NONRENEWABLE RESOURCE EXTRACTIONS WITH A POLLUTION SIDE EFFECT: A COMPARATIVE DYNAMIC ANALYSIS

ABSTRACT. In this paper, we present a nonrenewable resource model including environmental pollution as a state variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The costate variable for the resource stock is decomposed into a scarcity effect and a cost effect; and the costate variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.     

OPTIMAL REGULATION OF NATURAL RESOURCES IN THE PRESENCE OF IRREVERSIBLE THRESHOLD EFFECTS

ABSTRACT. Thresholds are an important physical consideration in the regulation of natural resources. This paper is the first to present a complete analytical framework in which to evaluate optimal regulation of a natural resource in the presence of irreversible threshold effects. Necessary conditions are presented for optimal regulation of these problems both for when the threshold has a known location in state‐space and for when the location of the threshold is unknown. In the case where the location is known, the literature is corrected on a seemingly minor technical point regarding the behavior of the co‐state variables that turns out to be of considerable importance. For the case when the location of the threshold is not known, it is shown that thresholds in state‐space implies a nonstandard risk structure.     

OPTIMAL TAXES FOR POLLUTION REGULATION: DYNAMIC,SPATIAL AND STOCHASTIC CHARACTERISTICS

The paper develops a model that incorporates the dynamic, spatial and stochastic aspects of environmental pollution. Conditions for optimal resource allocation between output production and pollution abatement processes are derived. Optimal emission (Pigouvian) taxes which may be used to efficiently regulate pollution in each region are determined. The pattern of emission taxes over time and their relative sizes among different regions are additionally explored with the help of a simplified numerical example.     

Optimal input substitution of a firm facing an environmental constraint

In this paper we consider the dynamic behavior of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim it can, among others, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments, abatement efforts, and the choice whether to leave some capacity unused or not. The abatement process is modeled as input substitution rather than end-of-pipe. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Different scenarios are considered, ranging from attractive clean input to unattractive clean input, and from a mild emission limit to a very tight one. It is shown that for large capital stocks and/or when marginal cash flow per unit of emissions is larger for the dirty input than for the clean input, it can be optimal to actually leave some production capacity unused. Also, since the convex installation costs suggest to spread investments over time, it can happen that investment in productive capital is positive although capacity remains unused.     

Effects of pollution restrictions on dynamic investment policy of a firm

The purpose of this paper is to determine the effects of different pollution standards on the firm's resource allocation decisions. To do so, a dynamic model of the firm is developed in which it is assumed that production causes pollution as an inevitable byproduct. Concerning its investment policy, we suppose that the firm can choose between investing in productive capital goods and investing in abatement efforts.It is shown that, in some cases, future abatement expenses have a negative impact on the present level of productive investment, even if the pollution standard is not binding at the moment. This implies a really dynamic optimal investment policy for the firm, which cannot be obtained within a comparative static analysis.This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Comments by Frank van der Duyn Schouten and Piet Verheyen (Tilburg University) and by Raymond Gradus (Dutch Ministry of Finance, The Hague) are gratefully acknowledged.     

Exploitation of natural resources and pollution

This paper provides some differential game models of natural resource exploitation when environmental pollution takes place. The classical approach to determine optimal harvest rates of renewable resources utilizes Optimal Control models, i.e. there is either a monopolistic market structure or there is pure competition. In case of pollution, however, all agents can be put together, forming the groups of the resource harvesters on one side and of polluters on the other side. So differential games can be used to analyze environmental problems. The models introduced in this paper are put together in order to showdifferent problems that can all be analyzed using differential games.     

Multi-resource investment strategies: Operational hedging under demand uncertainty

Consider a firm that markets multiple products, each manufactured using several resources representing various types of capital and labor, and a linear production technology. The firm faces uncertain product demand and has the option to dynamically readjust its resource investment levels, thereby changing the capacities of its linear manufacturing process. The cost to adjust a resource level either up or down is assumed to be linear. The model developed here explicitly incorporates both capacity investment decisions and production decisions, and is general enough to include reversible and irreversible investment. The product demand vectors for successive periods are assumed to be independent and identically distributed. The optimal investment strategy is determined with a multi-dimensional newsvendor model using demand distributions, a technology matrix, prices (product contribution margins), and marginal investment costs. Our analysis highlights an important conceptual distinction between deterministic and stochastic environments: the optimal investment strategy in our stochastic model typically involves some degree of capacity imbalance which can never be optimal when demand is known.     

