on long run trends in mineral prices is examined.     

Putting free-riding to work: A Partnership Solution to the common-property problem

The common-property problem results in excessive mining, hunting, and extraction of oil and water. The same phenomenon is also responsible for excessive investment in R&D and excessive outlays in rent-seeking contests. We propose a “Partnership Solution” to eliminate or at least mitigate these excesses. Each of N players joins a partnership in the first stage and chooses his effort in the second stage. Under the rules of a partnership, each member must pay his own cost of effort but receives an equal share of the partnership's revenue. The incentive to free-ride created by such partnerships turns out to be beneficial since it naturally offsets the excessive effort inherent in such problems. In our two-stage game, this institutional arrangement can, under specified circumstances, induce the social optimum in a subgame-perfect equilibrium: no one has a unilateral incentive (1) to switch to another partnership (or create a new partnership) in the first stage or (2) to deviate from socially optimal actions in the second stage. The game may have other subgame-perfect equilibria, but the one associated with the “Partnership Solution” is strictly preferred by every player. We also propose a modification of the first stage which generates a unique subgame-perfect equilibrium. Antitrust authorities should recognize that partnerships can have a less benign use. By organizing as competing partnerships, an industry can reduce the “excessive” output of Cournot oligopoly to the monopoly level. Since no partner has any incentive to overproduce in the current period, there is no need to deter cheating with threats of future punishments.     

How deep is the footprint? A 3D representation

Depletion of natural capital stocks and use of natural capital flows are the central issues in the sustainability debate. Differentiation of these two components, considering natural capital and its limits, is important for planning and management of land use. This paper offers insights into this issue and proposes a new perspective of the Ecological Footprint (EF) in three dimensions, considering not only its size but also its depth: according to this viewpoint the footprint is not an area but a volume, although maintaining the same value as the one in two dimensions. Use of annual flows provided by the Earth is represented by the footprint size, expressed in global hectares (gha) and plotted in the (x,y) plane. Footprint depth represents the demand for extra land to meet human needs through depletion of stocks of natural capital. It is plotted on the z-axis. It can be seen as the number of years necessary to regenerate resources liquidated in 1 year (and to absorb the respective wastes) or as the number of planets necessary to support the inhabitants of the planet Earth. The evolution of these two components in the last five decades is studied and discussed.     

Growth accounting in a fishery

Since 1950, the real value of fish catches in Norway has about doubled, while the number of fishermen has declined by about 85 percent. This has made it possible to maintain fishermen's incomes roughly on par with other occupational groups in Norway. It is investigated to what extent this increase in labor productivity is due to accumulation of capital, increasingly abundant fish stocks, or technological progress. Since the capital stock in recent years is not much greater in real terms than in the early 1960s, it is tempting to ascribe most of the increase in labor productivity to technical progress. This, however, would leave out the role of fish stocks; if stocks have increased over this period, this would explain some of what otherwise appears as a technical progress. Using data on labor, capital, fish catches, and fish stock abundance 1961–2004 the development of total factor productivity is examined. Ignoring changes in fish stocks, total factor productivity is estimated to have increased by 0.8 percent per year. Accounting for changes in fish stocks raises this to 1.7–4.3 percent per year, depending on the importance assigned to stocks as factors of production.     

North–South Investment Flows and Optimal Environmental Policies

In the context of a simple North–South model that focuses on the international movement of capital, we show how neglect of pollution-generating effects of foreign investment may lead to distorted and misleading policy recommendations. Such a neglect has recently received emphasis in the empirical literature on East Asian economies, as in Bello and Rosenfeld (1990, “Dragons in Distress: Asia's Miracle Economics in Crisis,” Food First, San Francisco), and was shown to overlook resulting tendencies in these economies toward specialization, away from agriculture and toward manufacturing. Our simple model formalizes this observation and allows us to show that even for an unspecialized capital-poor, resource-rich South, such pollution-generating effects provide incentives for the North to encourage, rather than to discourage, foreign investment abroad and strengthen Southern incentives to restrict foreign investment more sharply than is conventionally assumed. In a nutshell, it brings out the implications of Northern capital “creating its own demand” as a consequence of its adverse impact on the Southern resource base. Despite its simplicity, the model thus sheds light on three interrelated aspects of international trading relations: production asymmetry, incomplete markets, and monopolistic advantage.     

