Optimal harvest feedback rule accounting for the fishing-up effect and size-dependent pricing

Fishing leads to truncation of a population's age and size structure. However, large-sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size-related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon-Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon-Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size-dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies potentially causing rent dissipation and suboptimal utilization of renewable resources