Dynamic model of fishing: The relationship to conjectural variations

Abstract

The idea that a firm decides its level of output in an oligopolistic market on the basis of some conjecture about the reaction of the other firms to its decisions has been used in economic modeling since the work of Bertrand and Cournot. One of the first economists to have discussed the implications of “conjectural variations” is Ragnar Frisch in [F]. Recently there has been a renewed interest in this subject; see [KS]. The use of conjectural variations yield important insights into the effect of various market structures on equilibrium prices and outputs. This is especially the case when the conjectural variation term is set equal to zero, for it is precisely in this case that one gets the Nash or Cournot equilibrium. O ther market structures can also be inferred from different assumptions about the conjectural variation term. For example, if the conjectural variation is set equal to minus one then a perfectly competitive solution is implied. The monopoly solution follows from setting the conjectural variation to one. All previous work on the relationship between conjectural variations and market structure has been in the static framework. However, many interesting questions also arise in a dynamic context. It is the purpose of this paper to study how conjectural variations are related to market structures in the dynamic case and which assumptions about conjectural variations lead to outcomes associated with different market structures. A natural setting for this analysis is the market for a natural resource, e.g., fish. Various market structures have been studied in this context; e.g., see [LMM I], [LMM II], and [Ml. The dynamic model yields a large class of possible market structures since both a static (or short run) dimension and a dynamic (or long run) dimension are present. For example, in the competitive free entry case, i.e., in which there are no ownership rights to the fish, the dynamic aspect of the problem is less important than the static