A goal interval programming model for resource allocation in a marine environmental protection program

A multidimensional “goal programming” model is developed to aid resource allocation decisions in the U. S. Coast Guard's Marine Environmental Protection (MEP) program. It is then extended to a model of “goal interval programming” (GIP ) type where exact values for the indicated goals, as in ordinary goal programming, are replaced by ranges. Deviations outside these ranges are also accommodated by piecewise linear functions with slopes that vary with distance from the goal intervals. Uses and generalizations are discussed in the context of applications to allocating manhours and planning the activities of the Coast Guard's MEP program.     

Creation and preservation of vegetation patterns by grazing

Structural patterns of tall stands (“tussock”) and short stands (“lawn”) are observed in grazed vegetation throughout the world. Such structural vegetation diversity influences plant and animal diversity. A possible mechanism for the creation and preservation of such patterns is a positive feedback between grazing and plant palatability. Although some theoretical studies have addressed this point in a non-spatial setting, the spatial consequences of this feedback mechanism on the stability and spatial characteristics of vegetation structure patterns have not been studied.We addressed this issue by analyzing a spatially explicit individual-based plant-grazer simulation model, based on published empirical relations and the assumption of optimal foraging.In the model, the selection by the grazer of short stands (that have a higher energy content and are more palatable) is affected by traveling costs and the spatial organization of swards. Nevertheless, the most selected biomass in this type of short stands was the optimal biomass predicted by cropping and digestion constraints. As a result of the optimal foraging strategy, the grazers displayed Lévy-flight traveling behavior during the simulations with characteristic exponent μ ≈ 2.Patterns of short and tall stands created by grazing were preserved for at least a decade. Even in seasonal habitat, the spatial organization of the patterns remained relatively constant, despite fluctuations in the area of short stands. Heterogeneity of initial vegetation increased heterogeneity of the grazing-induced pattern, but did not affect its stability.The area of short stands that was preserved by grazing scaled with the herbivore mass to the power 0.4 and with the carrying capacity of the vegetation to the power −0.75.Patterns of tall and short stands can be created and perpetuated by optimally grazing ruminants, irrespective of possible underlying soil patterns. The simulations generate predictions for the stability and spatial characteristics of such structural vegetation patterns.     

Optimal harvesting of ecologically interdependent fish species

The optimal exploitation of a two-species predator-prey system is considered, using Lotka-Volterra-type equations. Due to the density-dependence of ecological efficiency, both species should be harvested simultaneously over a range of relative prices. Beyond the limits of this price range, either the prey species should be utilized indirectly by harvesting the predator, or the predator should be eliminated to maximize the prey yield. Neglecting harvesting costs, the simultaneous harvest of prey and predators requires that a unit of prey biomass increase in value by being “processed” by predators. Certain results from single-species fishery models are shown not to apply to multispecies models. These are as follows: (i) Optimal regulation of a free access fishery may call for subsidizing instead of taxing the harvest of predator species. (ii) Increasing the discount rate may, at “moderate” levels, imply that the optimal standing stock of biomass increases instead of decreasing. (iii) A rising price or a falling cost per unit fishing effort of a species may raise and not lower the optimal standing stock of that species.     

