of fish and fisheries management: an economic perspective · 2004-09-21 · discarding of fish and...

Discarding of fish and fisheries management:

An economic perspective

Vilhjilmur Hansson Wiium

M.A., Simon Fraser University, 1993

B.Sc., University of Iceland, 1991

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@ VilhjQmur Hansson Wiium 2001

SIMON FRASER UNIVERSITY Mar& 2001

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Abstract

This thesis uses economic analysis to gain understanding of the interaction between discarding of

fish and fisheries management. Fishers have in recent years faced accusations of wasting valuable

resources by excessively discarding low value catches, allegedly in order to replace them with higher

value fish. In the thesis a mathematical model is developed analysing a fishery where a fish stock has

both low and high value individuals. After deriving optimal levels of fishing effort and discarding,

various management policies are applied to an open access situation to evaluate how successful they

are in reaching the optimal situation in the presence of discarding. The model extends previous work

in this area by including long run effects on fish stocks in ordcr to assess whether management systems

can lead to a reduction in, or even depletion of, fish stocks through excessive discarding. The factors

determining discarding are identified as being economic in nature, especially fish prices and various

cost aspects of fishing. This indicates that any policy addressing a discarding problem should focus on

economic incentives. It is established that some management policies induce excessive discarding, in

particular, landing taxes and individual quotas. Management policies that lead to optimal harvesting

decisions in the absence of discarding are not optimal when discarding is present. For instance, there

will be too much discarding and too many fishers in an individual transferable quota system. -4

significant result of the thesis is that even if management policies, such as taxes or quotas, may

induce excessive discarding, they nonetheless increase the size of the fish stock through a reduction

in iishing effort. This indicates that discarding will not lead to the depletion of a fish stock as some

have thought. Finally, four remedies for the discarding problem are explored, but only a crime and

punishment approach, where iishers are fined for discarding, has the potential of bringing the fishery

to its optimal position. A subsidy low value fish or a tax on high value fish are both found to reduce

discarding, but are nonetheless suboptimal. .A rebate on landings costs is found to have no impact

at aii on discardiig behaviour.

Acknowledgments

Such a long ordeal as the road to a Ph.D. degee cannot be taken without the support of many

wonderful people. First of you, thanks are due to my senior supervisor, Terry Heaps. Your patience

when guiding me through the "wonders" of mathematical rnodelling is beyond belief. The role of

Panival Copes in my development as a hheries economist has also been vcry important. It is likely

that without your influence 1 would not have chosen fishenes as my speciality. 1 guess, Parzi, you

made me "see the light." Many other prolessors in the Department of Economics contributed to

my development as an economist. Rather than naming anyone in particular let me give you al1 a

collective thank you.

So many of my fellow students at SFU gave me continuing support through good times and bad.

1 hope my support to you was half as good as your support to me.

Bridget, what would 1 ever have done without your sweet personality? 1 often think back to

our little talks in the IF.4 office and our squash matches. They helped me keep rny perspective and

redise what things are r e d y important in life.

1 owe many thanks to B j h Dagbjartsson, the director of the Icelandic International Develop

ment Agency. Your insistence that 1 should finish this thesis really made a difference-without that

1 might not have made that one final effort.

Finally, there is the influence of my family. 1 do not think it is possible to quantify the support

my mother, Eygl6, has given me througliout the years, in particular, after 1 decided to go to college. I can only say thank you. To my wife, Gulla, you have followed me al1 over the world and you support

has meant more to me than 1 can ever express to you. Lady, tny dear daughters, Dagmar and

Tinna, your constant questions about ahen "the book:' will be finished have finally been answered.

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Acknowledgrnents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Economics of fish hanresting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Dynamics of fish populations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Fish harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Social optimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Openaccessequitibrium . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.3 Dynamics of fisheries . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Management in the absence of discarding . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1 A historicai backdrop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Objectives of management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.1 Taxes on effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.2 Taxes on landings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.3 Overview of taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 Restrictions on catches and entrq- . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.1 Total ailowabte catch . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.2 Effoa control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5 Individual quotas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5.1 Xon-transferable quotas . . . . . . . . . . . . . . . . . . . . . . . . . 42

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Transferabk quotas 44

3.5.3 Criticisms of individuai quotas . . . . . . . . . . . . . . . . . . . . . 45

4 A mode1 of discarding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Brief literature review 49

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Adding discarclhg to the mode1 53

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Maximising d u e to society 55

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 What to diard? 59

4.4 Open access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4.1 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.5 Discarding and dumping frontiers . . . . . . . . . . . . . . . . . . . . . . . . . 69

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Discussion 72 5 Management poiicies and discarding . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 -- 5.1.1 Taxeson effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ia

5.1.2 Taxes on landings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2 Individuai quotas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2.1 Non-transierable quotas . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.2.2 Transferable quotas . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W 6 Some policy alternatives for discarding . . . . . . . . . . . . . . . . . . . . . . . . . . 92

. . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Crime and punishment approach 94

. . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Subsidy on low quality Iandings 98 6.3 Taxing high quality landings . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.4 Reducing the mt of landings . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Discussion 108 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Summary and conclusions 110

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 115

List of Figures

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 A surplus growth mode1 7 2.2 Dynamics in the sixplus growth rnodel . . . . . . . . . . . . . . . . . . . . . . . . . . 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Schaefer modil 9

3.1 The effect on profits from a tax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 The discarding constraint of an individual fisher . . . . . . . . . . . . . . . . . . . . 57 4.2 Profit maximising situations of an individual fisher . . . . . . . . . . . . . . . . . . . 60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Discarding frontier 70

1.4 Discarding and dumping frontiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Chapter 1

Introduction

Discarding of fish is a behaviour that has always been part of fish harvesting. Fishecs throw out fish

that is unsuitable to sel1 in the market place. Perhaps the fishing gear has damaged the fish, perhaps

the fish is deerned too small, or perhaps it is a species that nobody wants to buy and eat. For these,

and other, reasons fishers discard fish. This was not a reaI cuncern as long as fishing capacity was

below nature's productivity of fish. However, with increased capacity of the world's khing fleets

combined with the decline of many important fish stocks, discarding has become a major concem.

In a report published by the Food and Agriculture Organization (FAO) in 1994, Alverson, Fceeberg,

Murawski, and Pope estimate global discards in commercial fisheries of 27 million metric tonnes per

year during 1988-1990. At the same time global annual landings of fish were 77 million tonnes. This

irnplies that 26% of total catches were thrown overboard. As said in the beginning, this activity is

by no means a new phenomenon. Holden (1994) claims that as early as 1960 it was known that in

the North Sea fisheries for haddock and whiting, 30% of haddock catches and 50% of whiting catches

were discarded. Canadians can see the problem right in their backyard. Storey and Smith (1995)

say tliat one factor contributing to the collapse of the east coast cod fishery were destructive fishing

practices such as highgading, discarding and dumping of undesirable fish and Gillis, Peterman, and

Pikitch (1995) point to research done in 1986 which indicates that 25% of cod caught by trawlers off

the Newfoundland coast was discarded.

Some might ask why we should be concerned about discardimg. -4fter d l , if fishers think that

26% of their catch is not worth holding on to, should they not be allowed to throw it out? An

intriguing question. By far the biggest problem for scientists caused by diicarding is in tems of stock

assesment. Discarding is rarely reported in a reliable way and since the mortality rate of diiarded

fish is in most cases high, this adds to the uncertainty that biologists are facing when estimating

stock sizes. Soehl(lW3), for instance, h d s that stock size estimates will differ substantially h m the

true stock size when dixarding takes place and is not incorporated into the estimation procedure.

be given property rights over the stocks themselves, not just the harvest. Many other problems have

been identiûed, Copes (1986), for instance, identifies various factors that may go wrong with an ITQ

system, including excessive discarding of fish.