Modelling effects of industrialization,population and pollution on a renewable resource

In this paper, a mathematical model is proposed and analysed to study the simultaneous effect of industrialization, population and pollution on the depletion of a renewable resource. Criteria for local stability, global stability and instability are obtained. It is shown that if the densities of industrialization, population and pollution increase, then the density of the resource biomass decreases and it settles down at its equilibrium level whose magnitude is lower than its original carrying capacity. It is further noted that if these factors increase unabatedly, the resource biomass may be driven to extinction. Computer simulations are also performed to illustrate the results.     

COST-BENEFIT ANALYSIS APPLIED TO WILDERNESS PRESERVATION—OPTION VALUE UNCERTAINTY AND DITONICITY

It has been recognized for some time that when cost-benefit analysis is applied to irreversible environmental decisions, such as that of developing or preserving wilderness land, there can be an option value associated with the preservation decision, which arises when there is future uncertainty with respect to the benefits of development or preservation. In this paper the provenance of option value is examined and it is shown that an important cause is a special kind of uncertainty, viz. the possibility of reversals in direction of the relative valuations of wilderness land and developed land, a property we refer to as ditonicity. It is shown that the more ditonic the relative valuation process the greater the deviance between the certainty-equivalence development policy and the stochastically optimal one, and thus by implication the greater the option value. In the two cases with zero ditonicity, when relative wilderness valuations always increase or always decrease (even though in a stochastic fashion), there is zero option value. The model used assumes that service flows from wilderness and developed land are size-dependent, with future relative values known only in terms of a stochastic process, which can take jumps up or down of the same proportional size, at random times. Development can be partial or total and can occur in impulses at any time over an infinite time horizon.     

INCENTIVE COMPATIBLE ENVIRONMENTAL REGULATIONS

This paper addresses the problem of designing environmental regulations when firms possess better information about the cost of pollution abatement than regulators. In the regulatory equilibrium derived in the paper, firms are induced to reveal the information they have concerning abatement costs through the judicious use of abatement standard-subsidy combinations. Offering firms a menu of regulatory contracts, each one specifying a required level of pollution abatement as well as a lump sum subsidy to be paid by the regulatory agency to the firm, is shown to be superior to optimal uniform standard-subsidy schemes. By appealing to the revelation principle and employing a second policy instrument (subsidies), albeit a costly one, in conjunction with an abatement standard, the incentive compatible approach to environmental regulation presented in the paper minimizes the economic inefficiency customarily attributable to a lack of initial information regarding pollution abatement costs.     

OPTIMAL RESOURCE DEVELOPMENT AND IRREVERSIBILITIES: COOPERATIVE AND NONCOOPERATIVE SOLUTIONS

This paper derives and compares free boundaries for the problem of irreversible development of an environmental resource under uncertainty, by explicitly taking into account the facts that: (i) there might be more than one private profit-maximizer decision-maker that acquires profits by developing the resource involved in the problem; (ii) there might be interactions among these decision-makers, in the sense that the development undertaken by a certain developer might affect the cost of the rest; and (iii) the undeveloped resource has an environmental value which is not taken into account by the individual developers but might be accounted for in the context of an optimal development problem faced by a social planner or environmental regulator. By comparing the three resulting free boundaries, it is shown that the noncooperative solution implies the fastest development as compared to cooperative outcomes. Policy schemes in the form of development fees and development limits which can secure the cooperative outcome are determined.     

Optimization of performance characteristics in a class of irreversible chemical pumps

A new irreversible cyclic model of a class of two-source chemical pumps, which are affected by not only finite-rate mass transfer and mass leak but also the internal dissipation resulting from friction, eddy currents and other irreversible effects inside the cyclic working fluid, is established. By using the optimal control theory, the optimal relation between the coefficient of performance and the rate of energy pumping for the two-source irreversible chemical pump cycles is derived. The maximum coefficient of performance and some other important performance bounds of the cycle are determined. The optimal mass-transfer time, minimum entropy production rate and minimum power input are calculated. Consequently, the influences of the main irreversibilities usually existing in real engineering systems on the performance characteristics of the chemical pump operating between two mass sources are revealed. Moreover, it is expounded that some relevant important conclusions in the literature can be directly deduced from the results in the present paper.     

