Download Ragnar Arnason*

Ragnar Arnason*
Ecosystem Management on the Basis of Catch Quotas
A background paper for the FAME workshop on
Biodiversity: Management, Economics and the Marine View
Esbjerg, June 11-13, 2004
A similar paper, titled Economic Instruments to Achieve Ecosystem
Objectives in Fisheries Management, was initially published in ICES
Journal of Marine Science 57 no. 3. 2000: 742-51
* Professor of Fisheries Economics
Department of Economics
University of Iceland
E-mail: [email protected]
1
Abstract
This paper develops an aggregative model of ecosystem fisheries. Within the framework
of this model, rules for optimal harvesting are derived and their content examined. An
important result is that in the ecosystem context unprofitable fisheries should usually be
pursued in order to enhance the overall economic contribution from the ecosystem.
Another interesting result is that in the multi-species context modifications of the usual,
i.e., single species, optimal harvesting rules are needed even when there are no biological
interactions between the species. The possibility of multiple equilibria and complicated
dynamics is briefly discussed.
The paper argues that only two classes of economic instruments capable of
optimal management of ecosystem fisheries have so far been identified. These are: (i)
corrective taxes and subsidies (Pigovian taxes) and (b) appropriately defined property
rights. Of these two classes of instruments, Pigovian taxes are informationally demanding
to the point of being infeasible. Property rights based regimes, on the other hand, are
informationally efficient and therefore appear to constitute the most promising overall
approach to the management of ecosystem fisheries. The employment of property rights
regimes for the management of ecosystem fisheries is then further discussed and some of
the implications explored.
2
1. Introduction
This paper considers the optimal utilization and management of ecosystem fisheries. It is
divided into two main sections. In the first section, a general aggregative ecosystem
fishery model is developed and its properties analysed. A major result of this part of the
paper is that ecosystem fisheries are very complicated and optimal utilization rules even
more so. Nevertheless, a number of results of apparently general applicability can be
derived. For instance, biological interactions between species are not necessary for
ecosystem or rather multispecies fisheries problems. For these to arise, it is sufficient to
have interspecies effects on the harvesting process or economic interactions between
different fisheries. Second, in the ecosystem case fishing effort can just as easily be
insufficient as excessive. Thus, the fisheries problem is just as much to encourage
inadequate fishing effort as to reign back excessive fishing effort.
In the second section of the paper, the problem of managing ecosystem fisheries is
considered. The main result is that direct controls are unlikely to improve the economics
of ecosystem fisheries. Due to ecosystem complexity and the costs of management they
may actually make matters worse. The most promising management tools for ecosystem
fisheries appear to be taxes/subsidies or property-rights based instruments. Of these two
property rights appear generally preferable, provided they are feasible, since they tend to
generate market prices that can offer important guidance to the fisheries manager.
2. A General Ecosystem Fisheries Model
This section deals with the modelling and analysis of ecosystem fisheries. In order to
focus on the key structural elements of the problem we restrict the modelling to
aggregative non-stochastic representations. We first describe the ecosystem then the
fishing activity and, combining the two, we examine the features of optimal harvesting
paths.
Ecosystem description
Consider an ecosystem containing I living species. Let us represent the biomass1 of these
species by the (1I) vector x. Let the biomass growth for the species be described by the
functions
(1)
x i = Gi(x,z), i = 1,2,....I
where the vector z represents habitat variables. In what follows it is often convenient to
refer to the (1I) vector of biomass growth functions i.e.
1
Or some other more pertinent measure.
3
(2)
x = G(x,z) = (G1(x,z), G2(x,z),....., GI(x,z))
Some logical and simplifying restrictions on (1) are now in order: First, as the
habitat is regarded as exogenous in this analysis we will in what follows generally drop
direct reference to this variable. Second, we assume that for each of the species included
in the ecosystem there exists a particular (non-negative) vector x such that biomass
growth is strictly positive. If this wasn't the case, the species could obviously not survive
and could be dropped from the analysis. Third, for analytical convenience we will assume
that the biomass functions are twice continuously differentiable and concave. This
implies that each of the Hessian matrices
Gixx  (Gi x j xk )  ( 2Gi / x j xk ) , i = 1,2,....I
is negative definite. Finally, we will assume that the growth function of each species has
the usual dome-shape with respect to own biomass. More precisely:
 xi2  xi1  0 such that Gi(xi1, x-) = Gi(xi2, x-) = 0 and Gixixi < 0,
where x- denotes the biomass vector with xi removed.
The representation in (1), even with the above restrictions imposed, is quite
general. All the species and all the habitat variables in the ecosystem potentially influence
the biomass growth of all the species. The species to species interrelationships are
captured by the Jacobian matrix
 G 1 x1

 .
Gx(x) = 
.

G I x
1

.
.
.
.
.
.
G 1 xI 

. 
,
. 