The primary aim of this thesis is to gain better understanding of the factors underlying discarding

behaviour of fishers. The research done to date has a number of gaps, some of which will be addressed

in the thesis. Gaining this understanàing will be useful for policy maken in the fisheries area for

at Ieast two reasons. Firstly, policy maken need to determine whether discarding is, in fact, a

problem or not in a particular fishery. As will be discussed below, there are many ITQ fisheries

where discarding is not believed to be of concern, while in othen discarding is believed to be a

serious problem. Policy makers need to be able to distinguish between the two in order to set an

appropnate policy. Secondly, if discarding is found to be a problem, policy makers need to have

some indication of how to deal with that problem. Understanding the factors influencing discarding

behaviour will assist greatly in developing effective policies to tackle discarding.

In this thesis the analysis begins with a fishery in the absence of discarding and various man-

agement policies are explored, a number of which may lead to an optimal fishery. Then discarding

is introduced, and its implications for management are shown. Finally, four possible remedies to the

discarùing problem are introduced and analysed. The specific outline of the thesis is as follows. in

Chapter 2, a mathematical model of fish harvesting is introduced; a model which is utilised through-

out the thesis. Two situations are analysed in the chapter, firstly, the optimal fishery where the

assumption is made that the objective with fishing is to maximise retums to society and, secondly,

an open access fishery where each fisher is assumed to maximise individual profits. Cornparison of

these two situations shows clearly the common pool extemality of fishing which is the reason why

management of fisheries is necessary.

The following chapter discusses various management policies, still in the absence of discarding.

Two types of taxes, effort and landings taxes, are explored. Then a brief discussion of effort control

and total catch restrictions is given, and finally individual quotas are brought into the model. Two

types of individual quotas are analysed, non-transferable and transferable.

Chapter 4 finally brings discarding into the picture. This chapter looks at the optimal and

open access situations, exploring in detail the reasons for discarding and why discardiig of 6sh will

under certain conditions be optimal from society's point of view. Chapter 5 continues the anaiysis

by investigating the implications discarding has on some of the management policies introduced in

Chapter 3. In Chapter 6 four possible remedies to the discarding problem are analysed, and 6nalIy

Chapter 7 highlights the main results and conclusions of the thesis.

Chapter 2

Economics of fish harvesting

Fish stocks are renewable resources. They consist of populations of individuals that reproduce, grow

and die. As with any renewable resource, it is important to distinguish between stocks and jiows.

The stock of fish, usually referred to as the biomoss, is a measure of the quantity of fish existing

at a given point in time. The fiow is the change in the stock over an interval of tirne. This change

may result from natural factors, such as the entry of new k h , referred to as recruitment, or the exit

of fish due to naturd death. Net natural growth is the difierence between recruitment and natural

mortality and is often referred to as surplw growth; if positive then the fish stock is growing, if

negative then the fish stock is declining. Alternatively, the change in a fish stock may result from

economic factors such as harvesting or aquaculture. The fact that fish possess a biological growth

capacity opens the possibility of harvesting fish without depleting the avaiiable stock. In fact, if the

removal of fish through harvesting in one time period is less than surplus growth, then the stock of

fish will be larger at the end of the period than it was at the beginning. -4 sustainable harvesting

strategy is obvious; harvest a quantity of fish exactly equal to the surplus growth, and the stock size

will remain constant over time.

in this chapter a general discussion of the harvesting of fish witl be giwn. To aid the discussion use

is made of a mathematical model. In the following chapters, this model will be extended to analyse

management policies and also discarding behaviour of fishers. The first section of the chapter looks

briefly at the biology of fish. To be able to understand the economics of fish harvesting it is essential

to have basic knowledge about the biological life of fish. For those who want a deeper discussion of

fish biology and stock assessment thm is given here, two excellent sources are Hiiborn and Walters

(1992) and King (1995). in the second section, harvesting is added to the discussion. A mathematical

model of fish harvesting is introduced; a inodel which will be used throughout this thesis. It will

first be developed under optimal conditions, but, as wiU be explained, few if any real world fisheries

are harvested under such conditions. That brings the aaalysis to open access bheries, where it is

CHAPTER 2. ECONOMICS OF FISH HARVESTING 6

recognised t int fisheries are usuaily plagued by a common pool extemality. A common pool resource

is a resource that is either commonly owned by a group of people, and is therefore the common

property of the people in question or the resource is not owned by anyone and therefore nobody has

the power to l i i t access to the resource. High seas fisheries are an example of unowned natural

resources. This common pool nature of fisheries usually leads to overexploitation of fish stocks where

economic rents are dissipated. Fiaily, the impact of changes in some of the exogenous variables in

the model will be analysed to gain a better understanding of the behaviour of fishen and its impact

on the biomass.

2.1 Dynamics of fish populations

Fish grow, reproduce, grow some more, and eventually die. If left alone, fish stocks tend to reach

a naturai equilibrium where the size of the population is in balance. In this equilibrium, growth

equds the decay of the fish stock. If a fish stock is ever to reach equilibrium, it must be that if

the stock size is below the natural equilibrium size, growth exceeds decay. In other words, there is

surplus growth. On the other hand, if the stock size is greater than the naturd equilibrium size, the

stock niust be declining if it is to return to equilibrium. That is to Say, growth is lcss than decay;

consequently the stock size is falling.

In the absence of fishing, a basic surplus growth model of a fish stock can be expressed either in

a discrete form as the difference equation

where xi is the stock size at time i , and F(z,) is the surplus growth a time i , or in a c~ntinuous forrn

as the differential equation

Whether the discrete or continuous version of population growth is used often depends on the sit-

uation at hand. The continuous version is easy to manipulate mathematically using caiculus, but

it ha3 the drawback of assuming instantaneous responses to externa1 forces (se e.g., Clark, 1990).

The discrete form, on the other hand, is usually better suited for computational manipulation, and

allows various complications to be incorporated into the model, such as seasonai pattetns.

The relationship between stock size and surplus growth is depicted in figure 2.1. At very Low

stock levels the fish stock is growing rapidly at an increasing rate, i.e., F'(x) > O. This rapid

growth of the stock can take place because at low stock levels there is plenty of food for the fish.

41~0, a small stock may be l e s vulnerable to predation, for instance, because hiding places are

easier to End. As the fish stock gets larger it will eventually reach its maximum growth potential.

This occurs at the maximum sustainable yield, m v , of the stock, shom as zb~sy in figure 2.1. A

necessary condition for a maximum is that F1(zersY) = O. At stock levels above z~sy growth is


decreasing, i.e., F1(z) < O. The stock is still growing, but the gowth fails as the biomass increases.

Now there is more competition among the fish for food and they may be more easily located by

predators. Eventudy the fish stock will reach a size that corresponds to the canying capacity of

the environment. The carrying capacity represents the maximum size of the fish stock that the

environment can support on a sustained basis. In figure 2.1 the carrying capacity is denoted as XK.

Crowth

- Biomass

Figure 2.1: A surplus growth mode1

If the stock becomes larger than z ~ , growth d l be less than decay and the fish stock declines

in size. Above ZK there is not sufficient food to support al1 this fish; consequently the population

of the stock fails. This iniplies chat equilibriurn is wached at point rK. It is a stable equilibrium

because the biomass aiways tends to return to t~ if a deviation from that level occurs. For instance,

one cold year might lead to a higher mortality rate than normal. This would reduce the stock level

below X K . But a t the new biornass level, there is surplus gowth and the biomass begins to increase

again, approaching XK asymptoticdly as time goes by as shown in figure 2.2. It can be seen that

regardless of the starting point of the biomass, it will tend toward z~ as time progresses,

There is a quaiification to the story told in figure 2.2. If the biomass level fails to a very 1ow

level-below point x, in figure 2.1-t hen the biomass begins to decline until it reaches a level of zero

fish. This is cailed criticol depensotion and point z, in figure 2.1 is the minimum viable stock size.