Towards a 3D National Ecological Footprint Geography

In the last decades several indicators have been proposed to guide decision makers and help manage natural capital. Among such indicators is the Ecological Footprint, a resource accounting tool with a biophysical and thermodynamic basis. In our recent paper (Niccolucci et al., 2009), a three dimensional Ecological Footprint (^3DEF) model was proposed to better explain the difference between human demand for natural capital stocks and resource flows. Such ^3DEF model has two relevant dimensions: the surface area (or Footprint size - EF_size) and the height (or Footprint depth - EF_depth). EF_size accounts for the human appropriation of the annual income from natural capital while EF_depth accounts for the depletion of stocks of natural capital and/or the accumulation of stocks of wastes. Building on the 2009 Edition of the National Footprint Accounts (NFA), global trends (from 1961 to 2006) for both EF_size and EF_depth were analyzed. EF_size doubled from 1961 to 1986; after 1986 it reached an asymptotic value equal to the Earth's biocapacity (BC) and remained constant. Conversely, EF_depth remained constant at the “natural depth” value until 1986, the year in which global EF first exceeded Earth's BC. A growing trend was observed after that. Trends in each Footprint land type were also analyzed to better appraise the land type under the higher human induced stress. The usefulness of adopting such ^3DEF model in the National Footprint Accounts was also discussed. In comparing any nation's demand for ecological assets with its own biocapacity in a given year, four hypothetical cases were identified which could serve as the basis for a new Footprint geography based on both size and depth concepts. This ^3DEF model could help distinguish between the use of natural capital flows and the depletion of natural capital stocks while maintaining the structure and advantages of the classical Ecological Footprint formulation.     

Pollution control in a simplified general-equilibrium model with production externalities

Pollution externalities of the producer-producer type are considered in a positive two-sector model with stationary capital and labor. By assumption, output from the polluting sector can be diverted to pollution abatement. Environmental authorities attempt to control the level of pollution to some minimum “acceptable” standard by requiring polluters to depollute through the mechanism of a uniform tax on production. Following discussion of short-run considerations, the stability of the tax-adjustment scheme is examined and the dynamic nature of growth paths in the economy is explored.     

The resistibility and shiftability of depletable externalities

In their recently revised book Baumol and Oates (“The Theory of Environmental Policy,” 2nd ed., Cambridge Univ. Press, Cambridge, UK 1988) accept Bird's argument on the optimal taxation policy when externalities are shiftable and depletable. Their conclusion is that the standard Pigouvian tax which is placed upon the generator of a negative externality can be extended to tax the victims who shift the externality to others or extended to compensate recipients in order to achieve Pareto optimality. It is shown in this paper that their conclusion is not free from error, because the possibility of resisting a shifted externality and conjectural variations by recipients is not recognized. Whether an externality is shiftable depends not only on the shifting activity of the original victim but also the resisting activity of his neighbors and their conjectures about each other's action. As such, the shifters should be taxed and the recipients should be compensated at the same rate per unit of externality shifted if the tax base is the output of the shifting and resisting activities. On the other hand, if the tax base is the input which produced the shifting of the externality, then both the shifters and the recipients should be subject to a tax (or subsidy) per unit of input that they have engaged in. Whether it is a tax or a subsidy depends on the direction and magnitude of the conjectural variation. The model and its policy implication can be generalized to cover the omnipresent and wasteful rent seeking activities.     

The models of niche and their application

Having studied the definitions of niche proposed by different ecologists, I have proposed a quantitative method of niche which can be applied to plants. Accordingly, the niche of an operational taxonomic unit (OTU) has been described by a mapping from its environmental set to the unit interval [0, 1], which enables a model of niche to be mathematically operational. The concepts of fundamental niche, realized niche, time niche, etc., may be described by using mathematical models related to each other, and the geometrical relationships between them can be revealed by a multi-dimensional surface. The uni-factor models are built upon the condition that the other factors are optimal for OTU, which are particular cases of the multi-factor models. The establishment of the quantitative relationship between these two kinds of models makes it possible to find out the plants' fundamental niche by doing uni-factor experiments. This may simplify the experiments in which the parameters in a practically applied model are to be estimated. The niche index introduced in this paper is related to average level and aftereffect of plant responses to the effects of its environment (i.e. “inertia”), thus it should be the basis of the simulation of plant seed yield and of its environmental evaluation. Accordingly, models of niche index, of plant seed yield, of plant growth and of environmental evaluation have been built which can be applied to the environmental evaluation or the prediction and management of plant (crop) production, etc.As an example of application, the models of wheat yield and its environmental assessment have been established and practically tested. The results of testing the model of wheat yield showed that the relative errors are 8% and 7.2%, respectively, in 1984 and 1986. The results of the environmental assessment of wheat reveal the fact that the insufficiency of the soil moisture at the 2th and 3th stages is the main restriction of the production of the wheat in Dinxi, Gansu Province, China.     

Do microbial processes regulate the stability of a coral atoll's enclosed pelagic ecosystem?

