Set-up costs and the existence of competitive equilibrium when extraction capacity is limited

Although set-up costs are prevalent and substantial in natural resource extraction, it is known that a Walrasian competitive equilibrium cannot exist in simple extraction models with set-up costs. This paper demonstrates that this result is sensitive to the assumption of unlimited extraction capacity and derives sufficient conditions for existence. An equilibrium exists if extraction is limited such that each firm earns sufficient surplus to cover its set-up costs or if firms choose extraction capacity subject to non-increasing returns. The resulting competitive equilibrium price either grows at the rate of interest when total extraction is below industry capacity or is constant when industry capacity is fully utilized. In the equilibrium, identical deposits are opened simultaneously, and set-up costs for new deposits are incurred when the industry has excess capacity rather than when capacity is fully utilized.     

Optimal management of a confined groundwater system

Dynamic programming is applied to a relatively simple economic and hydrologic model of a confined aquifer system in Southwest Montana to determine an optimal interseasonal allocation schedule. The derived decision rule demonstrates the economic advantage of maintaining a confined groundwater system. While localized intraseasonal loss of the artesian pressure may occur, it is important to maintain this pressure from year to year because of its role in reducing extraction costs. The welfare gap, as measured by differences in the net present value of economic returns to the basin under an optimal use policy versus an uncontrolled, “common pool” situation, is not trivial. Sensitivity analysis indicates that assumptions about uniformity of land productivity, vis-à-vis their impact on the shape of the returns function, the discount rate, and the level of electric power rates are particularly critical with respect to the magnitude of the commonality problem.     

Resource extraction and recycling with environmental costs

Extraction and use of a natural resource is assumed to affect the environment adversely. A perfect substitute for the resource can be supplied through a recycling process. Recycling may also have harmful effects on the environment, but to a smaller extent than extraction. The optimal path of extraction and recycling is studied under various assumptions about the environmental effects of recycling and the assimilative capacity of the environment. In particular, it is shown how the cost of recycling will affect initial resource extraction as well as the environmental quality at the time of resource exhaustion and in the long-run stationary state.     

On equilibrium in resource markets with scale economies and stochastic prices

In this paper, I show the existence and the characteristics of equilibrium in a non-renewable resource market where extraction costs are non-convex and market price is subject to stochastic shocks, an empirically relevant setting. In my model firms may be motivated to hold inventories to facilitate production smoothing, which allows them to continue producing at a smooth pace at any instant when extraction ceases, e.g. when reserves are exhausted. This aspect of the model then supports a competitive equilibrium in the presence of non-convex costs. Casual empirical evidence is provided that supports the central features of my model for a variety of non-renewable resources, lending credence to the explanation for equilibrium I propose.     

On equilibrium in resource markets with scale economies and stochastic prices

In this paper, I show the existence and the characteristics of equilibrium in a non-renewable resource market where extraction costs are non-convex and market price is subject to stochastic shocks, an empirically relevant setting. In my model firms may be motivated to hold inventories to facilitate production smoothing, which allows them to continue producing at a smooth pace at any instant when extraction ceases, e.g. when reserves are exhausted. This aspect of the model then supports a competitive equilibrium in the presence of non-convex costs. Casual empirical evidence is provided that supports the central features of my model for a variety of non-renewable resources, lending credence to the explanation for equilibrium I propose.     

Would hotelling kill the electric car?

In this paper, we show that the potential for endogenous technological change in alternative energy sources may alter the behaviour of resource-owning firms. When technological progress in an alternative energy source can occur through learning-by-doing, resource owners face competing incentives to extract rents from the resource and to prevent expansion of the new technology. We show that in such a context, it is not necessarily the case that scarcity-driven higher traditional energy prices over time will induce alternative energy supply as resources are exhausted. Rather, we show that as we increase the learning potential in the substitute technology, lower equilibrium energy prices prevail and there may be increased resource extraction and greenhouse gas emissions. We show that the effectiveness and the incidence of emissions reduction policies may be altered by increased potential for technological change. Our results suggest that treating finite resource rents as endogenous consequences of both technological progress and policy changes will be important for the accurate assessment of climate change policy.     

Sequential development and exploitation of an exhaustible resource: do monopoly rights promote conservation?