The idea is, that for a population of any species to increase, a criticai m a s is needed. For instance,

for mating to take place, two individuals of the opposite sex must be able to locate each other. If

there were only 100 cod fish left in the Atlantic Ocean, spread evenly over the ocean, there is only

a very remote probabiiity that they wiii be able to fmd one another. The point z, is an equilibrium

point, since net surplus growth quais zero, but it is unstable. If the biomass size becomes slightly

larger than z,, net gowth is positive and the biomass increases away from z,. If the biomass, on

the other hand, falls slightly below x,, then net gotvth is negative, and the biomass size again f d s

CHAPTER 2. ECONOMICS OF FISH HARVESTING

Figure 2.2: Dynamics in the surplus growth model

away from z, moving asymptotically towards zero.

The actual relationship between net growth and the size of a fish stock is very complex. Various

environmental factors d e c t this relation, such as food supply, available habitats, and the number of

predators. It is not possible to bring together al1 possible factors that affect the size of a fish stock. In

fact, it has to be admitted that knowledge about the biology of fish is rather poor. Notvithstanding,

biologists have developed models that greatly aid in understanding the dynamics of fish stocks.

One of the more widely used biologicai models is the Schaefer model (Schaefer, 1954, 1957). It

is a surplus growth model and is based on the logistic function. It can be expressed as

where r is a positive constant representing the intnnsic growth rote of the stock. The intrinsic growth

rate is the maximum proportional growth rate of the fish stock. The Schaefer model is shown in

figure 2.3. As in the mode1 in figure 2.1 in natural equilibrium, i.e., z = z ~ , the surplus growth is

zero and there is no tendency to move away from that point. One of the benefits of a logistic model,

surh as the Schaefer model is that it is symmetrical. As a consequence mathematicai manipulation

becomes rather straightforward. One result is that the maximum sustainable yield is at half the

carrying capacity, i.e., zbisy = ZK/2.

hnother cnnsequence of the simplicity of the model is that the minimum viable stock size, x,, is

equal to zero. This implies, that as long as there is any fish, the stock will grow. i f it is true that a

critical mass of fish is needed to sustain the stock, then this model does not capture that property.

However, it is argued that it is v e q unlikely that people will be able to reduce fish stocks to leve'els

close to 2,, and as a consequence worrying about that stock level is not a usefui exercise.

Growth

Figure 2.3: The Schaefer model

2.2 Fish harvesting

To harvest fish, various inputs are needed, such as vessels, fishing gear, crew and, of course, a skipper.

Tirne is also an important input. Some fish may be close to shore, while othen are out in the Iiigh

seas, and time is needed both ta get to the fishing grounds and to locate the fish to be caugfit. In

addition to these and other inputs, some fish must exist to be harvested. To focus on the distinctive

aspects of fishing, al1 inputs, except the fish stock, are mcrged into an index. This index rneasures

the use of al1 inputs in the fishery, and is referred to as eflort. In the model presented here there are

n individual fishers. The eEort of the i-th fisher is denoted e'. Fish can be harwsted by the individual fisher acmrding to the function

implying that al1 fishers have access to the sarne harvest technologl As before, z is the total biomass

of the fish stock. The stock size affects aii fishers, and therefoce enters the harvest function of al1 the individual fishers. The harvest hinction is assumed to have the following properties

h,i > O h, > O V i

h,,,; 5 O h,, 5 O V i

h,i, > O h,,, = h,,. V i

These standard assumptions regatding production functions imply diminishing marginal r e tum of

both inputs. The cross derivative h,i, has an interesting interpretation. If positive, a higher stock

level increases the productivity of each effort unit. One aspect of fish harvesting is the fact that to

catch any b h , it must 6rst be found. Some bheries are of the nature that as the biomass becomes

larger, the easier it is to locate &ih and the more productive each effort unit is, since less time musc


be spent searching for fish, i.e., h,iz > O. A ûshery of this type is called a seorch flshery (Neher,

1990). An example are many demersal fisheries, such as cod fisheries.' Some fish species, on the

other hand, tend to aggregate in large schools (Partridge, 1982). For such fish, once a school is

located, the size of the biomass has no effect on the productivity of each unit of effort. For such

schooling fisheties, h,,, will equal zero. Many pelagic fisheries, such as hemng and capelin hheries,

are examples of schooling fisheries. Throughout this thesis, h,i, is assumed positive.

in the economics literature on fisheries management, the harvesting function is frequently as-

sumed multiplicatively separable in effort and stock size. The commonly used Gordon-Schaefer

harvesting bnction

h(ei, x ) = kir (2.6)

whcre b is a constant called the catchability coefficient, is one example of such a function (see e.g.

Clark, 1990). in a general form, a multiplicative separable harvesting function can be rewritten as

Using a separable harvesting function simplifies the mathematical analysis. For instance,

h, = #(ex) and fi,, = O (2.8)

in other words, the partial derivative of the harvesting function with respect to the size of the stock

only depends on effort and not the stock sue. While assuming separability is not always needed in

the analysis in this thesis, there are occasions where this assumption is quite useful.

Until discardiig is introduced each fisher will land all of his harvest. The quantity of fish landed

by fisher i is denoted y', and in the absence of discarding it must be that

where Y measures total landings in the 6sbery.

Cost of fishing, in this model, depends on two factors; the effort level, and the amount of fish

landed. The cost bnction of the individual fisher in the fishery is

Landing cost includes cost from any fish processing done aboard the fishig vessel, in addition to the

cost of physicaiiy landing the fish. in the model as pcesented in this chapter, the amount of landed

fish equals the total harvest. However, once discarding is introduced in the next chapter, it becomes

possible to reduce this cost by discarding some, or aIi, of the 6sh catch. Fcr now, it is assumed not

'Demersd fish, often referred to as groundûsh, are tish that stay close to the bottom of the ocean and are often relatively stationary, while pelagic 6sh are i%h that tend to stay in upper layers of the ocean over deep waters often migrating over vast areas.

possible to throw out any part of the catch, so that for the current analysis the total cost could

be written ci(ei). However, for the purpose of comparing a fishery where discarding occurs, with a

fishery without discarding, the cast of landings is separateci from the cost of effort. The following

properties are imposed on the cost function

c:~ > 0, c i > O V i , and q,, = 7, where 7 is a constant, the same V i (2.11)

The first two conditions irnply that the cost of eflort increases at an increasing rate. The final

condition specifies that the marginal mst of landings is constant and the sarne across al1 fisbers.

The cost of landings will to a large extent be outside the control of the fisher. For instance harbour

dues and the cost of physicaily landing the fish will often by decidd by the port authorities and will

not differ among fishers. Therefore, this seems a reasonable assumption. The final condition also implies that the cost function is additively separable in its arguments. One reason is that effort and landings do not occur at the same time, and therefore do not affect each other's unit cost. Finally,

the average cost of a fisher as a function of hm-est,

is assumed to have the traditional U-shape, with minimum average cost denoted as i d . Individual fishers may have different cost functions, implying heterogeneity of fishers. Some

authors, such as Boyce (1992) and Terrebonne (1995), have introduced heterogeneity of fishers by

allowing for differences in harvest functions. In this thesis, on the other hand, al1 fishers are assumed

identical on the production side, while differences rnay occur on the cost side. Examples of modelling

heterogeneity through costs are Clark (1980), Heaps and Helliwell (1085) and Matthiasson (1997).

