\feesvsquotas




        Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks




                                              Abstract
       The paper analyzes the relative performance of two market-based fisheries management
instruments in the presence of a stochastic stock-recruitment relation. Regulators are forced to
choose either a fee per fish landed or a quota on the total fish harvest – at a time when they are
uncertain what will be the stock of fish recruits that will actually materialize during the next
fishing period. With such “ecological” or “environmental” uncertainty being the predominant
random variable in the fishery, some striking regulatory conclusions emerge, which go strongly
against conventional wisdom.




                                                                      Martin L. Weitzman
                                                                      Harvard University
                                                                      July 6, 2000
                                                                      Comments Appreciated
                Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks
                                             Introduction
       The model of this paper has its origins in some actual experiences of current Icelandic
fisheries. Iceland today relies upon a relatively sophisticated ITQ (Individual Transferable
Quota) fisheries management system to sub-allocate by tradeable permits the TAC (Total
Allowable Catch). The TAC itself is administratively set on an annual basis for all major fish
species found within the 200-mile offshore zone.
       Currently, there is some inkling of a national mood of discontent about at least one aspect
of the system. The major problem that the Icelandic public seems to be having now with the ITQ
system is not its perceived inefficiency relative to any alternatives, which is the subject of this
paper, but rather its perceived unfairness. To make a long story short, the original allocation of
ITQ’s was given free to vessel owners in proportion to their historical catch record over the
1981-83 period – at a time in the recent past when everyone in Iceland was concerned with
doing something about the then-existing bad state of over-fishing, and no one was much
concerned with hypothetical future windfall rents from handing out then, for free, potentially
valuable quota-harvesting rights. By now, of course, the rents have shot up just as predicted by
basic economic theory, in the form of increased quota prices. Furthermore, as might have also
been expected for Iceland, which has over ten-times more fisheries income per capita than the
second largest such fishing-industry-dominated nation in the world (and which additionally has a
super-Scandinavian-style work ethic), the windfall fishery rents are perceived as having caused
an unjust and disturbingly-large government-engineered alteration of income distribution.
       Thus, in Iceland today, there has arisen a sometimes-heated national debate concerning
what to do, or not to do, about spreading the existing quota wealth around more fairly. The key
issue is whether some mechanism should be institutionalized for taxing automatically the fishing
rents and transferring some of the proceeds to benefit the rest of the population, who was left out
of the original quota allocation even though the relevant law begins by declaring that “(t)he
exploitable marine stocks of the Icelandic fishing banks are the common property of the Icelandic
nation.” The Icelandic Parliament appointed a special Natural Resource Committee, whose
charge is “...to consider various aspects regarding the utilization of natural resources, especially
arrangements for optimal utilization and the advisability of taxation.”
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks                 page 3


       An outside economist asked to look in on all this could perhaps be forgiven for believing
that now might be a propitious time to try, at least as a kind of mental exercise, thinking through
again from first principles why a country or society that seems so concerned with distribution
does not just “tax the catch” – since, at least in principle, Pigouvian-style taxes on rents would
appear to be the ideal distortion-free instrument for such tax-and-transfer purposes, all the while
promoting simultaneously full economic efficiency in the fisheries.
       I think it represents a fair generalization to say that the conventional wisdom among
fisheries economists is that, for this specific application of regulating the fishing industry,
“prices” are an inferior instrument to “quantities.” The argument is grounded not so much in
anything having to do with equity or unearned-rent transfers, but is based more on the idea that
regulating fisheries with prices is less efficient than regulating with quantities – in part because
of the potential problems associated with highly-uncertain randomly-fluctuating fish stocks.1
       My own instinct on the issue of “prices vs. quantities” here was quite the opposite from
the prevailing wisdom. I tried to make the arguments heuristically, but was myself dissatisfied
with the resultant hand waving involved. This paper, then, represents my best attempt to capture
and to formalize the major part of that heuristic intuition in the simple standard dynamic fishery
model – augmented here by a fairly general stochastic specification of “ecological” or
“environmental” fish-stock uncertainty.
       There is a huge theoretical literature on the economics of the fishery. While most of this
literature deals with the deterministic case, stochastic models also appear. Perhaps the model in
the literature closest technically to the model of this paper is the outstanding contribution of
Reed [1979]. In Reed’s model there is multiplicative uncertainty about the future stock-


