Valuing satellite systems to support fishing in a dynamic competitive model

Abstract

This article investigates the technology adoption decision of a new satellite system aimed at locating tuna shoals. We propose a dynamic imperfect competition model with vertical differentiation in which each firm acts as a Cournot oligopolist and takes the evolution of the natural resource into account. In this dynamic setting, the model cannot be solved analytically and we rely on a numerical approach. Results are derived for the northern bluefin tuna. We find that high-quality firms value more the technology than low-quality firms. A direct implication of this result is that the market value of the new technology can be maximized while serving only the highest quality firms. We then evaluate how individual quotas can be used to increase the value that firms attach to the technology.

Acknowledgements

We would like to acknowledge the financial support of CNES, contract 4700015608/SIE491. We are garteful to Michel Moreaux and Alain Oustry as well as the participants to the CNES workshop and EEA 2007 for very valuable comments.

Notes

¹ For example Collecte Localisation Satellites (http://www.cls.fr/) and Orbimage (http://www.orbimage.com/) have both developed satellite system tracking tuna shoals over the world.

² See Motta (1993) for the detailed determination of the inverse demand functions.

³ This cost function is derived from a Cobb–Douglas production function with fishing effort and fish biomass as production inputs of the form where e is the effort of the firm. θ_i is productivity term that measures the catchability per unit of effort.

⁴ In the sequel, we denote .

⁵ In the fisheries economic literature, there is some ambiguity about the firms’ perception of the biomass constraint. Some studies retain the assumption that firms compete in the level of harvest and ignore the biomass growth constraint. Firms thus behave myopically. See for instance Okugushi (2003), Sandal and Steinshamn (2004) or Szidarovsky et al. (2002).

⁶ Note that this cost differs from the price paid by firms to obtain the technology.

⁷ Γ is assumed to be increasing with n.

⁸ We use a projection method that is detailed in Appendix C.

⁹ The reader is left to refer to Appendix D for a detailed description of the method.

¹⁰ The evolution of equilibrium market prices that supplements this benchmark can be found in Appendix A.

¹¹ Szidarovsky et al. (2002) perform a static comparative analysis of the steady state to a change in the harvest quantity. They find that an increase in the aggregate production either does not affect the asymptotic behaviour of the steady state stock of fish or makes it more unstable.

¹² This is described in Appendix E.