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Insights from a Simple Hotelling Model of the World Oil Market

Natural Resources Research volume 18, pages 19–28 (2009)Cite this article

Abstract

This paper uses annual data on world oil price and consumption from 1965 to 2006 to calibrate a Hotelling model of optimal nonrenewable resource extraction. Numerical solutions are generated for various specifications of the elasticity of demand for both isoelastic demand and linear demand under each of two possible market structures: perfect competition and monopoly. Prior to the 1973 oil crisis, the model that best fits actual data is one of perfect competition with linear demand and a demand elasticity of −0.4. For the periods 1973–1981 and 1981–1990, the model that best fits actual data is one of monopoly with linear demand and demand elasticities of −0.8 and −0.7, respectively, suggesting that the market was strongly influenced by OPEC during this time. Under the model that best fits the most recent period (perfect competition with linear demand and demand elasticity −0.5), the real oil price (in 1982–1984 U.S.$) should fall in the range $60.87–$66.31/barrel over the years 2010–2030.

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Figure 1

Notes

  1. Pindyck also compares the optimal and actual values to the myopic values that would occur if future depletion was ignored but the reserve-production ratio was maintained at its optimal level.

  2. I assume that, at any given time t, all the oil extracted at time t is sold on the market at time t.

  3. Much work has also been done in an attempt to measure the shadow price of the resource (see, e.g., Devarajan and Fisher, 1982; Halvorsen and Smith, 1984; Lasserre, 1985).

  4. Any common access problems that may arise in perfect competition are ignored. In other words, I assume, as does Pindyck (1978), that there is a large number of identical firms that all ignore each other, or, equivalently, that a social planner or a state-owned company has sole production rights and sets a competitive price.

  5. This holds because, assuming constant marginal utility of income:

    $$P(t)=\frac{\partial U(E(t))}{\partial E},$$

    so that the first-order conditions for the social planner’s problem are the same as those that arise in perfect competition.

  6. If then per-period net benefit function G(X, E) is concave in both X and E, then, since the control set \(\{E\mid E\,\geq\,0\}\) is convex, the first-order conditions are both necessary and sufficient for an optimum (Weitzman, 2003).

  7. A U.S. deflator rather than a world deflator is used because the original nominal time series was in current U.S. dollars.

  8. Because my data are in terms of barrels rather than mmBtu, these parameters are converted using the conversion factor: 5.8004 mmBtu = 1 barrel (USGS, 2004).

  9. The fixed cost to extraction c 0 is assumed to be constant with respect to the stock. As a consequence, the magnitude of the fixed costs to extraction does not affect the solution to the optimal control problem.

  10. I also run simulations in which I instead pin down the initial price P(0) to equal to actual real-world oil price at time t. Since the first year of price data in my data set in 1965, for these simulations t = 0 corresponds to 1965, when the real-world oil price was $4.51/barrel. However, because pinning down the initial price rather than initial stock often leads to solutions with negative stocks, and because the qualitative features of the results are robust to the type of initial condition chosen, the results of the simulations in which an initial condition was imposed on price are not reported here.

  11. As a robustness check, a base year of 1990 was also used, and the qualitative results were unchanged.

  12. No solution exists for monopoly under linear demand when demand is perfectly inelastic.

  13. Graphs for all scenarios using data from 1965 to 2001 are presented in Lin (2005).

References

  • Adelman, M. A., 1992, Finding and developing costs in the United States, 1945–1986, in Moroney, J. R., ed., Advances in the Economics of Energy and Resources—Energy, Growth and the Environment, v. 7: Greenwich, Conn., JAI Press Inc., p. 11–58.

  • Berndt, E.R., Wood, D.O., 1975. Technology, prices, and the derived demand for energy. The Review of Economics and Statistics 57(3), 259–268.

    Article  Google Scholar 

  • Chakravorty, U., Roumasset, J., and Tse, K., 1997. Endogenous substitution among energy resources and global warming. J. Polit. Econ. 105(6), 1201–1234.

    Article  Google Scholar 

  • Chapman, D., 1993. World oil: Hotelling depletion or accelerating use? Nat. Resour. Res., 2 (4), 331–339.

    Article  Google Scholar 

  • Chapman, D., and Khanna, N., 2000. World oil: The growing case for international policy. Contemporary Economic Policy, 18 (1), 1–13.

    Article  Google Scholar 

  • Cremer, J., Salehi-Isfahani, D., 1991. Models of the oil market. Harwood Academic Publishers, New York.

    Google Scholar 

  • Cremer, J., and Weitzman, M.L. 1976. OPEC and the monopoly price of world oil. Eur. Econ. Rev. 8, 155–164.

