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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 question of whether an exhaustible natural resource will be extracted at a socially optimal rate under imperfect competition, which first arose in the context of OPEC cartels in the 1970s, has reemerged in recent years in the context of new kinds of resources, such as antibiotics and crops genetically engineered to repel pests. Pesticides and antibiotics can be thought of as depletable resources, due to the selective pressure they place on susceptible bacteria or pests, which ensures that they become less effective with use [16]. The problems of suboptimally high rates of depletion that are associated with the open access nature of these resources are ameliorated to some extent by the existence of the patenting system. Although patents on antibiotics and pesticides are intended to reward innovators for undertaking the investment that leads to the innovation, they serve an additional purpose in the context of resistance-prone resources in that they give the patent holder an incentive to care about the rate at which resistance develops. Some have argued, therefore, that giving innovators longer patents would increase their incentives to internalize the problem of emergence of resistance [1] and [21]. Others have extended this argument to claim that the existence of patents relieves society from the burden of regulating for resistance since the patentee may have sufficient incentives to consider the depletion of product effectiveness. An additional feature of patents is that they often (though not always) give the patentee a head start in developing future drugs and pesticides that depend on the basic patent. This paper examines the issue of monopoly provision of a depletable resource when the patentee has the option of developing future resource pools after incurring some setup cost. It demonstrates that granting patents to firms may not necessarily give them a stronger incentive to protect their product from resistance. A number of authors have written on the implications of monopoly for the extraction of an exhaustible resource: Weinstein and Zeckhauser [31], Stiglitz [26], Kay and Mirrlees [14], Lewis [17], Sweeney [27] and [28], Dasgupta and Heal [2], Tullock [29] and [30], Lewis et al. [18], Eswaran and Lewis [5], Pindyk [23], and Gaudet and Lasserre [8], among others. Reviews of this literature are included in Peterson and Fisher [22], Dasgupta and Heal [2], Devarajan and Fisher [4], and Krautkraemer [15]. However, the role of future pools of resources and the associated setup costs in monopoly provision has received relatively little attention in these papers. Many traditional natural resources (and non-traditional ones like antibiotics and pesticides that are the focus of this paper) involve significant setup costs—fixed costs of exploration and development that must be incurred before any extraction can begin. Major investments in research and development, as well as the drug approval process, must occur before the products can be brought to market. Hartwick et al. [11] showed that in the presence of setup costs the social optimum dictates sequential exploitation of the natural resource pools, and the optimal path of marginal current net benefit will rise in a “saw-tooth” fashion. While any particular pool is being exploited, the marginal net benefit rises at the rate of interest, dropping down when a switch is made to the next pool, with the difference reflecting the marginal benefit of postponing the switch. Since setup costs create a non-convexity, they indicated and Fischer [6] proves that the socially optimal path cannot then be decentralized to a perfectly competitive equilibrium. Thus, the true extraction path would be characterized by some form of imperfectly competitive equilibrium. This paper analyzes the exploitation path that would occur with monopoly ownership of the resource pools and compares it to the planner's problem. Dasgupta et al. [3] considered setup costs in the form of the cost of inventing a new technology. With that technology functioning as a backstop substitute for the existing resource, the monopolist is shown to prolong extraction and delay implementation of the new technology compared to the planner. However, this result cannot be generalized when the setup investment produces the next in a sequence of exhaustible resources. The important difference is that with a non-exhaustible backstop, marginal costs are the same for the planner and the monopolist; thus, the relative stream of value from the new technology depends on consumer surplus and total revenue, given the same costs. However, when the new technology is also exhaustible, the marginal costs incorporate a scarcity value—and that scarcity value is different for the monopolist and the planner. Furthermore, the scarcity value also depends on how many more new technologies or resource pools remain in the sequence. Therefore, the planner and the monopolist face different kinds of tradeoffs in deciding when to exhaust the current resource and move on to the next, and those relative incentives depend further on the structure of demand and the availability of future sources. In this paper, we describe how these issues arise with new importance in application to problems of resistance, with the example of transgenic Bt crops and antibiotics (Section 2). We then present a model to analyze the general problem of sequential exploitation for both the planner and the monopolist (Section 3). 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, if consumer demand takes other forms, the monopolist may exhaust the resource more quickly, especially if many new options will follow. This result is demonstrated using a slight variation on the model in [26], which features constant elasticity of demand with zero extraction costs. In that case, without setup costs, the monopolist extracts at the same rate as the social planner. We find that in the presence of setup costs the monopolist is either more or less conservative than the social planner, depending on how many resource pools remain. If few resource pools are available after the current one is exhausted, the monopolist behaves more conservatively than the planner, extracting more slowly and delaying the setup of the next pool. However, if many resource pools remain in the queue, the monopolist extracts faster than the planner, more impatient to access the future revenue stream.