Pollution,unequal lifetimes and fairness

This paper characterizes the optimal level of pollution in a two-period OLG economy where pollution deteriorates survival conditions. We compare two long-run social optima: on the one hand, the average utilitarian optimum, where the long-run average well-being is maximized, and, on the other hand, the ex post egalitarian optimum, where the realized well-being of the worst-off at the stationary equilibrium is maximized. It is shown that the ex post egalitarian optimum involves, under weak conditions, a higher level of pollution in comparison with the utilitarian optimum. This result is robust to introducing health expenditures in the survival function. Finally, we examine the decentralization of those two social optima, and we compare the associated optimal taxes on capital income aimed at internalizing the pollution externality.     

带凸资源和恶化效应的单机松弛窗口排序

研究带凸资源和恶化效应的单机窗口指派排序问题,其中窗口指的是松弛窗口,凸资源和恶化效应指的是工件的实际加工时间是其开始加工时间的线性函数,是其资源消耗量的凸函数。目标是确定工件的加工顺序,资源分配量以及窗口的开始加工时间和长度使其在总资源消耗费用(与窗口有关的排序费用)有上界限制的条件下,极小化与窗口有关的排序费用(总资源消耗费用)。获得了求解上述问题的最优算法,证明了该问题是多项式时间可解的。     

POLLUTION, GOVERNMENT EXPENDITURE, TAXES AND STOCHASTIC GROWTH

This paper studies a stochastic endogenous growth model with pollution. It introduces government expenditure and exogenous pollution abatement technology to eliminate pollution and proves that under appropriate equilibrium conditions the main economic indexes （including economic growth rate, the optimal government expenditure rate） in the centrally planned economy and decentralized economy can be expressed by the parameters of the model uniquely. The optimal tax policy is analyzed ,and the optimal pollution is derived.     

一类具有资源限制的调度问题

研究了具有线性退化及学习效应作用下的单台机器调度问题,对于工件的到达时间是其资源消耗量的正的严格单调递减函数时,考虑了总资源消耗量限定情形下求最大完工时间最小化问题给出了最优算法.     

Single-machine scheduling problems with an aging effect

This paper considers single machine scheduling problems where the processing time of a job increases as a function of its position in the sequence. In this model, the later a given job is scheduled in the sequence, the longer its processing time. It is shown that the optimal schedule may be very different from that of the classical version of the problem. We introduce polynomial solutions for the makespan minimization problem, the sum of completion times minimization problem and the sum of earliness penalties minimization problem. For two resource constrained problems, based on the analysis of the problems, the optimal resource allocation methods are presented, respectively.     

具有恶化效应和凸资源分配关系的单机排序问题

研究工件加工时间具有恶化效应和凸资源关系的单机排序问题,其中工件的实际加工时间是其正常的加工时间,工件开工时间(具有恶化效应)及消耗资源量的函数。目标为在最大完工时间(总完工时间、总等待时间、完工时间总绝对差与等待时间总绝对差)小于或等于给定常数的条件下找到工件的最优排序和最优的资源分配使工件的总资源消耗量最少。在单机状态下,证明了此问题是多项式时间可解的,并给出了求解该问题的算法和数值实例。     

Optimal resource allocation across related channels

In this paper, we consider resource allocation strategies of a limited resource across two related channels in a multi-period setting. We study a stochastic control problem where the objective is to determine the optimal limited resource allocation policy across two related channels and optimal transshipment policy between these two channels. We characterize some structural results of the optimal resource allocation policy and show that it is determined by three monotone curves.     

Defence resource distribution between protection and decoys for constant resource stockpiling pace

The paper considers the optimal resource distribution between increasing protection of genuine elements and deploying decoys (false targets) in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed over this horizon. Series and parallel systems are considered. The defender optimizes the resource distribution in order to minimize the system vulnerability. The attacker cannot distinguish genuine and false elements and can attack a randomly chosen subset of the elements.