In the event that landings are constrained by harvest (i.e. μ1 > 0) there is an additional
near-term cost of increasing angler density in that it reduces angler welfare due to reduced
landings. This drives the optimal solution toward a lower density of anglers. In other words,
ceteris paribus, a fishery with strong retention preferences (high quality food fish species) should
have lower optimal levels of angler congestion than a technologically equivalent fishery
characterized by weak retention preferences (e.g. tarpon or marlin).
In considering the necessary conditions for the choice of inputs, there are several stylized
sub-cases to examine. An input can affect either catch or non-catch quality (or both) and can be
a fixed or variable input and vary with the choice of N (or not). We work at the maximum level
of generality, assuming that the input affects both catch and non-catch quality and that the factor
has both N-varying and non N-varying aspects. For the case of a fixed input at an interior
solution:
D*
∫[W¾ (∙)Hqqz(i) + MBsSz(i) ]dD - NV [rF.N(i)N + rF(i) ]+ μHqqz(i)
0
(15)
= λD*φHqqz(i).
The current net marginal benefits from an increase in an input must be balanced against the
dynamic costs of the mortality due to increased catch effectiveness.18 Additionally, if landings
are constrained by harvest (μ1 > 0), then there is a further benefit to increasing factors that
influence catch quality as doing so also increases landings.19
The necessary conditions for variable factors are as follows:
18 To ensure such interior solutions for all factors, we must supplement the properties of the catch and non-catch
quality production functions (given by (2) and (3)) with additional “Inada conditions” that all inputs are essential
and have an infinite marginal product as the quantity of the input approaches zero.
19 The corollary to this statement is that vessels pursuing species for which preferences for landings are strong
relative to the baseline “catchability” should optimally evidence a higher degree of catch-augmenting capital/labor
investment compared to fisheries with similar natural catchability but weak preferences for landings.
14