This paper explores the problem of sequential exploitation of exhaustible resources by a monopolist, when a setup cost must be incurred to access the next pool. Under certain circumstances, the monopolist will always follow a more conservationist path of extraction and delay the introduction of new resource pools compared to a social planner. However, with other forms of consumer demand, the monopolist may exhaust the resource more quickly, especially if many new options will follow. These results may apply especially to depletable resources like antibiotics or biotech products, for which significant research and development costs are required, followed by monopoly rights conferred by patents.     

The taxation of nonreplenishable natural resources revisited

The theory of nonreplenishable resource extraction has been extended to allow for extraction costs which increase as deposits are increasingly depleted. In these cases, profit maximization may result in the cessation of extraction before reserves are totally exhausted. The effect of various taxation policies on optimal extraction patterns in these models are derived. With a few exceptions, the results are that the imposition of a tax will cause operators to extract at faster rates over shorter periods of time and to reduce the total amount of ore extracted. The analysis allows for an output price which increases over time.     

Protected-Area Monitoring Dilemmas: a New Tool to Assess Success

Abstract:  Understanding factors that influence the success of protected areas in curbing unsustainable resource consumption is essential for determining best management strategies and allocating limited resources to those projects most likely to succeed. I used a law-enforcement and monitoring game-theory model from the political science literature to identify three key variables useful in predicting the success of a protected area: costs of monitoring for rule breakers, benefits of catching a rule breaker, and probability of catching a rule breaker if monitoring. Although assigning exact values for each of these variables was difficult, the variables had a strong predictive capacity even when coded as coarse ordinal values. A model in which such values were used correctly predicted the outcome of 88 of 116 protected areas sampled from the peer-reviewed literature. The model identified a critical zone of common mismatch between protected-area circumstances and management policies. In situations where the costs of monitoring were greater than the product of the probability of catching a rule breaker and the benefit of doing so, conservation was unlikely to succeed. Control of illegal use of protected resources was reported in only 8% of such cases, regardless of strategies to motivate potential users to cooperate with conservation. My model does not prescribe a best management policy for conserving natural resources; rather, it can be used as a tool to help predict whether a proposed management policy will likely succeed in a given situation.     

氨基苯甲酸稀溶液的络合萃取研究

本文利用三辛胺或磷酸三丁酯为络合剂，正辛醇或煤油为稀释剂，在不同的Ｐ则定了氨基本甲酸稀溶液的萃取相平衡分配系数，讨论了影响因素，提出了同时考虑络合萃取作用和物理萃取作用的平衡分配系数的表达式。     

The social and ecological determinants of common pool resource sustainability

We study a dynamic common pool resource game in which current resource stock depends on resource extraction in the previous period. Our model shows that for a sufficiently high regrowth rate, there is no commons dilemma: the resource will be preserved indefinitely in equilibrium. Lower growth rates lead to depletion. Laboratory tests of the model indicate that favorable ecological characteristics are necessary but insufficient to encourage effective CPR governance. Before the game, we elicit individual willingness to follow a costly rule. Only the presence of enough rule-followers preserves the resource given favorable ecological conditions.     

A free lunch in the commons

We derive conditions under which raising costs through a regulatory constraint or a fully expropriated tax can increase the profits arising from a common-pool resource. The basic model assumes a fixed number of identical agents with linear costs selling in a single period at an exogenous price. A necessary and sufficient condition for a cost increase to be profitable is that aggregate output from the resource be locally convex in aggregate effort. We also show that cost increases can be profitable even if price is endogenous, agents are heterogeneous, entry is costless, or agents are playing a Markov-perfect equilibrium of a dynamic game. We also discuss more general welfare implications of the result along with its relation to existing results for a Cournot oligopoly.     

Nonseparability and the voluntary approach to externality problems

Ronald Coase asserted that voluntary two-party bargaining with zero transaction costs results in an optimal resource allocation, which is invariant with respect to the liability rule. It has been argued that nonseparabilities destroy the validity of Coase's theorem. In this paper it is shown that this criticism is based on implausible assumptions about the externality-receivers adjustment to the externality level.     

