Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box

is that each vessel must be fully employed in every season for social welfare to be maximized.

In other words, the second constraint in (7) must strictly bind.¹⁷ Given that the second constraint
in (7) must bind, a generalized version of the maximum principle (c.f. Caputo, 2005, p. 152)
states that the necessary condition for the path of N_V through time can be found by taking the

partial derivative of (8) with respect to N_V yielding:

NV = -------DMAX-------ʌ μ

V  (( rFN‰ ) N + r∕ZF +Ψ)

Note the fundamental role of fixed costs in determining the optimum scale of the industry - the
higher are fixed costs the lower the optimal number of vessels. Since fixed costs are increasing
in the number of passengers, it is also the case that an increase in the optimum angler density
will lead to a decrease in the number of vessels. Also, the longer the natural season, the greater
the number of vessels since the fixed operating costs can be spread over a larger number of trips.
Finally, the number of vessels is rising in the marginal valuation of an additional day for the
entire fleet.

The necessary condition for the number of fishing days is:

MB(D^*,H(X,q(zq,N)),L,S(zs,N))-[(wVN'zVN)N+wV'zV]_N¹ -
=λ[φ(H(X,q(zq,N))-L)+L].

¹⁷ The proof for this assertion is intuitive and is easily arrived at by contradiction. Assume vessels are not fully
employed. This would imply that angler demand could be diverted to a smaller number of vessels while maintaining
the same angler density per trip. Benefits to consumers would remain constant while expenditures on variable costs
would also remain the same due to the linearity of expenditures in the number of trips. However, fixed costs would
decrease in this new state of affairs given the retirement of redundant vessel capital. Therefore it follows that any
non-full-employment outcome is suboptimal. This result is an artifact of the lack of any adjustment costs of
entry/exit in our model as well as the constant variable cost of trips. However, given our ultimate concern for long-
run bioeconomic equilibria, the omission of adjustment costs is immaterial since excess capacity cannot persist
indefinitely with finite costs of adjustment.

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