Economic Theory

, Volume 63, Issue 3, pp 687–721 | Cite as

Existence of equilibria in exhaustible resource markets with economies of scale and inventories

  • Antoine Bommier
  • Lucas BretschgerEmail author
  • François Le Grand
Research Article


The paper proves the existence of equilibrium in non-renewable resource markets when extraction costs are non-convex and resource storage is possible. Inventories flatten the consumption path and eliminate price jumps at the end of the extraction period, so that market equilibrium becomes possible. We distinguish between two types of solutions, one with immediate and one with delayed buildup of inventories. For both cases, we do not only characterize potential optimal paths but also show that equilibria actually exist under fairly general conditions. It is found that optimum resource extraction involves increasing quantities over a period of time. What is generally interpreted as an indicator of increasing resource abundance is thus perfectly compatible with constant resource stocks.


Exhaustible resources Non-convex extraction cost Equilibrium existence Resource storage 

JEL Classification

Q30 C62 D92 D41 


  1. Asheim, G.B.: Contestability in a resource market with non-convex costs. Scand. J. Econ. 94, 609–618 (1992)CrossRefGoogle Scholar
  2. Bommier, A., Bretschger, L., LeGrand, F.: Existence of equilibria in exhaustible resource markets with economies of scale and inventories. CER-ETH Working Paper 14/203 (2014). doi: 10.3929/ethz-a-010210631
  3. Cairns, R.D.: On non-convex costs and dynamic consistency in an exhaustible-resource market. Scand. J. Econ. 93(1), 89–100 (1991)CrossRefGoogle Scholar
  4. Cairns, R.D.: Exhaustible resources, non-convexity and competitive equilibrium. Environ. Resour. Econ. 40(2), 177–193 (2008)CrossRefGoogle Scholar
  5. Chakravorty, U., Moreaux, M., Tidball, M.: Ordering the extraction of polluting nonrenewable resources. Am. Econ. Rev. 98(3), 1128–1144 (2008)CrossRefGoogle Scholar
  6. Eswaran, M., Lewis, T.R., Heaps, T.: On the nonexistence of market equilibria in exhaustible resource markets with decreasing costs. J. Polit. Econ. 91(1), 154–167 (1983)CrossRefGoogle Scholar
  7. Fisher, A.C., Karp, L.S.: Nonconvexity, efficiency and equilibrium in exhaustible resource depletion. Environ. Resour. Econ. 3, 97–106 (1993)CrossRefGoogle Scholar
  8. Gaudet, G., Moreaux, M., Salant, S.W.: Intertemporal depletion of resource sites by spatially distributed users. Am. Econ. Rev. 91(4), 1149–1159 (2001)CrossRefGoogle Scholar
  9. Harstad, B.: Buy coal! A case for supply-side environmental policy. J. Polit. Econ. 120, 77–115 (2012)CrossRefGoogle Scholar
  10. Holland, S.P.: Set-up costs and the existence of competitive equilibrium when extraction capacity is limited. J. Environ. Econ. Manag. 46, 539–556 (2003)CrossRefGoogle Scholar
  11. Le Van, C., Schubert, K., Nguyen, T.A.: With exhaustible resources, can a developing country escape from the poverty trap? J. Econ. Theory 145(6), 2435–2447 (2010)CrossRefGoogle Scholar
  12. Lewis, T., Matthews, S., Burness, S.: Monopoly and the rate of extraction of exhaustible resources: note. Am. Econ. Rev. 69(1), 227–230 (1979)Google Scholar
  13. Lozada, G.A.: Existence of equilibria in exhaustible resource industries: nonconvexities and discrete vs. continuous time. J. Econ. Dyn. Control Elsevier 20(1–3), 433–444 (1996)CrossRefGoogle Scholar
  14. Mason, C.F.: On equilibrium in resource markets with scale economies and stochastic prices. J. Environ. Econ. Manag. 64(3), 288–300 (2012)CrossRefGoogle Scholar
  15. van der Meijden, G., Smulders, S.: Technological change during the energy transition. Tinbergen Institute Discussion Paper, TI 2014–108/VIII (2014)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Antoine Bommier
    • 1
  • Lucas Bretschger
    • 2
    Email author
  • François Le Grand
    • 1
    • 3
  1. 1.Chair of Integrative Risk Management and EconomicsETH ZürichZurichSwitzerland
  2. 2.Chair of Economics/Resource EconomicsETH ZürichZurichSwitzerland
  3. 3.EMLyon Business SchoolÉcullyFrance

Personalised recommendations