G I xI 
which is often referred to as the community matrix.
This ecosystem representation obviously includes the usual singles species model
as a special case, i.e. the one where I = 1. For concreteness we then have the biomass
growth function:
x = G(x),2
and the Jacobian (community) and Hessian matrices are reduced to the scalars Gx(x) and
Gxx(x), respectively.
2
This could for instance be represented by the logistic function.
4
Fisheries description
Let us for convenience assume that each of the species in the ecosystem can be targeted
for fishing.3 Let the (1I) vector e represent aggregate fishing effort for each of these
species. Each element in this vector, ei, say, represents fishing effort directed to a species
i. The corresponding harvest is given by the following generalized harvesting function:
(3) yi = Yi(e,x),
where yi is the harvest of species i This harvesting function is quite general. First, all
biomasses influence the harvest of species i, not only the biomass of the species itself. It
is easy to imagine situations where cross-species harvesting effects of this nature might
take place. For instance the catchability of a given species may be influenced by the
presence of other species. It is an empirical problem, however, to establish the relevance
of this effect in particular cases. Second, the catch of species i depends on the fishing
effort for all the species in the ecosystem. Thus, equation (2) allows for by-catch in a
natural way. For instance, Yiej(e,x)  Yi/ej represents the marginal by-catch of species i
when changing fishing effort for species j.
Now, a harvesting function like (3) is assumed to apply to each species. For
mathematical convenience we will generally take these harvesting functions to be twice
continuously differentiable, increasing in own fishing effort and biomass and concave.
Moreover, since some fishing effort is needed to generate harvest and some biomass of
species i to generate harvest of species i, we have:
Yi(0,x) = Yi(e,0) = Yi(e,x1, x2,..,xi-1,0,xi+1,..,xI) = 0.
The whole fishery can be represented by the vector of harvesting functions
(4)
y = Y(e,x).
Clearly, under our assumptions, the Hessian matrices for this vector are negative definite.
The costs function corresponding to the harvesting activity may be written as
(5)
ci = Ci(e,w), i = 1,2,....I
where the vector w represents the vector of input prices. These are regarded as exogenous
in this analysis so in what follows we will drop reference to this vector from the notation.
Note that (5) is a fairly general representation of the fisheries cost function in the
ecosystem context. In particular, the derivative Ciej(e) represents the marginal cost in
fishery i of increased fishing effort in fishery j. In the economic jargon an effect of this
kind is referred to as a production externality. While it's easy to think of situations where
3
This actually is totally unrestrictive since, as we will see, as any level of bycatch is permitted.
5
an effect of this kind might be important4, its empirical relevance clearly depends on the
particular situation in question.
We assume that the cost functions are increasing in own fishing effort (but
perhaps declining in the fishing effort for other species) and, for mathematical
convenience, convex.
Total fishing costs can be represented by the (1I) vector
(6)
c = C(e,w).
Equations (4)-(6) complete our description of the harvesting activity. The vector
of individual species fishing effort, e, plays a central role in this description. It is worth
noticing that if it is not possible to target fishing effort on specific species, this vector
collapses to a single variable or a scalar. Let us refer to this scalar as, e. It immediately
follows that all the species in the ecosystem have to be fished indiscriminately according
to their respective harvesting functions, yi = Yi(e,x) for all i. Therefore, ecosystem
management, in the sense of adjusting fishing effort on species is simply not possible and
the whole ecosystem has to be exploited as if it consisted of only one species. Thus, the
assumption that it is possible to target individual species, or at least subsets of the
species, separately is fundamental to the practical relevance of ecosystem analysis.
Profits and rents
Combining the economic and biological part of the model, the evolution of species
biomasses is defined by the following vector function:
(7)
x = G(x) - Y(e,x).
It should be realized that this representation implicitly assumes that the fishing activity
only influences biomass growth via its extraction of biomass in the form of harvests.
Profits from fishery i are
i = Yi(e,x) - Ci(e),
where the unit price of harvest has been normalized to equal to unity. This, of course is
equivalent to redefining the units in which the volume of harvest is measured to make the
price per unit equal unity.
For all the fisheries the profits are
 = Y(e,x) - C(e),
4
Crowding on the fishing grounds or in harbour is one obvious case.
6
where  is a (1I) vector of profits by fishery.
Total fisheries profits from the ecosystem as a whole are
 = i i  i Yi(e,x) - Ci(e)  1(Y(e,x) - C(e))  1,
where  represents total profits at time t. 1 represents a (1I) vector of ones and the
vector Y(e,x) - C(e))  1 is now a (I1) column vector.
Finally, the present value of profits is:

V =  exp(-rt) dt =
0


0
1(Y(e,x) - C(e))exp(-rt) dt,
where t represents time and r>0 is the rate of discount (interest). Thus, the expression,
exp(-rt)  e-rt is the discount factor appropriate to profits at time t.
Optimal ecosystem fisheries
We will first study the case where the social objective is to maximize the present value of
economic rents form the fisheries. This, of course, is the usual approach in analytical
fisheries economics.
The maximization problem is to find the time path for the fishing effort vector
that maximizes the present value of profits from the fishery. More formally we seek to:
(8)


