Ragnar Arnason
Department of Economics, University of Iceland
Basic Fisheries Economics
DRAFT
A paper prepared for the
Workshop on
Policy and Planning for Coastal Fisheries Resources
University of South Pacific,
Suva, Fiji, January 28 to February 8 2008.
Table of Contents
Page
A. Fundamentals of Fisheries Economics
1. The Simplest Fisheries Model: Basic Elements
1.1 Biology
1.2 Economics
1.3 Combining Economics and Biology
1
3
3
7
10
2. The Sustainable Fisheries Model
12
2.1 The sustainable yield function
2.2 The sustainable biomass function
2.3 The sustainable yield and biomass diagram
2.4 The sustainable fisheries model
2.5 Risk and uncertainty
2.6 Realism or lack thereof
Technical appendix 1
Technical appendix 2
13
16
17
18
19
21
3. The Optimal Fishery
24
3.1 What is optimal?
3.2 The optimal sustainable fishery
3.3 The shadow value of biomass
Technical appendix 3
24
29
32
4. The Competitive Fishery
36
4.1 The possibility of biomass depletion
4.2 The shadow value of biomass
Technical appendix 4
40
42
5. The Nature of the Fisheries Problem
46
5.1 The fisheries problem as an externality
5.2 The fisheries problem as a lack of property rights
5.3 Competitive fisheries as a game
5.4 The tragedy of the commons
5.5 The fisheries problem is not caused by ignorance
5.6 The fisheries problem is not caused by lack of communications
5.7 Summary
46
47
48
50
51
51
52
6. Fisheries over timeDynamics
54
6.1 Optimal dynamics
6.2 Competitive dynamics
Technical appendix 5
54
59
7. Summary
67
References
68
A. Fundamentals of fisheries economics
The annual ocean harvest from capture fisheries (as opposed to farmed fish) has in
recent years hovered around 90 million metric tonnes annually (FAO 1999). This
amounts to a global supply of about 12.3 kg per capita. The landed value of this catch
may be conservatively estimated in the neighbourhood of USD 80 billion.
Unfortunately, it appears according to the FAO, (1993, 1997) that we have
severely mismanaged these fisheries. First many of the world's most valuable fish
stocks are overexploited, some severely so, with the result that their annual yield is
much less than could be obtained on a sustainable basis. According to FAO (1997)
between 60 and 70% of commercial fish stocks are fully or over utilized. Some of
these stocks have been brought close to extinction. Second, instead of providing us
with substantial net economic benefits, i.e. benefits in excess of costs of harvesting,
the global fishery, according to the FAO, actually produces less than it consumes.
Thus, based on 1989 data, FAO in 1993 estimated that global fisheries costs exceeded
revenues by over 50%. According to the FAO (1993), the difference is accounted for
by government subsidies, especially by the industrial world. Thus, not only do the
world's fisheries fail to generate fisheries rents, thanks to the distortionary impact of
subsidies they seem to produce high overall losses.
So, a glance at the empirical evidence suggests that there is something very
wrong with the global fishery. An industry that on the basis of the richness of many
marine resources, should be able to generate a high economic return amounting to a
large fraction of its gross revenues, appears to be operating at a loss.
This observation is in full accordance with theoretical predictions. According
to standard fisheries economic theory (started by Warming, 1911 Gordon 1954)
fisheries are subject to specific socio-economic forces that tend to drive the fisheries
to a position of no economic benefits irrespective of the richness and value of the
underlying resource. The problem has been characterized as the common property
problem (Gordon 1954, Hardin 1968) and the process by which potential rents are
dissipated as the tragedy of the commons.
Thus, both the empirical evidence and economic analysis go hand in hand.
Both suggest the wastefulness of unmanaged (or mismanaged) fisheries and establish
the need for specific fisheries management if the potential benefits of fisheries
resources are to be realized.
To manage fisheries successfully we must obviously understand the basic laws
that govern them. In particular, we must understand the basic attributes of fisheries
that result in an economic inefficiency. For these are the attributes that the
management must be designed to alter or somehow render impotent.
In this paper we attempt to provide this general understanding. For this
purpose we provide a simple representation (or model) of the fishery. This
representation, while admittedly much simpler than any real life fishery, is
nevertheless hopefully realistic enough to provide us with a tool to understand the
basic problem of fisheries.
2
In a later section (Section 1 & Section 6) we will provide a sketch of more
detailed models that are more suitable to describe actual fisheries situations. These
models, however, are primarily useful to set the optimal TAC and other fisheries
management parameters and provide little additional insight of a general nature.
The chapter is organized broadly as follows: In the first section the basic
elements of the most simple fisheries model adequate for the purposes of this book are
presented. In the following section, section 1, these elements are brought together in
the sustainable fisheries model, a standard tool in fisheries analysis. The properties of
the optimal fishery are discussed in section 3 and those of the competitive, or
unmanaged, fishery in section 4. Comparison between the optimal and competitive
fishery suggests that the latter is generally severely suboptimal. This is the essence of
the so-called fisheries problem which is analysed in section 5. In section 6, the
analysis is extended to include dynamics, i.e. the evolution of fisheries over time.
Finally, in section 7 the main results of this chapter are summarized.
3
1. The simplest fisheries model: Basic elements
All fisheries models are composed of two sectors; the biological sector, describing the
evolution of the stock of fish over time, and the economic sector describing the
economics of the harvesting activity. The link between the two sectors is given by the
harvesting function which combines economic inputs (fishing effort) with the fish
stock to generate harvests.
In this section we will present a simplest possible fisheries model of this type
that is still adequate for the understanding of the basic fisheries problem.
1.1
Biology
Let us represent the stock of fish at a point of time by a single variable namely the
aggregate volume of fish or biomass. For analytical convenience we will often refer to
biomass at time t by the symbol x(t), where x is the biomass and t refers to time. Fish
biomass is frequently measured in metric tonnes.
Clearly, for most species of fish, this representation is overly simplistic. Most
species of fish consist of several yearclasses (or cohorts) and many also consist of
genetically and geographically distinct sub-stocks. To the extent that these yearclasses
and sub-stocks exhibit differential growth rates and are subject to differential harvest
rates, their aggregation into an amorphous collective, biomass, will result in
aggregation errors (see Arnason, 1984). Nevertheless, for analytical purposes, this
biomass representation of the fish stock is generally found to be adequate.
For our purposes the evolution of biomass over time, e.g. in response to
fishing, is of central importance. Let the instantaneous change in biomass at time t be
represented by the symbol x (t ) . Since all our variables are generally dependent on
time, we will in what follows, generally omit explicit reference to time and just write
x and x instead of x(t) and x (t ) . From a mathematical perspective, x is simply the
first derivative of biomass with respect to time, i.e., x x/t. For our purposes,
however, it is sufficient to regard x as the instantaneous change in biomass.
In the absence of fishing, biomass will evolve according to a biological growth
processes. Let us represent these processes by the function G(x). Thus, more formally,
biomass growth is defined by the expression
(1)
x = G(x).
Generally, for most species, biomass growth is negative at very low levels of
biomass. This is because at very low stock levels the species may be poorly equipped
to withstand predation and is unable to reproduce successfully. Biomass growth then
increases with biomass (at a decreasing rate) up to a certain point where maximum
growth is attained. It then declines and at a certain high stock level biomass growth,
drops to zero and beyond that point becomes negative. This effect is usually attributed
to environmental constraints, the lack of food or space. This general shape of the
biomass growth function is illustrated in Figure 1.1.
4
Figure 1.1
The biomass growth function, G(x)
Growth,
x
ymsy
x1
xmsy
x2
Biomass, x
As indicated in Figure 1.1, biomass growth is positive for biomass levels in
the interval (x1, x2) and non-positive everywhere else. If the biomass level ever drops
below x1 it will inexorably decline to zero. Consequently, x1 is referred to as the
minimum viable biomass. Notice that at the minimum viable biomass, x1, there is no
biomass growth. Thus, x1 represents a biomass equilibrium. Beyond biomass level x2
biomass growth is negative. Therefore, if biomass ever happens to exceed x2, it tends
to revert back to x2. For this reason x2 is often referred to as the carrying capacity of
the stock. Alternatively, since an unexploited stock is likely to find itself at or close to
x2, this biomass level is also often referred to as the virgin stock equilibrium.
As mentioned, positive biomass growth occurs between biomass levels x1 and
x2. Clearly, it is possible to harvest any biomass growth on a sustainable basis, i.e.
without affecting the biomass level. It follows that biomass growth at any biomass
level is the same as the sustainable harvest at that biomass level. Thus, the maximum
sustainable harvest or yield occurs at the biomass level where natural growth is at a
maximum. In Figure 1.1 this occurs at biomass level xmsy and the corresponding
sustainable harvest is ymsy. Note that, as indicated in the diagram, the sustainable
harvest can be anything from zero to ymsy.
Whenever biomass growth is nonzero (positive or negative) biomass will be
evolving over time. In the absence of fishing, this clearly happens at all biomass
levels in Figure 1.1 except 0, x1 and x2. Consequently, these points may be
5
characterized as biomass equilibrium points. The movement of biomass outside these
equilibrium points is indicated in Figure 1.2.
Figure 1.2
Biomass dynamics
Growth,
x
x1
x2
Biomass, x
The evolution of biomass outside the equilibrium points (0, x1, x2) is indicated
by the arrows in Figure 1.2. Clearly, small deviations of biomass from the minimum
viable level, x1, will lead to a continual growth to x2, or a collapse of the resource to 0.
Thus, x1 represents unstable biomass equilibrium. The virgin stock equilibrium, x2, on
the other hand, represents a (locally) stable equilibrium. From any biomass level
above x1, biomass will tend toward x2. Finally, the biomass of zero is also locally
stable. Any biomass deviation from this equilibrium up to x1 will return to zero again.
The exact shape of the biomass growth function below x1 is theoretically
interesting but of little practical importance. The biomass is doomed to extinction no
matter what. There are two main possibilities. First, the biomass growth function is
continuous and turns back to the origin as indicated in Figure 1.3(a). This means that
the biomass decline (albeit perhaps not the proportional decline) becomes slower as
zero biomass is approached. The other alternative is that the biomass decline
continues increasing and the biomass growth function is discontinuous at zero as
illustrated in Figure 1.3(b).
6
Figure 1.3
The biomass growth curve at the origin
Growth
Growth
Biomass, x
Biomass, x
(a)
(b)
It is of some importance for fisheries management which often requires a
rebuilding of the fish stocks to develop a feeling for the movement of biomass over
time. The adjustment of biomass toward the two stable equilibria, namely 0 and x2
according to the basic biomass growth function as illustrated in Figure 1.1 and 1.3(b)
is depicted in Figure 1.4.
Figure 1.4
The evolution of biomass over time
Biomass,
x
x1
x2
Time, t
7
As indicated in Figure 1.4, biomass according to the simple biomass growth
function approaches its equilibrium values asymptotically over time. While this
function is a greatly simplified version of reality, the basic property still applies. It
may take a very long time to completely rebuild fish stocks, especially if they have
been driven down to their minimum viable biomass levels.
1.2
Economics
Following the custom in fisheries biology (Ricker, 1975) and fisheries economics
(Gordon 1954, Clark, 1976) we represent the economic inputs used for fishing by a
single aggregate measure called fishing effort. It is important to realize, especially
from the perspective of fisheries management, that this representation of fishing effort
for all economic inputs, although standard in fisheries economics, is quite restrictive.
Fishing effort consists of a great number of variables including various types of
human capital (labour), various types of physical capital, fish-finding equipment, fuel,
fishing gear, and many other inputs. In a typical commercial fishing operation, the
number of different fisheries inputs is undoubtedly measured in the hundreds. Many
of these inputs, moreover, can be substituted for each other both before and after
capital investment in the vessel is made. This has major implications for fisheries
management.
The volume of harvest normally depends on fishing effort as well as the size
of the biomass to which this fishing effort is applied. More formally, we write this
relationship, generally referred to as the harvesting function, as follows:
(2)
y = Y(e,x),
where y represents the volume of harvest, e denotes fishing effort and x, as before, the
biomass of the fish stock.
Presumably, the volume of harvest increases with fishing effort for a given
level of biomass and, similarly, increases with biomass for a given level of fishing
effort. This general shape of the harvesting function is illustrated in Figure 1.5.
Figure 1.5
The harvesting function
Harvest,
y
[x3]
[x2]
[x1]
Effort, e
8
Figure 1.5 depicts harvest as a function of fishing effort for three different
levels of biomass, x1, x2 and x3, where x1 < x2 < x3. As indicated in the illustration in
Figure 1.5, harvest generally increases with increased fishing effort for a given
biomass but at a declining rate. This represents the economic law of diminishing
returns which is thought to apply, at least in the short run. The reason is that in order
to expand fishing effort, increasingly less efficient effort units (human capital,
physical capital etc.) have to be brought in. Presumably, the same effect holds for
biomass, i.e. for a fixed fishing effort harvest increases at a declining rate as biomass
grows. Here, however, the reason could be capacity bottlenecks aboard the fishing
vessels and in the landing places as well as the increased proportion of the operating
time spend by the fishing vessels steaming to harbour with the hold full of fish.
There is an interesting special case of the harvesting function that may be
useful to mention at this stage. This is the case of the so-called extreme schooling
species. Many species of fish, especially smaller fish that are subject to heavy
predation, tend to congregate in dense schools. Often these schools contain a huge
quantity of fish from which a particular fishing vessel harvests but a small fraction.
