Open AccessON THE OPTIMAL POLICY FOR COMBINED HARVESTING OF INDEPENDENT SPECIES
Author(s) -
MestertonGibbons Michael
Publication year - 1987
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1987.tb00028.x
Subject(s) - pontryagin's minimum principle , revenue , stock (firearms) , mathematical economics , economics , path (computing) , value (mathematics) , mathematics , function (biology) , mathematical optimization , interpretation (philosophy) , optimal control , computer science , statistics , biology , finance , mechanical engineering , programming language , evolutionary biology , engineering
By a combination of analytical reasoning and numerical experiment it is demonstrated that, for the combined harvesting of two ecologically independent species which grow logistically and are harvested at a rate proportional to both stock level and effort, there is a unique attainable equilibrium which yields positive revenue and to which the approach path satisfies all of Pontryagin's necessary conditions for maximizing the harvest's present value. A simple feedback law governs this approach and is conjectured to be the optimal policy. On that basis, criteria are found for the survival of the less productive species, as a function of the system parameters and initial stocks. An economic interpretation of the equilibrium is also given.