0
0
Maximize V =  exp(-rt) dt =  1exp(-rt) dt
{e}
Such that
x = G(x) - Y(e,x),
 = Y(e,x) - C(e),
x  0,
e  0.
A Hamilton function corresponding to this problem may be written as:
H = 01(e,x) + (G(x) - Y(e,x)),
where the (I1) vector   (e,x) represents profits, i.e. (e,x)  Y(e,x) - C(e). The scalar
0 and the (1I) vector are Lagrange multipliers. The vector  plays a crucial role in the
7
analysis. Along the optimal path, the elements of , namely (1, 2, ….I,), represent the
shadow values of the respective biomasses, i.e. (x1, x2, …. xI,). , in other words, provides
a measure of the true values of the biomasses in terms of the objective function.
Necessary conditions for solving problem (8) include5:
(8.1)
0 = 1,
(8.2)
1e - Ye = 0,
(8.3)
 -r = - 1Yx - (Gx – Yx),
(8.4)
x = G(x) - Y(e,x).
Expressions (8.2)-(8.4) provide 3I conditions that along with the appropriate
initial and transversality conditions are in principle sufficient to determine the optimal
time paths of the 3I unknown variables, namely the (1I) vectors , e and x.
Equations (8.2) and (8.3) are in many respects central to the solution. Equation
(8.2) gives the rule for the optimal behaviour of the fishing industry at each point of time.
According to this rule, fishing effort in each fishery should be expanded until the overall
marginal profits equal the marginal value of the biomass as measured by the term Ye.
This means that it is not optimal to maximize instantaneous profits. This temptation must
be modified according to the value of the biomass in the ocean. Equation (8.3), on the
other hand gives the equations of motion for the shadow value of the biomasses along the
optimal utilization path.
Equations (8.2) and (8.3) contain the derivatives that describe how system
variables respond to exogenous fishing effort changes. These derivatives are contained in
the (II) Jacobian matrices e, Ye and Gx.
Gx, of course, is the community matrix as previously discussed. This matrix has
long been regarded as one of the keys to the ecosystem fisheries problem. Expressions
(8.2) and (8.3), however make it clear that the economic matrices e and Ye  that may
be called the economic community matrices  play in general just as important role in
the optimal management of ecosystem fisheries. Typical elements of the Ye and e
matrices are marginal catch of fishing effort and marginal profits of fishing effort. More
precisely:
Ye = (Yi(e,x)/ej),
i.e. the marginal catch of species i in response to increased fishing effort on species j. If
there is no by-catch this matrix will be diagonal, i.e.
5
According to the so-called maximum principle (Pontryagin et al. 1962).
8
 Y 1e1

 0
Ye = 
.

 0

0 

0 
.
.
. 