Now, with modern day technology, these schools are relatively easy to locate. It
follows that for a schooling species, it is primarily the existence of schools rather than
the volume of biomass that determines the level of harvest. For an extreme schooling
species, i.e. one that always forms schools of equal size and density, if the stock level
is sufficiently large, this means that the harvesting function does not depend on the
biomass, provided the biomass is above a certain (relatively low) minimum.
Harvesting Functions: Examples
Many different forms of the aggregative harvesting function have been suggested in
the literature. The following are two simple examples:
y = aex
This widely employed harvesting function proposed by Schaefer (1957) and often
referred to simply as the Schaefer function is really a special case of the well
known Cobb-Douglas type of production functions (Cobb and Douglas (1928))
with returns to scale equaling two and elasticity of substitution between the two
factors, eand x, of unity. The coefficient a, is often referred to as the catchability
coefficient.
y = aebxc
This more general harvesting function has the general Cobb-Douglas form with
returns to equal to b+c and the elasticity of substitution equal to unity. It should be
noted that this equation includes the Schaefer function as a special case. It should
also be noted that for a schooling species c would be small perhaps close to zero.
For an extreme schooling species c=0 and the equation would be reduced to
y = aeb
9
Fishing costs, of course, depend on the use of economic inputs or, in the
current parlance, fishing effort. Let us write this as the function:
(3)
c = C(e).
Now, fishing costs may be taken to be increasing in fishing effort, most likely
at an increasing rate as more intensive usage of fishing effort drives up the associated
unit prices and costs. This basic shape of the fishing cost function is illustrated in
Figure 1.6.
Figure 1.6
The Fisheries Cost Function
Costs,
c
c0
Effort, e
The cost function as drawn in Figure 1.6 exhibits certain costs, c0, even when
there is no fishing effort. Thus, c0 represents what is usually referred to as fixed costs,
namely costs that are independent of the activity level. These costs, such as the costs
of maintaining the firms' assets; insurance, maintenance etc., are incurred if the firm is
in the business even if it is inactive. They disappear, however, if the firm goes out of
business.
Cost functions: Examples
Common forms for the aggregative fisheries cost function are:
c=ae,
c=aeb,
c=aeb+c0,
where a, b and c0 are parameters with c0 representing fixed costs.
10
The final economic elements necessary to complete our simple fisheries model
are prices. Three categories of prices are needed:
The price of landed harvest, i.e. the output price. This we denote by the symbol p.
The price of fisheries inputs, denoted by w.1
The rate of discount (interest), denoted by r.
Changes in input prices affect the fisheries cost function directly. More precisely,
at a given level of fishing effort, an increase in one or more input prices implies an
increase in the cost of that fishing effort. This is illustrated in Figure 1.7 for variable
input prices increasing from w1 to w2 to w3.
Figure 1.7
The Fisheries Cost Function: Increasing input prices
[w3]
Costs,
c
[w2]
[w1]
c0
Effort, e
1.3
Combining biology and economics
The biological and economic parts of our fisheries model are linked in two ways. First
biomass affects harvest via its role in the fisheries harvesting function discussed
above. Second, the harvesting activity affects biomass and consequently biomass
growth directly by its extraction from the existing biomass. The simplest way to
represent the latter is by simply subtracting the harvest from biomass growth. This
results in the net-growth function of the biomass as follows:
(4)
x G(x) – y,
where, it will be recalled, y represents instantaneous harvest.
1
Of course, as there are many inputs, input prices are actually better represented by a vector, w.
11
Although, expression (4) is almost universally taken for granted, it is important to be
mindful of its expression. Basically this assumption, that harvesting represents a
passive extraction from the biomass without affecting its growth process. This, of
course, may or may not be true. In fact it is easy to imagine ways by which the fishing
activity may affect the growth of the remaining fish. It may, for instance, disturb their
feeding and/or spawning behaviour. Alternatively, it may enhance growth of the
remaining fish by making prey more accessible to them.
A more general representation of the net-growth function of the biomass
allowing for general interactions between the biomass growth and harvest is:
(5)
x G(x,y).
To avoid unnecessary complications, we will, however, in what follows, restrict
ourselves to the standard approach as expressed in (4).
12
2.
The Sustainable Fisheries Model
Consider a fishery operating at a certain harvesting level. Clearly, if at this
exploitation level, biomass doesn't change, the fishery can be maintained indefinitely
at its current level. The fishery is said to be sustainable. Obviously, in a sustainable
fishery, harvesting amounts exactly to natural biomass growth so net biomass growth
is zero.
The concept of a sustainable fishery plays an important role in fisheries
management. There are various reasons for this, some more rational than others. A
sustainable fishery implies the long run survival of the fish stocks which is generally
taken to be desirable. Sustainability also implies a certain stability in the fishery
which is frequently an important aim of fisheries management. Finally, the study of
actual fisheries usually concludes that it is economically optimal to adopt a harvesting
path over time that leads to a long run sustainable equilibrium.
This, however, should not close our eyes to the limitations of the concept of
sustainable fisheries. First, sustainability may not be optimal. There are cases where it
is not optimal to operate the fishery on a sustainable basis, not even in the long run.
These include the so-called periodic or pulsating fisheries (see e.g. Clark, 1976 and
Arnason, 1991) where it is optimal to operate the fishery periodically. It also includes
the cases where it is optimal to exhaust the fisherymine it out, so to speak. For
commercially valuable fisheries this is most likely to happen in the case of slow
growing species such as some shellfish and deep sea species.
Second, even when sustainability is optimal in the long run, it is not a very
practical proposition. Any real life fisheries are continuously bombarded with more or
less random shocks and disturbances. The recruitment to the fishable stock is larger or
smaller than the average. Prices of inputs or outputs change. Fishing technology
evolves, quite often in discrete jumps.
Temporary aberrant fish behaviour
Figure 1.8
induced e.g. by a shift in ocean currents
Actual position of a fishery in the
makes fishing temporarily more or less
neighbourhood of a sustainable point
difficult (i.e. alters the catchability
coefficient). All these impacts alter the
optimal sustainable equilibrium for the
fishery. Therefore, fisheries hardly even
find themselves at a sustainable
equilibrium point. To the extent that a
sustainable equilibrium is relevant, they
are much better described as continually
on the path towards a sustainable
equilibrium. As far as sustainability is
concerned, the best that can be hoped
for is that over some period of time the
fishery may spend most of its time in the
neighbourhood of a sustainable equilibrium point. This is illustrated in Figure 1.8.
Note that the neighbourhood around the sustainable point, within which the fishery
moves, may be of any size. For some fisheries over some period of time it may be
quite small. For others it may be quite large.
13
Third, the concept of sustainability by itself is far too broad to be of much use
as a requirement for fisheries management. As should be evident from the two
preceding sections, a fishery can be sustainable at widely different stock levels. All
that is required is that the harvest equals natural biomass growth. Thus, we can for
instance have a sustainable fishery at
very low stock level. We can also have
Figure 1.9
sustainable fishery at a very high stock
level and the same harvest level. We can Possible fisheries policies
moreover have a sustainable fishery at
any stock level in between. Not all of
these sustainable points are equally
beneficial. Clearly, the requirement of
All fisheries policies
sustainability does not restrict the set of
possible fisheries policies very much.
Sustainable
Thus, assuming for the sake of argument
fisheries
that the optimal fishery should be at a
policies
sustainable point in the long run, then
we can say that the requirement of
sustainability is a necessary but not a
sufficient condition for the proper
Optimal
management of the fishery. This means
fisheries
policy
that the requirement of sustainability
may restrict the set of possible fisheries
policies but not sufficiently. This is
illustrated in Figure 1.9.
Notwithstanding these limitations, the concept of sustainability, it is
analytically useful to help us to think about fisheries problems and problems of
fisheries management. Also, it provides us with a very convenient reference point for
real life fisheries. This justifies developing our sustainable fisheries model.
2.1
The sustainable yield function
The sustainable yield function is the central component of the sustainable fisheries
model. The sustainable yield function is also widely used for studying and discussing
fisheries both in the biological and economic context.
The sustainable yield function links fishing effort to the sustainable harvest. It
is defined as the level of harvest that is sustainable at any given level of fishing effort.
Formally, we may write this relationship as:
(6)
y = (e),
where, as before, y denotes the volume of harvest and e aggregate fishing effort. The
function (.) is the sustainable yield function that maps fishing effort into sustainable
harvest.
14
The general shape of the sustainable yield function is illustrated in Figure
1.10.
Figure 1.10
The sustainable yield function
Sustainable
harvest,
y
yMSY
y1
e1
eMSY
e0
Effort, e
As indicated in Figure 1.10, at zero fishing effort, there is no sustainable
harvest. No fishing effort yields, no harvest. Now consider increasing fishing effort to
a positive level, e1 and keeping it there. The increase in fishing effort will produce a
jump in the harvest level that subsequently subsides as the biomass is reduced. After a
while (perhaps a few years) the biomass reaches a new (and lower) equilibrium and
the harvest level settles down to its sustainable level, y1. This level is the sustainable
harvest corresponding to fishing effort e1. We can now repeat this exercise for any
level of fishing effort to obtain the complete sustainable yield schedule as drawn in
Figure 1.1. Initially, as fishing effort is increased, the corresponding sustainable
harvest is also increased but at a declining rate. The reason is that with more fishing
effort (and harvest), biomass declines and it requires increasingly more fishing effort
to maintain and expand the sustainable harvest. At a certain point, eMSY, in the
diagram, sustainable harvest reaches a maximum. This point, or rather the
corresponding harvest, yMSY, is generally referred to as the maximum sustainable
yield (MSY) in the fisheries literature. The maximum sustainable yield corresponds
to the maximal natural biomass growth indicated in Figure 1.1 above. Remember that
sustainable harvest must equal natural biomass growth.
Increasing fishing effort beyond the maximum sustainable yield, eMSY, leads to
a declining sustainable harvest. The reason is that biomass is reduced even further and
can no longer sustain the same yield as before when fishing effort is increased. At a
certain point, e0, in the diagram, there is a gap in the sustainable yield diagram.
15
Fishing effort beyond e0 will produce no harvest on a sustainable basis. Thus, there is
a discrete jump to zero or a catastrophe in the sustainable yield function at this point.
It is of great importance to appreciate fully the importance of this gap. First,
obviously, the gap in the sustainable yield function has fundamental implications for
fisheries management. The gap implies a certain discontinuity in the relationship
between fishing effort and the sustainable harvest. This is often difficult for human
society to assimilate. It means that a fishery that has been continuously sustainable at
various previous fishing effort levels and is perfectly sustainable at a certain fishing
effort level may become unsustainable at just slightly (in fact, infinitesimally) higher
fishing effort level. The only consolation is that for most species, the sustainable
harvest (and stock) collapse doesn't occur instantaneously. Rather there is a steady
decline in harvest and stocks over a period of time until the species disappears.
Although there is usually a certain tendency to interpret this as just a temporary
contraction, it can certainly serve as a warning sign. Consequently, if fishing effort is
reduced sufficiently quickly, there is usually still time to move back to sustainability
and for the stock to recover. This, however, generally requires a drastic cut-back in
fishing effort.
Second, the gap, although often ignored when sustainable yield curves drawn2,
is not an exception from the rule. It is the rule! It is a definite feature of sustainable
yield functions for most, if not all, species. For instance, the gap will definitely exist if
the minimum viable biomass exceeds zero. Clearly, this holds for virtually all higher
animal species. In fact, for fish stocks, the minimum sustainable biomass appears in
most cases to be measured in thousands if not millions of individual fish. Even when
the minimum viable
biomass is zero, the
gap may still exist.3 Figure 1.11
Thus,
we
may Sustainable yield function: Extreme schooling species
conclude that the
only
difference
Sustainable
harvest,
between
the
y
sustainable
yield
yMSY
curves for different
species
is
not
whether they exhibit
a gap or not but
rather the size of this
gap. For instance, for
an
extreme
schooling species, it
may be shown (see
Effort, e
eMSY = e0
technical appendix)
that the gap occurs
right
at
the
maximum
sustainable
yield
effort level and is therefore very large.
2
3
An exception is C.W. Clark's (1976) book on mathematical bioeconomics.
A sufficient condition for it to exist is that there exist a level of biomass and fishing effort such that
Gx(x)=Yx(e,x) as further discussed in the technical appendix to this chapter.
16
2.2
The sustainable biomass function
Corresponding to the sustainable yield function there is a sustainable revenue
function. Although this function is rarely (if even) used in the literature, it is actually a
very useful tool for understanding and appreciating fisheries problems.
The sustainable biomass function gives the sustainable biomass as a function
of fishing effort. It, thus, belongs to the same conceptual category as the sustainable
yield function. Formally we may write the sustainable biomass function as:
(7)
x = (e),
where x refers to the volume of biomass and e to fishing effort. The function (e)
maps fishing effort into sustainable biomass. Since, the sustainable biomass function
corresponds precisely to the sustainable yield function, there is no need to explain the
derivation of this function in detail. The general shape of the function is illustrated in
Figure 1.12
Figure 1.12
The Sustainable Biomass Function
Sustainable
biomass,
x
e0
Effort, e
At zero fishing effort level, the sustainable biomass is x2, the virgin stock
equilibrium. Contrary to sustainable yield function which is dome shaped in fishing
effort, the sustainable biomass function is monotonically declining in fishing effort.
