Optimal population and capital dynamics in fisheries with irreversible investments

A multi-dimensional, non-linear dynamic model in continuous time is presented for the purpose of finding the optimal combination of exploitation and capital investment in optimal renewable resource management. Non-malleability of capital is incorporated in the model through an asymmetric cost-function of investment, and investments can be both positive and negative. Exploitation is controlled through the utilisation rate of available capital. A novel feature in this model is that there are costs associated with the available capital, whether it is utilised or not. And, in contrast to most of the previous literature, the state variables, namely the physical capital and the biological resource, enter the objective function. Due to the nonlinearities in this model, some of the results are in sharp contrast to previous literature.