Modelling species extinction: the case for non-consumptive values

Conservation of endangered species is a multifaceted problem with species facing pressure from competition for land, from direct exploitation and from a lack of effective management. A model is developed, using the African elephant as an example, to highlight the key economic factors that are influential in determining the fate of an endangered species. Particular emphasis is placed on the role of non-consumptive values as a key component of species’ survival. It is demonstrated that, in many cases, some existence value must be appropriated to the resource in order for extinction to be avoided.     

Theory and practice of monetary policy

Summary. We consider an optimally managed renewable resource with stochastic non-concave growth function. We characterize the conditions under which the optimal policy leads to global extinction, global conservation and the existence of a safe standard of conservation. Our conditions are specified in terms of the economic and ecological primitives of the model: the biological growth function, the welfare function, the distribution of shocks and the discount rate. Our results indicate that, unlike deterministic models, extinction and conservation in stochastic models are not determined by a simple comparison of the growth rate and the discount rate; the welfare function plays an important role.Received: 20 October 2004, Revised: 28 February 2005, JEL Classification Numbers: D90, O11, O41, Q32.Santanu Roy: Correspondence toResearch on this paper was completed when the second author visited Cornell University in July, 2003. We thank the Center for Analytic Economics and the Department of Economics at Cornell University for making this research visit possible. The current version has gained considerably from the comments made by an anonymous referee.     

A real option approach to the protection of a habitat dependent endangered species

We use a real option approach to determine when a social planner has to stop or resume logging in situations where an endangered species relies on forest habitat for its survival. Logging affects the stochastic process followed by the habitat of the endangered species, which disappears irreversibly if its habitat reaches a critical extinction level. As long as the endangered species is still in existence, the social planner manages logging in such a way as to balance the risk of extinction against the benefits from commercial wood exploitation. The model incorporates economic, ecological, and social features. It is solved analytically to characterize the optimal forest management rule. Then it is applied to the case of the Rangifer tarandus caribou, an endangered species in Central Labrador (Canada). The parameters of the habitat process are estimated by Monte Carlo methods. The policy implied by the model – alternatively banning and resuming logging according to appropriate habitat threshold levels – turns out to be quite attractive; it does not require long banning periods while it drastically reduces the extinction risk and increases forest value.     

Harvest and extinction in multi-species ecosystems

A potential cost of harvesting in multi-species ecosystems is the extinction of nonharvested species that are at the same trophic level as the harvested species. Existing analytical models are not well-suited for studying this harvest externality because they focus on species interactions across trophic levels instead of within them. We identify the conditions under which the harvesting of a single species causes at least one extinction of nonharvested species at the same trophic level. We compare two harvest regimes: uniform management, in which a privately optimal harvest rate is applied to the entire ecosystem; and specialized management, in which a portion of the ecosystem is intensively managed for the harvested species and the rest is left unharvested. Which regime is more likely to result in extinction depends on the discount rate and on the harvested species' competitive ability and colonization rate compared to those of the other species.     

Effect of total resource allocation effect and economic growth：Chinese experience of 1978-2004

The analytical method of total resource reallocation effect is an evolution of the analytical method of the factors of economic growth. Since the marketization reform in China in 1978, market mechanism has played a more and more important role in resource allocation, and Chinese economy has developed greatly, which is called ＂the Chinese Miracle＂. This paper analyzes the economic growth in China from 1978 to 2004 with the analytical method of total resource reallocation effect. The result shows that the annual growth rate of total resource reallocation effect was 0.2%, which was 5.1% of the comprehensive productivity and 0.21% of the gross output growth, i.e. the total resource allocation played a weak role in the economic growth in China. When analyzing it in Chenery＇s multinational model, we find that Chinese comprehensive productivity growth rate was higher than that in all the income phases of the model, but the total resource allocation effect was obviously lower than that in all the income phases of the model. It indicates that the total resource allocation in China has a great potential, and that to accelerate marketization reform is one of the important issues for Chinese economic development.     

自然资源、经济增长与创新三者的关系分析

自然资源是经济增长的过程中的一个要素,理论上这个要素能够扩大生产可能性边界,但是,现实生活中自然资源常常阻碍了经济增长的提高,而缺少自然资源的地区反而可能有更快的增长速度.本文考察了自然资源禀赋、经济增长与创新之间的关系,作为"资源诅咒"的传导机制的重要部分,并发展了一个基于内生经济增长理论,变化的拉姆齐-卡斯-库普曼斯模型来解释"资源诅咒"现象.资源收入通过直接减少工作动力和间接导致较小的从事创新的劳动力比例两种方式阻碍经济增长.     

