By Eugen (1879-1964) Varga
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Global warming, small pelagic fisheries and risk 3. 4. 5. 6. 7. 8. 9. 10. 11. 31 Possibly weakening the Gulf Stream substantially; see ACIA (2004). The most important exception would be ﬁsheries based on strongly schooling species, where the biomass has little eﬀect on the harvesting proﬁt function. This does not apply to the case of optimal extinction, that is when the optimal long-term biomass level is zero. Note that, in a perfect market system, proﬁts are synonymous with social beneﬁts. Note that the total catch is deﬁned as NиQ(x, t).
9) reduces to Gx(x, t)ϭr. 1) that if global warming has a positive eﬀect on biomass growth, that is Gt, Gxt Ͼ0, both equilibrium biomass and harvest will unequivocally increase, and vice versa. The optimal adjustment path of biomass and harvest from an initial equilibrium to a new one is, of course, no less important than the equilibria themselves. Unfortunately, this path is quite diﬃcult to characterize in general. 5 Now, as already seen, in the case of an advantageous climate change, the initial equilibrium biomass level is sub-optimal.
THE STOCHASTIC CASE As stated earlier, the impact of global warming on biomass growth in the future is highly uncertain. One way to model this is to represent biomass growth by a stochastic diﬀerential equation instead of the usual nonstochastic one. 15) 19 Biomass, x . 8 No. of firms, N . xϭ0 20 Climate change and the economics of the world’s fisheries where, as before, x refers to biomass, q to harvest and t to time. G(x, t)Ϫq is the deterministic part of biomass growth, as in the previous section.