       1
         Actually, I would have to go much further in saying that I was shocked at learning the
degree to which the regulatory agenda in this area had already been captured by some fisheries
economists with an extreme “property rights” interpretation of harvesting quotas, which
essentially precludes a serious consideration of Pigouvian-style landing fees from being placed
on the discussion table. A reader interested in checking whether my interpretation is fair might
begin by consulting recent comprehensive accounts, such as Arnason and Gissurarson (1999) or
National Research Council (1999), then followed up by checking out some of the many
references to the fisheries literature contained in these two books.
06.07.00                Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks           page 4


recruitment relation, but the fisheries regulators are allowed to know the current recruitment at
the time that the current harvest decision is made. Unfortunately, as Clark [1990, page 349]
notes, “in many fisheries the exact magnitude of the current stock is unknown at the time that
quotas are specified.” Since it is commonly accepted that “the central problem facing fishery
scientists and fishery managers is to understand and deal with recruitment variability,”2 in such a
spirit it seems somewhat self-defeating to postulate for a stochastic fisheries model that the
regulators know beforehand what will be the next period’s recruitment level.
       The aim of this paper is create and to analyze a stochastic fisheries model where
regulatory decisions must be made when the pertinent recruitment stocks are unknown. So far as
I am aware, the model of this paper is the first to examine analytically the regulatory issue of
instrument choice when there are such severe informational constraints about an uncertain
fisheries environment being placed upon the managers at the time they must make their
regulatory decisions.
       The paper works with a model whose informational timing forces the regulatory
instruments to be set when the size of the relevant resource stock is unknown, primarily because
of significant environmental or ecological uncertainty concerning the stock-recruitment relation.
The model is describing a situation where the regulators must be prepared to live with the
consequences of stock uncertainty, at least during that part of the next regulatory cycle where the
fishermen are reacting to lagged instrument values – throughout the pending fishing period –
which are different from what prevailed at the time when the instruments were set.
       It is within this general kind of informational and institutional context that the question of
“fees vs. quotas” is being posed and analyzed in the paper. Offhand, the usual tradeoff would
appear to be present: harvest quotas have the advantage of fixing the total quantity of fish being
caught, but suffer from the drawback of being unable to control the possibly-excessive effort
being exerted to fish down a stock that, it may just so happen by the laws of chance, is
coincidentally experiencing a low recruitment throughout this fishing period; landing fees, on the


       2
         Sissenwine [1984], from an article in Marine Resource Economics entitled “the
uncertain environment of fishery scientists and managers.”
06.07.00                Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks              page 5


other hand, are (relatively) better able to control the (marginal) fishing effort (or cost), but suffer
the drawback of being unable to prevent over-fishing in a situation where, again by the laws of
chance, the stock recruitment happens already to be low.
        The stochastic part of the simple fisheries model of this paper is sharply and almost
exclusively focused on what might be called “ecological” or “environmental” uncertainty. The
novel feature of this model is that instrument values are being chosen in a regulatory world where
“the central problem facing fishery scientists and fishery managers is to understand and deal with
recruitment variability” – in the form of a currently-uncertain stock recruitment. Even with the
stochastic component being limited to such ecological or environmental uncertainty, the fee-vs-
quota argument is sufficiently complicated that it may, quite reasonably, be unclear beforehand
which verdict the formal model will render. Therefore, I would say, the striking affirmation by
this simple model of the generic superiority of landing fees over harvest quotas in the presence of
stock uncertainties comes as somewhat of a surprise, which perhaps should merit a serious
reconsideration in fisheries economics of this entire set of issues.


