Optimal investment policies with exhaustible resources: An information-based model

An information-based model of the “optimal control” type is developed using concepts from information theory to explore the dynamics of fossil resource exhaustion and the phenomenon of substitution by other forms of capital and technological knowledge. All exhaustible resources stocks and forms of capital (and knowledge) are taken to be equivalent to forms of information in the physical sense. It is shown that, with optimal policies, the planning period, or cycle, has several distinct phases, with different optimal investment patterns. The model has two important qualitative implications: (1) economic growth rates are inherently discontinuous and (2) the model predicts an evolutionary structural change, viz., the creation of a new sector in response to the progressive exhaustion (or obsolescence) of previously essential resources or capital stocks. A multiperiod extension is suggested, leading to a tentative explanation for the Kondratieff long-wave phenomenon.     

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 resource curse revisited and revised: A tale of paradoxes and red herrings

We critically evaluate the empirical basis for the so-called resource curse and find that, despite the topic's popularity in economics and political science research, this apparent paradox may be a red herring. The most commonly used measure of “resource abundance” can be more usefully interpreted as a proxy for “resource dependence”—endogenous to underlying structural factors. In multiple estimations that combine resource abundance and dependence, institutional, and constitutional variables, we find that (i) resource abundance, constitutions, and institutions determine resource dependence, (ii) resource dependence does not affect growth, and (iii) resource abundance positively affects growth and institutional quality.     

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.     

A social benefit-cost analysis of mandatory deposits on beverage containers

This paper presents a social efficiency analysis of mandatory deposits on beverage containers. Five kinds of resource effects are identified, evaluated and added up: (1) litter (both pickup and “eyesore” costs); (2) solid waste collection; (3) container costs; (4) production and distribution costs; and (5) consumer convenience. It is shown that the desirability, on efficiency grounds alone, of mandatory deposits is not indisputable; it depends critically on one's evaluation of (1) the average value of the time it takes consumers to return empty containers and (2) the average value of the “eyesore” benefit of a dramatically reduced (i.e., by around three-fourths) volume of beverage container litter.     

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.     

Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta–Heal–Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the maximin problem in the case where production and utility are Cobb–Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show that it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb–Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resolution of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if it does not, whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.     

Renewable Resources in an Overlapping Generations Economy Without Capital

We incorporate a renewable resource into an overlapping generations model without capital and with quasi-linear preferences. Besides being an input for production the resource serves as a store of value. We characterize the dynamics, efficiency, and stability of the steady-state equilibria. The stability properties are sensitive to the type of resource growth. For constant growth there is only one steady-state equilibrium which is stable and efficient. In the general case of the concave growth function, there are usually at least two steady-state equilibria, one of which is stable and the other one unstable. The unstable steady state is efficient, but the stable one may or may not be. We study the robustness of our results by assuming a logarithmic utility function. We show that for the Cobb–Douglas production function the steady state is unique and stable regardless of whether the equilibrium is efficient or inefficient. Our analytical results are illustrated by numerical calculations.     

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.     

Scarcity, growth and R&D

The limits to economic growth due to resource scarcity can be alleviated only by the development of backstop substitutes. This paper combines resource-based economic growth with R&D to reduce the cost of backstop technologies. Characterizing the entire dynamics of optimal growth and R&D processes, we find that an economy's growth prospects depend on its type, as determined by its production technology and learning ability, and by its knowledge–capital endowment. A wide variety of growth patterns emerges, ranging from cases in which an economy that without R&D eventually stagnates (converges to a steady state) is diverted by R&D onto a path of sustained growth, to cases in which R&D is not warranted. Resource scarcity is shown to encourage R&D due to the increased reliance on the backstop technology.     

On the extraction of an exhaustible resource by a monopoly

Hotelling's r-percent rule does not hold for monopoly extractors of durable exhaustible resources. An example with a nondurable resource in which the rule also fails to hold is presented. An economy with a fixed average propensity to save is modelled. The monopoly extractor recognizes that resource extraction, by affecting output and hence capital accumulation, affects future demand. The firm exploits this effect by causing the marginal profitability of extraction to grow faster or slower than the rate of interest, depending upon initial conditions. Conditions are developed under which the growth rate will be less than the interest rate.     

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.     