The cost difference may, for instance, derive from dinecent wage demands of crew members. Imagine

a fishery where vessels of different nationalities target the same fish stock. Among these vessels labour

costs might differ, leading to differences in cost functions. One reason for different opportunity costs

of this son may be differences in ethnic backgrounds that have impact on acceptable wage levels

(Jacobson and Thompson, 1993). Another r e m n why costs may difier among fishers is that fishers

will often have different reasons for fishing. For instance, in a survey by Hanna and Smith (1993),

33% of fishers surveyed saw the opportunity of simply being on tlie ocean as a significant reward e

from being a fisher, while others did not share that feeling. Differences of this kind will affect

the opportunity costs of fishers. Yet another reason stems from the fact that sorne fishers will be

highliners, Le., fishers that tend to catch more h h than others. Often there is considerable prestige

associated with being a highliner and a fkher that wants to be considered a highliner will have a

lower opportunity cost of efTort than someone who is not interested or able to be a highliner. Some

hhers, on the other hand, are part tirne fishers, often combining fishing with other part tirne work.

They may value the option of being able to work flexible hours and like to spend some of their time

pursuing other interests. For instance, they may put a high value on leisure tirne and therefore are

not willing to spend as much time fishing as the highliner. Gautarn, Strand, and Kiriùey (19%) look at some of the implications for 6sheries management of including in the analysis tradeofh between

labour and leisure. These kind of considerations could be explicitly included in the cost function if

modelling the situation of a particular 6shery. The main point is that the heterogeneity of Gshers,

for whatever reason it exists, allows some of them to earn intramarginal rents reflecting that some

of them can hanrest fish at lower cwt than others. In the economic Iiterature, intramarginal rents

are also known as quasi-rents or producer's surplus (e.g. Copes, 1972).

2.2.1 Social optimum

Given a k e d output price for fish, p, the maximum value to society Bom fishing is found by maximising the function

which maximises the difference between total revenue from harvesting fish and the cost of catching

it, while, at the same time, assuring sustainability of the fishery, since only surplus growth, F ( z ) , is removed from the oceau.' The Lagrangian of this maximisation prohlem is

where X is the Lagrangian multiplier associated wit h the stock constraint measuring the shadow

d u e of the stock. The first order conditions are

f$ = ph,, (ei,z) - ci, (el, y') - cli (e',yi)hc.(ei,z) - Ah,; (ei,z) = O, V i (2.16)

By solving these n -t 2 equations simultaneously, the n d u e s for ei, and the values for x, and A that

maximise the sustainable d u e of üshing to soaety, can be found.

Equation 2.16 is the rnorginui effort condition For fisher i, it c m be rewritten as

Z'CVhether maximisirtg the difierence between revenue and cost results in the sustainable optimum for society is debated. This will be further d i s c d in section 3.2 below.


which States that effort is to be chosen such that marginal revenue fiom effort equals marginal cost.

Marginal cost of effort coasists of two factors, h t , the direct change in cost from using additional

effort, and second, the change in landings cost arising from the new harvest level. The difference

from other production activitics in the economy is that the output price needs to be adjusted to

recognise the fact that one factor of production, the fish stock, does not carry a market price. Since

the fish stock is a productive part of the econorny, it is d u a b l e for society, as given by its shadow

value, A. The shadow value shows the increase in profits from a marginal increase in stock size. It

can also be thought of as the opportunity cost of the marginal h m e s t and to reflect this cost, the

landed value of the harvest must be lowered accordingly.

Equation 2.19 can be rewritten slightly to give

The term given by the right hand side (~tis) of the equation is the marginal cost of fisher i l as can

be seen by differentiating total cost with respect to output, i.e., . . .

dc'(el, y') . dei 4. (et. Y') + = = cf,(ei,y')- + 7 =

dgi dyi he, (et7 z)

Since p- X is constant for ai1 fishers, equation 2.21 implies that marginal cost should bc equal across

iîshers. if this was not the case, geatet efficiericy could be achieved by assigning more harvest to

fishers with lower marginal cost and reducing harvest of fishers with higher marginal cost. Imagine

that al1 fishers are operating a t the same harvest level and some fishers have a lower marginal cost

than others given that harvest. Then reducing the harvest of a fisher with a high cost by one unit

and giving it to a h h e t with a lower cost will reduce overall costs of fishing while maintaining the

overall harvest level. As long as thcre are any differences between the marginal costs, it will pay

to redistribute harvest from those fishers with higher costs to those with lower costs. Yotice, that

equal marginal costs indicate that low cost fishers will harvest more and use a higher level of efTort

than high cost fishers. The logic is essentially the same as behiid the multiplant production decision

of a monopolist, where the monopolist will produce such that the marginal cost across plants is the

~ a r n e . ~

In the case where fishen are homogenous and marginal costs are constant the number of fishers

is irrelevant. If the aggregate effort is optimal then it does not matter how many fishers are active.

The marginal cost oE using one-tenth of an effort unit or one thousand effort units is the same.

However, if marginal costs are not constant then one question to be addressed is how many fishers

should be allowd to harvest fish in this fishery. Heaps and Helliwell (1985) look at this issue, and

determine that it is profitable to add vessels to a fishery, as long as the marginal benefit from doing

so is at least as high as the average cost of the new vessel. To understand thii, assume that ali n

3See any intermediary microeconornics textbook, such as Pindyck and Rubinfeld (1998), pp. 343-345.

CHAPTER 2. ECONOMICS OF FISH HARVESTWG 14

fishers are operating and re-allocate a harvest of Ayi from each fisher to fisher n + 1. This does not

change the overall harvest. In this case,

This can only be profitable if (p- A) 2 icn+'. Lf fishers are ranked by their average cost of harvest;

fisher 1 being the one with the lowevt average cost, fisher 2 having the second lowest, etc. this implics

that the average cost of the last fisher must q u a i margitial cost. The marginal fisher is therefore

making zero profits i.e.,

( p - A)yn -cn(e",yn) = O (2.23)

A fisher making zero profits is receiving normal returns on the use of al1 inputs. If rnaking less, it

would be beneficial from society's point of view to transfer that fisher to sonie other sector of the

economy, where he c m make nomal retums. However, if the marginal fisher is rnakiiig more than

zero profits, it is sociaily beneficial to transfer a person making normal returns in another sector to

the fishing sector where higher returns can be made. Oiily when the marginal fisher is making zero

profits will there be no gains from such transfers and an equilibriurn is reached.

The zero profit condition (equation 2.23) irnplies that fishers will continue to enter the fishery

until

icn 5 p- x < ~k"" (2.24)

where i c i refers to the minimum average cost for fisher i .

Equation 2.17 is the marginal stock condition. It specifies the optimal stock size in the fishery.

It commands that the biomass be kept at a level where the marginal cost of increasing the stock,

Le., the foregone profit from leaving the marginal fish in the ocean, be equd to the marginal benefit

of doing so, namely the increase in the vaiue of the resource frorn adding one fish CO the stock. From

the marginal stock condition, the shadow value oE the stock can be found to equal

evaluated at the optimal levels of ei, z, and n. The shaàow vaiue depends on the price of the fish,

the growth function of the fish stock, and aiso the cost and harvesting functions of al1 individual

fishers. Therefore, the shadow value is afiected by the efTort level of each fisher.


From the marginal stock condition it can be seen that

since otherwise equation 2.17 could not be satisfied. This is thus a necessary condition for a maximum

and keeping this in mind often aids in the comparative static exercises later on.

The final first order condition, equation 2.18, ensures the sustainability of the fishery, by restrict-

ing harvest to equal the surplus growth of the fish stock at the chosen stock size.

2.2.2 Open access equilibrium

The next step is to analyse what occurs in a free market situation, and how it compares to the

social optimum. This is effectively open access; anyone can harvest the resource without limitations.