                            The Model: Specifications and Assumptions
        The basic framework is a discrete-time metered model. Only a difference-equation set
up, with its inherent delay effects, can aspire to capture the measurement errors, informational
uncertainties, too-late observations, and lagged response features, which form such a critical part
of the actual fisheries management scene.
        Throughout the paper, the positive integer                will index a particular fishing
period. Let     represent the escapement (from capture) in period t. “Escapement” is a fisheries-
biology term for the stock of potential parent fish remaining alive at the end of the fishing period.
It should be noted throughout the paper that nothing in the technical construction of the model
prevents the interpretation that    represents the estimated escapement (in period t), as opposed
to the actual escapement.
        The recruitment of fish stock that actually shows up during period t is denoted         . Let
   represent the state of the fishery environment during period t. The fundamental stock-
06.07.00                  Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks            page 6


recruitment relation is given by the stochastic equation

                                                                                                      (1)



where the       are independent identically distributed (i.i.d.) random variables with a known
given probability density function. It is assumed that for all values of      having positive
probability measure,

                                                                                                      (2)



and, for all values of       ,



                                                                                                          (3)



        It is important to be very clear about the timing and informational sequence being
modeled here. The fisheries regulators first observe (or estimate) escapement            at the end of
period t-1. Then, operating in time on the thin border line between the end of period t-1 and the
beginning of period t, and before anyone can observe what will be the realization of the state of
the environment     , the regulators assign a “best value” to their management instrument, which
is here either a landing fee or a harvest quota. Finally, the fishermen react to the value of the
management instrument during the period t, in effect choosing their most economical level of
fishing effort, via the harvest they take, after they have observed the realization of the state of the
environment      – from the decks of their boats so to speak – in the form of                   . The
subsequent value of        is then the result of profit-maximizing fish-harvesting behavior, given the
imposed regulatory instrument value and the actual realization of       .
        The harvest of fish taken during period t is denoted      . The following formula must then
hold for all periods t:
06.07.00                 Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 7



                                                                                                      (4)



          Let the unit or marginal profitability when the fish stock is x be denoted       . If a total
of H fish are harvested during the period, starting from recruitment level R at the beginning of the
period, then the corresponding total fishing profit for the period is


                                                                                                      (5)




          In the standard fisheries model,      is typically assumed to be of the form

                                                                                                      (6)

where p is the unit price of fish, while      represents the unit cost of harvesting (at fish
population x) – but there is no reason to be so restrictive. The only critical assumption being
made here is that

                                                                                                      (7)

for all      , which corresponds to the standard assumption             .
          Loosely speaking, the fisheries managers are trying to pick instruments in such a way as
to induce harvest levels that will attain as high a level as can be achieved of an -expected-
present-discounted-profits expression having the general form




                                                                                                      (8)




subject to (1), (4) and some initial conditions. The operator notation         here stands for the
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 8


expected value of whatever is contained within the square brackets, taken over all relevant
realizations of     , while


                                                                                                      (9)



represents the relevant discount factor when is the one-period discount rate.
       The reduced-form core uncertainty in this model concerns the overall relationship
between last period’s estimated fish escapement stock and next period’s actual recruitment. Let
us call this kind of stochastic reduced-form relationship ecological uncertainty. It comes about
in this model by a compounding of two stochastic effects – (1) uncertainty about the actual
escapement; (2) uncertainty about the stock-recruitment relationship. Such kind of reduced-form
“ecological uncertainty” represents, arguably, the largest single source of fluctuations in the
fishing industry and the largest single kind of variability in the fishery regulatory process – but
there are many other important sources of uncertainty in fisheries management. (Actually, the
fishery seem to represent one of the most difficult industries in the world to regulate well, in part
because everywhere the regulators look they see uncertainty.)
       So, while I believe there are some very useful, and perhaps even important, insights that
will come out of this way of modeling fisheries management, there is no way I want to argue that
this model represents the final word or that the conclusions could not be undone by another
model constructed differently. The actual regulation of fisheries is more than a match for any
model. The model of this paper merely overlays just one type of uncertainty – ecological
uncertainty about fish stocks – on top of the standard bare-bones deterministic model, which is
itself the simplest meaningful dynamic model of the fishery. The most we can hope to
accomplish with such an approach is to develop a slightly better intuition about the direction of
the pure effect of the single extra feature being added (in this case the pure effect of ecological
uncertainty on the choice of regulatory instrument between fee or quota), when the rest of the
model is isolated away from all other forms of fisheries uncertainty.
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks            page 9