    Article  Google Scholar 

  • Dahl, C.A., 1993. A survey of oil demand elasticities for developing countries. OPEC Review XVII (4), 399–419.

    Article  Google Scholar 

  • Dahl, C.A., 1994a. A survey of oil product demand elasticities for developing countries. OPEC Review XVIII(1), 47–87.

    Article  Google Scholar 

  • Dahl, C.A., 1994b. A survey of energy demand elasticities for the developing world. Journal of Energy and Development 18(I), 1–48.

    Google Scholar 

  • Devarajan, S., Fisher, A.C., 1982. Exploration and scarcity. J. Polit. Econ. 90(6), 1279–1290.

    Article  Google Scholar 

  • Edmonson, N., 1975. Real price and the consumption of mineral energy in the United States, 1901–1968. The Journal of Industrial Economics 23(3), 161–174.

    Article  Google Scholar 

  • Farrow, S., 1985. Testing the efficiency of extraction from a stock resource. J. Polit. Econ. 93(3), 452–487.

    Article  Google Scholar 

  • Farzin, Y.H., 1992. The time path of scarcity rent in the theory of exhaustible resources. Economic Journal 102, 841–851.

    Article  Google Scholar 

  • Farzin, Y.H., 1995. Technological change and the dynamics of resource scarcity measures. Journal of Environmental Economics and Management 29, 105–120.

    Article  Google Scholar 

  • Gately, D., 1984. A ten-year retrospective: OPEC and the world oil market. J. Econ. Lit. 22(3), 1100–1114.

    Google Scholar 

  • Griffin, J.M. 1985. OPEC behavior: A test of alternative hypotheses. Am. Econ. Rev. 75 (5), 954–963.

    Google Scholar 

  • Halvorsen, R., Smith, T.R., 1984. On measuring natural resource scarcity. J. Polit. Econ. 92(5), 954–964.

    Article  Google Scholar 

  • Halvorsen, R., Smith, T.R., 1991. A test of the theory of exhaustible resources. The Quarterly Journal of Economics 106(1), 123–140.

    Article  Google Scholar 

  • Hanson, D.A., 1980. Increasing extraction costs and resource prices: Some further results. The Bell Journal of Economics 11(1), 335–342

    Article  Google Scholar 

  • Hnyilicza, E. and Pindyck, R.S. 1976. Pricing policies for a two-part exhaustible resource cartel: The case of OPEC. Eur. Econ. Rev. 8, 139-154.

    Article  Google Scholar 

  • Hoel, M., 1978. Resource extraction, uncertainty, and learning. Bell J. Econ. 9(2), 642–645.

    Article  Google Scholar 

  • Hotelling, H., 1931. The economics of exhaustible resources. J. Polit. Econ. 39(2), 137–175.

    Article  Google Scholar 

  • Hughes, J., Knittel, C., and Sperling, D., 2008. Evidence of a shift in the short-run price elasticity of gasoline demand. Energy Journal 29(1), 93–114.

    Google Scholar 

  • Huntington, H., 1994. Oil price forecasting in the 1980s: What went wrong? Energy Journal 15(2), 1–22.

    Google Scholar 

  • Khalatbari, F., 1977. Market imperfections and the optimum rate of depletion of natural resources. Economica 44(176), 409–414.

    Article  Google Scholar 

  • Krautkraemer, J.A., 1998. Nonrenewable resource scarcity. J. Econ. Lit. 36(4), 2065–2107.

    Google Scholar 

  • Lasserre, P., 1985. Discovery costs as a measure of rent. The Canadian Journal of Economics 18(3), 474–483.

    Article  Google Scholar 

  • Lin, C.-Y. C, 2005, Optimal world oil extraction: calibrating and simulating the Hotelling model, in Hogan, W. W., ed., Repsol YPF—Harvard Kennedy School Fellows 2003–2004 Research Papers, John F. Kennedy School of Government, Harvard University, Cambridge, p. 251–266. URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=616961

  • Lin, C.-Y. C., 2008a, An empirical dynamic model of OPEC and Non-OPEC. Working paper: University of California at Davis.

  • Lin, C.-Y. C., 2008b, Estimating supply and demand in the world oil market. Working paper: University of California at Davis.

  • Lin, C.-Y. C., Meng, H., Ngai, T. Y., Oscherov, V., and Zhu, Y. H., 2008, Hotelling revisited: oil prices and endogenous technological progress. Working paper: University of California at Davis.

  • Lin, C.-Y.C. &Wagner, G., 2007. Steady-state growth in a Hotelling model of resource extraction. Journal of Environmental Economics and Management, 54, 68–83.

    Article  Google Scholar 

  • Marcel, V., and Mitchell, J. 2006. Oil titans: National oil companies in the Middle East. Washington, DC: Brookings Institution Press.