... Y I eI 
0
Y
2
...
...
e2
.
.
The marginal profit matrix, e, is defined by
e = (i/ej) = (Yi(e,x)/ej – Ci(e) /ej).
So the typical element in e represents the marginal profit in fishery i of increased
fishing effort on species j. For this matrix to be diagonal there must be no by-catch and
no interfishery cost effects. This means that in addition to a diagonal Ye matrix the, the Ce
matrix must be diagonal as well, i.e. Ci(e) /ej = 0 for all ij.
Expression (8.2) contains I equations, one for each fishery or rather fishing effort.
A representative equation, the j-th one, say, may be written as:
(8.2´)
I
I
i 1
i 1
 (Y eij  Cei j )   i Y eij  0.
This representative equation measures the marginal impact of fishing effort directed at
species j on overall profits. These profits are defined as direct profits, i(Yiej – Ciej) less a
charge iiYiej due to the value of the biomass extracted by this marginal fishing effort.
According to equation (8.2´), this charge is equivalent to the summation over the
marginal catch effect of ej on all the species multiplied by its shadow price, i.
Notice that the summation is over all the species in the ecosystem, i.e. the
marginal impact of fishing effort directed at one species is evaluated according to its
harvest of all species in the ecosystem. Also, through the term iCiej, the effects of this
marginal fishing effort on the costs in all fisheries is included. Only if both the marginal
harvest matrix, Ye, and the marginal cost matrix, Ce are diagonal will the typical equation
in (8.2) be reduced to the familiar single species equation:
(8.2´´) Yeii  Ceii  i  Yeii  0.
Expression (8.3) also contains I equations. It provides us with the equations of
motion for the shadow prices for each species of fish. A representative equation, the j-th
equation, say, is
I
I
i 1
i 1
(8.3´)  j  r   j   Y xi j   i  (G xi j  Y xi j ) .
9
So, (8.3´) tells us first of all that the evolution of the shadow value of biomass j depends
not only on that biomass's impact on its own marginal growth but also on its impact on
the marginal growth of all the other species in the ecosystem. This effect is translated
through the relevant column in the community matrix, Gx represented in (8.3´) by the
summation iGixj: Secondly, (8.3´) informs us, that the evolution of the shadow value of
the biomass of species j also depends the marginal effect of this biomass on the harvest of
all the species in the ecosystem. This effect is reflected in the summation iYixj, which we
have previously referred to as the cross-species harvesting effect.
An interesting message of equation (8.3´) is that even if the community matrix is
diagonal, i.e. Gixj = 0 for ij, there will still be interspecies effects of biomass values
through the cross-species harvesting effects Yixj. Thus, only if both the Gx and Yx matrices
are diagonal will equation (8.3´) be reduced to the usual single species equation
 j  r   j  Yxj   j (G xj  Yxj ) .
j
j
j
Now, eliminating the Lagrange multipliers 0 and the vector from the necessary
conditions (8.1)–(8.4) we obtain two sets of differential equations describing the solution
to the maximization problem.
(8.5)
 = - 1Yx + (Yx + rI - Gx),
(8.4)
x = G(x) - Y(e,x),
where I is the identity matrix and the vector of biomass shadow values, , is defined by
(8.6)
 = 1e(Ye)-1,
where (Ye)-1 is the inverse of the matrix Ye. This expression for the shadow values of
biomasses is quite important for what follows. In principle it can be used to calculate
these shadow values provided the fishery is moving along the optimal path. In practice,
this is usually not feasible.
The two sets of differential equations (8.5) and (8.4), along with the appropriate
initial and transversality conditions6 will in principle suffice to determine the paths of
fishing effort and biomasses that solve the maximization problem (8). It is clear,
however, that this system, especially equations (8.5), is exceedingly complex. This has
several important implications. First, the system may exhibit very complex dynamics.
Therefore, even along the optimal path, the existence of multiple equilibria, bifurcations
and even chaos cannot be ruled out.7 Second, due to its complexity, the system is in
6
7
Usually, the initial stock of biomasses x(0) may be estimated. Terminal conditions in an infinite
programme may be complicated although usually tractable. Moreover, sustainability requirements may
impose certain terminal conditions.
The Bendixson-Poincaré theorem [REFERENCE] states that a set of three or more 1st order differential
equations is sufficient to generate chaos. Montrucchio (1992) has demonstrated that optimal systems
may exhibit chaotic behaviour.
10
general very difficult to analyse even with high powered numerical methods. Third, again
due to the systems complexity, just obtaining a particular numerical solution may be an
extremely difficult task.
An equilibrium solution to this system is slightly more informative. Imposing
equilibrium, i.e.  = x =0, we find after some rearranging that in optimal equilibrium:
(9.1)
[Gx + Ce(e)-1Yx - rI ] = 0,
(9.2)
G(x) - Y(e,x) = 0.
Expressions (9.1) and (9.2) yield 2I equations to solve for the 2I optimal equilibrium
values of fishing effort, e, and biomass, x. The corresponding shadow values of the
biomass, , can subsequently be calculated according to (8.6)
A number of observations concerning system (9.1) and (9.2) are in order:
(i)
The system may in principle exhibit many solutions. In that case, additional
considerations are needed to determine the truly optimal equilibrium.
(ii)
If some optimal equilibrium values of biomass or levels are zero, as seems likely,
the number of equations is reduced correspondingly (as is the number of
unknowns).
(iii)
In the single species case, I=1, the system reduces to a nonlinear version of the
usual modified golden rule equilibrium conditions for the fishery derived by Clark
and Munro (1982)
G(x) + CeYx/e = r
G(x) - Y(e,x) = 0.
(iv)
If all the Jacobian matrices, i.e. Gx, Ce,Yeand Yx, are diagonal the system reduces
to collection of Clark-Munro type of single species equilibrium conditions. So in
this case the single species theory applies even if the fishery is a ecosystem
fishery. Notice, however, that this is a necessary condition. For this result to hold,