Selecting parameters for calibration via sensitivity analysis: An individual-based model of mosquitofish population dynamics

A stochastic individual-based model (IBM) of mosquitofish population dynamics in experimental ponds was constructed in order to increase, virtually, the number of replicates of control populations in an ecotoxicology trial, and thus to increase the statistical power of the experiments. In this context, great importance had to be paid to model calibration as this conditions the use of the model as a reference for statistical comparisons. Accordingly, model calibration required that both mean behaviour and variability behaviour of the model were in accordance with real data. Currently, identifying parameter values from observed data is still an open issue for IBMs, especially when the parameter space is large. Our model included 41 parameters: 30 driving the model expectancy and 11 driving the model variability. Under these conditions, the use of “Latin hypercube” sampling would most probably have “missed” some important combinations of parameter values. Therefore, complete factorial design was preferred. Unfortunately, due to the constraints of the computational capacity, cost-acceptable “complete designs” were limited to no more than nine parameters, the calibration question becoming a parameter selection question. In this study, successive “complete designs” were conducted with different sets of parameters and different parameter values, in order to progressively narrow the parameter space. For each “complete design”, the selection of a maximum of nine parameters and their respective n values was carefully guided by sensitivity analysis. Sensitivity analysis was decisive in selecting parameters that were both influential and likely to have strong interactions. According to this strategy, the model of mosquitofish population dynamics was calibrated on real data from two different years of experiments, and validated on real data from another independent year. This model includes two categories of agents; fish and their living environment. Fish agents have four main processes: growth, survival, puberty and reproduction. The outputs of the model are the length frequency distribution of the population and the 16 scalar variables describing the fish populations. In this study, the length frequency distribution was parameterized by 10 scalars in order to be able to perform calibration. The recently suggested notion of “probabilistic distribution of the distributions” was also applied to our case study, and was shown to be very promising for comparing length frequency distributions (as such).     

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.     

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.     

Plant acclimation to elevated CO2—From simple regularities to biogeographic chaos

Upon exposure to altered levels of CO₂, plants express a variety of acclimations to CO₂ directly, over and above acclimations to indirect changes in temperature and water regimes. These acclimations commonly include increased photosynthetic CO₂ assimilation and increased water-use efficiency with reduced N content and reduced stomatal conductance. The robust generic acclimations are explicable by combining simple models of carboxylation, stomatal control, energy balance, and functional balance. Species- or genotype-specific acclimations are overlaid on these generic acclimations. Several such specific acclimations that are often seen are readily incorporated in an extended model. These specific acclimations generate a great spread of values in key performance measures of photosynthesis, water- and N-use efficiencies, and rates of water and N use, even among C₃ species that are the focus of this work. These performance measures contribute strongly to relative fitness and thus to evolving biogeographic distributions. The spread in fitness values is so large as to impend “chaotic” shifts in biogeography (and, ultimately, evolution) that are not understandable with models specific to species or functional groups; rather, a systematic study of key physiological and developmental parameters is merited. Also merited is a coherent extension of the model used here, or similar models, to include other phenomena, including mycorrhizal associations, transience in resource availability, etc. The composition of useful approximate fitness functions from physiological and allocational responses is a major challenge, with some leads originating from the model. In the search to extract patterns of responses, arguments based on the responses being close to optimal or adaptive will be misleading, in view of the absence of selection pressure to perform adaptively at high CO₂ for over 20 million years. I offer suggestions for more useful research designs.     

Stochastic bycatch, informational asymmetry, and discarding

The existing literature (i) examines bycatch and discard behavior in a static framework and (ii) treats bycatch as a deterministic process uniform across vessels. Using a dynamic representative agent model in a two-stock resource, this paper explores strategic interactions between a social planner and two groups of harvesters, one of which imposes a stochastic “technological externality” (bycatch) on the other. In addition to limitations on entry and the number of trips taken in each industry, three bycatch control instruments are compared to the unconstrained case: taxes, trip limits, and value-based quotas. Implementation and enforcement costs aside, taxes dominate both types of quota, and value limits outperform trip limits by eliminating one type of discarding. In simulations, relative performance depends upon variance in the bycatch process, differences in the ex vessel prices of stocks, relative efficiency of the harvester types, and fixed costs on the trip and industry margins.     

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.     

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.