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I think there is an approach problem in the constraint. (1) implies that: \begin{align} v_{n,t} - v_{n,t+1}=H_t - (\sum_{i=1}^{n-1} v_{it}-\sum_{i=1}^{n-1} v_{i,t+1}) \end{align} As the number of fish caught that are not the $n$ species increases, the number of fish that belong to the $n$ species decreases. This, i understand, may arise from a production ...