This is a useful property because it means that we can take it for granted that a higher
17
sustained fishing effort always results in a correspondingly lower biomass level. As
the sustainable yield function, however, the sustainable harvesting function has a gap
at a certain effort level, e0. Beyond this level of fishing effort there is no positive
sustainable level of biomass. Note that this is the same effort level as that at which the
sustainable yield collapses.
Derivation of the sustainable yield and biomass functions
The sustainable yield function is derived from the harvesting function,
equation (2) above, and the net growth function of the biomass, equation (4),
above. More precisely we have:
(2)
y = Y(e,x),
(4) x G(x) – y.
For sustainability, there must be no change in the biomass, i.e. x 0.
Therefore, equation (4) reduces to:
0 = G(x) – y.
Clearly, this equation and equation (2) define a system of two equations in
three variables, namely the biomass, x, the harvest, y and fishing effort, e.
Given some unrestrictive technical conditions we may solve this system to
obtain the sustainable harvest as a function of fishing effort, i.e. the sustainable
yield function:
y = (e).
A corresponding equation for biomass, the sustainable biomass function, is:
x = (e).
2.3
The sustainable yield and biomass diagram
It is helpful for later purposes to bring the sustainable yield and biomass functions
together in one diagram. This can be done by measuring biomass along the negative
part of the vertical axis as in Figure 1.13.
18
Figure 1.13
The sustainable yield and biomass functions
Sustainable
harvest,
y
eMSY
Effort, e
xMSY
x2
Sustainable
biomass,
x
In the diagram in Figure 1.13, biomass is measured downward along the
negative part of the vertical axis. This means the further down on this axis the higher
the biomass. Thus, as shown in the diagram, biomass is monotonically declining in
fishing effort up to the point of collapse, e0. One of the great advantages of the
sustainable yield and biomass diagram is that is shows immediately the biomass level
corresponding to any level of sustainable harvest. Thus, at no fishing effort level, the
sustainable biomass is at x2, the virgin stock equilibrium. At the maximum sustainable
yield effort level, eMSY, the corresponding biomass level is xMSY as can be read from
the diagram.
2.4
The sustainable fisheries model
Multiplying the sustainable yield function by the price of fish, p, provides us with the
sustainable revenue function. Subtracting the cost function, (2) above, provides us
with sustainable profits. Formally, we may write this as:
(8)
= p(e) – C(e).
19
This equation coupled with the sustainable biomass function, (7) above, defines the
sustainable fisheries model. A diagrammatic representation of this model is expressed
in Figure 1.14.
Figure 1.14
The sustainable fisheries model
Sustainable
revenues
$
Costs
eMSY
Effort, e
xMSY
x2
Sustainable
biomass function
Sustainable
biomass,
x
The sustainable fisheries model comprises all the basic information relevant to the
fisheries problem in a sustainable state, harvest, biomass, fishing effort and profits.
Consequently it constitutes our basic static tool for analyzing the fisheries problem.
2.5
Risk and uncertainty
Generally the sustainable yield function is not known with any certainty. Two reasons
(a) shifts in the sustainable curve (environmental shifts, biomass growth parameters,
technology etc.). This implies that knowledge about the exact location of the
sustainable yield function at a given time is imperfect. (b) Pure lack of knowledge.
The sustainable yield function is constant but only has an imprecise knowledge of the
coefficients.
The upshot is that the sustainable yield function is not precisely known. It
follows that the location of the gap or the maximum sustainable yield is also not
20
known with any precision. The appropriate way do deal with this is to specify the
appropriate probability distribution for the yield function. A simpler way is to specify
upper and lower limits for the yield function. This can also be represented
diagrammatically as indicated in Figure 1.15.
Figure 1.15
The sustainable yield function: High and low estimates
Sustainable
harvest, y
Medium estimate
yMSY
High estimate
Low estimate
Effort, e
eMSY
e0
In Figure 1.15 three sustainable yield curves are depicted. The so-called
medium estimate represents the most likely yield curve. The high estimate represents
an optimistic view of the yield curve and the low estimate a pessimistic view. The
probability the true curve lies within these estimates could be for instance 95%.
This uncertainty about the exact location of the yield function leads to a
corresponding uncertainty about the appropriate fisheries policy. For instance, as
shown in the diagram, the fishing effort corresponding to the maximum sustainable
yield is now represented by an interval. The actual volume of the maximum
sustainable yield lies in a corresponding interval. Similarly, the fishing effort that
corresponds to un-sustainability of the fishery is represented as an interval. It follows
that a precautionary approach would avoid taking fishing effort into this interval.
Actually, as the diagram is drawn, the cost of this type of precaution is zero, for the
optimal fisheries policy would hardly ever want to exceed the MSY level.
This has a number of implications. First, any fisheries policy is bound to be
erroneous. At each point of time there is a best policy. Since the actual situation is not
known with certainty (and is probably unknowable anyway), mistakes are
unavoidable. Second, the optimal fisheries policy must take risk and risk attitudes
explicitly into account. Third, additions to knowledge that allows a more precise
21
determination of the sustainable yield curve or for that matter any fisheries parameter
are valuable, perhaps very valuable. This justifies investment in economic and
biological research.
2.6
Realism or lack thereof
The above representation of the fishery is obviously quite simplistic compared to the
intricacies of real life fisheries. For instance, in the sustainable fisheries model above,
the state of the fish resource is described by only one variable, the biomass. This we
know is, in general not sufficient. Similarly, the activity of the fishing fleet is
represented by only one variable, fishing effort. Again, we know that this degree of
aggregation is not really feasible. The model, moreover, only provides a description
of the fishery in a sustainable state or equilibrium. It doesn't include any evolution
over time which, of course, is a basic feature of virtually all real-life fisheries. All
these simplifications raise the question of realism. How realistic is this sustainable
fisheries model? Does the extreme simplicity of the model distort the outcomes
derived? Can the results be applied in the real world?
The answer, as far as we know, is a qualified yes. The basic results that (a)
biomass declines with fishing effort, (b) there is a maximum sustainable yield, (c)
there is a gap in the sustainable yield function (d) competitive utilization leads to
more or less complete waste of economic rents and (e) optimal utilization generally
implies substantially more conservation of the fish stocks and much less fishing effort
than competitive utilization, all seem to apply in real fisheries and certainly in more
detailed and complicated models.
The qualification in the affirmative answer above refers primarily to the
details. The simple, aggregative, sustainable fisheries model cannot be expected to
provide a very accurate picture of real world fisheries. Thus, the detailed predictions
of these types of models, the calculated optimal fishing effort and so on should not be
regarded as anything like precise estimates. To obtain more reliable estimates of the
pertinent statistics of this kind, more detailed models must be constructed. At the
same time, it must be realized that the building of increasingly more detailed fisheries
models is quickly subject to significantly diminishing returns. Therefore, there is a
limit to the modeling details that it is sensible to aim for. In many cases a more
simplistic aggregative model is quite sufficient for the needs at hand.
22
Technical appendix 1
The fisheries model: Equilibrium and stability
Consider the fisheries model:
y = Y(e,x),
x G(x) – y,
where y denotes the volume of harvest, e fishing effort and x denotes biomass.
x x / t , where t is time. The functions Y(e,x) and G(x) are assumed to be
increasing in their arguments and twice continuously differentiable over the relevant
range.
Equilibrium and sustainable curves
Equilibrium is defined by x 0. Imposing this condition transforms the system to two
static equations in three unknown variables, y, e and x. This system implicitly defines
the following two sustainable equations
y = (e),
x = (e),
provided all the derivatives of the partial derivatives of the initial system exist and are
continuous and the determinant of the Jacobian matrix for the system, namely
Gx Yx
0
Yx
1
0.
This condition translates to the simpler condition:
Gx – Yx 0.
So, over the domain of x where this condition holds, the existence of the
sustainable functions, y = (e) and x = (e), is guaranteed.
Stability
The dynamics of the biomass is obviously given by the equation:
x G(x) – Y(e,x)
According to standard differential equation theory (Apostol, Shone) stability requires:
x / x Gx – Yx <0.
23
Obviously, if x / x 0, small (positive or negative) deviations from an equilibrium
biomass would imply that the biomass would never again revert to that equilibrium.
This complements the implicit function theorem condition for the existence of
sustainable yield and biomass function, namely that Gx – Yx 0. This is an example of
what Samuelson (1947) called the correspondence principle. The stability analysis
shows that although sustainable functions may exist for the region where Gx – Yx>0,
the instability of this part of the sustainable fucntions implies that this is of very little
practical relevance.
Technical appendix 2
Estimation and application of the sustainable fisheries model.
[To be supplied]
24
3.
The optimal fishery
In this section we will employ the sustainable fisheries model developed in the
previous section to identify the optimal sustainable fishery and examine its properties.
The sustainable fishery is, as already discussed, a fishery in a steady state or
equilibrium. The optimal dynamic fishery will be considered in section 7.1 below.
To be able to describe the particulars of the optimal fishery, we obviously
need to have a clear notion of what is optimal. This is the concern of the first
subsection of this section. Having covered this, we turn our attention, in subsection
3.2 to the optimal sustainable fishery.
3.1
What is optimal?
Fisheries management is concerned with the optimal utilization of fish stocks. This
raises the question of what is optimal. For instance, is it optimal to maximize the total
sustainable output from the fishery? Is it optimal to maximize employment in the
fishery? Is it optimal to maximize the net profits (or economic rents) obtained from
the fishery?
The answers to these basic questions are provided by standard economic
theory (see e.g. Layard and Walters, 1978 and Varian, 1984). Unfortunately, however,
the theory is somewhat abstract and difficult to apply in practice. Nevertheless, we
will now attempt to briefly recount the essential contents of this theory as it can be
applied to fisheries.
The first element of the theory is that all individuals are taken to harbour a set
of desires than they seek to satisfy. Obviously, these desires are the basic motivation
for people to act. The desires are assumed to be sufficiently well developed to be
translated into preferences over all relevant options. Actually, this is not much of an
assumption. If it did not hold, people would not be able to act. Thus, individuals are
assumed to be able to determine whether they for instance prefer a bowl of rice to a
can of tuna, a trip to London to a night with the family and so on. These preferences
are often represented by the so-called utility function which basically provides a
measure of a person's level of satisfaction or happiness.
A person's utility function contains everything that affects his satisfaction. Let
us refer to this generally extremely long list of items, as utility items. Some utility
items (like good food) increase utility. Others (like excessive labour or bad odors)
reduce it. The first class of items is usually referred to as goods and the second as
bads. However, it is more convenient to think about all utility items as goods and
represent the bads as negative amounts of goods.
The basic aim of economic production is to increase the availability of goods
in society. To produce goods, generally, some use of other goods (such as materials
and/or labour) has to take place. Thus the production of a positive amount of goods is
usually accompanied by a negative production (use) of some other goods. Therefore,
it is necessary to regard the success of production in terms of the net production of
goods, i.e. the gross production less the use of other goods.
25
In all societies, the net production of goods is bounded by the society's
production capacity. This means that it is not possible to produce more than a limited
amount of goods. The production capacity is determined by a number of factors
including the availability of labour, human and physical capital and natural resources
as well as the available technology. This maximum capacity for net production of
goods over a period of time may be regarded as society's opportunity set. This is often
represented diagrammatically as in
Figure 1.16:
Figure 1.16
The social opportunity set The Social Opportunity Set
drawn in Figure 1.16 gives all the
combinations of two goods, good 1
Good 2
and good 2 that are available to
society given its current productive
x2
capacity. If all the production
capacity is used to produce good 1
the maximum production is given by
Social
x1 in the diagram. Alternatively, if all
opportunity
set
the production capacity is used to
produce good 2 the maximum
x1
amount obtained is given by x2 in the
Good 1
figure. Finally, if all the available
production capacity is used to
produce combinations of good 1 and good 2, we obtain the upper (or rather upperright) boundary of the social opportunity set.
The social opportunity set is probably the most basic part of economic welfare
theory. It defines the possibilities society has to meet the desires of its members by
providing them with goods. These possibilities cannot be exceeded. They are
determined by the available economic resources and the production technology.
Given these possibilities, the remaining task is to choose the optimal point in the
social opportunity set and to allocate the production to the citizens according to some
social welfare function.
The upper boundary of the social opportunity set which we may refer to as the
frontier (often called the production possibility frontier in economics) is of particular
relevance for optimality. This represents the maximum combinations of good 1 and
good 2 that can be enjoyed by society. Since goods are desirable by definition, it
follows immediately that all points below this frontier are less than optimal (suboptimal). Obviously, any such point can be improved upon by moving to the frontier.
So, points below the frontier represent economic waste.
These considerations provide us with a basic characterization of optimality in
production. Optimality in production requires us to locate the production on the
frontier of the social opportunity set. This maximizes society's opportunities for utility
or satisfaction.
The implication for optimality in the fishery is obvious. It is simply that net
production, i.e., production less costs, should be maximized. The above argument
26
shows that this will automatically maximize the fishery's contribution to the social
opportunity set.
While the above result is really the crux of the matter, there is a certain
bothersome loose end we have to deal with. This is the practical problem of
calculation. The only way to calculate the net production from a production activity is
to measure everything on the same scale. We cannot compare apples and oranges.
One way to do this is to use prices to calculate revenues and costs and the net
production as profits. In most societies this is an extremely convenient procedure as
prices are readily available in the market. However, for this method to be accurate the
market prices must first of all be complete, i.e. there must be a price for every item (a
good or a bad) that is involved in the production activity. Second, the prices must be
true, i.e. they must correctly measure the true social value of each unit of the item in
question. In well developed and smoothly operating market economies, both of these
conditions are met to a large extent. In economies where the market system is less
well developed or where the economy is subject to persistent market disequilibria, this
may not be the case. In these cases, some of the existing prices have to modified and
new ones constructed. It may even prove necessary to construct artificial price for
non-existing ones.
