In the latest issue of Marine Resource Economics (vol. 28, no. 1) I co-author an article together with colleagues at the Norwegian School of Economics. We explore what optimal management looks like when capital has to be managed as well as the fish stock. In fisheries, fleet investments are to some degree irreversible; fishing boats has little alternative use. While little has been written on the multidimensional decision problem of how large a fleet to own (the capital decision) and how much of it to use (the fishing decision), we also look at the effect of stochasticity. Things quickly become messy in these models as the number of potential scenarios is large. While it is manageable in our present case, I do not look forward to seeing further extensions. Or rather, I would love to see creative takes on analysis and presentations of high dimensional problems.
We present a continuous, nonlinear, stochastic, and dynamic model for capital investment in the exploitation of a renewable resource. Both the resource stock and capital are treated as state variables. The resource owner controls fishing effort and the investment rate in an optimal way. Biological stock growth and the capital depreciation rate are stochastic in the model. We find that the stochastic resource should be managed conservatively. The capital utilization rate is found to be a nonincreasing function of stochasticity. Investment could be either higher or lower depending on the interaction between capital and the resource stock. In general, a stochastic capital depreciation rate has no strong influence on optimal management. In the long run, the optimal harvest for a stochastic resource becomes lower than the deterministic level.