However, before this can be done, the issue of how fishen regard the effects of their harvest on

the fish stock must be addressed. Even if it may be obvious that total harvest in a given year

affects the biomass, it is not as obvious how the harvest of one fisher affects the stock size-if at dl.

Traditionaily, fish stocks have been commonly used resources, which can lead to perverse incentives

once a stock is heavily exploited. For instance, a fisher may feel that a fish, just harvested, is too

small and it would be more beneficial to release it and allow it to grow for a year, rather than hanest

it now. However, if the fisher actudly releases the fish, he is unlikely to catch it later. Therefore, the

first fisher rnay decide to keep the fish rather than release it. This situation is a consequence of what

Hardin (1968) refers to as the tmgedy of the commons. Because of the common use of the fish stock,

no fisher has an incentive to husband the resource. The result is that it wiIl become overexploited.

One result of this common pool externality is that fishers seem to behave as they do not recognise

the effects that their harvesting activities have on the fish stock. The more fishers there are, the

more pronounced this effect will be, and this is the situation that will first be analysed.

No recognition of stock effects

In thi case, fishers behave as if they do not redise that their harvesting decisions afFect the stock

size. Perhaps, they consider their own operations so small that their hwest is insignificant relative

to the stock. Here, fishers take the stock size as given, wanting to maximise their individuai profits,

as given by

mexi = ph(e';x) - c'(ei $) V i (2.27) e'

The semicoIon in the harvesting function indicates that the stock size, z, is considered an emgenous

variable. Sice the fisher does not recognise the stock effect, there is no stock constraint. AS before,

it is assumed that the fisher lands aU his hmest, i.e., yi = h(ei;x) . The k t order condition for

thii maximisation problem is

The marginal effort condition now does not take into account, at ail, the shadow value of the fish

stock, A. By comparing with the sociaily efficient marginal effort condition (equation 2.16) it is clear

that the fisher does not use an efficient level of effort. if the 6sher operates a t the socially optimal

effort level, as given by equation 2.16, marginal revenue is greater than marginal cost, since the fisher

does not recognise the shadow value of the stock. The fisher will therefore increase the effort level

to equate marginal revenue and marginal cost.

The second order sufficient conditions for maximisation for the individual fisher are satisfied

when

@ - 7)heiee - ceie* < O (2.29)

This condition will be utilised in sorne of the discussion below.

In addition to excessive effort of each fisher,the open access fishery will attract more fishers than

is optimal. Since marginal benefit of effort is higher than in the sociaiiy optimal case, new fishers

will enter the fishery. As long as there are positive profits to be made, and entry and exit is costless,

more fishers will join the fishery. If fishers are ranked by their average cost, as in section 2.2.1, the

number of fishers, n, wiH be determined by the condition

Since X is excludecl Crom the marginal benefit, the minimum average cost Car the marginal fisher in

this case is higher than in the socially optimal case. Consequently, some high cost fishers will enter

the fishery, where the term high cost refers to fishers nith minimum average cost above the minimum

average cost of the marginal fisher in the socially optimal situation.

It is clear from the discussion that, when compared to an optimal fishery, effort in the open

access fishery is higher as a result of two factors. Firstly, each 6sher will use more effort than is

socially optimal, and secondly, more fishers will be attracted to the fishery, as well.

With regard to stock size, the increase in effort must lead to a smaller biomass than is socially

optimal. To show this, keep in mind that the fishery must be sustainable, i.e.,

Even if each ûsher does not recognise the stock effect, for equilibrium this last condition must hold

for the fishery as a whole. Differentiating equations 2.28 and 2.31 with respect to effort, stock size,

and the price, results in the following equation system -

-

de1 *

de'

den

dz _ - -

* -h,r -h,o

- h e m O

CHAPTER 2. ECONOMCS OF FISH HARVESTiNG 17

where rii,, has dready be shown to be less than zero, af,, = (p-y)h, > 0, and 0, = F 1 ( x ) -C h, < O. For the coefficient matrix, A, it can be shown that its determinant equds4

i= 1 > O if n odd

Denoting the matrix when the last column of A has been replaceri with the RHS vector as A,, its determinant can be shown to be

IA.I= 5 3 ( > O if n even

i= l , i < O if n ~ d d

Cramer's rule can be used to find 8% IAZIC0 -=- a~ IAI

which implies that in open access an increase in the landed value of fish leads to a smaller stock

size. As was argued abow, the diRerente between the optimal situation and open access is chat the

shadow value of the stock is nut considered by fishers in open access. In other wrds, the landed

value in the optimal situation is lower than in open access. Therefore, if the open access îishers were

to face the lower land4 value, according to equation 2.35 the biomass would increase from the open

access equilibrium.

h l 1 recognition of stock effects

Perhaps by assuming non-recognition of harvesting effects on fish stocks, fishers are given less credit

than is due. Many fishers are knowledgeable about the biology and behaviour of fish stocks, and

realise that their harvest affects the size of the tish stock. Arnason (1990) argues that when modelling

the behaviour of fishers, the m a t ceasonable assurnption is rationality where fishers take al1 relevant

variables into account, including the stock constraint and effort levels of other fishers. Also, Hanna

and Smith (1993), when surveying fishers, finds that fishers have an understanding of the effects that

too many fishers can have on the resource. Following . ha son (1990) by assuining, therefore, that

al1 fishers acknowledge the effects of their harvest on the fish stock, each fisher wiil maximise profits

41n general, it can be shown by induction that

a i O W . - O h

O a2 : h -. O :

0 ... O a. b. CI cz . - C, d


as follows

There are two differences from the case of non-recognition. Fintly, each fisher redises, and takes

into account, that the size of the fish stock is endogenous, deterrnined by the harvesting decisions of

al1 fishers. Fishers could, for example, behave in a Cournot fashion, forming expectations about the

behaviour of other fishen and making their own decision such that a desired biomass level is reached,

contingent on these expectations. Secondly, fishers know that for a sustainable fishery, total harvest

may not exceed surplus growth. Given this, the Lagrangian of thii optimisation problern is

where a' is the shadow value of fisher i. The first order conditions for fisher i are

ph,, (e', x) - c:, (e', y') - ci, (ei , yi)h,i (e', z ) - a'h,, (e', z) = O (2.39)

The hi11 maximisation problem has n effort equations, n equations for the shadow value, u', and one

stock equation. There are n effort levels to solve for, as well as n shadow values and the stock size.

Since the number of equations is equal to the number of choice variables, a solution to this problem

may exist . Looking Grst a t the marginal stock condition, equation 2.40, it can be rewritten to express the

shadow value of the stock, for the individual fisher as

As long as there are at least two fishers participating in the fishery, the marginal increase in harvest

for the individual fisher from an increase in the stock size, h,(ei,x), must be less than the overall

increase in harvest, C h,(ei,z). S i ce the individual ûsher gains less from aiiowing one more fish to

grow larger than society does, each M e r wiU use a higher effort level than is sociaüy optimal. The

reason is straightforward. The fisher has very ü t l e chance of reaping the benefit of dlowing fish

to grow larger. The greater the number of fishers, the l e s chance the fisher has of benefiting from

letting the marginal fish grow larger, hence vaiuing an increase in stock size less than society does.


It is worth noting, that if fishers are heterogeneous, i.e., have different cost functions, they

will have different shadow values for the fish stock. This arises since the optimal effort level will

d i e r among fishers, thus, on the margin, hz(ei,x) will differ from one fisher to the next. This has

consequences for management as will be discussed below.