all these matrices must be diagonal. If only one of them is not, the single species
theory is inapplicable. Thus, for instance, a diagonal community matrix, i.e. no
biological ecosystem interactions, is by no means a sufficient justification for
employing single species analysis.
(v)
The shadow values of biomass, i.e. the s, do not have to be positive. They may
just as easily be zero or negative as is made clear by equation (8.6). This, of
course, makes perfect sense. The biomass value of a species that has little
conservation or commercial value but is detrimental to the biomass growth of a
very valuable species can hardly be positive. In fact, most likely it is negative
meaning that harvesting of that species is encouraged beyond the point where
marginal profits are zero.
11
3. Economic Instruments
According to the results of the previous section optimal fishing behaviour, i.e. fishing
effort, is given by the vector equation:
(8.2)
1e - Ye = 0
where  is the appropriate vector of shadow values of the ecosystem biomasses. For a
particular fishery, fishery j, say, the relevant equation is:
(8.2´)
I
I
i 1
i 1
 (Y eij  Cei j )   i Y eij  0.
According to this equation the “correct” application of ej takes account of its impact on
all the biomasses, all the harvests and all the cost functions.
In an unmanaged fishery, by contrast, the fishing firms maximize their own
profits. As is well established (see e.g. Clark 1976, Hannesson 1993) this means in
general that they take insufficient account of the shadow value of the biomass.8 In fact,
for most fisheries with a reasonable number of participants, the fishing firms imputed
value of  is not only too small, it is very close to zero (Arnason 1990). This means that
instead of (8.2) the firms approximately follow the rule :
(10)
1e = 0.
As a result the fishing firms and the fishing industry as a whole behaves suboptimally.
This is the essence of the fisheries problem. The fishing firms do not take full account of
their impact on the biomass growth and therefore they apply the wrong fishing effort. In
the usual single species fisheries models aggregate fishing effort is generally too great
and the stocks too small. In the ecosystem context, by contrast, fishing effort can just as
easily be too small and the corresponding species biomass too great.
To solve the fisheries problem, a great number of different management methods
have been suggested and tried. Most of theses, however, are conveniently grouped into
two broad classes; (1) biological fisheries management and (2) economic fisheries
management. Economic fisheries management may be further divided into (i) direct
restrictions and (ii) indirect economic management as illustrated in Figure 1
8
They will also ignore other externalities their fishing activtiy may impose on other fishing firm such as
crowding, gear conflict, dispersing fish concentrations etc. These types of externalities, included in the
I
general ecosystem fisheries model analysis in the terms
 (Y
i 1
analysis.
i
ej
 Cei j ) , are ignored in the following
12
Figure 1
Fisheries Management Methods: Classification
Biological
Fisheries
Management
Economic
Fisheries
Management
Direct
Indirect
Taxes
Property
Rights
Biological fisheries management, such as mesh size regulations, total allowable
catch, area closures, nursery ground protection etc., may conserve and even enhance the
fish stocks. They, however, fail to improve the economic situation of the fishery because
they do not impose the appropriate shadow cost of harvesting on the fishing firms as
required by equation (8.2´). As a result, the fishing firms will respond to a successful
biological management simply by expanding fishing effort thus eliminating any
temporary gains generated by the managment measures.
Much the same applies to direct economic restrictions. Such restrictions take
various forms. There are limitations on days at sea, fishing time, engine size, holding
capacity of the vessels etc. These methods also fail to generate economic improvements
because they impose a the shadow cost of harvesting on the fishing firms. As a result, the
fishermen are still encouraged to expand uncontrolled inputs until all profits in the fishery
have been wasted.
In addition to this, it is important to realize that setting and enforcing biological
and economic fisheries restrictions is invariably costly. Usually, these costs are quite
substantial. Since, these measures do not generate any economic benefits, at least not in
the long run, these costs represent a net economic loss. Consequently, we are driven to
the conclusion that these fisheries management methods may be worse than nothing!
The only fisheries management methods that on theoretical grounds have any
chance of success are indirect economic ones. The most prominent of these are (a)
corrective taxes/subsidies and (b) property rights based instruments such as individual
transferable quotas.
13
Taxes on harvests
Comparison of equations (8.2) and (10) suggests that the imposition of unit harvesting
taxes (or subsidies) equivalent to the shadow value of biomasses  will solve the fisheries
problem.9 Under those circumstances the fishing companies will experience an additional
marginal cost of effort equivalent to Ye as required by equation (8.2) and modify their
behaviour accordingly.10
There are severe practical problems with this approach, however. Most
importantly, it has immense computational and informational requirements. First, there
must be one tax rate for every biomass. In the ecosystem context this implies a high
number of taxes. Second, the taxes are dynamic: they must be adjusted continuouly over
time if they are to be optimal. For these reasons, just calculating the taxes poses a
formidable problem. In addition to this, there are apparently insurmountable problems to
obtaining the information needed to do the calculations. The previous section gives the
formula for the shadow value of biomasses, i.e. the appropriate tax rates as:
(8.6)
 = 1e(Ye)-1,
and its dynamics as
(8.5)
 = - 1Yx + (Yx + rI - Gx).
Now, all the relevant information about the fishery is contained in the biological
growth functions, G(x), the harvesting functions, Y(e,x), and the profit functions, (e,x).
Therefore, expressions, (8.5) and (8.6) make it clear that the fisheries manager must have
