A note on CES Preferences in Age-Structured Models

In a biomass model a CES function generates an exploitation rate that is directly proportional to the scarcity of the resource: resources with less biomass are subjected to lower exploitation rates. In this paper we investigate the implications of introducing invariant intertemporal preferences as to yield stability in age-structured fishery problem. Our results show that a CES function in an age-structured bioeconomic model produces links between the scarcity of the resource (measured as the weighted sum of the size of the cohorts, which is similar to the Shannon index) and the exploitation of the resource over a complete cycle, the duration of which is equivalent to the number of age groups of the resource. Given that multiple paths can be constructed that regenerate the population of the resources (the age pyramid) over the course of the cycle, optimum harvest allocation means selecting the one that permits the biggest catch at the beginning of the cycle. Smoother exploitation path towards the stationary values are achieved by catching more in periods when there is less biomass in exchange for catching less when the biomass recovers, which results in exploitation rates that are not directly proportional to the scarcity of the resource. Moreover, we show that introducing non-constant discount rates into age-structured models enables exploitation rates proportional to the scarcity of the resource to be recouped