Environmental and Resource Economics 13: 75–94, 1999. 75 c 1999 Kluwer Academic Publishers. Printed in the Netherlands. Sharing a Fish Resource – Bioeconomic Analysis of An Applied Allocation Rule CLAIRE W. ARMSTRONG Department of Economics, Norwegian College of Fishery Science, University of Tromsø, Norway (e-mail: clairea@nfh.uit.no) Accepted 13 January 1998 Abstract. Political and economic factors usually determine the harvest shares allotted to heteroge- neous fisher groups harvesting upon the same fish stock. Given that the fishers harvest upon different segments of a fish stock with, for instance, cannibalistic tendencies, the shares allotted may have con- siderable effect upon the well-being of the stock and the economics of the fishery. This paper analyses an existing allocation rule defining harvest shares allotted to two vessel groups (trawlers and coastal vessels) in the Norwegian cod fishery. We apply a model with two interacting age groups within a single fish stock, where the interaction has both biological and economic implications. Requiring a first best approach to an optimal stock size results in no harvest in the first years studied. In order to ensure harvest amounts close to the historic harvest, we design a second best model giving optimal biological shares in the build-up phase of the stock, and bioeconomic optimal shares at the optimum fish stock level. The second best model recommends that for an increasing stock size the trawlers should obtain decreasing shares. We find that the actual allocation rule functions in a manner opposite to the second best model, since this rule allocates an increasing share to the trawlers for an increasing stock size. Key words: bioeconomics, cod, cannibalism, harvest allocation JEL classification: Q22, Q28 1. Introduction In addition to deciding harvest levels, fisheries managers must often take into account the well-being of several competing heterogeneous harvest groups. The fact that allocations to heterogeneous harvest groups affect the age structure of the remaining fish stock, and that this again gives biological and economic effects for future allocations, is seldom taken into account. A vast number of theoretical bioeconomic studies have paid attention to two- agent management of one common stock, or two interacting stocks or age groups of fish. Mostly, however, the approaches have been non-cooperative, with focus on efficient solutions. Some cooperative approaches have been studied, using bargain- ing solutions to determine the final distributions (Munro 1979; H¨ am¨ al¨ ainen et al. 1984; Armstrong and Flaaten 1991; Larkin et al. 1996). All the existing work is of a prescriptive type, describing how solutions should be. In addition these studies are preoccupied with optimal steady state equilibria, not the build-up period leading to