The ghost of extinction

The second complication relates to the inclusion of the in situ benefits of wildlife into the analysis. [...] The optimal population of the wildlife species occurs when the social discount rate equals the marginal rate of substitution between leaving an animal (or unit of biomass) in situ and harvesting it today plus the growth rate. [...] It is clear from (10) that an increase in the marginal in situ value of a species, B'(x), will raise the optimal stock x*, and that an increase in marginal harvest benefits will reduce the optimal population for a given discount rate r. Finally, notice that, if the value of harvest is constant (say equal to p) and c'(h)=c also constant, then λ=p–c and (10) reduces to the simpler form B'(x*)/(p–c) [...] Clearly Proposition 1 holds because marginal benefits are a function of at least M and T, as indicated in equations (14) and (16), as well as the slope of the marginal benefit function and the allocation of total WTP in the case of quadratic benefits. [...] It is obvious that M is determining if the optimal solution is x*≥M – the value of x* depends on the value of the minimum viable population as is evident from (18) or (19).