                  The Optimal Regulatory Quota Under Ecological Uncertainty
       In this section of the paper we assume a market-based ITQ (Individual Transferable
Quota) management system is in place, within which sub-allocations of the TAC (Total
Allowable Catch) are automatically determined via competitively traded permits. The task of the
regulators here is to determine the optimal TAC in the presence of ecological uncertainty.
       The “harvest-quota” system works as follows. Given a TAC of Q, which is set by the
fisheries manager, let the ITQ-fishery harvest response function

                                                                                                   (10)



be defined implicitly by the pair of conditions

                                                                                                   (11)



representing a corner solution where H=Q, and

                                                                                                   (12)



representing an interior solution where H<Q.
       Taken together, conditions (11) and (12) mean that the fishermen are expending their
optimal effort to attain the profit-maximizing harvest level, given the actual ecological
environment, and subject to the total allowable catch being no greater than Q. (In equation (12)
we impose the convention that whenever            , then        .)
       The manager’s optimal TAC is most readily explained in this model by going straight to
the dynamic-programming formulation. In the framework of this paper, the fisheries manager
contemplating the setting of a total quota for period t takes the previous period’s escapement
     as the relevant state variable upon which to condition the setting of a TAC.
       Let
06.07.00              Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks              page 10



                                                                                                   (13)



be the expected present discounted value from following a optimal TAC policy starting from state
S. The optimizing manager’s corresponding dynamic programming equation is:


                                                                                                   (14)




where              is defined by (11) and (12).
        Let the value of Q that maximizes the right hand side of (14) be denoted

                                                                                                   (15)

        In period t the managers just prorate the TAC

                                                                                                   (16)



equally per existing quota unit, and then let the market-based ITQ system automatically take care
of the sub-optimizing cost-minimizing part of the “quota” system. Note that fisheries regulation
with quotas seems relatively direct and straightforward, at least by comparison with a fees
system, to which subject we now turn.


                     The Optimal Landing Fee Under Ecological Uncertainty
        The landing-fee regulatory control system is dual to the quota-based TAC system. The
two systems are symmetric opposites – in instrument they are controlling, but also on the issue
of whether or not relevant within-period new information (available to the fishermen within the
fishing period) is being utilized by the endogenous profit-maximizing fishing “response.” A
quota controls directly the TAC quantity output but leaves uncertain next period’s escapement
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 11


“response,” and is informationally inflexible in not permitting to be utilized some relevant
within-period new information. A fee controls marginal profitability (or marginal effort), and is
informationally flexible in allowing some use of within-period relevant new information about
recruitment levels, but leaves uncertain the harvested catch “response.”
       The “landing-fee” system works as follows. Given a landing fee of         per unit of fish,
which is set by the fisheries manager, let the landing-fee-fishery harvest response function

                                                                                                     (17)



be defined implicitly by the pair of conditions

                                                                                                     (18)



representing an interior solution where        , and

                                                                                                     (19)



representing a corner solution where the profit from catching the first fish is less than the landing
fee. Taken together, conditions (18), (19) mean that the fishermen are expending their optimal
effort to attain the level of harvesting which maximizes their profits, given the environment and
subject to the fee   being imposed on each unit of their landings.
       The manager’s optimal landing fee is most readily explained in this model by going
straight to the dynamic-programming formulation. In such a framework, the fishery manager
contemplating the setting of a landing fee for period t takes the previous end-of-period’s
estimated escapement        as the relevant state variable upon which to condition the setting of
the landing fee.
       Let

                                                                                                     (20)
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks              page 12


be the expected present discounted value of following a optimal-landing-fee policy starting from
state   . The corresponding dynamic programming equation for the optimizing fishery manager
is:


                                                                                                      (21)




where               is defined by (18) and (19).
        Let the value of      that maximizes the right hand side of (19) be denoted

                                                                                                      (22)

        For period t, the fisheries manager selects the fee

                                                                                                      (23)



to be charged per unit of fish landed in period t. Thereafter, self-interested decentralized profit
maximization by the fishermen determines the level of fishing effort during the period.
        Compared with the relatively-more-straightforward quota system, fishery regulation with
a landing fee seems somewhat indirect and difficult to explain, or, for that matter, may even be
difficult to understand. It is no wonder, perhaps, that the direct quota system is typically
preferred to the indirect fee system in most of the fisheries economics literature. As we shall see,
however, exactly the opposite conclusion is warranted, at least for the case treated here of pure
ecological uncertainty.


