Abstract
The theoretical literature following Hotelling (J Polit Econ 39:137–175, 1931) assumed that all nonrenewable resource needs are satisfied by one type of resource (e.g. “oil”), extractible at different per-unit costs. This formulation implicitly assumes that all users are the same distance from each resource pool, that all users can switch costlessly from one type of resource to another (e.g. liquid fossil fuels to coal or vice-versa), and that all users are subject to the same regulations. These assumptions imply, as Herfindahl (Extractive resources and taxation. University of Wisconsin Press, Madison, pp 63–90, 1967) showed, that in competitive equilibrium all users will exhaust a lower-cost resource completely before beginning to extract a higher-cost resource: simultaneous extraction of different grades of oil or of oil and coal should never occur. In trying to apply the single-demand curve model during the last twenty years, several teams of authors have independently found a need to generalize it to account for users differing in their (1) location, (2) resource needs, or (3) regulatory environment. Each research team found that Herfindahl’s strong, unrealistic conclusion disappears in the generalized model; in its place, a weaker Herfindahl result emerges. Since each research team focussed on a different application, however, it has not always been clear that everyone has been describing the same generalized model. The goal in this paper is to integrate the findings of these teams and to present an easily accessible generalization of the nonrenewable resource model to multiple demand curves.
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Notes
The multiple demand model explains why exhaustible resources with different, constant per-unit costs of extraction should in theory be simultaneously exploited, a prominent feature of the real world which cannot be explained by the the single demand model. Of course, depending on the particular situation, other factors also need to be taken into account if Hotelling’s model of expected wealth maximization is to be reconciled with empirical observation. Once account is taken of these other factors, the Hotelling model no longer predicts that prices will rise at r-percent, a property of only the simplest toy Hotelling model. See Gaudet (2007) for a fairly thorough discussion of some of those other factors, and Anderson et al. (2014), where Hotelling’s assumptions of expected wealth-maximization and foresight are maintained but recognition that some resources are driven to the surface by underground pressure is shown to improve the model’s predictions of well drilling and oil production in Texas.
Sources may need to be converted in order to satisfy a particular use (j) but, after conversion, they are assumed to be perfect substitutes. Otherwise the utility (\(U_{j}\)) would depend, even after conversion, on a vector of consumptions instead of a single aggregate. Even with linear costs, users would then simultaneously access multiple sources since they would be imperfect substitutes; they would also utilize multiple sources if the flow of production from each source was capacity constrained. Capacity constraints on the flow of production will be discussed in Sect. 4.
Source 3 will eventually be exhausted as well. If there are more than three sources, it will be exhausted in finite time at the date a switch occurs to the next highest cost source, as for sources 1 and 2; and so on for all the other sources.
The resumption of usage of a source by one user after it has been abandoned by another user and has remained idle is illustrated in Figure 1 of Im et al. (2006).
Chakravorty et al. (2005, Sect. 2.4) introduce various notions of comparative advantage, including this one, which they refer to as “pairwise comparative advantage.” Prior to that the concept of comparative advantage was also mentioned in Chakravorty and Krulce (1994, pp. 1445 and 1448) and Chakravorty, Roumasset and Tse (1997, p. 1222).
The paths depicted in Fig. 4 are compatible with the following entirely plausible assumptions: \(w_{21}> w_{11} > w_{31}\); \(w_{12}> w_{22} = w_{32}\); \(\lambda _2 > \lambda _3 > \lambda _1\); \(w_{11} < \lambda _{3} - \lambda _{1}\); \(w_{12} - w_{22} > \lambda _{1}\) (see Gaudet et al. (2001, pp. 1156–1157)).
Unlike the case in Im et al. (2006), discussed in footnote 5, the same user returns to the source he had abandoned.
To be concrete, suppose when charged the same price per barrel equivalent, all users regarded oil and coal (once liquefied) as interchangeable. Then coal (resource i) could be considered just another grade of oil with its own cost (\(w_{ij}=w_{ij^{\prime }}\)) and multiplier (\(\lambda _{i}\)). There would then be no need to extend Hotelling’s model to the case of multiple demand curves and the standard Herfindahl results would apply. Solow (1974, p. 5) discusses this case under the assumption that liquefied coal has the higher cost (w) but the lower Hotelling rent (\(\lambda \)). It is because these two resources are not perfect substitutes in all uses that the multiple demand curve model is needed.
