A note on the extinction of renewable resources

We consider in this chapter Hotelling’s classic model of the economics of exhaustible resources and its extensions. The social planner’s problem in this model is to maximize the discounted social benefit from consumption of a homogeneous resource under the constraint that cumulative consumption is no greater than the initial resource stock. The marginal resource rent for the optimal extraction path grows at the real rate of interest, and the equilibrium resource price meets this condition, known as “Hotelling’s rule”. This rule modifies under the model extensions to heterogeneous resources: the marginal rent falls if extraction switches from low-cost to high-cost resource stocks. We consider the models of resource pricing in the presence of a backstop technology, the Herfindahl principle that a lower-cost resource stock depletes before extraction switches to a higher-cost stock, and the principle of comparative advantage for a more general case of heterogeneous resources and consumers.

We study the optimal extraction of a polluting nonrenewable resource within the following framework: environmental regulation is imposed in the form of a ceiling on the stock of pollution and a clean unlimited backstop technology can be developed by research and development. More specifically, the time taken to develop a new technology depends on the amount spent on R&D. A surprising result is that the stringency of the ceiling and the size of the initial stock of the polluting nonrenewable resource have a bearing on whether environmental regulation speeds up the optimal arrival date of this new technology. Compared to a scenario with no environmental externalities, stringent environmental regulation drives up the optimal R&D investment and brings forward the optimal backstop arrival date only in the case of a large initial resource stock. Otherwise, if the initial resource stock is small, regulation reduces optimal R&D and postpones the optimal backstop arrival date. These results are explained by the two roles played by the backstop technology. First, the backstop serves to replace oil once it has been exhausted. As extraction is slowed down by regulation, the exhaustion of the nonrenewable resource is postponed and the long‐run gains of innovation are lowered. Second, environmental regulation raises the short‐run gains of innovation by increasing the cost of consuming just oil.

A qualitative characterization of the competitive nonrenewable resource extracting firm

The optimal extinction of a renewable natural resource

Equilibrium transitions from non-renewable energy to renewable energy under capacity constraints

A fundamental issues in designing any fiscal regime for non-renewable resources is the balance between rent taxes and royalties. This paper reviews the core issues that arise, in terms of both efficient rent extraction and correcting various market failures. Issues of asymmetric information, for instance, can rationalize using both instruments. The paper also shows that, even though they effectively involve the choice of distinct parameters at several dates, rent taxes are not subject to the time consistency problem that is central to the extractive industries, but royalties are (although time consistent royalty policy is efficient conditional on initial resource stocks).

Women entrepreneurs have long been argued to suffer from disadvantages in initial resource stock, which makes it difficult to establish and maintain a sustainable competitive advantage. Prior work suggests that planning may assist in overcoming these disparities; however, few studies have examined these relationships while considering context. We explore the role of strategic business planning activities on entrepreneurial firm performance and whether such planning activities yield greater benefit for women than men. We find that business planning provides greater performance benefits to women, which we argue may give women an opportunity to compensate for initial resource disadvantages.

On the profitability of cross-ownership in Cournot nonrenewable resource oligopolies: Stock size matters

We examine the profitability of cross-ownership in an oligopolistic industry where firms compete as Cournot rivals. We consider a symmetric cross-ownership structure in which a subset of k firms engage in cross-shareholding and each firm has an equal silent financial interest in the other firms, while the remaining (n – k) firms stay independent. We show that a symmetric cross-ownership is never profitable for any levels of non-controlling minority shareholdings if the participation ratio (k/n) is less than or equal to (n+1)/(2n), while there exists a large range of cross-ownership for which it can be profitable beyond that participation ratio. This result may be called a cross-ownership paradox, analogous to the merger paradox. With the presence of stock constraints, however, we find some of the results from the cross-ownership paradox do not carry over to the case of non-renewable resource industries. The profitability of a symmetric cross-ownership can be positive even when the participation ratio (k/n) is less than or equal to (n+1)/(2n) and is always positive when the participation ratio (k/n) is greater than (n+1)/(2n), provided that the initial resource stock owned by each firm is small enough. We also highlight that cross-ownership can be preferable to a horizontal merger under Cournot competition. Not only is it more profitable to do so, more importantly, it constitutes a shrewd strategy to avoid possible legal challenges.