Open- and closed-loop equilibrium control of trophic chains

If a nearly natural population system is deviated from its equilibrium, an important task of conservation ecology may be to control it back into equilibrium. In the paper a trophic chain is considered, and control systems are obtained by changing certain model parameters into control variables. For the equilibrium control two approaches are proposed. First, for a fixed time interval, local controllability into equilibrium is proved, and applying tools of optimal control, it is also shown how an appropriate open-loop control can be determined that actually controls the system into the equilibrium in given time. Another considered problem is to control the system to a new desired equilibrium. The problem is solved by the construction of a closed-loop control which asymptotically steers the trophic chain into this new equilibrium. In this way, actually, a controlled regime shift is realized.     

芳香酸稀溶液的络合萃取研究

络合萃取法分离极性有机物稀溶液具有高效性和高选择性。本文利用三辛胺或磷酸三丁酯为络合剂，四氯化碳、三氯甲烷、正辛醇或煤油为稀释剂，实验测定了苯甲酸、邻硝基苯甲酸稀溶液的萃取相平衡分配系数，讨论了影响因素。     

Optimal escapement levels in stochastic and deterministic harvesting models

A constant-escapement feedback policy is shown to be optimal in maximizing expected discounted net revenue from an animal resource whose dynamics are described by a stochastic stock-recruitment model, provided that unit harvesting costs satisfy certain conditions. The optimal escapement in this model is compared with that in the corresponding deterministic model and it is shown how the way in which unit harvesting costs vary with population abundance can be important in determining the relative sizes of the optimal escapements. In most cases, the optimal stochastic escapement is no less than the optimal deterministic escapement.     

Voluntary Auctions for Noxious Facilities: Incentives to Participate and the Efficiency of Siting Decisions

This paper explores the efficiency properties of a voluntary auction under which the city submitting the low bid hosts the region′s noxious facility and receives the high bid as compensation. In the Nash equilibrium of the auction game, the auction mechanism is individually rational (participation is rational for all values of the local environmental costs of the facility), incentive-compatible (the facility is located in the low-cost city), and revenue-neutral. If the compensation of the host city distorts location choices, participation in the auction is rational for all values of local environmental costs if the scale economies associated with the noxious facility are large relative to the average local environmental cost and the distortionary cost per dollar of compensation.     

Entry Deterrence and Signaling in a Nonrenewable Resource Model

We analyze a nonrenewable resource model in which an incumbent firm faces potential entry from a rival firm. The incumbent has private information about its stock size but the rival can observe extraction. With observable extraction and unobservable stock, the rival can use extraction as a signal about stock, from which it can infer whether entry is likely to be profitable. We characterize the necessary conditions for pooling and separating perfect Bayesian equilibria in a signaling game of resource extraction and provide examples of each. We show that the incumbent will often prefer pooling to separating even though welfare is higher in separating equilibrium.     

Adaptive strategies of territory formation

How do territorial animals gain ownership of an area? Early modelling has considered the evolution of fighting when the winner can claim the right to the resource. Recently, alternative hypotheses have been offered where repeated interactions lead to division of space through 'nagging' instead of one decisive fight. However, these models assume that animals avoid areas in which they have taken part in aggressive interactions, but do not consider whether avoidance itself is adaptive. We aim to bridge this gap between mechanistic and adaptive explanations, by presenting a game-theory model where individuals choose whether to return to an area after a fight with a specific outcome (win, loss, draw). We show that avoidance of areas where fights have occurred can be adaptive, but only if benefits of access to the area are low compared to costs of fighting. Otherwise, one individual (typically the winner) responds by returning to the area, and the other (loser) avoids it. In such cases, space is gained by winning fights. We also consider the role of conventions. If responses to fights were purely conventional, paradoxical strategies where losers of fights gain ownership would be equally logical as common-sense ones where winners claim ownership. Paradoxical solutions can be stable but only when there is little difference in fighting ability between the competitors, when individuals adhere very strictly to a behavioural rule without much random variation, and when the population in its ancient state used a paradoxical strategy.     

Monopoly exploitation of an exhaustible resource

The popular notion that a monopolist will exhaust a nonrenewable natural resource at a slower than socially optimal rate is examined. Contrary to the prevailing belief, instances do exist for which the monopolist uses the resource faster than the social maximizer. This is demonstrated first by finding conditions for which the expected result—a monopoly rate which is slower than optimal-will always hold, and second, by showing that for situations where these conditions are violated the result may be reversed.