The marginal effort condition (equation 2.39) for the individual fisher can be rewritten as

Since ai < X it must be that if the fisher is operating at the socially optimal effort level, as determined

by equation 2.19, the marginal cost of effort is less than the marginal benefit. Consequently, the fisher

will increase effort, and continue doing so until marginal costs equal marginal benefits. This leads to

overexploitation of the fish stock. However, as long as ai is greater than zero, the overexploitation

will be less than in the case of non-recognition. Al1 active fishers will even be earning rents equal to

their shadow value. Another consideration is that the greater is the number of fishers, the smaller ai

becomes, as h,(ei,z) is reduced when the number of fishers increases (Arnason, 1990). On the other

hand, if there was oniy one owner of fishing vessels, this owner would fully take the stock effect into

account, i.e., C hz(ei,z), and ai = A. The sole owner would choose effort, stock size and the number

of fishen that would maximise the resource rent in the fishery (Scott, 1955). Whether this would

be socially optimal depends on the potential for intramarginal rents in the fishery. It was shown by

Copes (1972) that mavimising only resource rent leads to a different solution than when the sum of

resource rent and intramarginal rents is maximi~ed.~ Empiricaily, Cook and Copes (1987) showed

this result for the Pacific haiibut fishery in Canada. Keeping this in mind and looking at a sole owner

of a fishery, he cannot capture any intramarginal rents unless there was only one fisher operating

in the fishery, namely himself. if more fishers are needed, the sole owner will only maximise the

resource rent, and disregard intramarginal rents as they will accrue to the fishers thernselves.

As in the case when not recognising the stock effea, not only will each fisher increase effort, as

compared to the optimal situation, but more fishers will enter the fishery as well. Again, as long as

positive profits can be made in the fishery, more fishers will join. The condition that determines the

number of fishers is now

icn < p - un < ~ 2 ~ + ~ (2.44)

It seems reasonable to assume that on = O. A positive an indicates that the marginal fisher is making

profits higher than normal profits. Therefore, someone outside the fishery will find it profitable to

enter, forcing on down, increasing the minimum average cost on the margin. This process wili not

stop, until an = O. This implies that there be the same number of fishers in both the open

access situations, regardless of whether the behaviour recognises the stock effect or not. However,

'Capes (1972) also looked at the possibity of including consàmer's surplus in the maximisation problem. Not surprisiigly that would lead to yet another optimal solution. .As the price is taken as given in the an&& here, there is no consumer's surplus to analyse in this case.

the intramarginal fishers with a positive shadow value wil1 make cents by restricting their effort.

Therefore, overall effort wiU be lower than in the open access situation with fishers not recognising

the stock effect. However, as more fishers enter, the lower will h, be for an individual fisher and the

closer to zero ui wiU become for al1 fishers, implying that the difference between the non-recognition

and full information cases will be small.

Analysing the €uH information case is both comptex and cumbersome. Assurnptions must be

made of the perception eacb 6sher has regarding the behaviour of other fishers. Such assumptions

bring the analysis into the realrn of p m e theary. The discussion in this section has assumed that

each fisher knows how much catch other fishers harvest. One way of modelling this is to assign

Cournot behaviour to fishers, where each fisher assumes that other fishers do not change their effort

decisions from the previous tirne period. Then each Gher c h m an effort level based on beliefs

regarding the effort of other fishers, and their preference regarding stock size. This apiild then lead

to a Nash equilibrium, where no hher ha. an incentive to change hi decision, given the behaviour

of the other fistiers. However, it rnay well be that multiple Nash equilibria exist or that no Nash

equilibrium exists at dl, and its analysis is very dificult as n rises. Game theory is becoming increasingly important in fisheries economics, as in other branches of

econoniics. However, it has been niost appiied in situations where there are distinct groups that are

competing, rather than individual fishers. Normally, papers applying game theory to fisheries only

analyse the interaction between two agents. Considerable work has been done analysing actions and strategies where more than one country has access to the same fish resource. This work really began

after the introduction of 200 miles exclusive economic zones in the late 1970s. Some examples of this

literature are Munro (1979), Levhari and Mirman (1980), Kaitala and Munro (1993), -4rmstrong

(1994), Ferrara and Missios (1996), Hannesson (1997) and Li (1998). Other game theory models

have looked at different sectors within the fishing industry, such as the relation between fishers

and fish processors (e.g., hIunro, 1981), and vesse] ownera and crew members (e.g., Sutinen, 1979;

Himalainen, Ruusunen, and Kaitaia, 1990).

2.2.3 Dynamics of fisheries

The harvesting of iîsh is a dynamic process. Fish stocks are natural assets and a decision has CO

be made whether each i%h should be harvested today or allowed to live longer and be harwsted at

some time in the future. Taking the asset value of fish stocks into account , brings discount rates into

the analysis. in thii thesis so far no explicit assumptions have been given regarding discount rates.

However, both the optimai aod open access situations make implicit assumptions about ùiicounting.

The mode1 of the optimal fishery in section 2.2.1, sometimes referred to as the static optimum,

assumes that every p e t i d is the same, that a dollar earned thii par is exactly the same as a dollar

earned ten years from now. This impües a discount rate of zero which can &e considered one extrerne. The open access ûshery as presented in section 2.2.2, on the other hand, is a situation where no 6sher


cares the least about the future. Al1 that matters is the current time period. The reason is that

even if one fisher tries to behave in a way that may bring benefits in the future, the actions of other

fishers is almost certain to nullib this action. Not caring about the future implies an infinite discount

rate, which is the other extreme of discount rates. Discount rates between the two extrernes will

have effects on the equilibrium solution (e.g., Clark, 1990; Hannesson, 1993). For instance, while

in the static optimum the biomass is always larger that X ~ s y this is not necessariiy the case when

the discount rate is positive (see e.g., Hartwick and Olewiler, 1998, p. 358). Nonetheless, discount

rates will be ignored in the formal analysis in this thesis. The airn of the thesis is to explain and

understand the discarding behaviour of fishers. As will become clear this behaviour is complex and

is difficult enough to analyse in a static framework. Addiig a discount rate to the analysis will not

add rnuch to the anaiyticai results of the thesis and is therefore left out!

Another issue related to the dimension of time is the steady-state nature of the anaiysis in this

thesis. A11 equilibria derived here are long-run steady-state equilibria, and al1 comparative statics

are comparing one steady-state to another. There is no attempt made to analyse the path from one

equilibrium to another. It is assumed that in the long run al1 costs are variable and therefore there are

no costs of entry and exit, removing any complications due to possible irreversibility of investments

in the fishery? One of the benefits of looking at long-run models is that the effects different policies

have on the biomass can be analysed. AS will be discussed below, the previous work on discarding

has been short-run analyses assuming a h e d biomass, thus neglecting the impact discarding may

have on the biomass.

Finally, the model does not look at various production externalities that may apply to fisheries.

For instance, a fishing season is assumed to be instantaneous which implies that the length of the

season is not a factor in the decisions made by fishen. It may well be that a fishing season of one

month induces a different fishing behaviour than a season of twelve months. Also, diierent fishing

grounds may have different levels of productivity such that fishers rnay spend resources in assuring

that they get to fish from the most productive grounds. Examples of literature looking at such issues

are Clark (1980), Boyce (1992), and Homans and Wilen (1997). While production externalities will

undoubtedly affect the behaviour of fishers, including their discarding behaviour, the current model

does not address such externalities as there are a number of basic issues relating to discarding that

need to be addressed first. This thesis aims to look at some of these basic issues, as explained in

section 4.1 below.

'1f a positive discount rate is included in the anaiysis the equation for the optimal stock level (quation 2.17) becomes L, = 6X, where 6 is the discount rate. In this thesis this would complicate, but not change the qualitative comparative statics results.

'~rreveïsibilit~ of investment in ikheries has been analysed by a number of authors, e.g., Clark, Clarke, and Mumo (1979), Charles (1983) and Boyce (1995).