A fundamental issues in designing any fiscal regime for non-renewable resources is the balance between rent taxes and royalties. This paper reviews the core issues that arise, in terms of both efficient rent extraction and correcting various market failures. Issues of asymmetric information, for instance, can rationalize using both instruments. The paper also shows that, even though they effectively involve the choice of distinct parameters at several dates, rent taxes are not subject to the time consistency problem that is central to the extractive industries, but royalties are (although time consistent royalty policy is efficient conditional on initial resource stocks).

Path-dependence in a Ramsey model with resource amenities and limited regeneration

We study an optimal control problem with a man-made capital stock, and a stock of renewable natural resource. They are substitutable inputs in the production of the final good. Starting from low levels of both stocks, the optimal policy consists of three phases. In phase I, the planner builds up the stock of resource above its steady state level, while the man-made capital stock is kept below its steady state level. In phase II, the resource stock declines steadily, while the man-made capital stock continues to grow, until the steady state is reached, and the economy stays thereafter. The model exhibits “overshooting” property.

In a recent paper Levhari and Liviatan (1977) present a refinement of the analysis of Hotelling's (1931) paper on the economics of exhaustible resources. While they examine various aspects of the problem of determining the optimal time-path for the rate of extraction of a mineral deposit, they do not develop an important point raised by Hotelling (1931, 163): that the 'capital investment in developing the mine ... is a source of a need for steady production.' A large initial capital investment is typically required before a mineral deposit can be exploited: investment in infrastructure, overburden removal, shaft-sinking, mining and milling plants, and housing for employees may be necessary. The traditional model tends to ignore these preproduction expenses and treats all extraction costs as variable costs. The present paper argues that when the capital investment which must be undertaken before mining can commence is introduced into the conventional analysis of Hotelling, the optimal rate of extraction is constant over much of the mine's life and does not decline over time as the traditional model prescribes. The results of the present paper are derived from a model of non-renewable resource extraction in which the firm uses physical capital to extract the resource from a fixed resource stock of uniform quality. The rate of extraction, or disinvestment in the resource stock, is constrained by the amount of physical capital owned by the firm. The rate of investment in physical capital is assumed to have no upper bound and disinvestment in physical capital is assumed to be impossible, reflecting the fact that much of the capital invested in exploiting a resource stock may not be transferable to another use once extraction terminates. Various elements of the problem addressed in the present paper have received attention in the recent natural resource economics literature. Heaps and Neher (1980) investigate the optimal harvesting policy for a forest when the harvest rate is constrained; Clark, Clarke, and Munro (1979) use a model of renewable resource extraction to analyse the implications of various assumptions about the degree of malleability of capital (its ability to be transferred to an alternative use) for the optimal exploitation of a commercial fishery; and Puu (1977) discusses models of the extraction process of renewable and non-renewable resource stocks in which the rate of extraction is constrained by the size of the physical capital stock. Puu's model of nonrenewable resource extraction differs from that of the present paper in that the resource stock is assumed to be of nonuniform quality, the rate of investment in physical capital has an upper bound, and disinvestment in

This paper studies maximin paths in the context of a standard exhaustible resource model. Under the assumption that the resource is important in production, it establishes the efficiency and uniqueness of non‐trivial maximin paths. It uses these results to study the nature of the maximin value and policy functions. The value function is shown to be differentiable with respect to the initial resource stock, and the derivative of the value function is related to the shadow prices associated with the maximin path starting from that resource stock. We show how maximin policy functions can be derived, using the maximin value function, and the fact that the maximin path always follows Hartwick's investment rule.

Harvesting and Replenishment Policies for Renewable Natural Resources