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UBC Theses and Dissertations

The optimal management of an ocean fishery Bjørndal, Trond


The objective of this thesis is to study the optimal management of North Sea herring. The analysis is based on a dynamic bioeconomic model for a fish resource, consisting of a model of population dynamics and a net revenue function. The model of population dynamics is described by a delay-difference equation. The model distinguishes between natural growth and mortality in the existing stock as opposed to new recruitment to the stock, which takes place with a time lag. The model is estimated based on time series data for the period 1947-82. The net growth function is shown to exhibit depensation, a phenomenon not uncommon for schooling fish like herring. In fisheries economics, the production function is often treated in a rather restrictive manner. The approach of this thesis is to specify a general production function, where output (harvest) is a function of variable inputs, stock size and other fixed factors. Cross-sectional (1968, 1971 and 1975) and aggregate time series (1963-77) data sets for the North Sea herring fishery are available. The cross-sectional data facilitate direct estimation of the production function (Cobb-Douglas). The time series data are used to estimate a harvest supply function (Cobb-Douglas), and by duality theory the parameters of the corresponding production function are derived. A hypothesis of increasing returns to scale in all inputs is accepted in all model specifications. The stock output elasticity generally varies between 0.1 and 0.5. Bionomic equilibrium--i.e., the open access stock level--is estimated to be close to zero. The last two results are attributed to the fact that the resource in question is a schooling one. The model is extended by introducing stock dynamics and the concept of a sole resource manager. An intertemporal profit function is maximized and an expression for the optimal stock level is derived. Some new analytical results with regard to the relationship between the optimal stock level and the production technology are derived. The quantitative results show that the inclusion of costs in the intertemporal profit function causes a considerable increase in the optimal stock level. The assertion that a low stock output elasticity implies that costs have a negligible effect on the optimal stock level is therefore not necessarily true. This is a result of the nonlinear nature of the production technology. The optimal stock level is shown to be not very sensitive to moderate changes in the discount rate. It is illustrated that costs have a stabilizing influence on the stock level. The optimal harvest quantity is quite insensitive to changes in the stock level, a result caused by the properties of the estimated model of population dynamics. Lastly, the model is found to be robust in the sense that the different specifications of the model of population dynamics and the production technology give rise to the same qualitative results.

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