2.3 Discussion

This chapter has looked at two static long-run equilibria for the harvesting of a fish resource. Firstly,

it looked at the optimal situation deriving the optimal levels of effort, stock size and the number of

fishers. This equilibrium f ' l y takes into account the value of the fish resource to society. Secondly,

the chapter andysed an open access situation, the situation that prevails if no limits are set on the

exit or entry of fishers, and each bher can harvest as he pleases. This analysis has brought out

a striking result. For fisheries where the free market is left to its own devices, resources are not

allocated efficiently. There will be tao many fishen attracted to the fishery and each will use more

effort than is optimal. The reason is clear; one input-the resource itself-does not carry any price

to the fishers, even if it is of value to society. This gives rise to a market failure and any andysis of

fisheries must begin from this €undamental result.

Increased pressure on fish stocks is a serious matter from a conservation view point, but it is

not the only burden of excessive fishing effort. Since too much fishing effort is employed, economic

resources are being wastefuily used. In a free market, the opportunity cost of the fishing resource

is not fully taken into account by the users of the resource. This cost, represented in the current

model as A, measures the rent that should accrue to the owner of the resource; a rent often referred

to as resource rent. .As Gordon (1954) showed, hhers will compete for this resource rent with the

consequences that it is wasted through excessive use of effort. If fishers do not recognise the effects

of their fishing on the fish stock, then dl of this rent is dissipated. If fishen take the effect on the

stock into account, some of the rent will be reaiised by the fishers. However, the greater the number

of fishers, the less is realised.

From this discussion, two types of overexploitation do therefore exist; biological and economic.

Biologists consider any fish stock that is harvested at a level where the stock size is less than qlsy

to be overexploited, as the long-run harvest level could be achieved at larger stock size. Economic

overexploitation, on the other hand, occurs when the effort level in a fishery is larger than the one

that will produce the maximum resource rent. These two do not necessarily go hand in hand, but in the static case an economically efficient solution will never biologically overexploit the stock, while a

solution that does not biologically overexploit the stock may overexploit for an economic view point

(see e.g., Hartwick and Olewiler, 1998, p. 108).

The chapter has given the building blocks that dl be used to analyse the effects discardig have

on the various aspects of fisheries. It is mrth keeping in mind that, as stated above, this analysis is

comparing long-nin equilibria and therefore alI costs are variable. This also implies that there are

no costs of entry into, or exit from, the fishery.

In the discussion and analysis that foiio~s, 6shers wüi be assu~ned not to recognise the impact of

harvesting on the fish stock. As has been discussed above, this situation may well represent fishers

who actually know and understand this impact. As soon as the number of fishers begins to increase,


each fisher only has a minuscule effect on the overd üshery, thus behaving as not recognising stock effects. As most üsheries have a considerabte number of fishers, this case will give a reamnably accurate picture of the behaviour of fishers.

Chapter 3

Management in the absence of

discarding

In this chapter some of the possible management policies for fisheries will be analysed. For each

policy, three main issues will be discussed. Firstly, whether the policy is capable of bringing an

unregulated tîshery from the open access equilibrium to the optimal situation. Secondly, whether

improvements wiU be achieved by using the policy, even if it falls short of the socially optimal

situation, and thirdly, whether these policics are practical and what drawbacks and difficulties rnay

be expected in the irnplernentation of each policy. It must, nonetheless, be kept in mind that no two

fisheries are the sarne and it is not possible to cover al1 the possibilities that may arise. However,

a general analysis such as the one provided here will give good indications on what factors to keep

in inind when a management system for a fishery is being considered. The analysis still will not

include the pmsibility of discarding. The following chapters look at discarding in detail comparing

the discarding results with the results from the current chapter.

3.1 A historical backdrop

As long as the fishing capacity of the world's fishing fleet was relatively low, there was little concern

over the state of fish stocks. In fact, for a long time it was thought that the oceans had plentiful

and inexhaustible resources. As fishing capacity increased with improved technology, concern over

the state of fish stocks began to surface and the need to manage fishing for conservation purposes

was identifieci. Prior to that the limited management of M i n g that existed was done more for

economic and social reasons. Gough (1993) describes how England, France and Holiand set policies

to promote 6shing because their governments saw a link between a strong fishing fleet and the

growth of their empires. For instance, France was subsidising its fishing fleet as early as the 1700s.

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DISCARDING 25

Conservation objectives, however, were not a priority at all. There is the odd exception to this.

In Newfoundland, in 1876, in a modification to the Pallister Act, which was set 11 years earlier to

promote the development of a British fishery at Newfoundland, a minimum mesh size of four inches

was set in the groundfishery, apparently to allow small fish to escape. However, this kind of policy

was an exception, not the d e .

Eventually, governments began to realise that actions needed to be taken to curtail fishing effort.

In the 1800s fears of ovefishing and pollution were growing in Canada due to depletion in many

inshore fisheries (Gough, 1993). This lead to regdations on mesh size, gear type, and even time and area closures around the turn of the century. However, management of this type was testricted to

three miles from shore, since that was the limit of national fishing jurisdiction at the time.

It was not until the 1970s that goveniments began to take conservation actions in a serious way.

Canada was one of the pioneering nations in this respect. The management plan introduced in the

Salmon fisheries in British Columbia in 1968 was a bold and innovative initiative in thii direction

(Pearse and Wilen, 1979). Not only was the plan intended to address conservation, but also to

rationalise the fishery economically. In order to reduce effort a management system of limiting entry

and reducing vesse1 numbers through a buy-back scheme was implemented. However, thii plan was

eventually regarded as a failure, resulting in fishing capacity much higher than when the scheme was

put in place (Copes, 1990).

Even if governments were willing to take conservation action, the effect was insignificant in m a t

cases, since international waters began only twelve nautical miles from shore. The nurnber of fish

stocks that stayed within twelve mifes were relatiwly few. In 1972, Iceland declared a 50 miles

exclusive economic zone (EEZ), and only three years later increased its EEZ to 200 miles. This burst

the dam, and within very few years 200 miles EEZS had become widespread throughout the world.

This drastically changed the policy environment for fisheries management since many fish stocks now

fall under the national jurisdiction of only one nation as opposed to being in international waters.

However, it still took governments some time to act.' The European Union (EU), for instance,

did not take any conservation action to speak of, until the introduction of its Common Fisheries

Policy (CFP) in 1983, which sets national quotas for commercially important species that are fished

within the fishing zone of the EU. in addition, various measures have been adopted to curtail fishing

effort. However, the CFP is generally viewed as having failed in reducing fishing effort (e-g., Holden,

1994).

In addition to conservation, otber objectives, such as economic efficiency, have begun to play

a bigger role in policy discussions and decision. For instance, since the early 1980s, a number of

countries have introduced individual quotas as a management tool and as will be argued below,

the primary objectives of quotas are economic. New Zealand and Iceland control ail commercially

'For the interested reader, Parsons (1993) looks at select management issues in a few countries from a historical perspective and NRC (lm) looks at some more recent examples.


important fisheries in this manner, whiie countries such as Canada, Australia, Namibia, and others

use such quota systems to manage some of their fisheries. Individual quota systems are highly

controversid, some analysts declare them as a success, while others claim them to be failures.

3.2 Objectives of management

if fisheries are to be managed, it must first be asked what the purpose of management is. if it is

simply to prevent the extinction of k h species and ensure sustainability, then the only role of the

management authocity is to prevent overfishing. For instance, this could be established by deter-

mining the allowable catch of fish each season, and to enforce closure of the fishery once the limit

is reached. if, on the other hand, there are other objectives of managing fisheries, then such simple

management may not be sufficient. if economic efficiency is an objective, then measures need to

be put in place to somehow prevent dissipation of the rents that can be generated from a fishery.