                           The “As-If-Omniscient” First-Best Fishery Policy
        At this point we are almost ready to compare the relative performance of landing fees
with harvest quotas under ecological uncertainty. But first we briefly make here a seeming
digression to characterize, as a benchmark reference point, the hypothetical “perfect-information”
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 13


solution of the stochastic fishery problem when it is known beforehand what will be the
environment one period ahead.
       In this section of the paper, but only in this section, we assume that an as-if-omniscient
fishery manager can “see” before setting the regulatory-instrument values the complete
resolution of the ecological uncertainty of the next fishing period. In all other sections of the
paper we make the more realistic assumption that only the fishermen themselves can observe the
realization of ecological uncertainty, as it unfolds around them in the ocean, and while they are
reacting to the quasi-fixed regulatory instruments that have already been imposed upon them.
More technically, we are assuming in this section of the paper, but only in this section of the
paper, the following highly unrealistic timing sequence concerning what the regulators know.
       In this section of the paper, it is assumed that the omniscient fishery manager, operating
in time on the thin border line between the end of period       and the beginning of period t, can
observe not only the variable       at the end of period     , but here (in this section of the paper
only) knows beforehand also the yet-to-be-realized value of      . The omniscient fishery
manager then conditions regulations on both S and , with corresponding dynamic
programming problem


                                                                                                        (24)




where the operator notation       stands for the expected value of whatever is contained within
the square brackets, being taken over all relevant realizations of the dummy random variable .
       Let the solution of the problem on the right hand side of (24) be denoted

                                                                                                        (25)

       Now, at last, we are ready for the main result of the paper.


                                          The Basic Result
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 14


       Define the immediate-harvest-value function


                                                                                                      (26)




where A is an arbitrarily-fixed lower bound, defined, for example, by the free-access zero-profit
condition

                                                                                                      (27)

       Next, assume that for all possible states of the environment the immediate-harvest-value
function always shows non-increasing-returns to escapement levels. This is the analogue in the
fisheries context of assuming a reduced-form convex production structure.
       Assumption: For all possible values of , the function

                                                                                                      (28)

is concave in S.
       The following proposition shows that, with ecological uncertainty, the optimal landing
fee attains the “as-if-omniscient” first-best fishery policy, and therefore is always superior to a
TAC quota system.
       Theorem: Under the assumptions of the model, for all possible values of          and of S,

                                                                                                      (29)



and for all S (in every case except the singular deterministic case)

                                                                                                      (30)



       Proof: Define by induction for each positive integer n the function
06.07.00                Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks           page 15




                                                                                                      (31)




where              . Making the substitution                , it is readily confirmed by inspection
that if the function sequence             defined by (31) converges, then the limiting function
must obey equation (24).
        Next, define the function

                                                                                                      (32)



        Using definitions (26) and (32), rewrite equation (31) as

                                                                                                      (33)



        We now prove by induction that for all n (and for all possible ), the function            is
concave in S. It is clearly true for     , because            . Suppose the concavity assumption
is true for     . It then follows, making use of (7) and the fact that a convex combination of
concave functions is concave, that          defined by (32) is concave in X.
        For any possible value of      , choose any   and   . Let the corresponding values of X
that maximize the right hand side of expression (33) be denoted, respectively,     and     . Thus,

                                                                                                      (34)



and

                                                                                                      (35)
06.07.00                  Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks       page 16


Also, from feasibility,               and             , implying from the concavity assumption (3)
that

                                                                                                 (36)



for         . Thus, the policy                     is feasible for                . Therefore,
from the maximum part of the equation (31), it follows that,

                                                                                                 (37)



       From concavity of (28) and (32), it follows directly that

                                                                                                 (38)



and

                                                                                                 (39)



       Combining (38) and (39) with (37), and rearranging terms in the latter expression, we
have

                                                                                                 (40)