This procedure of modifying the price system for use in optimality
calculations is a standard one in the so-called cost-benefit analysis (see e.g. Layard
and Glaister 1994, Dasgupta and Pearce 1978). According to this theory, the most
common prices that need to be modified are the price of labour, the price of foreign
currency and the rate of interest. The reason is disequilibrium in the corresponding
markets. For instance, in the case of substantial and persistent (hidden or explicit)
unemployment, there is ample reason to infer that the market price of labour, i.e. the
wage rate, overestimates the true social value of labour. Therefore, in determining
what would be the optimal fisheries policy, the wage rate should be modified
accordingly. Similar arguments hold for price of foreign currency (the exchange rate)
where in the case of persistent balance of payments disequilibrium this value is
typically underestimated, and the rate of interest which is often distorted by an
underdeveloped financial market. The most common prices that need to be
constructed from scratch are the prices of natural resources and other valuables that
are not subject to private property rights. Due to the lack of private property rights,
these goods cannot be traded often it is said that the corresponding markets are
missing and, consequently, they have no market prices.
27
Example
Modifying input prices and, consequently, the optimal fisheries policy
A fisheries manger is charged with the responsibility of determining the optimal
fisheries policy in a given fishery. This is a very simple fishery that only uses labour
as an input. The harvest is exported fresh.
Consulting the appropriate fisheries biologists and economists, the fisheries
manager is told the optimal use of labour in this fishery is given by the equation:
L=
pw
,
2 p
where L represents labour, p the unit price of the harvest and w the unit price of
labour.
The corresponding sustainable harvest function is:
y = 2*L - L2,
where y represents harvest.
The current export price of fish is 1 and the current wage rate is also 1.
Accordingly, the fisheries manager calculates the "optimal" labour use and harvest
as:
L* = 0.5,
y* = 0.75.
The fisheries manager observes, however, that the labour market is
characterized by perennial disequilibrium with heavy unemployment and that foreign
exchange is rationed by the banks with a black market rate 10% above the bank rate.
He therefore suspects that the "true" prices for fish and labour may differ from the
market rates. Consulting the economist again, he is told that the correct (social) value
of labour is only 0.5 instead the market price of 1 and that the fish price evaluated at
the appropriate exchange rate would be 1.1 instead of 1. Armed with this new
information, the fisheries manager recalculates the optimal labour usage in the
fishery and the corresponding harvest level to find:
L** = 0.77,
y** = 0.95,
which is substantially different from before.
Maximizing the contribution of the fishery to the social opportunity set does
not, of course, guarantee that the opportunities will be well used. In particular,
28
although one may rest reasonably certain that the additional net benefits will increase
the satisfaction of some individuals, there is no guarantee that they will go to the most
needy or deserving. This is the question of the distribution of income which is
captured by the social welfare function. There is obviously no guarantee that
maximizing the net production from a fishery will actually maximize the social
welfare. In fact, in a real life situation, it is actually quite likely that the utility level of
some individuals will decline as a result of a fisheries rationalization in spite of it
being hugely beneficial to society as a whole. The same, of course, applies to any
other project.
What the maximization of fisheries profits evaluated at the socially
appropriate prices does is to maximize the contribution of the fishery to the social
opportunity set. This creates the social opportunity to improve the situation of
everyone. It does not guarantee that this will actually happen. That is more of a social
and political problem than a fisheries problem. Therefore, in the design of a fisheries
policy, it is not unreasonable to ignore these distributional problems, relegating them,
so to speak, to another process of a socio-political nature. Thus, any fisheries policy
that increases the net contribution of the fishery to the social opportunity should be
undertaken. This is actually a well-known and respected approach in applied welfare
economics usually called the Hicks-Kaldor criterion after the early proponents of this
approach (See Harberger, 1971).
This gives rise to the following basic conclusion regarding the socially optimal
fishery:
Fisheries optimization rule
Maximize fisheries profits evaluated at the socially correct prices of inputs
and outputs.
This rule, basically embraces the Hicks-Kaldor criterion. From the perspective
of social welfare, where the distribution of costs and benefits may be important, the
implicit assumption is that the actual distribution of the net benefits gained will be in
accordance with the social welfare function. Thus, according to this rule, in designing
the optimal fisheries policy, we can ignore questions regarding the distribution of the
net benefits.
The adoption of the Hicks-Kaldor criterion basically means that the optimal
fishery is the one that maximizes society's opportunity set with respect to the
fisheries. This basically relieves us of the need to consider the distribution of the
benefits and costs. This is simply relegated to the socio-political decision process. In a
democratic political system, where distributional issues are routinely dealt with by the
political system this approach appears reasonable. In other situations we may not be
so sanguine.
In cases, where it is little reasonable to expect that the costs and benefits of
fisheries rationalization will be distributed according to prevailing social sentiments,
the above procedure may not be entirely satisfactory. In these cases, an explicit social
29
welfare function with the appropriate weights for different social groups and
individuals may be brought to bear upon the optimal fisheries policy. An exercise of
this nature is usually quite demanding. In effect, it means that the various costs and
benefits will be assigned different weights according to whom they accrue.
Finally, it is important to realize that, irrespective of the inclusion of a social
welfare function or not, the distribution of the costs and benefits may actually impinge
on the feasibility of adopting an efficient fisheries policy. Usually, a new fisheries
policy requires a degree of social and political support in order to be adopted. If those
that do not benefit (or benefit less than others) are strategically placed, they may be
able to prevent the implementation of a socially beneficial fisheries policy. In this
case, it may be appropriate to try and redesign the policy in order to redistribute the
burden of costs and benefits. This clearly has major implications in terms of social
welfare and ethics.
3.2
The optimal sustainable fishery
We can use the tools developed above, in particular the sustainable fisheries model to
characterize the profit maximizing fishery. Profits are defined as the difference
between revenues and costs (receipts and expenses). In terms of the sustainable
fisheries diagram, this occurs where the distance between the revenue curve and the
cost curve is greatest. This is illustrated in Figure 1.17.
30
Figure 1.17
Maximum profits
$
Costs
Sustainable
revenues
eOSY
xMSY
xOSY
eMSY
Effort, e
Sustainable
biomass function
Sustainable
biomass,
x
As indicated in Figure 1.17, the optimal sustainable fishing effort occurs at
effort level eOSY. Thus, it’s important to notice, that it is less than the maximum
sustainable effort level, eMSY. The corresponding sustainable biomass level, xMSY, is
greater than the biomass level corresponding to the maximum sustainable yield, and
the harvest, yMSY, smaller. Thus, the optimal sustainable fisheries policy is more
conservative of the fish stock than the maximum sustainable fisheries policy. This is
an important result and is of general validity in sustainable fisheries models. Only in
dynamic models with a comparatively high rate of discount is it conceivable that the
equilibrium effort level exceeds the maximum sustainable yield level.
Why is it not efficient to go for the maximum sustainable yield level? Why is
it economically optimal to operate the fishery at an effort level below the one
corresponding to the maximum sustainable yield? From the diagram in Figure 1.16
this is not overly difficult to understand. Begin at the claimed optimal effort level
eOSY. Imagine a small increase in fishing effort. From the diagram it should be clear
that this will increase revenues. But, alas, it will also increase costs and the increase in
costs is greater than the increase in revenues. For this reason it is not economically
optimal to increase fishing effort beyond eOSY. The additional benefits are simply not
sufficient to pay for the additional costs. A corresponding argument can be employed
to show that it is not optimal to reduce fishing effort below the eOSY level. In that case
31
the reduction in revenues would exceed the savings in costs. Therefore, eOSY must be
optimal.
The above argument is an example of the economic principle that at the
maximum marginal (or additional) costs must equal marginal (additional) costs.
Mathematically, this is achieved by differentiating the revenue function (equation (8)
in the previous section) with respect to fishing effort and setting the outcome equal to
zero. Formally this is expressed by the equation:
(9)
e = pe – Ce = 0,
where the subscripts indicates differentiation of the function with respect to the
subscript variable. Thus, e/e etc. The approach expressed in equation (9) is very
useful in analytical work as well as empirical determination of the optimal fishing
effort. Among the several interesting messages of equation (9) is that maximal profits
are located at a point where the slope of the revenue function equals the slope of the
cost function.
Example
Determination of the optimal fishing effort
Let us assume that biological and economic research has produced the
sustainable yield function:
y = 2e - 1e2,
and the cost function
c = 0.5e,
and that the unit price of landed catch is
p = 1.
Then the profit function is:
= p(2e - 1e2) - 0.5e = 1.5e - e2
Differentiating this equation and setting the result to zero yields
1.5 - 2e = 0.
So, the profit maximizing level of fishing effort is e = 0.75
Substituting into the sustainable yield function we find the corresponding
harvest as y = 0.94 and profits as =0.56.
32
3.3
The shadow value of biomass
Now we need to talk about a very important but unfortunately somewhat technical
concept in fisheries management, namely the shadow value of biomass. In producing
harvest, the biomass of stock usually plays an important role. This implies that the
biomass has a certain economic unit value. This value is just like a conventional
market price for a commodity. The difference, however, is that biomass can normally
not be bought and sold in the market place. Consequently, there is no market price for
biomass. For this reason this value is referred to not as the price but the shadow price
of biomass.
The shadow price of biomass is essentially the price a sole user of the resource
would be willing to pay for increasing the biomass by one more unit. In the case of
the optimal fishery, this is equivalent to the net benefits that the collection of all users
can obtain if the sustainable biomass increases by one unit. We refer to this as the
social shadow value of biomass. Now, if the biomass is very small, i.e. relatively
scare, the shadow value of biomass becomes correspondingly higher. If, on the other
hand, the resource is bountiful, its shadow price is relatively low. Thus, in a
fundamental sense, the shadow value of biomass is a measure of the relative scarcity
of the biomass. Similarly, the higher the price of fish the higher the shadow value of
biomass. We can express these ideas with the help of the following diagram
calculated on the basis of a particular example.
Figure 1.18
Shadow value of biomass
(p1>p0)
Shadow value
of biomass
[p1]
[p0]
Biomass
Figure 1.18 depicts the relationship between the shadow value of biomass and
the availability of biomass. If the biomass level is very low, the shadow value of
33
biomass is relatively high. It may even approach infinity as the biomass approaches a
certain critical level (such as the minimum viable biomass). Similarly if the biomass
approaches a certain upper bound (usually beyond what is biologically possible), the
shadow value of biomass generally goes to zero.
To understand the nature of the optimal fishery and the fisheries problem it is
important to understand the role of the shadow value of biomass in the behaviour of
the fishing industry. The shadow value biomass represents the social cost of
extracting or harvesting one unit of biomass. This cost must, of course, be subtracted
from the benefits. Therefore, the net social price of a unit of harvest is not the market
price but the market price less the shadow value of biomass. More formally let us
represent this by the equation:
(10)
p* = p - q,
where p* is the true social price of a unit of harvest, p is the market price and q the
shadow value of biomass.
Of course, the shadow price of biomass is not actually paid to anyone and the
fishery actually receives the market price for its landings of fish. The point, however,
is that the optimal fishery behaves as if it was faced with the true social price of fish,
p*. As a result it behaves in the socially optimal fashion.
34
Technical appendix 3
Static optimum:
The problem is to adjust fishing effort, e, and biomass, x, so as to solve the following
problem:
(A2.1)
Max = pY(e,x) – C(e)
e,x
s.t. G(x)-Y(e,x) = 0.
One way to solve the problem is to set up the Lagrange equation
L(e,x,q) = pY(e,x) – C(e) + q( G(x)-Y(e,x)),
where q is the Lagrange multiplier which at the optimal solution equals the shadow
value of biomass.
The necessary conditions for solving problem (A2.1) include:
(A2.2)
pYe – Ce - qYe = 0,
(A2.3)
pYx + q(Gx - Yx) = 0,
G(x)-Y(e,x) = 0.
Eliminating the Lagrange multiplier, q, from the first two equations and
rearranging yields the basic optimality conditions:
Gx +YxCe/(pYe-Ce) = 0
(A2.4)
G(x)-Y(e,x) = 0.
Solving these equations for e and x yields the corresponding optimal fisheries policy.
Shadow value of biomass
Solving equation (A2.3) for q gives us the shadow value of biomass as
(A2.5)
q = pYx /(Yx - Gx).
Note that this goes to infinity as the denominator, (Yx - Gx), goes to zero. This may
occur at any biomass level below the one corresponding to the maximum sustainable
yield. The empirical evidence is that for most fisheries, this occurs at fairly low
biomass levels or not at all.
Equation (A2.2) may be regarded as the behavioural rule of the fishing
industry in the optimal fishery. According to this rule, marginal benefits adjusted by
the shadow value of biomass should be equated to marginal costs. More precisely:
35
(A.2.6)
(p- q)Ye p*Ye = Ce.
where p* is the adjusted fish price, i.e. the gross fish price less the shadow value of
the fish harvested.
36
4. The Competitive Fishery
In this book the term ‘competitive fishery’ refers to a completely unmanaged fishery,
i.e., a fishery that is totally without management. This means perfectly free entry and
no restrictions on catch levels, fishing methods, fishing areas, vessel power or
anything else. Thus, outsiders enter the fishery if they please and the fishery
participants choose whatever harvesting intensity and methods they want to without
any interference.
