Environmental Economics and Policy Studies

, Volume 2, Issue 3, pp 167–185 | Cite as

Growth or environmental concern: which comes first? Optimal control with pure stock pollutants

  • Kjell Holmåker
  • Thomas Sterner


This paper models an economy with a stock pollution problem that must choose between productive and environmental investments. Both increase consumption, but only the former leads to economic growth. An optimal control model is solved giving four different paths depending on the initial parameters. For small values of pollution maximizing economic growth is optimal; and for massive pollution all investments are dedicated to environmental abatement. Similarly, the role of discount and savings rates, the relative profitability of abatement and productive investments, and the length of the time horizon are analyzed. Optimal control models simple enough to solve analytically often give intuitively unsatisfactory, boundary-type solutions. Our model, however, does have a large domain of parameter values for which “interior” solutions are optimal. These may start with a period of exclusive productive or environmental investments and then switch over to a mix of investments that corresponds to real-life expectations.

Key words

Growth Stock pollutant Environmental investments Optimal control Application of the Pontryagin maximum principle 


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  1. Barrett S (1991) Optimal soil conservation and the reform of agricultural pricing policies. Journal of Development Economics 36(2): 167–187CrossRefGoogle Scholar
  2. Berkovitz LD (1974) Optimal control theory. Springer, Heidelberg Berlin New YorkCrossRefGoogle Scholar
  3. Brazee RJ, Southgate D (1992) Development of ethnobiologically diverse tropical forests. Land Economics 68:454–461CrossRefGoogle Scholar
  4. Cacho OJ, Kinnucan HW, Hatch LU (1991) Optimal control of fish growth. American Journal of Agricultural Economics 73(1):174–183CrossRefGoogle Scholar
  5. Chappell D, Dury K, Straker C (1992) A differential game model of Canada’s Pacific halibut fishery. Journal of Economic Studies 19(4):43–47CrossRefGoogle Scholar
  6. Clark CW, Munro GR, Charles AT (1985) Fisheries, dynamics, and uncertainty. In: Scott A (ed) Progress in natural resource economics. Oxford University Press, Oxford, pp 99–120Google Scholar
  7. Clark CW, Munro GR (1980) Fisheries and the processing sector: some implications for management policy. Bell Journal of Economics 11:603–616CrossRefGoogle Scholar
  8. Falk I, Mendelsohn R (1993) The economics of controlling stock pollutants: an efficient strategy for greenhouse gases. Journal of Environmental Economics and Management 25:76–88CrossRefGoogle Scholar
  9. Gisser M, Sanchez DA (1980) Competition versus optimal control in groundwater pumping. Water Resources Research 16:638–642CrossRefGoogle Scholar
  10. Kim CS, Moore MR, Hanchar JJ (1989) A dynamic model of adaptation to resource depletion: theory and an application to groundwater mining. Journal of Environmental Economics and Management 17:66–82CrossRefGoogle Scholar
  11. Ko ID, Lapan HE, Sandler T (1992) Controlling stock externalities: flexible versus inflexible Pigouvian corrections. European Economic Review 36:1263–1276CrossRefGoogle Scholar
  12. Van Kooten GC (1993) Bioeconomic evaluation of government agricultural programs on wetlands conversion. Land Economics 69(1):27–38CrossRefGoogle Scholar
  13. Kort PM, van Loon PJJM, Luptacik M (1991) Optimal dynamic environmental policies of a profit maximizing firm. Journal of Economics (Zeitschrift für Nationalökonomie) 54:195–225CrossRefGoogle Scholar
  14. McDonald AD (1991) A technique for estimating the discount rate in Pindyck’s stochastic model of non-renewable resource extraction. Journal of Environmental Economics and Management 21:154–168CrossRefGoogle Scholar
  15. Noel JE, Howitt RE (1982) Conjunctive multibasin management: an optimal control approach. Water Resources Research 18:753–763CrossRefGoogle Scholar
  16. Snyder DL, Bhattacharyya RN (1990) A more general dynamic economic model of the optimal rotation of multiple-use forests. Journal of Environmental Economics and Management 18:168–175CrossRefGoogle Scholar
  17. Steinkamp EA, Betters DR (1991) Optimal control theory applied to joint production of timber and forage. Natural Resource Modeling 5:147–160Google Scholar
  18. Vanzetti D, Kennedy J (1990) Strategic trade policy with competitive storage. European Review of Agricultural Economics 17:465–483CrossRefGoogle Scholar

Copyright information

© Springer Japan 1999

Authors and Affiliations

  • Kjell Holmåker
    • 1
  • Thomas Sterner
    • 2
    • 3
  1. 1.Department of MathematicsChalmers University of Technology and the University of GöteborgGöteborgSweden
  2. 2.Department of EconomicsThe University of GöteborgGöteborgSweden
  3. 3.Resources for the FutureWashington, DCUSA

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