       Finally, substituting (34) and (35) into (40) yields the desired induction conclusion

                                                                                                 (41)



       From the general theory of dynamic programming, we know that the successive
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 17


approximation (31) converges to the unique solution of (24). (Any standard mathematical
textbook on dynamic programming will contain this contraction-mapping result.) The concavity
condition (41) then proves that the function

                                                                                                       (42)



which uniquely satisfies (24), is concave in S. In its turn, this implies that the function

                                                                                                       (43)



is concave in X.
       Thus, we have proved that            is a concave function defined on the extended real line
      . Let the maximum value of               be attained at the point       , meaning that for all
values of      ,

                                                                                                       (44)

       Now rewrite (24) in the equivalent form

                                                                                                       (45)



       The argmax solution of the right hand side of (45) is just the function

                                                                                                       (46)

       In other words, equation (46) means that the “as-if-omniscient” optimal fisheries policy is
a most-rapid-approach to the constant escapement level S* defined by (44). The remainder of
the proof consists of confirming from the harvest reaction functions (18) and (19) that a most-
rapid-approach to the “as-if-omniscient” escapement level         is automatically induced from any
possible values of S and      by imposing the constant landing fee
06.07.00                Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks              page 18



                                                                                                       (47)

while it is impossible for any quota system to attain this same “as-if-omniscient” first-best
solution unless      essentially has a degenerate distribution with all probability mass effectively
concentrated at one singular point.


                                              Discussion
       The result that a landing fee is able to attain the “as-if-omniscient” first-best fishery
policy seems so striking that it cries out for elucidation. How does the landing fee “know” before
period t what will be the realization of the state-of-the-environment random variable       ?
       The answer here is yet another example of the powerful general theme of economics that
a “price signal” can compress into a simple reduced form all relevant information for inducing
correct decentralized decisions. The point is that by using the instrument of a landing fee, the
fishery manager obviates or shunts aside the need to know the actual recruitment of fish stocks.
       After all, the only use to the fishery manager of knowing recruitment in this model is to
be able to set accurately the harvesting quota that will attain the desired escapement level. The
knowledge of recruitment stocks and the setting of harvesting quotas are just the two means to
the single reduced-form end of hitting accurately an escapement target. The “as-if-omniscient”
first-best policy in this model is a most rapid approach to the (constant) escapement level
defined by (44). By casting the regulatory problem into the mold of the dual price side, in the
form of an optimal landing fee         defined by (47), the fishery manager can automatically
induce the fishermen to attain most rapidly the escapement level         irrespective of the actual
recruitment level.
       Such economizing on information is the hallmark of a price system. All that the current
fishermen need to know, really, is the expected marginal efficiency cost to future fishing of their
landing one more current fish – i.e., the optimal landing fee       . Decentralized self-interested
profit maximization will take care of all the rest.
       To intuit more vividly why prices systematically outperform quantities here, imagine that
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks              page 19


fishing is done by a kind of floating “suction machine,” whose operation is analogous to that of a
vacuum cleaner. In this analogy, there are two natural candidates for regulation: either (1) the
power (i.e., effort) setting at which the floating vacuum cleaner is operated; or (2) the number of
fish actually “siphoned up” by the machine.
       A harvest quota corresponds to a restriction on how many fish can be “siphoned up” by
the machine. When recruitment is higher than anticipated and fish are relatively abundant, the
fishermen operators will most profitably attain their quotas by running their suction machines at
lower power settings, thereby saving on power (i.e., effort) costs. But if fish recruitment levels
are lower than was expected by the managers, and fish are unexpectedly relatively hard to find or
catch, then the profit-maximizing operators will attempt to meet their quotas by revving the
suction machines up to higher power settings, thereby drawing down fish escapement stocks to
undesirably low levels. It is not control of the harvest that is socially desirable per se, but
control of the escapement. Setting the harvest quota gives the fisheries regulators the sensation
of being in direct control of an important quantity, but this is essentially an illusion because they
are unable to control the really important quantity, which is escapement.
       I think the model is trying to tell us that with ecological uncertainty in fish recruitment, it
is a better policy to effectively set an upper limit on the power at which the fish vacuum cleaners
may be run than to attempt to regulate directly the total volume of fish that the suction machines
are allowed to ingest. In the presence of such basic stock uncertainty, it is far better to control
marginal fishing effort, which is what the price/fee accomplishes indirectly, than to control
directly the quantity/harvest level. The fact that fish stocks are highly variable is not, in and of
itself, a valid argument for the preferment of harvest quotas to landing fees. Just exactly the
opposite is true. Pure ecological uncertainty, in and of itself, constitutes a powerful generic
argument for the superiority of landing fees, as a regulatory instrument, over harvest quotas.
       Of course, such conclusions come only from a model. In this model there is just one
source of variability – the fluctuations in fish stocks, which we are here calling “ecological
uncertainty.” What happens to these conclusions where there are also present other sources of
uncertainty, namely “economic uncertainty” about the           profit function? Which regulatory
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks             page 20