The competitive fishery, of course, is an abstraction. Nowadays, few fisheries,
if any, are perfectly competitive (or laissez-faire) in the above sense. Most are subject
to a variety of restrictions, if only those informally imposed by custom and social
pressure. Usually, however, these restrictions are of little consequence. We will see
later that most restrictions imposed on fisheries have little or no impact on the crucial
outcome of the fishery, i.e. its generation of fisheries rents. In spite of these
restrictions, the fishery will still behave as the competitive fishery. For this reason it is
useful to study the competitive fishery.
The fundamental proposition regarding the competitive fishery is that, this
fishery will converge to a state where profits are zero. In other words, cost must equal
revenues.
The basic argument for this proposition is not difficult to understand. For
instance, assume for a moment that the fishery is generating positive profits4. Then, of
course, outsiders will want to enter the fishery in order to partake in these
supernormal profits. Also, existing firms in the fishery will want to expand
operations, by doing so they will apparently be able to increase their profits. So,
fishing effort will expand and it will keep on expanding while there are positive
profits in the industry. However, as we have seen (e.g. Figure 1.14), increasing effort
will sooner or later, result in declining profits. Therefore, this process of effort
expansion will eventually lead to zero profits in the industry. In Figure 1.19 below,
this occurs at effort level, eCSY.
Assume now, on the other hand, that the industry is experiencing negative profits,
i.e. losses. This induces a contraction in the industry. The least efficient firms will
exit. The other firms will reduce operations. Thus, fishing effort declines and this
continues until the industry breaks even again. Again, as shown in Figure 1.19, this
occurs at effort level eCSY.
This simple argument is sufficient to establish that the competitive fishery
finds an equilibrium only at a point where profits are zero. This is our fundamental
proposition regarding the competitive fishery.
4
I.e. profits in excess of normal profits in the economy.
37
The Competitive Fishery
Fundamental Proposition
In the competitive fishery sustainable profits are approximately zero
Before proceeding we must slightly qualify our notation of profits. First, by
profits here we mean profits in excess of normal profits, i.e., the usual profit enjoyed
in other economic activities in the economy (that are open to new entry). So the
fundamental proposition is that only at a point where profits in this sense are zero will
the competitive fishery find an equilibrium, i.e. become economically sustainable.
Second, it is not clear that aggregate industry profits will be precisely zero in
the competitive equilibrium. In the first place, even in competitive equilibrium, it may
be the case that the more efficient fishing firms are enjoying some profits in excess of
the normal. These types of profits, often referred to as intra marginal rents, are the
result of operational efficiency that cannot be replicated neither by the other firms nor
the firm itself. Otherwise it will be and aggregate fishing effort will expand. In the
second place, it must be realized that fishing is an unusually risky activity. This
suggests the need for a risk premium to induce firms and individuals to undertake the
fishing activity. If this is the case, one would expect correspondingly higher normal
profits in the fishery compared to most other production activities. Counteracting this,
however, are indications that many fishermen are actually risk lovers. I.e. they are of
the type, a bit like gold-diggers, that like to take the chance of a great return even if
the expected value of the activity is negative. To the extent that this is the case, the
aggregate profits in a competitive fishery equilibrium may well be negative.
Third, we should mention that many real-life fisheries enjoy social support and
subsidies in various forms. This means that while individual fishing firms may be
breaking even, the industry, from a social standpoint, is operating at a loss.
The essential features of the competitive fishery can be captured with the help
of the sustainable fisheries model developed in the previous section. This is provided
in the diagram in Figure 1.19.
38
Figure 1.19
The competitive fishery
Costs
$
Sustainable
revenues
eOSY
eCSY
Effort, e
xCSY
xOSY
Sustainable
biomass function
Sustainable
biomass,
x
In Figure 1.19, the competitive fishery equilibrium occurs at the effort level
corresponding to the competitive sustainable yield or eCSY. At this fishing effort the
cost function intersects the sustainable revenue function and profits are zero.5 This
outcome should be compared to the maximum attainable profits at the optimal effort
level, eOSY. Clearly, at this level of effort substantial economic profits (or rents) are
generated. So, the competitive fishery wastes these rents by applying too much fishing
effort.
Note also that, as shown in the lower half of the diagram in Figure 1.19, the
competitive sustainable yield effort, eCSY, corresponds to a biomass level, xCSY, that is
much lower than the optimum sustainable yield biomass level, xOSY. Similarly, as can
be inferred from the diagram, the competitive sustainable yield, CSY, corresponding
to eCSY, is lower than optimal sustainable yield. It is important to realize, however, that
this last result is not a general rule. Whether or not the OSY is higher or lower than
the CSY depends entirely on the location of the cost function. This is illustrated in
Figure 1.20.
5
The observant reader may notice that the cost function also intersects the revenue function at a low
level of fishing effort. This point, however, is not an equilibrium for the competitive fishery. The
reason is that a slight increase in fishing effort (which enterprising fishermen will always try) will
generate positive profits. Therefore, fishing effort will expand beyond this point.
39
Figure 1.20
Optimal vs. competitie sustainable yield: Two examples
Harvest,
y
Sustainable
yield
Harvest,
y
CSY
OSY
OSY
Sustainable
yield
CSY
Effort, e
Effort, e
We are now in a position to summarize our most crucial conclusions for the
competitive fishery relative to the optimal fishery. :
The Competitive Fishery
Basic Conclusions
Profits are approximately zero
Fishing effort is greater than the optimal sustainable fishing effort.
Biomass is lower than the optimal sustainable biomass.
The harvest level may be higher or lower than the optimal sustainable
yield.
40
Example
Outcomes of the competitive and optimal fisheries
Assume, as in the corresponding example for the optimal fishery, that biological
and economic research has produced the sustainable yield function:
y = 2e - 1e2,
and the cost function
c = 0.5e,
and that the unit price of landed catch is
p = 1.
Consequently, the profit function is:
= p(2e - 1e2) - 0.5e = 1.5e - e2
In the competitive fishery profits are approximately zero. Thus,
1.5 - e = 0.
So, the profit maximizing level of fishing effort is e = 1.5.
Substituting this fishing effort into the sustainable yield function, we find the
corresponding harvest as y = 0.75.
Comparing these outcomes with the optimal fishery we find:
Fishing effort
Sustainable yield
Profits
Optimal
0.75
0.94
0.56
Competitive
1.50
0.75
0.00
So, for this example the competitive fishing effort is double the optimal one, the
competitive sustainable yield is only about 80% of the optimal one and the
competitive fishery forgoes profits amounting to almost 60% of the gross
revenues.
4.1
The possibility of biomass depletion
It has already been established that the competitive fishery implies a lower, in most
cases much lower, equilibrium biomass than the optimal fishery. Moreover, from
Figures 1.19 and 1.20 it is obvious that this biomass equilibrium is much closer to the
gap in the sustainable yield and biomass curves than the optimal sustainable fishery.
41
In fact, while the optimal sustainable fishery is generally to the right of the maximum
sustainable yield where there is no danger of biomass extinction, there is really
nothing preventing the competitive fishery to be unsustainable. All that is needed is
for the cost function to pass through the gap in the sustainable revenue (yield)
function. Figure 1.21 illustrates this possibility. If the cost function passes through the
gap in the sustainable revenue function as in Figure 1.21, the fishery is obviously
profitable at e0, the highest
sustainable fishing effort level.
Therefore,
the
competitive Figure 1.21
fishery will expand beyond this A nonsustainable fishery
point and the fishery will not be
sustainable. In fact, unless the
$
fishing effort is somehow
curtailed, the stock will not
survive.
The cost function may
pass through the gap in the
sustainable yield function for
two basic reasons. First, it may
happen for biological reasons,
e0
i.e. because the gap is large as
Effort
for instance in the case of
schooling species. Second, it
may happen for economic reasons, i.e. because harvesting costs are low relative to the
landings price of fish. The latter is especially worrying as technological progress
tends to reduce harvesting costs over time. This, in fact, appears to be one of the main
reasons why so many species of fish have come under the threat of stock depletion
and even exhaustion in recent decades. This process of technological process reducing
the cost of harvesting over time is
illustrated in Figure 1.22. Three Figure 1.22
cost curves are illustrated in A reduction in harvesting costs over time
Figure 1.22. The first, and
probably the earliest one in time is
[1]
labelled [1]. According to this cost
function, the fishery would not be
[2]
profitable at any fishing effort
$
level. Hence it would not be
pursued, at least not in a
sustainable fashion. The second
cost curve, labelled [2] implies a
[3]
sustainable competitive fishery at
effort level eCSY. This represents a
sustainable competitive fishery.
The third and lowest cost curve,
e0
Effort
[3], represents the highest
technological level. This curve
passes through the gap of the
sustainable revenue curve. Hence, the fishery is profitable at the minimum viable
biomass level and, unless protective measures are taken, the fishery will be wiped out.
42
4.2
The shadow value of biomass
As discussed at some length in section 3.3 above, the shadow value of biomass is one
of the crucial variables in the economics of fisheries. To determine the optimal fishing
effort it is necessary to take full account of the shadow value of biomass. One way to
do that is, as outlined in section 3.3, to employ the true social price of fish (calculated
as the difference between the market price of fish and the shadow value of biomass)
in calculating the profits of increased fishing effort.
It can be shown, (see the technical appendix to this section) that the
competitive fishing industry generally greatly undervalues the social shadow value of
biomass. This is not difficult to understand. The competitive fishing industry is
generally composed of many firms. A rational firm contemplating whether to harvest
one unit more will compare the benefits to the costs. Among the costs is the impact
the harvest will have on the biomass and, consequently, the firm's harvesting
conditions in the future. This, of course, is the shadow value of biomass from the
perspective of this particular firm. There are many firms, however. Leaving one fish
unharvested in the ocean is going to benefit all of them. The rational firm will, of
course, only take its own private benefits into account when doing its calculation.
Therefore, its private evaluation of the shadow value of biomass will be too low and
it’s fishing effort correspondingly too large.
Obviously, everything else being the same, the greater the number of fishing
firms, the lower their private evaluation of the shadow value of biomass. More
precisely for, identical fishing firms, the relationship between the social shadow value
of biomass, the private evaluation of the shadow value of biomass and the number of
fishing firms may be expressed as follows6:
q = Nq(i),
where q is the social shadow value of biomass, q(i) the private evaluation of this
shadow value and N the number of fishing firms. This relationship shows that the
private shadow value of biomass falls very fast with the number of fishing firms.
Thus, if there are 10 identical firms in the industry their shadow value of biomass is
only 10% of the social shadow value etc. The relationship is further illustrated in
Figure 1.23.
6
See technical appendix 3, equation (A.3.4).
43
Figure 1.23
The shadow value of biomass and the number of
firms. (Social shadow value = 1)
Privte sahdow value of biomasss
As
demonstrated in
Figure 1.23, the
private
shadow
value of biomass
falls very fast
with the number
of
(identical)
firms
in
the
fishery.
For
anything above
30-40 firms this
private evaluation
of the shadow
value
is
negligible.
1,2
1
0,8
0,6
0,4
0,2
0
1
11
21
31
41
51
61
Number of firms
71
81
91
44
Technical appendix 3
The optimal and competitive fisheries: Shadow value of biomass
Consider a fishery composed of N fishing firms, each with a profit function of the
form:
(i) = pY(e(i),x;i) – C(e(i);i), i=1,2,...N,
where, as before, e refers to fishing effort, x to biomass, p to the fish price and the
functions Y(e(i),x;i) and C(e(i);i) refer to the harvesting and cost functions,
respectively. Note that both of these functions, and therefore also the profit function
may differ across firms.
For a sustainable fishery we must have:
x = G(x)-iY(e(i),x;i) = 0.
The social problem is to maximize aggregate profits subject to the biomass constraint.
I.e.
Maximize
i (i)
All e(i) and x
S.t. G(x)-iY(e(i),x;i) = 0.
Solving this problem yields inter alia the following necessary conditions.
(p-q)Ye(i) – Ce(i) = 0, i=1,2,...N,
piYx + q(Gx - iYx) = 0,
where q is the appropriate Lagrange multiplier, equal to the shadow value of biomass.
From the second of these necessary conditions, we immediately derive an
important expression for the optimal (social) shadow value of biomass as:
(A3.1) q= piYx /(iYx - Gx).
Individual competitive firms on the other hand, attempt to solve their own
profit maximizing problems. Thus firm i for instance will want to
Maximize (i)
e(i) and x
S.t. G(x)-iY(e(i),x;i) = 0.
Note that in realizing the biomass constraint the firm takes full account of all the facts
of the situation. In this sense it is perfectly rational. Assuming that the firm cannot
control the effort of other firms, i.e., e( j ) / e(i ) 0, all i and j, we can derive the
45
necessary conditions for profit maximization corresponding to the ones for the
optimal fishery above:
(p-q(i))Ye(i) – Ce(i) = 0,
pYx(i) + q(i)(Gx - iYx) = 0,
Where q(i) is the appropriate Lagrange multiplier for firm i's problem. It is equal to its
private evaluation of the shadow value of biomass.
From the second of these necessary conditions, we can immediately derive the
expression for the private evaluation of the shadow value of biomass as:
(A3.2) q(i)= pYx(i) /(iYx - Gx).
Comparing (A3.2) with its optimal counterpart we see that they are identical
apart from the numerator on the right hand side. In the optimal case this is a
summation over all firms reflecting the fact that a reduction in biomass affects the
harvesting opportunities of all the firms in the industry. In the competitive case, only
the impact of biomass reduction on the firm itself appears in the expression. This
means that firm i ignores the negative impact, its extraction from biomass has on the
harvesting opportunities of all other firms in the industry. Since, iYx is generally
much greater than Yx(i), this is potentially of great quantitative importance.