The monopolist reacts differently to setup costs in exploiting exhaustible resources than would a social planner. Understanding how is important, since setup costs make competitive provision unlikely for a resource that does not exhibit significant, increasing variable costs of extraction. This situation can occur in some traditional resource markets, but it is perhaps more common for newer resources like antibiotics or biotech products. For these products, the major costs are incurred in the development process, rather than production. Once complete, patents ensure the developer a monopoly over provision of the product. Furthermore, scarcity is an important issue, since consumption depletes the resource—resistance increases with greater use of antibiotics or of crops genetically engineered to repel pests. How the monopolist's incentives differ from those of the social planner depends on several factors. First is the question of how scarcity value affects the path of consumption. For the monopolist, marginal profits rise at the rate of interest during the exploitation of a particular resource pool. Depending on the structure of demand and extraction costs, this can lead to either a faster or slower extraction path than the planner. However, even with identical scarcity incentives, as in the case with constant-elasticity demand and no extraction costs, extraction can differ according to the incentives for timing the switchover to the next resource pool. These incentives involve tradeoffs between prolonging the life of the current resource pool and postponing a move to the next one. Prolonging use of the current pool means another period of profits, but that extraction comes at a cost of slightly less extraction—and thereby profits—in all the preceding periods over the life of the resource pool. This net effect can be larger or smaller than the net benefits to the planner of prolonging use of a pool, which involve the excess of total surplus in the last period over the scarcity value (marginal surplus) of the last period's extraction. Postponing the switch to the next resource pool postpones not only incurring the setup cost, but also receiving the present value of that resource pool and all the subsequent ones. Thus, for the monopolist, waiting one more period means giving up the interest that would have been gained on the value of the subsequent profit stream, which is necessarily less than the subsequent stream of surplus for the planner. This latter effect tends to make the monopolist more patient—and thus more conservationist than the planner—since the costs of postponing are smaller. The overall effect then depends on the relative magnitudes of these differences. With certain forms of demand, like the constant-elasticity case, the monopolist's net benefits of prolonging use of the existing pool are smaller than those of the planner. When the costs of postponing the switch are relatively small, as when there are fewer resource pools left in the queue, the monopolist prefers to wait longer and conserve the existing pool. However, when the opportunity costs of postponing loom relatively larger, as when many more resource pools will be available, the monopolist becomes more impatient than the planner and follows a less conservationist path. The assumption of the constant-elasticity demand function is useful for analytical convenience that the monopolist's and social planner's incentives are perfectly aligned in case of zero setup costs. However, assuming a different demand specification would not alter our basic result that the availability of a large number of additional resource pools, each with its own setup costs, would imply a relatively faster rate of extraction for the monopolist (relative to the social planner), than if there were few additional resource pools. For resources like biotech products, an important research question is whether the patent system offers good incentives for the monopolist to exercise the proper care for managing resistance and inventing new substitutes. This question has been raised not only regarding agricultural biotech products, but also in the case of antibiotics and the need for direct regulation for drug resistance.14 The extensive use and misuse of antibiotics has resulted in rapidly increasing levels of bacterial resistance to these valuable drugs that form the bedrock of modern medicine. Pharmaceutical firms, which typically have 7 to 10 years to recover the significant investments made in drug development, may have insufficient incentives to care about drug resistance. Some have suggested the extending patent length or breadth on antibiotics may give pharmaceutical firms a greater incentive to conserve the effectiveness of their products (Tisdell 1982, OTA, 1995, Laxminarayan 2002). The results of this paper indicate that extending the firm's patent on antibiotics may or may not be in society's best interests depending on whether or not there are derivatives of the existing product that could be modified to counter the effects of drug resistance. This paper indicates that more needs to be understood regarding not only the structure of demand but also the scope for future technologies. For example, a new antibiotic is often a variation of the same basic chemical entity; the scope for new derivatives not subject to the same resistance may then naturally be limited. Furthermore, in view of the uncertain nature of the arrival time and quality of new discoveries in the real world, future research is needed to understand how a monopolist may respond to these uncertainties compared to society's preference. These questions involve not only investment strategies, but also how early arrivals of substitute resources affect the use of current stocks—are they abandoned, exploited simultaneously, or exhausted while the new patent “sleeps”? More generally, our results indicate that the characteristics of a new invention—specifically, whether or not it is depletable—are important for determining whether the monopolist is indeed a conservationist's friend.