بهره برداری استراتژیک از یک منبع مشترک تحت خطر زیست محیطی

We study the effect of environmental risk on the extraction of a common resource. Using a dynamic and non-cooperative game in which an environmental event impacts the renewability and the quality of the resource, we show that the anticipation of such an event has an ambiguous effect on extraction and the tragedy of the commons. A risk of a reduction in the renewability induces the agents to extract less today while a risk of a deterioration in the quality has the opposite effect. Moreover, when environmental risk induces conservation, the tragedy of the commons is worsened.

Natural common resources are susceptible to increasing environmental risks as reported in recent scientific studies. The most common prediction is a widespread reduction in the renewability (i.e., the future quantity) of the stock of natural resources. Declining fish stocks (Backlund et al., 2008); a decrease in global water availability (IPPC, 2007); an overall decline in crop yields for global temperature increases above View the MathML source3°C (IPPC, 2007); and a decrease in growth rates of tropical forests (Hopkin, 2007) are just a few examples. There is also scientific evidence regarding the negative effect of climate changes on the quality of natural resources. The US Department of Agriculture reports that an increase in extreme events brought on by climate changes, such as more frequent flooding, will reduce water quality (Backlund et al., 2008).1 Complementary to the scientific research, there exists a large literature in economics that asks how economic behavior is altered in anticipation of events that have detrimental effects on natural resources.2 While many papers have found conservative behavior in the context of single-agent dynamic models, less is known about the link between conservative behavior and the tragedy of the commons. Specifically, there remains the question of whether the intensity of conservation differs in the non-cooperative outcome and the social planner's solution and if so, what the effect is on the tragedy of the commons.3 It is the purpose of this paper to consider whether the tragedy of the commons is reduced or exacerbated in the presence of environmental risk. To that end, we embed environmental risk in a dynamic and non-cooperative extraction game à la Levhari and Mirman (1980) and show that strategic interactions are key in explaining the effect of environmental risk on the tragedy of the commons. We focus on two effects of environmental risk consistent with the scientific evidence exposed above: renewability and quality. We consider a purely exogenous risk, i.e., the exploitation of a lone resource has a relatively small effect on regional or global environmental risk.4 This is in contrast to a strand of the literature on (single-agent) optimal control which considers the problem of resource management under uncertainty when the agent can reduce the likelihood of the environmental risk (Clarke and Reed, 1994, Tsur and Zemel, 1995, Tsur and Zemel, 1996 and Tsur and Zemel, 1998). Specifically, Tsur and Zemel (1995) study the management of groundwater resources at risk of a permanent and catastrophic event (ceasing exploitation activity).5 Optimal exploitation is also studied in the context of managing the level of pollution in the case of environmental events (Clarke and Reed, 1994, Tsur and Zemel, 1996 and Tsur and Zemel, 1998).6 In all these cases, conservation can occur to prevent or reduce the likelihood of such events. In contrast, by focusing on a completely exogenous event, the change in behavior is solely due to reducing exposure to risk (instead of altering it).7 Hence, we are able to provide results about the pure effect of environmental risk, thereby abstracting from any manipulation by the agents.8 We first show that when the environment becomes riskier, harvesting behavior is altered in order to reduce exposure to risk.9 On the one hand, if environmental changes lead only to a lower renewability, agents reduce their exposure to this type of risk by harvesting less. The substitution toward future harvesting (and, thus, consumption) is due to precautionary motives since saving more allows one to compensate for a possibly less renewable resource and less future availability of the stock. On the other hand, if environmental changes lead only to lower quality, then agents reduce their exposure to risk by harvesting and consuming more in the present so as to face less risk in terms of future utility flows. When both quality and renewability are at risk of being deteriorated, the direction of the effect depends on the relative strength of the two effects. For instance, if the deterioration in quality is small compared to the negative change in renewability, then agents reduce their exposure to risk by harvesting less. In that case, precautionary motives dominate over concerns for lower future (per-unit) utility flows. In view of our results, the reason for a change in behavior due to environmental risk is solely motivated by a reduction in the exposure to risk (and not manipulation of likelihood of risk as discussed above). In that sense, our framework is close to Lafforgue (2005), which provides such an analysis in the context of a single-agent optimal control problem of resource extraction when there is amenity value for the exploited stock. The effect of uncertainty is shown to be ambiguous as well, and can lead to conservation. However, the overall effect depends on the size of uncertainty and not on the type of uncertainty, as in our paper (i.e., quality vs. renewability uncertainty). After explaining how different types of risk affect harvesting, we turn to the tragedy of the commons. We show that when environmental risk induces conservation (i.e., when the risk of less renewability is more important than the risk of quality deterioration), the presence of the risk leads to a stronger decrease in present harvesting under social planning than in the non-cooperative game. Hence, the ratio between aggregate harvesting in the Cournot–Nash outcome and the socially optimal level of harvesting is increased, which makes the tragedy of the commons worse. Although agents choose to harvest less, they do not internalize the risk that too much extraction creates for others, and, thus, decrease their own extraction too little. The social planner, on the other hand, internalizes this effect and decreases harvesting more. This disparity in conservation leads to a worsening of the tragedy of the commons. We also show that when the risk of quality deterioration is the greatest of both risks, a larger stock means more uncertainty regarding future utility flows. In the non-cooperative game, the agents only care about their own exposure to risk without considering the overall risk in terms of future utility flows, which leads to a weaker increase in harvesting relative to the social planner. As a result, the tragedy of the commons is lessened because the agents fail to reduce exposure to risk in a socially optimal way. The rest of the paper is organized as follows. In Section 2, we present the model. In Section 3, we characterize the Cournot–Nash equilibrium and the benchmark socially optimal solution. We then study the effect of environmental risk on behavior and the tragedy of the commons in Section 4. Section 5 concludes and suggests possible extensions.

We study the economic behavior of agents who extract a common resource when the renewability and the quality of the resource are at risk of being altered by environmental change. In particular, we show that when the agents engage in conservative behavior, the tragedy of the commons is exacerbated due to strategic interactions. In order to obtain the existence of a Markov-perfect Nash equilibrium, we have relied on the Levhari-Mirman model of resource extraction with strategic interactions. While this specification may seem too restrictive,19 our results on conservation in a non-cooperative game are consistent with the results derived from the different functional forms used in the literature described in the Introduction. The only difference is that we show that whether conservation occurs or not depends on the source of risk. However, in this aspect, our explanation is not specific to the log utility, or the Cobb–Douglas production function, but rather due, in general, to the motivation to reduce the exposure to risk. When risk concerns quality, a reduction in risk exposure is possible by harvesting more. When risk concerns quantity, harvesting less in order to have a buffer saving yields less risk. Similarly, the link between conservation and the tragedy of the commons does not depend on the functional form of the utility and the production functions. Rather, it is due to the presence of strategic interaction and its effect on conservation. For instance, when there is conservation, strategic interactions induce each agent to conserve less (relative to the social planner) because they can benefit from the conservation of the other agents. Finally, we note that our model abstracts from two important aspects. First, we have focused on an exogenous environmental change. Endogenizing the probability of a climate change as in Clarke and Reed (1994) and Tsur and Zemel, 1995, Tsur and Zemel, 1996 and Tsur and Zemel, 1998 should a priori strengthen the result. If agents could reduce the likelihood of the environmental risk by decreasing present extraction, then this extra conservation motive would further increase the tragedy of the commons. Second, we have assumed that society does not display a protection motive for the resource, i.e., there is no amenity value. 20 Assuming that the stock enters directly into preferences as in Lafforgue (2005) should also alter the effect of environmental risk on the tragedy of the commons.