To explore this, let (i)Yx(i)/iYx. Thus, (i) is in a certain sense firm i's
share in the total catch.7 Given this definition, we can readily derive:
(A3.3) q(i)= (i)q.
Thus, e.g. if firm i has 1% of the fishery, its evaluation of the shadow value of
biomass is 1% of the optimal social value.
If the firms are all identical (A3.3) reduces to:
(A3.4) q(i)= q/N
7
For the Schaefer harvesting function, it is actually precisely its share in the total catch.
46
5.
The nature of the fisheries problem
Our analysis, so far, shows that the competitive (or unmanaged) fishery is
economically inefficient. It employs too much fishing effort. It overexploits the fish
stocks and may even threaten them with extinction. It may reduce the overall
sustainable harvest. Most importantly, however, it squanders the potential net
economic benefits obtainable form the fish resource.
The forces that induce the competitive fishing industry to operate in this
inefficient manner are in many respects fundamental to the theme of this book. The
purpose of fisheries management is to find ways to nullify or at least counteract these
forces so as to enable the fishery to operate at or at least close to the optimal point. In
order to achieve this, it is, of course, necessary to gain as complete an understanding
of the nature and operation of these forces as possible. Therefore, although we have to
a certain extent done so in the previous sections, we will now return to this topic in
more detail. This will help us judge the effectiveness of various fisheries management
methods that have been proposed and to devise new ones.
5.1
The fisheries problem as an externality
Fishermen harvest from a common resource, the stock of fish. The catch of one
fisherman reduces the available stock of fish (at that moment of time) by the same
amount. This means that the harvesting opportunities of the other fishermen are
correspondingly reduced.8 This kind of impact on production possibilities between
firms are generally referred to as external effects or externalities in economic theory.
(For a basic treatment of the subject see e.g. Bator 1958 and Buchanan and
Stubblebine 1962). We find it convenient to refer to this particular externality in
fisheries as the fish stock externality or, more briefly, the stock externality.
In making their harvesting decisions fishermen, of course, consider all the
implications of these decisions on their own operations. However, they are extremely
unlikely to take into account the external effects their harvesting imposes on other
fishermen. In fact, if they did, their fishing activity would be less profitable than that
of other fishermen and would soon be driven out of business. So, this externality is
not taken into account by the fishermen. This is equivalent to underestimating the
shadow value of the resource. As a consequence, each fisherman finds it
advantageous to employ too much fishing effort. Hence, aggregate fishing effort is
also excessive and the fisheries problem emerges.
From this perspective, the basic cause of the fisheries problem is the stockexternality.9 It is therefore natural to ask: what causes this externality? And, can it be
eliminated? To this we now turn.
8
9
Actually, the effect is both a short term and a long term one. In the short run, the availability of fish
for harvesting is reduced. The long run effect is that the regenerative ability of the stock, i.e. its
growth, is affected.
This, of course, is not supposed to imply that there are not other externalities in fisheries. For a
further treatment of that issue see Johnston 1992.
47
5.2
The fisheries problem as a lack of property rights
Externalities are the result of missing markets.10 Externalities are essentially just a
synonym for the economic importance of goods (or for that matter bads) that are not
bought and sold in the market. Since the good cannot be purchased, economic agents
simply take the good.11 This means that the good is not available to someone else,
hence the externality. In the fisheries case, this good is the fish stock. Usually, fish
stock or its services cannot be bought and sold. In other words, the market for the fish
stock is missing. So there is no price either. Therefore, fishermen underestimate the
value of the resource.
Why is there not a market for the fish resource, because there are no property
rights. With a few exceptions, no-one owns the fish in the ocean. Therefore no-one
can charge for its use. As a result the fish is simply taken without proper
compensation to those that are harmed by it. This, of course, is the stock externality.
If, on the other hand, the resource were in private ownership the owner would of
course only part with it (or pieces of it) for anything less than an alternative buyer
would offer and certainly for no less than its benefits to him. The potential buyers, in
turn, would certainly offer no more for the resource than they would benefit from
using it. Hence, we see that first, a market price would emerge and second, this
market price would normally be in the neighbourhood of the social shadow value of
the resource.
The current situation in most ocean fisheries is like farming where no-one
owns the land. In that situation agriculture would be very different from what we are
accustomed to. For instance, the land would hardly be carefully tended and improved.
On the contrary, it would most likely be overexploited and its productivity severely
diminished. This is very much like the outcome in competitive fisheries.
So, it seems that the fisheries problem derives fundamentally from the lack of
private property rights in the fish stocks and, more generally, the underlying natural
resources, the aquatic habitat. It is the lack of these property rights that prevents
markets for the use of the fish stocks to emerge, i.e. results in missing markets. It is
the missing markets for the fish stocks, that causes the basic stock externality in
fisheries.
This fundamental observation raises the question why these property rights in
fisheries are missing. The basic reason seems to be that the appropriate property rights
in fisheries are difficult to define and implement. Fish are not stationary. They cannot
normally be restricted to a certain area. They swim around more or less as they please.
In this sense they are like cattle or sheep grazing on a common pasture. There are
fundamental differences, however. First, fish cannot normally be herded. They have
to be harvested more or less where they are found. Second, and perhaps more
importantly, it is generally not feasible to define private property rights in individual
fish. Therefore, individual fishermen cannot claim ownership of particular fish from a
common harvest as is done in cattle and sheep ranching on common land. Thus, there
are technical obstacles to introducing the appropriate property rights in fisheries as
10
11
A market of a particular good is missing, if the good cannot be purchased at any price.
Sometimes goods are taken although markets for them exists. This is basically stealing and it
constitutes an externality.
48
has been done in most economic activities on land. Technology simply hasn't, at least
not yet, provided us with the ability to implement strong private property rights in
common fish stocks. Although, social inertia undoubtedly also plays a role in the
situation, the lack of good property rights technology in fish stocks is probably the
main reasons why fisheries around the world are still, for the most part, organized as a
hunting activity.
The situation in ocean fisheries is not dissimilar to the situation on land during
the early stages of human development. Then it was also technologically difficult to
define and enforce property rights on land. As a result, the human race had to suffer
huge land-externalities. With an improved technology and the corresponding
adjustment in social organization it gradually became feasible to bring land into
communal and later private ownership with the result that huge improvement in land
productivity (agriculture) became possible. It seems likely that eventually the same
progress can be made in the fisheries. In fact, as will become clearer in later chapters,
there are now certain property rights techniques that can be applied to commercial
fisheries. What is still, to a certain extent, missing is the adjustment in social
organization that makes the adoption of these techniques socially feasible.
5.3
Competitive fisheries as a game
The impact of the basic stock-externality in fisheries may be usefully examined with
the help of simple game-theoretic techniques. Game theory is an analytic tool to study
the actions and reactions of individuals when their actions impinge on each others'
possibilities and returns. Since each fisherman’s harvest has an impact on the
opportunities of other fishermen, they find themselves in a game-theoretic situation
(Bjorndal and Scott, 1996). Their situation is not unlike that of the famous prisoners
dilemma game (Kreps, 1990).
In the prisoners' dilemma game, two perpetrators of a crime have been
apprehended. There, is no proof of their guilt and the only way to get a guilty verdict
is that one of them confesses. The police therefore place them in separate
interrogation rooms to prevent them from communicating and present them with the
following: Confess and you will get off with only one year of prison time. If you don't
confess, your partner will certainly confess and you, as a hardened criminal, will
receive three years in prison. The prisoners now face a certain dilemma, the prisoners'
dilemma. Thus, for instance prisoner A is faced with the following situation. If he
confesses he will get the mild sentence for sure. If he doesn't confess his fate is
basically in the hands of his partner. If the partner confesses he will get the three year
sentence but if his partner doesn't confess both he (and both of them) will be set free.
The other prisoner, prisoner B, is faced with exactly the same situation.
Games are often described in terms of tables that list the possible options
(usually called moves or strategies) and the resulting outcomes or pay-offs. In our
prisoners' dilemma game the prisoners' pay-off matrices look like this:
49
Payoff matrix for A
B
Confess
Deny
A
Confess
-1
-1
Payoff matrix for B
Deny
-3
0
A
Deny
Deny
B
Deny
-1
-1
Deny
-3
0
Obviously, the two prisoners can maximize their utility by denying the
charges. In this case there will be no penalty indicated by the "zero" in the bottom
right hand corner of the pay-off matrices. So to deny is clearly their best overall
strategy. However, this is an unlikely outcome.
Look at the situation from the perspective of prisoner A. If he denies he risks a
prison term of three years. Moreover, this outcome is quite likely because he knows
there is a good chance, his partner B will confess to save his own hide. If on the other
hand, he confesses, his worst possible outcome is a prison term of 1 year. Under these
circumstances most people choose to confess. It is actually possible to show that (See
e.g. Kreps 1990) that given that the two prisoners cannot communicate this is indeed
the dominant (best) for each of them.
Thus, we see that in the prisoners' dilemma game the equilibrium outcome is
inefficient. Because of the structure of the game (lack of ability to confer and
coordinate) the two prisoners are basically forced to select the less efficient strategy.
The fisheries situation exhibits many of the characteristics of the prisoners'
dilemma game. The best overall strategy, the one that maximizes the joint (and
individual) return, is prudent harvesting by every fisherman. However, each
fisherman that elects his strategy runs the risk that the others will fish full-out, in
which case he will be much worse off with his prudent fishing. More formally, the
essentials of this situation may be described with the help of the following pay-off
matrices.
Payoff matrix for A
Payoff matrix for B
A's strategies
B's
Full-out
Prudent
strategies fishing
fishing
Full-out
0
-10
fishing
Prudent
95
100
fishing
B's strategies
A's
Full-out
Prudent
strategies fishing
fishing
Full-out
0
-10
fishing
Prudent
50
100
fishing
50
As illustrated in the above pay-off matrices, if A chooses the strategy of fullout fishing the pay-off will be either 0 or 95. It will be 0 if the other fishermen also
fish full-out. It will be 95 if the other fishermen all elect to do prudent fishing. If A,
on the other hand, chooses the strategy prudent fishing his pay-off will be -10, if all
the other fishermen fish full-out, and it will be 100, if all the other fishermen follow
suit and adopt prudent fishing.
Obviously the optimal overall strategy is for everyone to adopt prudent
fishing. This, however, is not a likely outcome. Just like in the prisoners' dilemma
game, the rational strategy for each fisherman is full-out fishing. Only, if each
fisherman can reasonably trust all the others to exhibit prudent fishing, it will be
optimal for him to follow that strategy himself. In the competitive fishery with more
than a few participants, this is far-fetched. With free entry, where we have new
entrants whenever there are positive gains to be made, it is virtually out of the
question. So, the equilibrium outcome of the fisheries game is that everyone plays the
full-out fishing strategy and the aggregate (and individual) gains will be zero.
5.4
The tragedy of the commons
The prisoners' dilemma fisheries game neatly captures the essence of what has been
called the 'tragedy of the commons' (Hardin 1968). It is basically the common
property arrangement of the competitive fishery that pits fisherman against fishermen
in the prisoners' dilemma fisheries game. If the fishery was organized on the basis of
private property, there would be no externality and the fishermen would not find
themselves trapped by the prisoners' dilemma game. Thus, it is the social institution of
common property that basically forces fishermen to overexploit the fish stocks even
against their own better judgement. When many fishermen have access to a common
fish stock, each one of them has every reason to grasp as great a share of the potential
benefits as soon as possible before the other fishermen manage to reap all the benefits
the resource can offer. Prudent harvesting exhibited by one fisherman in order to
maintain the stocks will, for the most part, only benefit the other, more aggressive
fishermen without preventing the ultimate decline of the fish stock. Thus, each
fishermen acting in isolation, is powerless to alter the course of the fishery. His best
strategy is to try to grasp his share of the benefits as quickly as possible while the
resource is still large enough to yield some profits.
This, in a nutshell, is the 'tragedy of common property resources'. No matter
how great the resource and highly priced each unit of harvest, all the technically
achievable economic benefits of the resource tends to become dissipated by the
multitude of users operating under the common property regime. If this waste is not
tragedy enough, we may add that this occurs in spite of everyone realizing what is
happening and detesting it. Like actors in a Shakespeare play, fishermen are
powerless to prevent the inevitable.
51
5.5
The fisheries problem is not caused by ignorance
It is sometime suggested that the fisheries problem is somehow caused by the
fishermen's ignorance of the basic facts of the fishery in which they find themselves.
This is false. The fisheries problem has nothing to do with the fishermen's
understanding (or lack thereof) of their predicament. For instance, our discussion of
the prisoner's dilemma fisheries game assumes full knowledge of the situation by all
the participants. Nevertheless, the outcome is a waste of all fisheries rents. Indeed this
is the essence of the tragedy of common property resources discussed above, was that
that it happened spite of everyone realizing it.
This result is confirmed by our study of the shadow value of the resource in a
previous section. There we showed that the difference between the private evaluation
of the shadow value of biomass between uninformed and fully informed fishermen
falls very fast with the number of fishing firms and becomes negligible for any
reasonable number of fishing firms (above 20-30). The application of fishing effort, of
course, behaves accordingly. Even for a very small number of fishing firms, the
difference between the fishing effort of uninformed and informed fishing firms is very
small. For a reasonable number of firms (20-30) the difference becomes virtually
indistinguishable. The common property arrangement basically forces every fishing
firm to behave as if it was ignorant of the evolutionary laws of the fishery irrespective
of whether it is or not.
