simply imposes diminishing marginal returns on increases in harvest, landings and non-catch
9
quality.
As previously mentioned, the catch and non-catch aspects of trip quality are produced
with multiple compensated and uncompensated factors of production. In the case of per-trip
harvest, we assume that it is a continuous, differentiable and increasing function of the current
stock of the target species, X, and a “catch effectiveness” argument, q, analogous to the
catchability term commonly employed for analysis of commercial fisheries. Catch effectiveness
is itself a function of a Qx1 vector of capital and labor inputs selected by the vessel owner,zq ,
that serve to enhance the skill of fishermen.10 For instance zq may include the use of additional
fishing rods for each angler to increase catch per unit effort, investment in engine horsepower to
allow faster access to productive fishing grounds and greater fishing time, the use of chum to
attract certain species, or the diversion of crew time to education on fishing techniques and the
baiting of gear. In agreement with conventional production theory, we assume that each of these
inputs has a positive and diminishing marginal effect on catch effectiveness.
In addition to these purchased factors, we also assume that the number of anglers onboard
a given vessel, N, has a negative, continuous, differentiable and decreasing effect on the marginal
effectiveness of effort - this to account in a generic fashion for a variety of possible intra-vessel
congestion externalities (e.g. from entangled fishing lines). The mathematical summary of these
properties of the catch quality production function, H(X,q(zq,N)) , are summarized as follows:
9 Given our focus on aggregated demand, we do not entertain the possibility of “corner solutions” in demand (i.e.
individual non-participation). Anderson (1993) exposits a model where free entry of anglers combined with
heterogeneity yields an equilibrium where fishing benefits to anglers are dissipated, much as in the classical
commercial fisheries model thus leading to partial exit of some anglers. While useful, this approach seems to lack a
firm basis in consumer theory and also begs the question of what economic mechanism (if any) would guide angler
demand so that some common minimal level of well-being is achieved across anglers in equilibrium.
10 To simplify the formal analysis, we presume fishermen are equally skilled and that their per-trip catch is
predetermined from their perspective. The implications of relaxing these assumptions are considered in the later
discussion.