Optimal age-structured harvest in a dynamic model with heterogenous capital

A dynamic optimization model with four state variables and two control variables is developed in order to analyze a fishery where on fleet-segment is targeting young fish and another fleet-segment is targeting older fish of the same species. The state variables are the biomass levels of young and old fish and the stock of capital in each fleet-segment. The control variables are investment or de-investment in each type of capital which again determine the harvest rates. Irreversible investments are represented through an asymmetric cost of investment. In addition market conditions, cost structure and technologies differ between the two fleet-segments. The model contains both biological interaction between young and old fish (stock-recruitment, cannibalism) and economic interaction (inter-dependent market prices).