It is interesting, however, that since, in the competitive fishery, knowledge of
the evolutionary law of the fisheries has no behavioural implication to speak of, there
is no reason for the well run fishing company to gather knowledge of this nature. In
fact, since the procurement of knowledge is costly, it is actually optimal to be ignorant
of these laws. For this reason, it is commonly observed that actual fishermen are
found to be quite ignorant about the biological and economic facts of the fishery. The
smaller they are (as a proportion of the fishery as a whole) the more likely they are to
be found in this situation.
5.6
The fisheries problem is not caused by lack of communication
It is sometimes suggested that the fisheries problem would be solved, if only the
fishermen were in a position to communicate amongst themselves. Thus, if somehow
the fishermen could be informed about the fisheries situation, the social distance
between them and other similar social obstacles sufficiently reduced and they brought
together in one negotiation room they would be in a position to more or less solve the
fisheries problem.12
This argument has a certain basis in the analysis of the prisoners' dilemma
game. There, as we have seen, the problem stems partly from the inability of the
participants to communicate. On a more fundamental level this argument appeals to
the so-called Coase theorem (Coase 1960) According to the Coase theorem, the
12
It may be noted that theory forms the basis for the idea of communal fisheries management and
similar notions (Leal, 1996, .Jentoft 1898).
52
detrimental effects of externalities may be corrected by negotiation between the
parties involved. Let us now briefly examine this.
Now, the fisheries problem is certainly an externality problem. Therefore, at
first glance, it may appear that the fisheries problem might be solved by the fishermen
getting together and negotiating a sensible fisheries joint policy. This, however, is far
too optimistic. The Coase theorem is based on two crucial premises. The first is that
negotiation costs are sufficiently small. The second is that the rights of the parties
participating in the negotiations are sufficiently well defined. It is doubtful that the
first premise holds for most ocean fisheries. Such fisheries are typically characterized
by a high number of participants (hundreds or even thousands). These participants are,
moreover, often spread over wide distances with different attitudes and social
cultures. In some cases, they even belong to different nations. Therefore, in general,
the assumption of low negotiations costs is hardly justified. It is important to realize,
nevertheless, that there are certain fisheries - frequently inland or small inshore
fisheries - where the number of participants is relatively small, living in the same
general area and sharing the same culture. In these fisheries the assumption of
sufficiently low negotiation costs may be appropriate.
The other premise that of well defined rights, is even less likely to hold. In
fact, in the case of the competitive (i.e. perfectly unmanaged) fishery it doesn't apply
at all. A defining characteristic of the competitive fishery is that the existing
fishermen have no exclusive rights in the fishery. Hence, any fisheries management
agreement they might be able to negotiate amongst themselves would, if even
minutely successful, immediately be undermined by new entrants to the fishery. It
follows that any rent increasing fishing agreement among the existing would not be
sustainable. So, the first necessary condition for a fishermen's agreement of this kind
is that they be able to form a sufficiently closed club. This means, of course, that this
group of fishermen is now the de facto owners of the fishery. So, we have basically
moved out of the competitive fisheries framework, where the fisheries problem arises.
In this situation, communication amongst the fishermen leading to a fisheries rent
enhancing agreement could alleviate the fisheries problem. Note, however, that there
are still severe obstacles to actually arriving at a workable agreement. For instance,
the bothersome problem of free riders enforcement raises its head. Will the fishermen
be able force their agreement upon everyone in the group? Will they be able to
enforce the agreement? It is clear that an affirmative answer to both questions
presupposes extensive rights (property rights) in the fishery which is, of course, even
further removed from the concept of the competitive fishery.
Thus, we must conclude that the fisheries problem does not fundamentally
stem from the lack of communication between the fishermen. The fundamental
problem is again lack of property rights. Nevertheless, fishermen's self-management
along the above lines remains an interesting possibility with apparently a good deal of
promise.
5.7
Summary
The fisheries problem is not caused by the fishermen’s lack of knowledge or
understanding of the situation in which they find themselves. It makes very little
53
difference to the final outcome whether the fishermen are all-knowing or not. Neither
is the fisheries problem caused by the lack of communication or social cohesion
amongst the fishermen. Without the foundation of some exclusive rights attempts at
communication and co-operation amongst the existing fishermen is doomed to failure.
The immediate cause of the fisheries problem is the external effects each
fisherman imposes on others by his extraction from the common stock of fish. These
external effects lead to a private undervaluation of the shadow value of the resource
and they give rise to a competitive game situation with an severely sub-optimal
equilibrium solution.
On a more fundamental level, the basic stock-externality in fisheries is a
consequence of deficient or lacking property rights in the fish resource. If the
appropriate property rights were in place, the fishermen would have to pay for the
privilege of extracting fish from the stock just like a theatergoer has to pay for the
privilege of taking a seat away from someone else. And the price exacted would
amount precisely to the social shadow value of the biomass. The externality would
still exist but it would be transformed into what economists call pecuniary externality
(Johnston, 1992) which is economically harmless.
So, from this perspective, the fisheries problem derives most fundamentally
from the lack of property rights over the relevant natural resource, i.e. the fish stock.
When property rights are lacking or severely deficient, the institution of private
enterprise (laissez faire) is inappropriate. Only with well defined property rights and,
therefore, reasonably complete markets will the invisible hand be in a position to
guide private enterprise toward the social optimum. In this sense we may say that the
fisheries problem is caused by an inappropriate institutional framework.
54
Fisheries over time Dynamics
6.
Fisheries are rarely encountered in an equilibrium (sustainable state). Most of the time
fisheries are found on a dynamic adjustment path towards one equilibrium or another.
Usually, no sooner an equilibrium is reached, it is shifted by a new development in
one of the pertinent variables and the fishery finds itself out of equilibrium again and
must embark on a new adjustment path. Thus, the evolution of the fishery over time is
somewhat akin to an everlasting missile trying to hit a continuously moving target. It
is not difficult to see that this will generally result in the missile spending most of its
time circulating in the neighborhood of the target. This holds equally for the
unmanaged fishery as the optimally managed one although the specifics of the
dynamic paths may differ.
It follows from this that in order to gain sufficient understanding of fisheries
for management purposes we must study their dynamic evolution. Unfortunately, it
turns out that the analysis and characterization of fisheries dynamics is much more
complicated and, consequently, more difficult to understand than the corresponding
study of sustainable fisheries. Therefore, in our treatment of this topic here, we will
only attempt to provide the most basic intuitions.
6.1
Optimal dynamics
In the dynamic context the appropriate fisheries objective is to maximize the present
value of profits from the fishery forever. Invariably, this implies choosing a time path
for the available fisheries controls, e.g. fishing effort or harvest, so as to bring the
fishery on to an optimal evolutionary path. In our simple aggregative fisheries model
we can describe the optimal time paths of fishing effort and biomass with the help of
the following diagram.
Figure 1.24
Optimal fishery adjustment paths: An example
.
e, effort
e=0
.
x=0
x, biomass
55
Two equilibrium curves are drawn in Figure 1.24, the biomass equilibrium
curve, x 0, and the economic equilibrium curve, e 0 . The meaning of these two
curves is as follows:
The biomass equilibrium curve traces out the combinations of biomass and
fishing effort that keeps biomass constant. Thus, for intermediate levels of biomass,
natural biomass growth is high, so fishing effort must be relatively high also to
generate sufficient catches to keep the biomass constant. On the other hand at the
minimum viable biomass level, there is no natural biomass growth, so fishing effort
must be zero to maintain an unchanged biomass. Similarly at a very high biomass
level, biomass growth is low and, consequently fishing effort must be low also to
maintain the biomass level. Thus, for instance, to maintain the virgin stock
equilibrium, fishing effort must be zero. Everywhere off the biomass equilibrium
curve, biomass is changing. Above the curve it is declining (fishing effort is too great
for equilibrium) and below the curve biomass is rising (fishing effort is too small to
keep biomass constant).
The economic equilibrium curve traces out the combinations of biomass and
fishing effort that maximize present value of profits (with the shadow value of
biomass appropriately accounted for). Thus at a high biomass level, it is optimal to
use high fishing effort to harvest a great deal while at a low biomass level, it may be
optimal to employ no fishing effort at all. Everywhere off the fishing effort
equilibrium curve, optimal fishing effort is changing. It is growing above the curve
and declining below it.
Although, this would constitute economic equilibrium, it is generally not
possible to stay at the economic equilibrium curve. Assume that the fishery is for
some reason on the economic equilibrium curve at a given point of time. Then it is
optimal to maintain an unchanged fishing effort. However, an instance later, biomass
will have changed and the fishery is off the economic equilibrium curve. A
corresponding argument applies to points on the biomass equilibrium curve. Since
fishing effort is generally changing there, it is not possible for the fishery to come to a
rest on there.
An overall equilibrium is found at the intersection of the two equilibrium
curves, the biomass and economic equilibrium curves, and indicated by a dot in the
diagram. At this point, there is no reason to adjust fishing effort, since the fishery is
on the economic equilibrium curve, and biomass does not change since the fishery is
operating on the biomass equilibrium curve. This overall fishery equilibrium
constitutes the optimal sustainable state of the fishery.
It can be shown that for an infinitely long management time horizon, actually
a prerequisite for sustainability, it is optimal to move the fishery to an optimal
sustainable equilibrium point of the type indicated in the diagram. The movement
toward the equilibrium, however, must be along optimal adjustment paths. Only two
such paths exist, one from above and the other from below, as illustrated in Figure
1.24.
56
According to these optimal adjustment paths, if the fishery, finds itself initially
at a high biomass level, e.g. close to the virgin stock equilibrium, it is optimal to
select a fairly high fishing effort and run the biomass down fairly rapidly to the
optimal sustainable level. If on the other hand the fishery management period starts
with a low biomass level (but above the minimum viable level),it is optimal to select
initially a low fishing effort, perhaps even zero, in order to rebuild the fish stocks at a
rapid rate and then gradually increase fishing effort until the optimal sustainable
equilibrium is reached.
Obviously, the exact nature and shape of these optimal adjustment paths, as,
indeed, that of the optimal equilibrium itself, depends on the particulars of each
fishing situation. However, these broad features of the optimal adjustment paths are of
fairly general validity. I.e. if the biomass is below the optimal sustainable level, the
optimal dynamic policy calls for relatively low fishing effort (and therefore catches)
initially to rebuild the biomass and, contrariwise a relatively high fishing effort (and
therefore catches), if biomass is above the optimal sustainable level.
The extremity of the optimal adjustment to the biomass level varies primarily
as a function of the economics of harvesting. In the most extreme case, where both the
harvesting and cost functions are linear in the control variables (i.e. fishing effort in
our case) the optimal course calls for the most rapid approach path. This means that
the biomass is adjusted to the optimal sustainable as fast as possible. Thus, whenever
biomass is below the optimal sustainable level, fishing effort (and therefore also the
harvest rate) is set at zero to build up the biomass level as quickly as possible.
Similarly, when the biomass is above the optimal sustainable level, fishing effort (and
therefore harvest) is set as high as possible in order to reduce the biomass level as
quickly as possible to the optimal sustainable level. This policy, often referred to as
the “most rapid approach path” or “bang-bang” policy is illustrated in Figure 1.25
Figure 1.25
The most rapid approach path
Fishing
effort,
e
emax
e*
x*
Biomass, x
57
Figure 1.25 shows the most rapid optimal approach or “bang-bang” paths to
the sustainable equilibrium. With a large initial biomass, the optimal policy requires
an initial “bang” to the maximum possible fishing effort and then, when the biomass
has been reduced to the optimal sustainable level, x*, another bang to the optimal
sustainable effort level, e*. Similarly, for a low initial biomass, the optimal policy is
an initial “bang” to no fishing effort whatsoever, followed by another “bang” to the
optimal sustainable effort level, e*, when the optimal sustainable biomass, x*, has
been reached. The reader should notice that this fisheries policy, although quite
extreme, is really qualitatively similar to the more normal smooth adjustment policy
illustrated in Figure 1.24.
The optimal approach paths illustrated in Figures 1.24 and 1.25 provide us
with the general principles involved in operating a fishery in an optimal sustainable
manner. The principle is to place the fishery at all times on the optimal paths toward
the optimal sustainable equilibrium. It is important to realize that since this
equilibrium is a moving target, this fishery may never actually reach this equilibrium.
The best that a fisheries management can actually hope for is to spend most of the
time fairly close to this equilibrium. In this connection it is also important to realize
that apart from sustainability, the optimal sustainable equilibrium does not have any
particular economic welfare properties. Most importantly, it does not correspond to
maximal instantaneous or annual profits. Higher profits will generally be realized
along the optimal approach paths from above, when biomass is being reduced.
It is important to realize that the dynamic equilibrium is in general different
from the static equilibrium discussed above. The difference stems from the rate of
discount that is ignored in the static model. The inclusion of the rate of discount in
formulating the optimal fisheries policy leads generally to more fishing effort and a
lower optimal equilibrium biomass than would otherwise be that case. The
relationship between the rate of discount biomass and fishing effort is illustrated in
Figure 1.26.
