Management of a renewable resource with a backstop substitute (original) (raw)
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Optimal transition to backstop substitutes for nonrenewable resources
Journal of Economic Dynamics and Control, 2003
We analyze the optimal transition from a primary, nonrenewable resource to a backstop substitute for a class of problems characterized by the property that the backstop cost decreases continuously as learning from R&D e orts accumulates to increase the knowledge base. The transition policy consists of the R&D process and of the time proÿles of the primary and backstop resource supply rates. We ÿnd that the optimal R&D process follows a most rapid approach path (MRAP): the knowledge process associated with R&D should approach some (endogenously derived) target process as rapidly as possible and proceed along it thereafter. Thus, if the initial knowledge level is su ciently low and the cost structure justiÿes R&D activities, the R&D e orts should be initiated without delay at the highest a ordable rate and slow down later on. This pattern contrasts previous ÿndings that typically recommend a single-humped R&D process with a possible initial delay.
Optimal control of renewable resources with alternative use
2009
"We study the optimal harvesting of a renewable resource that cannot be continuously exploited, i.e. after the harvest the released space cannot be immediately reallocated to the resource. In the meantime, this space can be given an alternative use of positive utility. We consider a discrete time model over an infinite horizon with discounting, and characterize the optimality of two myopic policies, the greedy and the sustainable ones. We then show that the optimal strategy consists in applying one of these policies after a finite number of time steps. Value function and optimal feedback are explicitly determined."
On strategic incentives and the management of stochastic renewable resources
2005
The thesis consists of four theoretical articles that can be read independently of each other on the common topic-strategic incentives in the management of natural resources. Article I concerns biodiversity conservation of essential species in sustaining the ecosystem. The issue is what forces that may explain why a natural resource stock declines although the government is running a conservation programme in a second-best solution. The focus is on the government's strategic behavior against the industry being a polluter. Ten forces are identified that explains why a resource may decline under a conservation programme. One result is that an increase in the variance of the natural growth process does not lead to an increase in investment in the emission-generating industry in the second-best solution, as in the first-best solution. In article II, a marine natural resource stock is exposed to harvest as well as damage by pollution from N countries. Each country has four decision variables: harvest effort, domestic production (generating transboundary pollution), abatement and research in environmental technology. It is shown that the marine resource is damaged 'twice' as a result of a 'chain effect' in the strategic incentives among the countries. A harvest function is introduced, which results in 'tough' harvest efforts, implying that agents' effort increases the smaller the expected stock size as an extreme case of the 'tragedy of the commons'. In article III, the classical upstream-downstream case is analyzed under the assumptions of the Coase theorem in a dynamic model. Different assignments of rights to determine the level of externality are compared to the case of no-cooperation. It is shown that the 'efficiency proposition' does not necessarily hold. Specifically, a bargaining outcome may not be possible when downstream society has the right to determine the level of externality in the dynamic model as it may violate individual rationality of upstream society. In the fourth article-a technical note-it is shown in a that in most models with private provision of public goods, there exists a simple mechanism determining the reaction functions of the players.
Management of a Renewable Resource with a Finite Demand Elasticity
Natural Resource Modeling, 1990
Optimal management policies are derived for a renewable resource when the demand for output has finite elasticity. The analysis modifies traditional views of this problem by allowing for the possibility that static optimizing policies, which maximize myopic net revenues, may be superior to "Golden Rule" policies which account for longer-run stock effects.
Non-Renewable Resource Supply: Substitution Effect, Compensation Effect, and All That
SSRN Electronic Journal, 2000
Particular thanks go to xx. Financial support from the Fonds Québécois de recherche pour les sciences et la culture, the CER-ETH at ETH Zurich, and the CIREQ is gratefully acknowledged. The non-renewable-resource-extraction literature has extensively studied the e¤ects of several policy instruments on the market equilibrium extraction quantities. In this note, we examine the reaction of an individual resource supplier to given prices. In a synthetic resource supply theory, we compute instantaneous supply functions and decompose the e¤ects of price changes on supplied quantities. In a pure Hotelling model, we show that price changes entail an intertemporal substitution which is reminiscent of a green paradox. When the reserves stock is endogenous, this e¤ect is completed by a stock e¤ect of opposite direction. This gives rise to a resource supply decomposition equation, which is the counterpart of Slutsky equation in demand theory. We show that the substitution e¤ect always dominates so that a price decrease at some date always causes supply to increase at all other dates. Moreover, there is no phenomenon of the kind of the Gi¤en paradox. When this supply picture is introduced into a partial equilibrium framework, we …nd that the above results explain the e¤ects of demand-reducing policies.
