Too Many or Too Few? On the Optimal Number of Firms in the Commons

Resource industries are industries that extract resources from nature. Common-pool nonrenewable resource industries, in particular, are industries in which multiple firms jointly exploit the same nonrenewable resource. Examples include multiple firms extracting oil from the same reservoir or multiple firms pumping water from the same deep water, slowly recharging aquifer. The extracted resource is then either directly sold in the marketplace or used as a vital input in the production of homogeneous goods to be sold in the marketplace.

Most resource industries around the world are either oligopolies or good approximation of them. From Ancient Greek ὀλίγος (olígos) “few”, and πωλέω (pōléō) “to sell”, the term “oligopoly” indicates a market characterized by few large firms, each with significant market power (defined as the ability of a firm to raise the price above the marginal cost of production). When it comes to standard oligopolies, it is well-known that increasing the number of firms leads to a decrease in market power and to an increase in social welfare: increased competition pushes prices down, thus making consumers better off, and even though firms’ profits decrease, social welfare (defined as the sum of consumers’ and producers’ surplus) increases.

In common-pool nonrenewable resource industries, however, market power is not the only source of inefficiency.

When market power coexists with one or more sources of inefficiency, as is the case for common-pool nonrenewable resource industries, traditional competition policies might have unintended consequences. Reducing market power does not necessarily lead to an increase in social welfare.

The trade-off between market power and the tragedy of the commons

In common-pool nonrenewable resource industries, market power coexists with the “tragedy of the commons”, which refers to the tendency of overexploiting a shared resource compared with social optimum, eventually leading to resource depletion. The tragedy of the commons can be thought of as an intertemporal externality: when extracting an extra unit of resource, a firm does not consider that the resource stock available for future extractions by other firms decreases, thus increasing the shadow price of the resource (defined as the price that a firm would be willing to pay to have an extra unit of the resource stock). A social planner instead would internalize such an externality and therefore would exploit the resource less than in an oligopoly equilibrium. Indeed, in the social planner’s welfare-maximization problem, the shadow price of the resource is higher than in a firm’s profit-maximization problem, implying that the resource is more valuable to the social planner than to a firm. Not surprisingly, the tragedy of the commons (defined as the difference between the shadow price in the social planner’s problem and the shadow price in a firm’s problem) becomes more of a tragedy the higher the number of firms. On the other hand, market power decreases when the number of firms increases, since the intensity of market competition intensifies as the number of firms gets larger. Consequently, there exists a trade-off between market power and the tragedy of the commons.

An increase in the number of firms decreases market power while increasing the tragedy of the commons.

The optimal number of firms: when market power and the tragedy of the commons offset each other exactly

Both market power and the tragedy of the commons change as the resource stock is reduced. Intuition suggests that when the resource stock is abundant the market power aspects dominate, whereas when the resource stock is scarce the tragedy of the commons aspects dominate. Following this line of reasoning, the number of firms should be increased when the resource stock is abundant and decreased when the resource stock is scarce, implying that the optimal number of firms cannot be constant. This reasoning is correct if the extraction cost does not depend upon the resource stock. Assuming that it is more costly to extract a scarcer resource than an abundant one, as done in the present study, it is theoretically possible that the optimal number of firms be independent of the resource stock, therefore constant. Specifically, if changes in the resource stock impact market power and the tragedy of the commons “in the same way” (i.e., if market power and the tragedy of the commons have the same elasticities with respect to the resource stock), there exists a number of firms that is intermediate, ranging from 1 to infinite, and constant over time such that the two sources of inefficiency offset each other exactly. With this resulting number of firms, social welfare is maximized.

Achieving efficiency by regulating firms’ entry

The objective of a regulator seeking to maximize social welfare is to regulate firms’ access to the resource in such a way as to make the actual industry size equal to the socially optimal one. This can be achieved by means of licensing fees to be paid by firms before starting resource exploitation. In an equilibrium with regulated entry, firms will enter until the discounted value of their future profit streams are equal to the licensing fee. Since the discounted value of future profit streams is decreasing in the number of firms, the higher the fee the lower the equilibrium number of firms. By increasing the fee, a regulator can ensure that fewer firms enter the industry. Vice versa, by decreasing the fee, a regulator can ensure that more firms enter the industry. Clearly, the optimal license fee must be set at a level so that the equilibrium number of firms entering the industry corresponds to the socially optimal number of firms. The constancy of the socially optimal industry size implies that there is no need for further regulations. It is worth remarking that the objective of the regulation is to maximize social welfare. Important environmental, social, and political issues such as resource conservation and income distribution are not included in the analysis.

Methodology

In this study, the authors develop and solve a continuous-time (a.k.a. differential) game model of oligopoly exploitation of a common-pool nonrenewable resource. A key assumption in the model is that for resource stocks below a certain threshold the extraction cost, assumed to be decreasing in the resource stock, exceeds the benefit from selling the resource. As such, not all resource stock is extracted. The extraction path in the oligopoly equilibrium is compared with the extraction path that maximizes social welfare (defined as the sum of consumers’ and producers’ surplus). In deriving the extraction path in the oligopoly equilibrium, both open-loop and closed-loop (feedback) strategies are considered.

Applications and beneficiaries

The results of this research have clear policy implications for the regulation of resource industries. Under certain conditions involving the market demand and the extraction cost functions as well as the shadow prices of the resource, efficiency can be achieved with an optimal licensing fee, which should be set at a level ensuring that the number of firms in the equilibrium with regulated entry coincides with the socially optimal number of firms. This research is innovative and may possibly serve to guide decision making for resource utilization (renewable vs nonrenewable resources). It may genuinely benefit strategic C-level decision makers in production industries, NGOs, political activists, those concerned with corporate responsibility, academics, policymakers, and legislators.

Reference to the research

Colombo, L., Labrecciosa, P., Simon, L.K. (2023). Too many or too few? On the optimal number of firms in the commons. Journal of Environmental Economics and Management 121, 102825.

Consult the research paper