instantaneous knowledge about everything in the fishery to be able to calculate the
optimal tax. Clearly this is beyond the capabilities of any realistic fisheries manager.
In addition, there is generally substantial socio-political opposition to the
imposition of heavy taxes, as would be required for many fisheries, and to continuously
varying them over time. Moreover, there are significant equity problems involved. For
instance, it has been shown that the optimal tax should vary across firms of different sizes
(Arnason, 1990). This is probably quite unacceptable.
So, although taxes are theoretically attractive as a fisheries management tool, they
are subject to serious practical problems. Nevertheless, it should not be forgotten that
taxes have the great advantage that any tax collection in excess of collection costs must
represent fisheries rents. Therefore, even in an environment of limited information, it is
difficult to avoid improving the fisheries situation with a regime of corrective taxes.
Therefore taxes/subsidies remain an intriguing possibility as a fisheries management tool.
9
10
This type of taxes/ subsidies are generally referred to as Pigovian taxes (Pigou 1912).
Other taxation schemes such as taxes on fishing effort are also possible to achieve the same result.
14
Property rights, ITQs
Individual transferable quota a (ITQs) are probably the most widespread and flexible
property rights system currently employed in ocean fisheries. Let us now consider the
option of regulating an ecosystem fishery by means of ITQs. We will restrict our
attention to the following basic ITQ system:
1.
2.
3.
4.
5.
The fishing firms hold fractions or shares in the total allowable catch (TAC) for
each species. These shares are referred to as share quotas.
Each firm's permitted catch of a given species is defined as the multiple of its
share quota for that species and the corresponding TAC. This constitutes the
firm's catch quota11 for that species.
The share quotas are permanent in the sense that they allow the holder the stated
share in the TACs in perpetuity.
The share quotas as well as the catch quotas are transferable and perfectly
divisible.
A central authority, which may be referred to as the fisheries manager, issues the
initial share quotas and subsequently decides on the TAC for each species in the
ecology at each point of time.
Note that this multispecies ITQ system requires that all quotas be met exactly.
This important point warrants an explanation. If a particular fishery is profitable, profit
maximizing firms will obviously not choose to hold unused catch quotas in this fishery.
Therefore, the quota constraint only needs to be set as an upper bound. In the ecosystem
context, however, optimal fisheries management will typically require the reduction of
the stock of some species that are themselves not valuable but compete with or prey on
valuable species. Such fisheries will not be privately profitable and the respective quota
holders would like to avoid filling their quotas. Therefore, in the ecosystem context, the
requirement that all quotas be exactly met is needed12.
Under this ITQ system, the quotas, being tradable, assume a market value. Let us
refer to this set of prices at a point of time by the vector s. Clearly, s  0 according to
whether the fishery is privately profitable or not. Therefore, the use of quotas for fishing
implies an opportunity cost (or benefit) to the user just as a tax (or a subsidy). More
formally, the marginal benefits of fishing effort is now:
(11)
1e - sYe = 0.
Thus, by comparison with equation (8.2), it is clear that if the quota prices, s, were equal
to the shadow value of biomasses, , the fishing firms, under an ITQ system, would act in
a socially optimal fashion.
11
12
Note that the catch quotas are denominated in the same units as the TAC, i.e. volume per unit time.
Actually, the requirement could be relaxed to state that the share quotas stipulate the upper limit on the
permitted rate of catch for profitable fisheries and a lower limit for unprofitable fisheries.
15
Now, the market price of quotas obviously depends on the vector of TACs
(Arnason, 1990). Therefore by setting the appropriate TACs the authorities can induce
the fishing industry to utilize the ecosystem in the optimal manner. The drawback is that
selecting the correct vector of TACs, one TAC for each species in the ecosystem, is a
formidable problem. With regard to its computational and informational requirements it
is formally equivalent to the taxation problem above. Under the ITQ system, however,
this problem can to a large extent be bypassed. The fundamental reason is that the
information processing and number crunching abilities of the market actually solve a
good deal of the problem.
It may be taken for granted that all information that fisheries authorities can
possibly obtain about the biological and economic aspects of the fishery already exist
within the fishing industry. First, the fishing firms have at least as much knowledge about
their own operating conditions as the most determined fisheries authority could possibly
hope to obtain. Secondly, since the state of the stocks and their ecosystem interactions is
a major determinant of fishing firms' profitability, not the least in an ITQ environment,
the fishing firms or, more generally, quota traders can be relied on to assemble and to
make the best possible use of the available biological and ecosystem data. In fact, given a
reasonably competitive industry, only those firms that efficiently collect and interpret all
the relevant information will survive.
All this information is conveyed to the market in the form of offers and bids for
quotas. The resulting quota prices churned out by the market reflect the sum total of all
the information brought to the market and the best aggregate judgement of all market
participants. After all, market participants are betting their money on being right.
It can be shown (Arnason 1990, 1996) that under fairly nonrestrictive situations
the prices of permanent quotas or, equivalently, quota shares reflect the present value of
expected profits from using that quota. Moreover, the sum of all ecosystem quota values
equal the expected profits from exploiting the ecosystem as a whole. More formally:
(13)