Optimal Supply of a Depletable Resource with a Backstop Technology: Heal's Theorem Revisited
Operations Research, 1985
Heal's theorem states that if the extraction cost of a depletable resource increases with cumulative extraction, and if a backstop technology exists, the user cost of the depletable resource declines to zero at the date of exhaustion. In this paper, we first present a simple method for proving this proposition, using a social planning model that determines the optimal rates both of extraction of the depletable resource and of production of the backstop technology. We then present two examples that show how this method can be used to solve more difficult problems in the theory of resource economics. The first example involves learning-by-doing in the backstop sector; that is, backstop costs decline with cumulative production. The second example involves uncertainty of backstop costs. JN A 1976 article in the Bell Journal, Geoffrey Heal established the following important proposition concerning the role of extraction costs in determining the socially optimal price of a depletable resource. Assume the resource is available in infinite amounts, but that its extraction cost rises with cumulative extraction. The resource cost is bounded from above by a so-called "backstop" technology, which provides unlimited amounts of the resource at a constant cost. Heal claimed that in such a world the socially optimal price for the resource must start out well above the marginal extraction cost of the depeletable resource, and move toward it as cumulative extraction grows. Equivalently, the user cost of the resource is initially high, but declines to zero at the instant of transition to the backstop technology. This result contrasts sharply with the case in which extraction costs are constant and the total stock of the depletable resource is finite. With these alternative assumptions, the socially optimal price starts out close to the cost of extraction and rises steadily above it as the resource stock is consumed. The user cost of a constant-cost depletable resource reaches its maximum at the transition to the backstop. Subject classification: 131 Heal's theorem revisited, 473 optimal supply of a depletable resource.
The supply of non‐renewable resources
Canadian Journal of Economics/Revue canadienne d'économique
There exists no formal treatment of non-renewable resource (NRR) supply, systematically deriving quantity as function of price. We establish instantaneous restricted (fixed reserves) and unrestricted NRR supply functions. The supply of a NRR at any date and location not only depends on the local contemporary price of the resource but also on prices at all other dates and locations. Besides the usual law of supply, which characterizes the own-price effect, cross-price effects have their own law. They can be decomposed into a substitution effect and a stock compensation effect. We show that the substitution effect always dominates: A price increase at some point in space and time causes NRR supply to decrease at all other points. This new but orthodox supply setting extends to NRRs the partial equilibrium analysis of demand and supply policies. Thereby, it provides a generalization of many results about policy-induced changes on NRR markets. The properties of restricted and unrestricted supply functions are characterized for Hotelling (homogeneous) as well as Ricardian (non homogeneous) reserves, for a single deposit as well as for several deposits that endogenously come into production or cease to be active.
The Australian Journal of Agricultural and Resource Economics, 2006
In this paper we analyse the optimal management of a renewable resource (groundwater) with stock-dependent extraction cost and a backstop substitute, facing two-sector linear demands. Application to the Kiti region in Cyprus demonstrates the model's performance and is used to test for the difference between optimal and myopic behaviour. It is found that the presence of a backstop resource diminishes the importance of optimal dynamic behaviour, whereas in the absence of backstop the optimal control solution yields a value for social welfare significantly larger than the myopic policy.
Regulation of Renewable Resource Exploitation
SIAM Journal on Control and Optimization, 2020
We investigate the impact of a regulation policy imposed on an agent exploiting a possibly renewable natural resource. We adopt a principal-agent model in which the Principal looks for a contract, i.e. taxes/compensations, leading the Agent to a certain level of exploitation. For a given contract, we first describe the Agent's optimal harvest using the BSDE theory. Under regularity and boundedness assumptions on the coefficients, we express almost optimal contracts as solutions to HJB equations. We then extend the result to coefficients with less regularity and logistic dynamics for the natural resource. We end by numerical examples to illustrate the impact of the regulation in our model.
Non-use values and the management of transboundary renewable resources
Ecological Economics, 1998
It has long been recognized in economics that individuals can derive bene ts from a resource stock without directly or indirectly utilizing that resource. Such non-use values, including existence values and bequest values, however, are often ignored in models of resource management. In this paper, a simple, two-country model of the management of a renewable resource is developed in which at least one country has a non-economic interest in the conservation of the sh stock to examine the impact of such a non-use value on the end-of-period harvest and self-enforcing sharing rule. The model shows that this non-lucrative pursuit serves to decrease the total allowable catch for each period at the expense of the catch share of the more conservation-oriented country, a result is consistent with the September 1995 decision by NAFO ending the dispute between Canada and the European Union over turbot. * The comments of Charles Plourde, Mike Fraidenburg, Charles Paulsen, and an anonymous referee are greatly appreciated.