The total fleet profit Πt in year t   is given by equation(10) ∏t=nt⁎(Ptht−Ct),with ht=Ht/nt⁎ and Ct=cf+cve⁎. From society’s point of view, it is desirable to consider that consumers and fish processors benefit from buying cheap fish, and hence, policy-makers may take consumer surplus into account. Consumer surplus in year t is given by equation(11) St=12(p¯−Pt)Ht Total welfare is given by the sum of total fleet profit and consumer surplus, equation(12) Wt=∏t+StWt=∏t+St This study analyzes the performance of several HCRs.

First, the BEZ235 in vivo HCR that has been implemented in 2004 [6], will be referred to as the “current HCR”. We only consider the core of the HCR that relates TAC to SSB; in order to facilitate comparisons between alternative HCRs, we have ignored the additional elements in the current

HCR that aim at reducing annual variability in TACs. Second, alternative HCRs that result from the optimization of specific objectives will be analyzed and referred to as “optimized HCRs”. The current HCR for NEA cod is determined by two parameters in the form of reference points, Bpa and Fpa. The optimized HCRs are also characterized by two parameters: (i) the maximum fishing mortality Fmax, and (ii) the level Bmax of SSB at which the maximum fishing mortality Fmax starts to apply. Each of the optimized HCRs were derived by allowing Fmax and Bmax to vary across a wide range of values (see below), without constraining Daporinad in vivo them to existing reference points, and by then choosing those combinations of Fmax and Bmax that best fulfil the specific objective aimed to optimize. The current HCR is recovered as a special case by setting Fmax=Fpa and Bmax=Bpa.

For all considered HCRs, the fishing mortality rate resulting for a particular SSB is determined as follows: if the SSB is between 0 and Bmax, the instantaneous fishing mortality rate for that year is Fmax SSB/Bmax; otherwise, the instantaneous fishing mortality rate is Fmax ( Fig. 2c). The HCR parameters were optimized for three different objectives, maximizing either total Acesulfame Potassium welfare, total profit, or total yield. For all considered combinations of Bmax (varied over the range 0–800,000 tonnes in steps of 20,000 tonnes) and Fmax (varied over the range 0.1–1.3 yr−1 in steps of 0.01 yr−1), the discounted total welfare, total profit, and total yield over the period 2004–2053 were calculated. This gives a grid of 4961 different HCRs. The particular parameter combination that maximizes one of these three measures is identified as the corresponding optimal HCR.