Complex marine ecosystems contain multiple feedback cycles that can cause unexpected responses to perturbations. To better predict these responses, complicated models are increasingly being developed to enable the study of feedback cycles. However, the sparseness of ecological data often limits the direct empirical parameterization of all model parameters. Here we use a Bayesian inverse analysis approach to synthesize empirical data and ecological theory derived from published studies of a coral atoll's enclosed pelagic ecosystem (Takapoto Atoll, French Polynesia). We then use the estimates of flux magnitudes to parameterize probabilistic compartment models with two forms of heterotrophic consumption: (1) “bottom-up” donor-controlled heterotrophic consumption and (2) “top-down” mass-action heterotrophic consumption. We explore how the flux magnitudes affect the ecosystem's stability properties of resilience, reactivity, and resistance under both assumptions for heterotrophic consumption. The models suggest that the microbial uptake of dissolved organic carbon (DOC) regulates the long term rate of return to steady state following a temporary or pulse perturbation (resilience), and the cycling of carbon between abiotic pools and heterotrophic compartments regulates the short-term response (reactivity). In the bottom-up process model, the sensitivity of steady state masses following a sustained or press perturbation (resistance) is highest for the DOC pool following a sustained change to the microbial uptake rate of DOC. Further, a change in the microbial uptake of DOC propagates through the ecosystem and affects the steady state values of zooplankton. The analysis suggests that the food web is highly dependent on the recycling between the abiotic and biotic carbon pools, particularly as mediated by the microbial consumption of DOC, and this recycling determines how the ecosystem responds to perturbations.     

Harvesting in an eight-species ecosystem

The theory for a general equilibrium ecosystem model that can include large number of interacting species is presented. Features include: (1) individual plants and animals are assumed to behave as if they are maximizing their net energy intake, (2) short- and long-run equilibriums are obtained, (3) species’ population adjustments depend on individual net energies. The theory is applied using simulations of an eight-species Alaskan marine ecosystem for which a “natural” equilibrium is calculated. Humans are introduced by adding a regulated open access fishery that harvests one of the species. Fishing impacts the fish population as well as the populations of other species, including Stellar sea lions, an endangered species. The sensitivity of fish and nonfish species populations to harvesting are calculated.     

Pollution Permits and Sustainable Growth in a Schumpeterian Model

In Chapter 4 of their book (“Endogenous Growth Theory,” MIT Press, Cambridge, MA (1998)), Aghion and Howitt introduce environmental pollution in an aggregate Schumpeterian model and characterize the optimal path. In this paper, we study the equilibria in a decentralized economy compatible with their model. First, we study the trade-off between environmental quality and growth and identify the channels of transmission of environmental policy into growth performance. Then, we compute the levels of the tools which are used to implement the optimum.     

The effects of larval experience with a complex plant latex on subsequent feeding and oviposition by the cabbage looper moth: Trichoplusia ni (Lepidoptera: Noctuidae)

Summary. Leaf disc choice and oviposition bioassays were used to examine the effects of larval experience with a Hoodia gordonii latex on subsequent behaviors. The latex deterred feeding and oviposition by “naïve” cabbage looper (Trichoplusia ni, Noctuidae) larvae and moths with no previous exposure to the material. “Experienced” insects, reared on a diet with the H. gordonii latex (1000 ppm), exhibited lesser feeding deterrence relative to naïve insects. Experienced female moths actually preferred to lay eggs on treated rather than control leaves. There was no observed transfer of behavioral preferences from experienced parents to their offspring. Our results suggest that moths may be acquiring oviposition preferences from larval feeding experience as described by Hopkins’ host selection principal (HHSP) or through chemical legacy.     

Theory of equity in pricing for resource conservation

This paper seeks to construct some theoretical tools that can be used to examine formally the equity issues raised in the use of pricing as a means to conserve scarce resources, in particular, the criteria that can be used to judge the equity of such a price change and the special problem raised by differences in elasticity of demand of different customer groups are considered. Toward this end the concept of a “superfair” distribution (a distribution under which each and every participant obtains a share of the total which is equal to or greater than that individuars pro-rata share, in his own estimation) is introduced and discussed.