isi = 1s =  1exp(-rt) dt = V,
0
where si represents the price of (100%) quota share for species i and V, it will be recalled
from the previous section, represents the total value of all ecosystem fisheries.
Thus, under ecosystem ITQs, the task of the fisheries manager is greatly
simplified. He only has to adjust the current vector of TACs for all the species in the
ecosystem until the total market value of permanent quota shares, which he can readily
observe in the market, is maximized. The fisheries manager does not have to collect data
on the fish stocks and the economics of the fishing firms. The firms themselves13 can be
relied on to gather and interpret the pertinent biological and economic information in the
most efficient manner. This information will be reflected in quota prices. By selecting
TAC vectors that maximize the total market value of share quotas, the fisheries manager,
13
Or, for that case, market speculators.
16
however, acts as if he had command of all this information. Clearly this management
method is informationally extremely efficient. Therefore, it is sometimes referred to as
the minimum information management (MIM) procedure.
Ecosystem fisheries management with the help of ITQs has some interesting
implications. For instance, negative TACs and negative quota prices for some species are
quite possible and have a meaningful economic interpretation.
For privately profitable fisheries, those that are normally observed in the real
world, share quota price would be positive. On the other hand, in the ecological
framework, the MIM procedure may well result in negative share quota prices for some
other species. The reason is that the optimal ecological fisheries policy will usually
require a reduction in the stock size of some species of fish that are themselves not
valuable but prey on or compete with commercially valuable species. The quota price for
these species would be negative representing harvesting subsidies. This is not at all
surprising. There are many parallels under the more developed property rights system
ashore.14
When share quotas prices are negative, profit maximizing quota holders would
clearly prefer not to spend economic resources catching their share quota. Therefore, in
this case, the ITQ requirement that quotas be fulfilled must be imposed.15 Clearly, profit
maximizers will only assume such an obligation for a payment. For this reason, the initial
allocation of share quotas in a privately unprofitable fishery will normally require a
payment or subsidy.16 The firms requiring the lowest subsidy, i.e. the most efficient ones,
would normally be the recipients of these share quotas.
Another interesting feature of ecological fisheries management with the help of
ITQs is that optimal TACs for some species might be negative. A negative TAC means
that the corresponding share quotas holders would be under the obligation of adding to
rather than extracting from the stock of the species to the extent stipulated by their quota
holdings. Thus, it appears that ecological fisheries management with the help of share
quotas naturally accommodates fish stock enhancement as a dual to harvesting. Again, if
a quota price for a negative total quota is negative it represents a subsidy for fish stock
enhancement. That would occur in the case of socially optimal but privately unprofitable
stock enhancement. An example of this would be the hatching and releasing of valuable
marine fish into the ocean. Alternatively, stock enhancement may be privately profitable.
A case in point might be ocean ranching of valuable species such as scallops or salmon.
For ecological reasons the quota price would often be positive indicating that the ocean
ranching firms would pay for the privilege of releasing fish into the ocean.
14
15
16
Rewards for killing low value predators such as wolves and foxes and the eradication of pests in general
provide a case in point.
Moreover, for a similar reason it may become necessary to keep track of who actually holds negatively
priced share quotas.
This is different from the case of privately profitable fishery where the firms will be pleased to accept
share quotas for free.
17
It should now be clear that there are four polar cases of ecological fisheries
management in the ITQ framework as summarized in Table 1 below.
Table 1
Total Quota and Share Quota Price: Polar Cases
Total Quota (TAC), Q
Quota Price, s
__________________________________________
Negative
Positive
______________________________________________________________
Negative
Unprofitable Stock
Enhancement
Unprofitable Fishery
Predator/competitor
stock reduction
Positive
Profitable Stock
Enhancement
(Ocean ranching)
Profitable Fishery
(Commercial Fishery)
Applying the MIM procedure to a given marine ecosystem will normally produce
entries in one or more of the boxes in Table 1.17 Notice, however, that a prerequisite for
an entries with negative quota price (top-half of Table 1), is that there is at least one entry
with a positive quota price. Hence, if the ecology is not economically useful at all, all
share quota prices would be zero.
It is important to realize that the MIM procedure actually compares the overall
costs and benefits (as judged by the quota market) of any TAC change including stock
enhancement quotas. For instance, if the stock enhancement of a given species is
regarded as detrimental to valuable fisheries (presumably through ecological interactions)
the share quota prices in these fisheries would decline making it less likely that the MIM
procedure recommend the stock enhancement TAC. For that to happen, the increase in
the market price of the stock enhancement share quota must exceed the decline in the
market price of the share quotas of the other fisheries.
Obviously, changes in relative prices, environmental conditions and other
variables would induce corresponding modifications in TACs. The same applies to new
ecological or economic information in general.
17
