of fish capital from the system via the discard process.21 Finally, the effect of increased angler
demand on the valuation of the stock is ambiguous, depending upon the sign and magnitude of
the derivative of the biological growth rate.
Having derived the necessary conditions for the optimal management of the fishery, we
now contrast them with what we would expect in a perfectly competitive open access industry.
III. The Open Access Outcome
In competitive equilibrium the market determines the number of fishing days and
landings (holding other variables fixed) so as to maximize the sum of short-run consumer and
producer surplus:
D*
m*ax ∫MB(D, H(X, q(Zq, N)), L, S(zs, N)) dD - NV * c(z , Zs, N, NumTrips, w, r) (21)
D ,L 0
subject to the aforementioned constraints on landings and the maximum number of trips per
vessel where the vessels’ choice of angler density, number of vessels and quality inputs are taken
as given by anglers. The first order condition for D * is as follows:
MB(D*,H(X,q(Zq,N)),L,S(Zs,N))-[(wVN'ZVN)N+wV'ZV
=0.
(22)
This expression differs from (10) in that the full user cost of the mortality from additional angler-
days is missing from the right hand side. As a result, there will be excessive demand for days at
sea by anglers in the competitive case relative to the social optimum.22
The analogous condition for L is:
21 The effect of the mortality parameter in our model on the costate variable is analogous (although not perfectly
equivalent) to the role of depreciation in the literature on investment.
22 In the event that vessels are fully employed in a competitive equilibrium (an unlikely event as we will later
demonstrate), a fisherman desiring an extra day at sea would have to pay a discretely higher price than those
immediately preceding him due to the necessity of covering the fixed costs of the marginal increase in vessel capital
required to satisfy demand - thus the final term in (22).
17