Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box

ɪ>0 & ^{d q}<0 ∀i = 1,...,Q, '^q<0& ^q <0

∂z_q (i)       ∂z_q (i)²                ∂N      ∂N²

Non-catch quality is similarly dependent upon a Mx1 vector of inputs, z_s , which is

subject to the same continuity, differentiability and concavity restrictions as previously stated for
catch quality inputs. However, to account for the fact that some inputs that aid in the production
of catch quality may actually reduce productive capacity for non-catch quality (and vice versa)
we allow both “goods” and “bads” in the production relationship with sufficient curvature
restrictions to ensure the overall concavity of the marginal benefit function with respect to all
benefits. Note that all inputs are defined so that they are positive contributors to catch quality
production. As with catch quality, we assume that non-catch quality is influenced by the number
of passengers onboard a vessel in a negative and decreasing fashion so as to reflect negative
attitudes toward crowding apart from its impacts on catch.¹¹

In mathematical notation we assume S(z_s,N) satisfies the following properties:¹²

∂²S         ∂S         ∂²S

0 &-----< < 0 or-----< 0 &-----< < 0 ∀i = 1,...,M,

∂zs (i)²           ∂z_s (i )          ∂zs (i)^{2               , , ,}

_∂2S

—< < 0.

∂N²

¹¹ Although convenient, such an assumption may not be true in general. Individuals may initially derive utility from
the company of fellow anglers (apart from their effects on catch) with diminishing returns eventually leading to a
threshold density where the marginal effect of an additional angler on the production of non-catch quality becomes
negative. For the sake of mathematical tractability we assume that these preferences for “social” fishing are
sufficiently weak or exhibited at such low angler densities as to be negligible.

¹² In our specification of the production processes of catch and non-catch quality we have assumed that the two
processes are separable and thus represented by production functions. In reality, however, there may be significant
jointness in production. We confront this issue in two ways. First, certain inputs are likely to contribute to the
production of both forms of quality in a completely non-rivalrous fashion, such that their appearance in both
production processes causes no problem. This is potentially the case for many characteristics of vessel capital such
as deck size for which its usefulness in fostering catch (due to the dilution of congestion effects) is likely to in no
way affect its contribution toward perceptions of non-catch quality. Secondly, for inputs that are clearly rivalrously
consumed, a non-rivalrous relationship can be constructed by careful redefinition of inputs. For instance, labor
inputs that can be utilized for either fostering catch or non-catch quality (but not both simultaneously) can be
redefined as “catch related labor” and “non-catch related labor”, thus subsuming the factor allocation decision
within our analysis.

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