Optimal fishery harvesting rules under uncertainty

This paper derives the optimal fishery harvest policy in a real-option model with a stochastic logistic growth process, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. The optimal policy is illustrated with data from the Pacific Halibut Fishery. For this particular case, the optimal policy recommends harvesting when the fish stock rises to about three-quarters the environmental carrying capacity, and the amount harvested should be approximately a quarter of the prevailing stock. This harvesting policy maximizes the value of the fishery, and importantly, the resulting risk of extinction is negligible. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate and volatility of the stock, and also the economic parameters that have been ignored in previous papers (price sensitivity and fixed cost). If the optimal policy is followed, the risk of extinction will be negligible, except for very low growth rate and high volatility.     

Hyperbolic discounting and the time-consistent solution of three canonical environmental problems

In this paper I propose a time-consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open-access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.     

Natural Resource Dependence and Economic Performance in the 1970–2000 Period

We look at the type of natural resource dependence and growth in developing countries. Certain natural resources called point‐source, such as oil and minerals, exhibit concentrated and capturable revenue patterns, while revenue flows from resources such as agriculture are more diffused. Developing countries that export the former type of products are regarded prone to growth failure due to institutional failure. We present an explicit model of growth collapse with micro‐foundations in rent‐seeking contests with increasing returns. Our econometric analysis is among the few in this literature with a panel data dimension. Point‐source‐type natural resource dependence does retard institutional development in both governance and democracy, which hampers growth. The resource curse, however, is more general and not simply confined to mineral exporters.     

The ghost of extinction: Preservation values and minimum viable population in wildlife models

The inclusion of a minimum viable population in bioeconomic modeling creates at least two complications that are not resolved by using a modified logistic growth function. The first complication can be dealt with by choosing a different depensational growth function. The second complication relates to the inclusion of the in situ benefits of wildlife into the analysis. Knowledge about the magnitude of the in situ benefits provides no guide for policy about conservation management. Simply knowing that people are willing to pay a large amount each year to protect a species says nothing about whether one should manage habitat to protect or enhance the species' numbers, unless the species is in imminent danger of extinction. If willingness to pay is to be a guide, it needs to be better tied to population numbers, especially the minimum viable population.     

Harvesting to Extinction: Is It Socially Rational?

This paper presents a critique of the neoclassical view of the optimal use of renewable resources and offers an alternative view based on the method of classical thermodynamics. The presentation is forwarded via the issue of harvesting to extinction. Based on simple models, the traditional theory suggests that society would benefit from wiping out any renewable resource whose intrinsic growth rate, though positive, is smaller than the social rate of time preference. The latter is the rate society is using to discount its future benefits and costs. To bypass this ecologically implausible outcome, the simplistic assumptions have been modified in various ways. For example, either the costs or the benefits of harvesting have been made to depend on the stock of the resource as well as on the yield. The modifications offered make society less prone to wipe out resources intentionally, but they still disregard a more fundamental difficulty: The traditional theory is not consistent with the second law of thermodynamics; it describes a process that defies the second law, which no known system is able to be undergoing. No doubt, the theory should be challenged first and foremost on this ground, but none of the offered modifications is capable of annulling this inconsistency. A deeper change is needed because the social values of the resource as perceived by a society that behaves in manners consistent with the second law and as defined by the traditional theory necessarily differ. The paper identifies the socially consistent value and shows that harvesting to extinction is never optimal socially. Were society to follow the socially inconsistent value, it would always underestimate the importance of self-sustained resources. However, the unlikely refutability of the second law turns this possibility and the socially favored extinctions into arguable outcomes of an untenable theory rather than undesirable outcomes of a sound theory. Potentially growing renewable resources are wiped out in real life for various reasons, but when they are preyed to extinction, their unfortunate fate is an outcome of the dynamics of a socially unregulated system rather than a social objective coming to fruition. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fishing Technology and Optimal Distribution of Harvest Rates

This paper examines the problem of the optimal management of a joint-ownership fishing exploitation, where agents use different fishing gears. We consider a model in which the fishing activity may affect resource growth, not only through the harvest function but also through the natural growth rate of the resource. This allows us to capture the fact that some fishing gears alter the natural growth rate of the resource. We find that when the natural growth of the resource is altered by the fishing technology, the optimal stock is not independent of how harvest quotas are distribute among the agents. As a result, a fishing policy that firstly determines the optimum stock and, secondly, decides how to distribute the harvest among the different agents, will not be efficient. We also analyze the joint determination of optimal stock and harvest quotas and show that positive harvest quotas will only be optimal when countries are characterized by certain asymmetries.     

