Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box

fishing rods per angler. Such capital expenditures would be reflected in the vector z_FN .

Alternatively, crew time spent in training and baiting gear for each passenger could be captured
in the z_VN term. Finally, it may be that certain inputs enter both the portion of costs increasing in

N and the portion without. For instance, the fuel costs associated with traveling a given distance
from port (the endogenous variable input) could be parsed between the costs associated with a
boat devoid of anglers and the extra per-angler costs due to increased payload.¹⁵

Having established the nature of both costs and benefits, we now require an expression
linking the behavior of anglers and vessel owners to the evolution of targeted biomass through
time. We employ the following standard relationship:

X^& =g(X)-D^*(φ(H(X,q(zq,N))-L)+L)                      (5)

where D^* is the total number of fishing days demanded and φ is a discard mortality parameter
indicating the fraction of discarded catch that dies before returning to the reproductive stock.

The growth function g(X) is assumed to be strictly concave and to prescribe zero growth at zero
biomass and at a positive carrying capacity.

Having fully defined the notation of our problem we state the welfare maximizing
objective:
subject to (5), non-negativity constraints on the state and control variables and the following
additional constraints:

¹⁵ Note that the linearity of the expenditure function with respect to N does not mean that optimized costs possess a
linear-in-N relationship. Given the endogeneity of both the number of passengers per trip and all inputs, it is
possible for the allocation of inputs to vary as N varies - leading to a non-linear relationship in minimized costs.

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