instrument – landing fee or harvest quota – is then superior?
       A formal analysis of exactly how “ecological uncertainty” and “economic uncertainty”
interact to determine the optimal choice of fishery regulatory instruments involves a complicated
tradeoff that is properly the subject of another paper. Nevertheless, the outlines of a tentative
answer seem intuitively clear and can be indicated roughly here. As this paper has shown, pure
ecological uncertainty unambiguously favors fees over quotas. By contrast, pure economic
uncertainty is a typical “prices-vs-quantities-type” mixed situation where the answer can go
either way depending, among other things, on the relative slope of the marginal profit function.
A relatively flat marginal profit function by itself tends to favor quotas. In order to end up
favoring harvesting quotas to landing fees overall, then, it should be the case both that ecological
uncertainty is relatively less significant than economic uncertainty, and that the marginal profit
function        is relatively unresponsive to fish stock levels x.
       It is a useful task for future theoretical research to develop rigorously the mathematical
formulas that may show exactly how the comparative advantage of landing fees over harvesting
quotas depends quantitatively upon the various relevant specific features of the problem –
including economic and ecological uncertainty. And it will be a useful applied problem of
fisheries economics to attempt to categorize, however crudely, which types of fisheries are more
likely to be better managed by landing fees and which types of fisheries are more likely to be
better regulated by harvest quotas. The current paper may then perhaps be seen as a first
tentative step in the direction of such a research program.


                                             Conclusion
       The implicit point of departure for this paper has been the familiar prototype fisheries
model where a fictitious sole owner harvests a fish population to maximize present discounted
profits. In the deterministic case, it does not matter whether the fishing externality is corrected
by a market-based quantity instrument, in the form of a total harvest quota, or a market-based
price instrument, in the form of a landing fee. What happens to this theoretical equivalence,
though, when there is uncertainty?
06.07.00               Landing Fees vs. Harvest Quotas with Uncertain Fish Stocks                page 21


       The most significant form of uncertainty present in the fishing industry is usually held to
be the “ecological” uncertainty associated with a stock-recruitment relation that is inherently
stochastic and whose realization cannot be observed by the fishery managers at the time when
they issue regulations. It seems fair to say that the conventional wisdom in fisheries economics
favors harvest quotas over landing fees, often, or even typically, citing as justification the
inherently-unknowable randomness of this very stock-recruitment relation. The basic result of
the model of this paper shows that such logic is exactly backwards. The primacy of ecological
uncertainty tends to make a generic argument in favor of landing fees over harvest quotas –
rather than the other way around.




                                             References
Arnason, Ragnar, and Hannes H. Gissurarson (1999), Individual Transferable Quotas in Theory
and Practice. Reykjavik: The University of Iceland Press.


Clark, Colin W. (1990), Mathematical Bioeconomics, second edition. New York: John Wiley
and Sons.


National Research Council (1999), Sharing the Fish: toward a national policy on individual
fishing quotas. Washington: National Academy Press.


Reed, William J. (1979), “Optimal Escapement Levels in Stochastic and Deterministic
Harvesting Models.” Journal of Environmental Economics and Management 6, 350-363.


Sissenwine, M. P. (1984), “The Uncertain Environment of Fishery Scientists and Managers,”
Marine Resource Economics, vol. 1, no. 2, 1-30.