Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box

Given this structure of preferences and production relationships, we now consider the
nature of costs to vessel owners. We assume that there is an endogenously determined number
of identical vessels N_V . Each of these vessels faces three basic types of costs: 1) those that vary
according to the number of trips, 2) avoidable fixed costs (costs that are invariant in the number
of trips but are nevertheless avoidable without quitting the industry) and 3) fixed costs that are
only avoidable by exiting the industry altogether (e.g. license fees, minimal vessel insurance,
etc.) which we henceforth designate by Ψ . The first category may include expenditures such as
labor and fuel while the second includes expenditures on capital inputs.¹³ Note that inputs in
each category can enter into the production functions for both catch and non-catch quality in a
completely unfettered fashion.

Since part of our focus in this analysis is to investigate the use of inputs under optimal
and open access scenarios, we work with the seasonal vessel expenditure function rather than the
cost function resulting from quality-constrained expenditure minimization:

c(Zq_l, Zs, N, NumTrips, w, r) = [(w_m ' Zv_n )N + w_v 'z_v ]* NumTrips
+ [(rFN'zFN)N+(rF'zF)]+Ψ.

Note that seasonal costs are a function not only of inputs and their exogenous market prices
(indicated by the vectors w and r for variable and fixed inputs, respectively) but also of the
number of trips taken in the season and the number of anglers per trip.¹⁴ Both the fixed and trip-
variable cost components are partially comprised of costs that vary in a linear fashion with the
number of passengers. For instance, a vessel owner may elect to allocate a given number of

¹³ Since many aspects of vessel capital are best characterized as heterogeneous bundles of valued characteristics (e.g.
horsepower, fuel capacity, length, tonnage) we adopt the language of hedonic pricing in our descriptions of capital
inputs. Accordingly, the rental rates for a characteristic are interpreted as the first derivatives of the bid function
with respect to the quantity of that characteristic (Rosen, 1974).

¹⁴ We assume trips are reproducible at a constant variable cost when inputs and the numbers of passengers per trip
are fixed. In the context of day-trips it seems eminently reasonable that the variable cost of taking a trip today
should be independent of whether a trip was executed on the previous day.

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