Strategic Preemption in a Common Property Resource: A Continuous Time Approach

The threat of future entry affects the exploitation of common property resources in important ways. An incumbent has a strategic incentive to manipulate the resource stock to deter entry or to harvest more stock prior to entry rather than share the resource with the entrant. It is possible that the threat of potential entry can lead to the extinction of the resource even though actual competition would result in a steady state with a positive stock level.     

自然资源与经济增长:资源瓶颈及其解决途径

本文试图在新古典经济学框架内,解析古典经济学关于自然资源制约经济增长的传统,并揭示克服资源瓶颈的可能途径。文章首先扩展新古典索洛模型,证明在特定技术条件下,自然资源的固定禀赋最终将使经济增长停滞。然后分别探讨了解决资源瓶颈的两种机制。其一是产业转移,即开放条件下,厂商为摆脱本地资源瓶颈,通过向外地转移资本和劳动以利用该地的自然资源,从而带动了该后起地区的经济增长。其二是技术进步,即在封闭条件下,厂商将把一部分产出投入于研发活动,不断开发出自然资源增进型技术,从而推动本地区的又一波长期增长。     

资源约束不断加深下的可持续增长

该文借用一个资源约束不断加深的经济增长模型,重点分析资源开采成本、环境质量要求、污染税对经济增长的影响,发现在资源开采成本不断上升时,如果效用函数中环境质量要求足够大、折现率足够低、那么污染税能够促进增长;当资源开发效率较低时,污染税对经济增长率有正效应。中国的进口资源—粗加工—再出口模式同时承担了巨大的资源价格上涨压力和粗加工过程中的环境污染压力,在新的资源来源难以保证的情况下,尤其需要在立法和执法过程中提高环境质量要求,降低环境效用的折现率,以通过严格执行污染税实现经济的可持续增长。     

产业生态化:人工产业系统的生态性回归

产业系统所创立的单向线性经济模式的反生态特征,在私人资本的获利性和生态环境的无价性的经济制度下,导致资源枯竭和生态退化。产业系统必须向生态性回归:变线性增长模式为循环增长模式,形成一个损耗与利用优化、环境自净和人工净化相结合的相对闭合的能量与物质的循环系统,不断提高循环利用自然资源和恢复自然生态系统的能力。     

A viability analysis for a bio-economic model

This paper presents a simple dynamic model dealing with the management of a marine renewable resource. But instead of studying the ecological and economic interactions in terms of equilibrium or optimal control, we pay much attention to the viability of the system or, in a symmetric way, to crisis situations. These viability/crisis situations are defined by a set of economic and biological state constraints. The analytical study focuses on the compatibility between the state constraints and the controlled dynamics. Using the mathematical concept of viability kernel, we reveal the situations and, if possible, management options to guarantee a perennial system. Going further, we define ‘overexploitation’ indicators by the time of crisis function. In particular, we point out irreversible overexploitation configurations related to the resource extinction.     

International trade, exhaustible-resource abundance and economic growth

Countries with oil and other natural resources have grown less rapidly than those countries without. This phenomenon is known as the “natural resource curse”. We develop an infinite-horizon, two-country model of trade in which countries are identical, except that one country is endowed with deposits of an exhaustible resource and the other is not. Within the context of the model, we show that this phenomenon can be explained in part by an inelastic demand for the exhaustible resource that increases growth in trade revenues and induces the resource-abundant country to invest relatively less than the country lacking in exhaustible resources. These results are derived analytically and illustrated by an empirical analysis based on plausible parameters obtained from data.     

On the dynamics of renewable resource harvesting and pollution control

The paper presents a dynamic partial equilibrium model which combines optimal renewable resource harvesting and optimal pollution control. Pollution accumulates as a slowly decaying stock and is assumed to affect the growth and the quality of the renewable resource stock. The aim is to maximize a social welfare functional which gives the present value of the difference between natural resource benefits and pollution control costs. The existence, uniqueness and the dynamic properties of the steady states are investigated. The analysis also gives a general result concerning the steady state of any two state variable optimal control problems.     

绿色生态资源的规整性开发策略模型与算法求解

综合考虑绿色生态资源规模、技术创新、开发成本等不确定因素,对归属于不同存储路径的绿色生态资源开发顺序与开发时间进行规整性决策。构建了考虑满足开发优先级顺序与净现值最大化的前提的绿色生态资源开发模型。根据绿色生态资源开发的实际特点,构建了整数规划开采决策模型。基于异步次梯度法的拉格朗日松弛算法求解出稳态下绿色生态资源价格和产量的增长率,并对求解进行数值模拟与敏感性分析。研究表明,技术创新对绿色生态资源的规整性开发起到决定性作用。最终产品供给部门和资源开发部门的资源开发优先级约束、生产约束与资源开采净现值水平将显著影响绿色生态资源产量增长率。