Notice that the intermediate cases of zero total quotas and/or share quota prices, while not entirely
without interest, are not included in Table 1.
18
Thus, we may conclude that an ITQ system, coupled with the MIM procedure,
offers quite flexible and promising way to the problem of ecosystem fisheries
management. It is important to realize, however, that it by no means solves the problem.
First, the effectiveness of the ITQ system hinges critically on the ability of the
fisheries manager to enforce the quota constraint. This, as is well known is always costly,
often difficult and sometimes impossible. To the extent that the ITQs cannot be enforced,
the system will not work.
Second, it should be emphasized that the ITQ system coupled with the MIM
procedure will generally not yield the optimal fisheries policy, even with the system is
perfectly enforced. What the MIM procedure maximizes is expected rents in the fishing
industry. Economic rents are not necessarily the same as profits. More importantly, the
MIM procedure maximizes expected rents according to the expectations of the fishing
industry and other traders in the quota market. These expectations are bound to be
erroneous to some degree. Hence the MIM procedure will be correspondingly led astray.
Finally, an interesting byproduct of the ecosystem ITQ fisheries mangement
system is that the fishing firms are given an incentive to engage in their own fisheries
research. Any company that will acquire better information about the pertinent ecological
or economic relationships will be able to make money in quota trades. So, under the ITQ
system, one would expect increased private and privately funded research in fisheries.
Thus, it appears that an ITQ fisheries management system facilitates a transition from a
publicly funded research program to privately funded one.
There are limitations to the desirability of this process, however. The most
fundamental problem has to do with the public good nature of knowledge and
information. This, as is well known (Varian, 1984), implies that the private production of
knowledge, i.e. scientific research, tends to be less that socially optimal. To a certain
extent, it also subtracts from the ability of the private sector to outperform a centralized
fisheries authority in the generation of fisheries information and knowledge. Therefore, it
seems that even under an ITQ system, public fisheries research or at least subsidies for
private research would still be called for.
4. Conclusions
Ecosystem fisheries are extremely complicated. Most ecosystems contain thousands of
species and the number of potential biological and economic interactions increases
exponentially with the number of species. Thus, ecosystem quickly become quite
inscrutable even from a static perspective. Ecosystem dynamics add to this complexity.
Even with few species it is easy to generate multiple equilibria, bifurcations and even
19
chaos. In a real ecosystem, the scope for complicated dynamics is much greater. It is
therefore to be expected that they be characterized by strange dynamics, volatility and
unpredictabilty. Indeed, this seems to be the experience in many ocean ecosystems.
Under these circumstances, the question is whether it possible to manage
ecosystem fisheries in a useful manner. The answer to this question is probably yes. The
reason is that the outcome of unmanaged fisheries is so poor that, in spite of the
complexity of ecosystem fisheries, it is not too difficult to improve upon the situation.
The paper shows that optimal management rules are very complicated. This means that it
is very difficult to calculate optimal management paths let alone implement them.
Therefore, anything close to an optimal utilization of ecosystem fisheries may be far
away.
A reasonable objective for ecosystem fisheries management, therefore, is the best
possible management. The paper argues that of the myriad of management measures that
can be applied only two; taxes/subsidies and property rights, are suitable in this respect.
Of these two, property rights, when they can be applied, appear distinctly more
promising. The fundamental reason is that existence of property rights allows the market
to generate prices that not only steer market participants to the common good, but also
provide valuable management guidance to the fisheries manager.
The ITQ approach to ecosystem fisheries seems to offer the promise of the best
possible ecosystem management. Under this system, the fishery will operate efficiently
subject to the vector of TACs that has been set. Moreover, ITQ market prices provide the
fisheries manager with the best possible information about the advisability of different
TAC vectors. More precisely, under the usual assumptions concerning market efficiency,
the TAC vector that maximize the aggregate value of all outstanding ITQ-shares also
maximizes the present value of expected profits from the fishery.
20
References
Arnason, R. 1990. "Minimum Information Management in Fisheries", Canadian Journal
of Economics 23. pp. 630-53.
Arnason, R. 1998. Ecological Fisheries Management Using Individual Transferable Share
Quotas. Ecological Applications 8(1) Supplement. pp S151-159.
Clark, C.W. 1976. Mathematical Bioeconomic: The Optimal Management of Renewable
Resources. John Wiley.
Clark, C.W. and G.R. Munro. 1982. The Economics of Fishing and Modern Capital
Theory: A Simplified Approach. In L.J. Mirman and D.J. Spulber (eds.)
Essays in the Economics of Renewable Resources. North-Holland.
Hannesson, R. 1993. Bioeconomic Analysis of Fisheries. Fishing News Books.
Montrucchio, L. 1992. Dynamical Systems that Solve Continuous-Time Concave
Optimization Problems: Anything Goes. In J. Benhabib (ed.). Cycles and
Chaos in Economic Equilibrium. Princeton University Press.
Pigou, A.C. 1912. The Economics of Welfare. Macmillan.
Pontryagin, L.S., V.S. Boltyanskii, R.V. Gramkrelidze and E.F. Mishchenko. The
Mathematical Theory of Optimal Processes. Wiley.
Varian, H.T. 1984. Microeconomic Analysis. 2nd ed. Norton.