Acta Biotheoretica

, Volume 62, Issue 3, pp 305–323

A Mathematical Model of a Fishery with Variable Market Price: Sustainable Fishery/Over-exploitation

  • Fulgence Mansal
  • Tri Nguyen-Huu
  • Pierre Auger
  • Moussa Balde
Regular Article

DOI: 10.1007/s10441-014-9227-7

Cite this article as:
Mansal, F., Nguyen-Huu, T., Auger, P. et al. Acta Biotheor (2014) 62: 305. doi:10.1007/s10441-014-9227-7
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Abstract

We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource.

Keywords

Dynamical systems Fishery Variable price Market price equation Demand function Equilibrium Stability Sustainable exploitation/overexploitation 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Fulgence Mansal
    • 1
  • Tri Nguyen-Huu
    • 2
    • 3
    • 4
  • Pierre Auger
    • 1
    • 2
    • 4
  • Moussa Balde
    • 1
  1. 1.Département de mathématiques et informatique, Faculté des Sciences et techniques, UMI IRD 209, UMMISCO, IRDUniversité Cheikh Anta DiopDakarSenegal
  2. 2.UMI IRD 209, UMMISCOBondy CedexFrance
  3. 3.IXXIENS LyonLyonFrance
  4. 4.UPMC, Sorbonne UniversityParisFrance

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