V.2 Could Controls on Catch Effectiveness or its Inputs be Employed Instead of Discard Fees?
Since the choices of vessel owners are the only determinants of harvest rates in our
simple model, one might logically infer that a tax on catch effectiveness (i.e. a tax on some index
of a vessel’s productivity), if it could be reliably measured, would prove equivalent to a discard
tax. This is not generally the case, however, as we shall see.
First of all, if we derive the optimal tax on q from a revision of (30) where the discard tax
is simply replaced by a catch effectiveness tax (τq = λSSφH q), we find that some of the necessary
implicit tariffs listed in (29) fail to hold for all functional relationships between catch
effectiveness and harvest. Specifically, the first condition in (29) fails to hold except for the case
where the following condition is satisfied:
Hqq=H(X,q),∀q>0. (32)
In other words, the harvest function must be linear in catch effectiveness. This is a
commonplace assumption, but if this condition fails then the implicit tax on trips is:36
τD* =λSS((1-φ)L+φHqq). (33)
If Hq q > H for all q (i.e. harvest is strictly convex in q), then the implicit tax on days is too high
relative to that prescribed at the optimal solution, driving trip demand to too low a level - this
despite the fact that catch-augmenting inputs are all optimally determined.37 The imposition of
a linear tariff on catch effectiveness fails to work in general for the reason that a non-linear tariff
is required to account for the harvest-related mortality from additional fishing trips. A corrective
tax or subsidy on fishing days is required in combination with the tariff on catch effectiveness to
achieve the same outcome as the single levy on discards.
36 Note that the tax on landings from (30) has been altered to (1 -φ)λSS to compensate for the now-missing
“subsidy” on landings implicit in the discard tax but missing in the catch effectiveness tax.
37 The reverse applies for the case where harvest is strictly concave in catch effectiveness.
32