    Google Scholar 

  • Miller, M.H., Upton, C.W., 1985. A test of the Hotelling valuation principle. J. Polit. Econ. 93(1), 1–25.

    Article  Google Scholar 

  • Moazzami, B., Anderson, F.J., 1994. Modelling natural resource scarcity using the “error-correction” approach. Canadian Journal of Economics, 27 (4), 801–12.

    Article  Google Scholar 

  • Nordhaus, W.D., 1980. Oil and economic performance in industrial countries. Brookings Papers on Economic Activity 1980(2), 341–399.

    Article  Google Scholar 

  • Organization of the Petroleum Exporting Countries [OPEC], 2007, OPEC Brief History [Online: web], Cited 9 November 2007. URL: http://www.opec.org/aboutus/history/history.htm.

  • Pesaran, M.H. 1990. An econometric analysis of exploration and extraction of oil in the U.K. Continental Shelf. The Economic Journal 100 (401), 367–390.

    Article  Google Scholar 

  • Pindyck, R. S., 1976, Gains to producers from the cartelization of exhaustible resources. MIT Energy Lab working paper (No. MIT-EL 76-012WP).

  • Pindyck, R.S., 1978. The optimal exploration and production of nonrenewable resources. J. Polit. Econ. 86(5), 841–861.

    Article  Google Scholar 

  • Pindyck, R.S., 1980. Uncertainty and exhaustible resource markets. J. Polit. Econ. 88(6), 1203–1225.

    Article  Google Scholar 

  • Salant, S.W., 1976. Exhaustible resources and industrial structure: A Nash-Cournot approach to the world oil market. J. Polit. Econ., 84 (5), 1079–1094.

    Article  Google Scholar 

  • Slade, M.E, 1982. Trends in natural resource commodity prices: An analysis of the time domain. Journal of Environmental Economics and Management, 9 (2), 122–137.

    Article  Google Scholar 

  • Solow, R.M., Wan, F.Y., 1976. Extraction costs in the theory of exhaustible resources. Bell J. Econ. 7(2), 359–370.

    Article  Google Scholar 

  • Sperling, D., and Gordon, D., 2007, Two billion cars. Book manuscript: University of California at Davis.

  • Stiglitz, J.E., 1976. Monopoly and the rate of extraction of exhaustible resources. Am. Econ. Rev. 66(4), 655–661.

    Google Scholar 

  • Sweeney, J.L., 1977. Economics of depletable resources: Market forces and intertemporal bias. The Review of Economic Studies 44(1), 124–141.

    Google Scholar 

  • Ulph, A.M., and Folie, G.M. 1980. Exhaustible resources and cartels: An intertemporal Nash-Cournot model. The Canadian Journal of Economics, 13 (4), 645–658.

    Article  Google Scholar 

  • U.S. Geological Survey [USGS], 2004, United States Energy and World Energy Production and Consumption Statistics [Online: web], Cited 7 April 2004. URL: http://energy.cr.usgs.gov/energy/stats_ctry/Stat1.html

  • Watkins, G.C., 1992. The Hotelling Principle: Autobahn or cul de sac? The Energy Journal 13 (1), 1–24.

    Google Scholar 

  • Weitzman, M.L., 2003. Income, Wealth, and the Maximum Principle. Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Yergin, D., 1992. The Prize: The Epic Quest for Oil, Money, and Power. Free Press, New York.

    Google Scholar 

  • Young, D., 1992. Cost specification and firm behaviour in a Hotelling model of resource extraction. The Canadian Journal of Economics 25(1), 41–59.

    Article  Google Scholar 

  • Zimmermann, E.W., 1951. World Resources and Industries: A Functional Appraisal of the Availability of Agricultural and Industrial Materials. Harper and Brothers, Publishers, New York.

    Google Scholar 

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Acknowledgments

I thank Gary Chamberlain, Jon Conrad, William Hogan, Nancy Stokey, George Richardson, James Smith, Howard Stone, and Martin Weitzman for helpful comments and discussions. The time series data used in this study were acquired with the help of Brian Greene and with funds from the Littauer Library at Harvard University. I received financial support from an EPA Science to Achieve Results graduate fellowship, a National Science Foundation graduate research fellowship, and a Repsol YPF—Harvard Kennedy School Pre-Doctoral Fellowship in energy policy. All errors are my own.

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  1. Agricultural & Resource Economics, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    C.-Y. Cynthia Lin

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Lin, CY.C. Insights from a Simple Hotelling Model of the World Oil Market. Nat Resour Res 18, 19–28 (2009). https://doi.org/10.1007/s11053-008-9085-6

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