See also Holland (2003), who shows that similar results can be obtained in a partial equilibrium framework.
If it were, and the constraint was also binding at time t, we would then observe user 1 being served by more than two sources simultaneously.
The volume of space contained in a landfill at any given time can be viewed as a stock of nonrenewable resource that is being depleted: dumping solid waste in the landfill is equivalent to extracting the displaced volume of space from it and shipping it to satisfy a demand for solid waste disposal.
The term leakage is used here to describe a situation where, for instance, an increase in a carbon tax at a particular date (or in a particular region) would result in an increase in emissions at another date (or in another region). The latter can be referred to as “spatial leakage” and the former as “intertemporal leakage”.
References
Amigues J-P, Favard P, Gaudet G, Moreaux M (1998) On the optimal order of natural resource use when the capacity of the inexhaustible substitute is constrained. J Econ Theory 80:153–170
Anderson ST, Kellogg R, Salant SW (2014) Hotelling under pressure. Working Paper 20280, National Bureau of Economic Research, Cambridge, MA
Chakravorty U, Krulce DL (1994) Heterogeneous demand and order of resource extraction. Econometrica 62:1445–1452
Chakravorty U, Krulce D, Roumasset J (2005) Specialization and non-renewable resources: Ricardo meets Ricardo. J Econ Dyn Control 29:1517–1545
Chakravorty U, Roumasset J, Tse K (1997) Endogenous substitution among energy resources and global warming. J Polit Econ 105:1201–1234
Fischer C, Salant SW (2014) Limits to limiting greenhouse gases: intertemporal leakage, spatial leakage, and negative leakage. Resources for the Future, DP 14–09
Gaudet G (2007) Natural resource economics under the rule of Hotelling. Can J Econ 40:1033–1059
Gaudet G, Salant SW (2015) The Hotelling model with multiple demands, Chapter 2. In: Halvorsen R, Layton DF (eds) Handbook on the economics of natural resources. Edward Elgar Publication, Cheltenham, pp 23–40
Gaudet G, Moreaux M, Salant SW (2001) Intertemporal depletion of resource sites by spatially distributed users. Am Econ Rev 91:1149–1159
Herfindahl OC (1967) Depletion and economic theory. In: Gaffney M (ed) Extractive resources and taxation. University of Wisconsin Press, Madison, pp 63–90
Hoel M (2011) The supply side of \({\rm CO}_2\) with country heterogeneity. Scand J Econ 113:846–865
Holland SP (2003) Extraction capacity and the optimal order of extraction. J Environ Econ Manag 45:569–588
Hotelling H (1931) The economics of exhaustible resources. J Polit Econ 39:137–175
Im EI, Chakravorty U, Roumasset J (2006) Discontinuous extraction of a nonrenewable resource. Econ Lett 90:6–11
Kemp MC, Van Long N (1980) On two folk theorems concerning the extraction of exhaustible resources. Econometrica 48:663–674
Ley E, Macauley MK, Salant SW (2002) Spatially and intertemporally efficient waste management: the costs of interstate trade restrictions. J Environ Econ Manag 43:188–218
Ley E, Macauley M, Salant SW (2000) Restricting the trash trade. Am Econ Rev 90(2):243–246
Nordhaus WD (1973) The allocation of energy resources. Brookings Pap Econ Act 3:529–570
Nordhaus WD (1979) The efficient use of energy resources. Yale University Press, New Haven
Solow RM (1974) The economics of resources or the resources of economics. Am Econ Rev 64(2):1–14
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This is a somewhat expanded version of Gaudet and Salant (2015). It builds on that paper and a keynote lecture delivered at the SURED 2014 conference, June 10, 2014, in Ascona, Switzerland.
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Gaudet, G., Salant, S.W. Modeling Nonrenewable Resources Use with Multiple Demands and Multiple Sources. Environ Resource Econ 70, 737–755 (2018). https://doi.org/10.1007/s10640-016-0003-9
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DOI: https://doi.org/10.1007/s10640-016-0003-9