Figure 1.26
Relationship between the rate of interest and the optimal biomass and
fishing effort
Biomass
1.15
1
x
0.8
0.715 0.6
0
0
0.5
1
1.5
r
Rate of discount
1.5
58
As illustrated in Figure 1.26, the rate of interest encourages increased fishing
effort and discourages conservation of the fish stocks. Thus, contrary to the results of
the static mode, for a sufficiently high rate of interest, the optimal dynamic
equilibrium may be to the right of the maximum sustainable yield. This is illustrated
in Figure 1.27 for the same example as Figure 1.26.
Figure 1.27
The effect of the rate of interest on the optimal sustainable yield.
Sustainable yield
1
y
0.919
1
0.95
0.9
0
0
0.5
1
r
Rate of discount
1.5
1.5
b
Figure 1.27 shows that as the rate of discount is increased from 0%, the optimal
sustainable yield increases at first, reaching the maximum sustainable yield at about
40% rate of discount and then moves to the right hand side of the sustainable yield
curve. Note, however, that even at a very high rate of discount, the impact on the
optimal sustainable yield is relatively small.
Although the maximization of the present value of profits usually implies a
sustainable fishery, there are important exceptions that should be mentioned. First, if
the fishery cannot be sustained, i.e. the biomass has already fallen below the
minimum viable level, it clearly doesn’t make sense to try for a sustainable policy.
Second, if the initial biomass is very low, although sustainable, it may still be optimal
to go for an exhaustion policy, i.e. fish out the stock. (See e.g. Clark, 1973).The
higher the rate of interest the more likely this is. In practice, however, this is unlikely
to be the case because as the stock declines the value of the fish usually increases
substantially do to the scarcity and the conservation motive. This normally works
against exhausting the stock. Third, some fisheries, especially those characterized by a
low biological growth rates and a high harvesting set-up costs are best operated on an
irregular basis. This, thus may suggest an optimal fisheries policy that calls for
intensive harvesting for a few years and then a fisheries rest for several years. This is
not unlike rotational harvesting methods similar to those used in forestry (Pearse,
59
1990). Of course this might type of a fisheries policy might be regarded as
sustainable. However, it is definitely not anything like constant over time.
6.2
Competitive dynamics
The evolution of the competitive (i.e. unmanaged) fishery over time is qualitatively
different from the optimal one. The biomass dynamics, being determined primarily by
biological processes, are of course qualitatively the same as before. This means that
the biomass equilibrium curve, x =0, is the same as before. The economic equilibrium
curve, e =0, however, will be different. The reason is that in the competitive fishery,
effort will expand whenever there are positive profits in the fishery and contract
whenever profits are negative. So, for the competitive fishery, there can be no
economic equilibrium unless profits are zero. This then is the economic equilibrium in
the competitive fishery, i.e. all the combinations of biomass and fishing effort that
results in zero profits.
Examples of the two equilibrium curves in the competitive fishery (based on
our simple fisheries model of the previous sections), namely the biological
equilibrium curve and the economic equilibrium curve are illustrated in Figure 1.28.
For comparative purposes we also draw in Figure 1.28 an example of the optimal
economic equilibrium curve discussed in the previous section. Since, the optimal
fishery implies positive profits this economic equilibrium curve is, of course,
generally at a lower effort level and higher biomass level than the competitive one.
Figure 1.28
Equilibrium curves
Fishing
effort, e
Optimal economic
equilibrium, e 0
Competitive economic
0
equilibrium, e
ec
x 0
e*
xc
x*
Biomass, x
60
An overall fishery equilibrium (often referred to as bionomic equilibrium), is
found where the biomass and the economic equilibrium curves intersect. At this point
biomass and fishing effort are simultaneously constant. Consequently, the fishery as a
whole has come to a rest. In other words, it has reached an equilibrium. In the
diagram in Figure 1.28, this occurs at biomass xc and fishing effort ec. Note that this
point corresponds exactly with the competitive sustainable yield in the static model
depicted in Figure 1.19 above. Note also that this competitive equilibrium is at a
lower biomass and higher fishing effort than the optimal equilibrium indicated by x*
and e* in Figure 1.28. This, of course, is also in accordance with the static results in
the previous section.
In a sense the crucial part of the description contained in Figure 1.28 is the
competitive economic equilibrium curve, e =0. Although in Figure 1.28, this curve is
drawn for a fairly simple description of the harvesting economics, it nevertheless
captures the essential part of the general competitive situation. The economic
equilibrium curve basically splits the possible states of the fishery into three subsets
or parts. The first subset is along the curve itself. On the curve, as already discussed,
profits are zero and the competitive fishery is in equilibrium in the sense that there is
no tendency to either increase or reduce fishing effort. The second subset is to the
right of the curve. There profits are positive (more biomass). Consequently, under the
competitive regime, if the fishery at any time finds itself to the right of the curve,
fishing effort would normally expand. The third possible state of the fishery is to the
left of the economic equilibrium curve. There, profits are negative and fishing effort
would normally be contracting.
It is important to realize that changes in the economic condition of the fishery
will generally shift the economic equilibrium curve. Thus, a higher price of landings,
lower costs of fishing and an improved fishing technology shift the curve to the left,
while a lower price of landings, higher costs and less efficient technology shift the
curve to the right.
Example
Comparison of the competitive and optimal equilibria
Consider the following simple fisheries model:
Biomass growth:
x = 2x - x2 –0.1,
where, as usual x is biomass.
Harvesting:
y = ex,
where y represents volume of harvest and e represents fishing effort.
Costs:
c = 0.5e,
where c denotes costs.
61
Profits
= ex - 0.5e,
where represents profits. Note that this formulation implies that the unit price of landings is unity.
Competitive economic dynamics
e = .
Fishing effort
The biomass equilibrium curve (solid) and the competitive (dashed) and optimal
equilibrium curves (dotted) in
biomass, fishing effort space
are illustrated in the following
3.
diagram.
Where these
economic equilibrium curves
intersect
the
biomass
e( x )
2
equilibrium curve, overall
fishery equilibrium is found.
ee( x )
From the diagram, it is
ecomp( x )
obvious that the competitive
equilibrium occurs at much
lower biomass level and much
higher fishing effort level than
0
0
the optimal equilibrium (the
0
1
2
right –hand intersection).
0
x
2
More precisely the difference
Biomass
between the two is listed in the
following table:
Table
Biomass
Fishing effort
Harvest
Profits
Competitive
Optimal
Percentage
difference
0.50
1.50
0.75
0.00
0.89
1.00
0.89
0.39
+78%
--33%
+19%
+%
The dynamic evolution of the competitive fishery toward equilibrium is very
different from that of the optimal fishery. As already discussed, we may assume that
in the competitive, unmanaged fishery fishing effort will expand whenever there are
profits in the fishery. The reason for this, as was discussed in section 2.4 above, is that
if there are (supernormal) profits being made in the fishing industry new fishing firms
will enter the industry to partake in the profits. Most likely, also, existing firms will
expand their own fishing effort for instance by adding new vessels. In our simple
aggregative fisheries model we may describe the resulting dynamics with the help of
the following diagram.
62
Figure 1.29
Competitive fishery dynamic paths
Fishing
effort, e
e 0
ec
x 0
xc
x2
Biomass, x
Figure 1.29 provides examples of the possible evolution of the competitive
fishery from some initial level. Take for instance the path that starts at the virgin stock
equilibrium, x2 and zero fishing effort. Given the location of the economic equilibrium
curve, e =0, this biomass level represents an opportunity for a profitable fishery.
Fishing effort therefore expands and biomass declines. The expansion of fishing effort
is fast at first, but as biomass declines and profitability subsides, the expansion of
fishing effort is reduced until, eventually the fishery crosses the economic equilibrium
line of zero profits, where profits turn negative and fishing effort starts to contract.
When fishing effort has contracted sufficiently, biomass starts to recover and
profitability to improve. At a certain point, when the economic equilibrium line is
crossed again, the fishery becomes profitable again and fishing effort starts to expand.
Thus, the adjustment to a competitive equilibrium is a cyclical one. It is
characterized by periodically profitable fishery, a consequent expansion in fishing
effort and harvest followed by a decline in biomass and economic losses in the
industry. This type of cyclical adjustment paths are illustrated in Figure 1.30.
63
Figure 1.30
Cyclical adjustent to equilibrium: An example
Biomass & effort
2
2
x( n )
e( n )
0.01
1
0
0
0
20
n
T ime
40
50
It is important to realize that this cyclical adjustment to equilibrium is a
general feature of the competitive fishery and not just an artifact of our simple
representation here. This, of course, is entirely different from the optimal dynamics
that are normally characterized by a monotonic, often smooth, adjustment to the
optimal equilibrium.
Finally, let us consider the evolution of the competitive bionomic equilibrium
over time. This, as already pointed out will evolve with advances in fishing
technology, the price of landings and costs. In the long run, one may assume that
accumulation of technological progress dominates the other factors. This means that
the economic equilibrium curve tends to move to the left. Thus, we may visualize the
following historical evolution of competitive fisheries. Initially, at a fairly low level of
technological proficiency, the economic equilibrium line is to the right of the virgin
stock equilibrium and there is no fishery. With technological progress, however, the
economic equilibrium line moves to the left as illustrated in Figure +.+. Eventually, it
becomes profitable to pursue the fishery and an equilibrium point like x1 in the figure
is established. With further technological progress, the bionomic equilibrium moves
to the left, fishing effort rises and the biomass declines. Eventually, fishing effort may
be so great that the fishery collapses altogether.
64
Figure 1.31
The Impact of Techniological Advance
Competitive economic equilibria,
e 0
Fishing
effort, e
x 0
xmin
x-
x2
x1
x0
Biomass, x
It is important, in this context, to be aware that, a fishery collapse does not
require the economic equilibrium line to be to the left of the minimum viable biomass,
xmin in Figure 1.31. It is actually sufficient for the economic equilibrium line to
intersect the biomass equilibrium line to the left of the maximum of the latter,
indicated by x- in Figure 1.31. The reason is that, in that case the resulting overall
equilibria will not be stable. This means that the cyclical movement of fishing effort,
biomass will diverge from this equilibrium, not converge to it. Therefore, the class of
possible equilibria will generally not be attained. Therefore, in spite of the existence
of equilibria involving biomass above the minimum sustainable level, the fishery may
quite possibly be depleted. An example of these divergent cyclical paths away from
equilibrium is illustrated in Figure 1.32.
65
Figure 1.32
Divergent cyclical movements
Fihing effort
1.48
2
Z
n 2
1
0.221
0
0
0.083
0.5
Z
n 1
Biomass
1
1.5
1.194
Figure 1.32 is based on a particular numerical example (similar to the one in
the above example). In the figure there is a bionomic equilibrium at x= and e= . The
picture is drawn for a initial state of the fishery just outside this equilibrium. As
indicated in the diagram, the dynamic paths diverge ultimately resulting in the
collapse of the fishery.
66
Technical Appendix 4
Dynamic equilibrium optimum
The dynamic optimization problem is to find the time path of fishing effort that
maximizes the present value of profits from the fishery. More formally:
(A.2.3)
Max ( p Y (e, x) C (e)) exp( rt )dt
0
{e}
s.t. x = G(x)-Y(e,x).
One way to solve the problem is to set up the present value Hamiltonian
equation
H(e,x,w) = pY(e,x) – C(e) + w(G(x)-Y(e,x)),
where w is the dynamic Lagrange multiplier.
The necessary conditions for solving problem (A2.3) include:
pYe – Ce - wYe = 0,
r w -pYx – w(Gx - Yx),
w
x G(x)-Y(e,x).
= 0, and eliminating the dynamic
Imposing the equilibrium conditions, x w
Lagrange multiplier, w, from the first two equations, we can derive the basic
optimality conditions in equilibrium:
Gx +YxCe/(pYe-Ce) = r
(A2.4)
G(x)-Y(e,x) = 0.
Solving these equations for e and x yields the corresponding optimal equilibrium.
67
7. Summary [This is just a sketch. the final version should be appropriately
redone]
The following summarizes the main conclusions of this chapter.
(1)
The purpose of the fishing activity is to generate benefits for human use.
(2)
A fishery is said to be optimal if it produces the maximum possible benefits.
(3)
If all relevant prices are true, this is equivalent to maximizing the profits (or
rents) in the fishery.
(4)
Theoretical analysis and empirical observation suggest that fisheries around
the world are, with few exceptions, operated in a severely suboptimal fashion.
(5)
This means that the net economic benefits actually obtained from these
fisheries are far less than what is achievable.
(6)
Examination of the issue with the help of a simple fisheries model shows that
the competitive (i.e. unmanaged) fishery in general (i) exerts more fishing
effort, (ii) results in lower fish stocks and (iii) generates lower rents than the
optimal fishery.
(7)
This result applies to the fisheries equilibria and, with minor exceptions, to the
evolutionary paths toward these equilibria.
(8)
The risk of stock exhaustion (depletion) is high in the competitive (i.e.
unmanaged) fishery but almost nonexistent in the optimal fishery.
(9)
This outcome of the competitive fishery is referred to as the fisheries problem.
(10)
The fisheries problem is not a consequence of ill-informed fishermen.
(11)
The fisheries problem is not caused by a lack of communication between
fishermen.
(12)
The fisheries problem is caused by the external effect the fishermen exert on
each other by harvesting from common scarce fish stocks.
(13)
The external effect is the result of missing markets for the fish stocks.
(14)
The missing markets are a consequence of the lack of property rights in the
fish resource.
(15)
So, the fisheries problem stems most fundamentally from the common
property arrangement of ocean fisheries.
(16)
Given that property rights are a matter of social organization, we may say that
the fisheries problem is caused by an inappropriate organizational framework
in the fishery
68
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