Regional considerations often play an important role when fishery management objectives are consid-

ered. The nature of fishing is such that in many countries small remote communities depend heavily

on fishing as a provider of employment and income. Changes in fisheries management may have

enormous repercussions in such communities and consequently the welfare of fishing communities is

often a major consideration in the development of fisheries management plans. Different objectives

will lead to different effort levels and consequently different harvest levels. Cook and Copes (1987)

cdculate optimal harvesting levels for Canada's Pacific halibut fisheries using three different criteria;

maximising resource cent, maximising benefits for the harvesting sector, and mavimising social sur-

plus, where the social surplus includes consumers' surplus. Not surprisingly three different optimal

harvesting levels emerge, depending on the objective used.

Copes (1999), following previous work by Charles (1992)' points to three policy areas that need

government action in order for fisheries management to be optimal. The first is biological sustain-

ability, the second is economic efficiency, and the third is social equity. Copes calls for a balanced

approach where each of these three areas is given some weight. He points to the Newfoundland fish-

eries where for a long time the emphasis of management was to improve the social situation of the

Kewfoundland fisheries with a policy aimed at improving incomes and employment through various

grants and subsidies. This, Copes argues, lead to a fishery with too high effort levels resulting in

stock decline and harvest reductions, which in tum lead to reductions in income. Atlantic Canada

can dso provide an example of a fishery where economic efficiency became the primary target of

management policy. After the declacation of a 200 miles EEZ, individual quotas-called enterprise

quotas-were introduced in the Atlantic groundfish fishecies, giving priority to economic efficiency.

The result was disastrous. By 1992, groundfish stocks had collapsed leading to a closure of the

fishery with enormous adverse impacts on the communities in Atlantic Canada. Findy, Copes takes

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DlSCARDING 27

the example of the salmon fisheries in British Columbia where in 1998 a very large part of the k h -

eries was closed to protect coho stocks, a relatively minor part of the total salrnon harvest. This

conservation policy neglects the economic and social aspects of fishery and has lead to significant

codicts between fishers and the govemment; conflicts that tend to undermine the credibility of the

management authority.

One diculty facing policy makers that look at the three policy areas identified by Charles

(1992) and Copes (1999) arises from the fact that these objectives may lead to conflicting results.

For instance, an objective arising from social equity considerations rnight be to maximise empIoy-

ment in a particular region. However, an economic efficiency objective might require a reduction in

employment. These conflicts give rise to a multiple objectives approach where the aim is to give

a fair balance to each of the identified objectives. Examples of work using this kind of analysis

are Healey (1984) and Charles (1989). Mardle and Pascoe (1999) give a comprehensive revicw of

published research that applies a multiple objective approach to fisheries management.

Such alternative and sometirnes conflicting objectives have tumed some attention to cemanage-

ment of fisheries and community based management. The underlying assumption is that those who

have the most at stake will look after the resource in the best way possible. Under such schemes

the participants in the fisheries have a much greater influence on management, than under the

govertment controlled management systems that are dominant in mast of the western world (e.g.,

NRTEE, 1998). For instance, in Japan, fisheries have been managed on a community based level for a

very long tirne (e.g., Yamamoto, 1995). Anthropologists have recorded a large nurnber of community

b d management systems Gom al1 over the world. Wilson, Acheson, Metcalfe, and Kleban (1994)

review the anthropological literature and list 14 cases of coinmunity based management from various

countries. Pinkerton and Wcinstein (1995) look at ten case studies from a cernanagement point of

view, trying to isolate factors that lead to success or failure.

In this thesis, the social equity aspect of fisheries management will, for the most parts, not be

considered. The motivation behind the work camed out here, arose from claims that individual

quota systems lead to excessive discarding of fish. The analysis focuses on the effects that the

different management policies will have on the discarding behaviour of fishers, and vice versa. For

that analysis, the question of social equity is not important as it seems reasonable to assume that

fishers maximise their individual profits (e.g., Arnason, 1990). However, in parts of the thesis,

economic analysis is used to derive socialiy optimal situations. This has already be done in Chapter 2

for a situation where discarding is absent, and wiU be done again in Chapter 4 in the presence of

discarding. These socialiy optimal situations assume that the objective of the management authority

is to maximise economic returns from the fishery, subject to a sustainable harvest h m the 6sh stock.

In other words, the analysis includes the first and second poiicy areas identified by Charlez (1989)

and Copes (1999). Trying to expiicitly include social equity in this analysis muid not serve much

purpose, and have Little effects on the results. The mathematical functions used are of a very general


nature and could be manipulated to include some measure of social equity. However, as the definition

of social equity is likely to differ from one fishery to another, and from one country to another, it is

not obvious that including social equity will benefit the analysis. Nonetheless, social equity issues

are raised in some of the discussions in the thesis, since such issues will be of importance when it

comes to choosing among the policy alternatives provided here. Again, the purpose of this thesis

is to gain insights and understandimg of the factors that lead fishers to discard fish. These insights

will undoubtedly prove useful to fisheries managers and policy makers when developing management

policies in situations where discarding is a critical issue.

As just stated, the effects of individual quotas on discarding was the main motivation behind this

thesis. However, it is important to understand how other management alternatives affect discarding

behaviour. Therefore, a number of management measures will be investigated. These are the ones

typically suggested when fisheries management in the developed world is king discussed. Firstly,

two types of taxation are analysed; tax on effort and tax on landings. Secondly, managing a fishery

by limiting total allowable catch is looked at. Thirdly, restrictions on the effort level in a fishery

are reviewed, and finally, individual quotas are brought into the picture, both transferable and

nontramferable. Community based management schemes, on the other hand, will not be andysed.

These are difficult to generaiise, as they are normally "custom made" for the particuiar situation,

and therefore it is difficult to draw general conclusions from their analysis.

3.3 Taxes

Various forms of taxation in fisheries are possible (see e.g., Heaps and Helliwell, 1985). Only two

wiU be analysed here, taxes on the effort level in the fishery, and taxes on landings of fish. Without

discarding, these can both lead to optimal behaviour of fishers. However, once discarding is allowed,

the effects of these two tax types will be markedly different.

3.3.1 Taxes on effort

Since the open access situation leads to excessive effort, any management policy shouid a h to reduce

effort. One possible method is to make effort more costly by charging a tax on every unit of effort

used. For instance, a fisher might be required to pay a tax based on engine size, or the hoid size

of the fishing vessel. Also, the days a vessel stays at sea could be taud, or the time fishing gear

is kept in the water. Any dimension of effort that can be measured could be taved in this manner.

Disregarding any measurement and enforcement difficulties for the moment, the 6sher will have to

pay a tax, t i i , on each unit of effort used. Note, that the tax rate may differ among fishers. The

maximisation problem is now:

In this case a new cost term has been added to the profit function of the fisher. This term, &ei,

measures the total tau bill of the fisher. The first order condition for the individual fisher is given

by = phei (ei; X) - cf, (e', y') - cii(ei, y ' )hei(ei ;~) - tf, = O (3.2)

Rom comparing the first order condition with a tax with the first order condition in the open access

situation (equation 2.28), it is straightforward to see that each fisher will use less effort once an effort

tax is introduced. With the tau, each effort unit is more expensive than before. .4t the open access

effort level marginal cost is now higher than marginal benefit, due to the tax, and effort must be

reduced to equate marginal cost and marginal benefit. Alternatively, it c m be said that fishers will

lower effort in order to avoid payments of some of the tax.

By comparing equation 3.2 with the optimal marginal effort condition (equation 2.19) a candidate

for the optimal tax is

t:, = Me, (ei; z) (3.3)

edua t ed at the socially optimal effort and stock levels. It is worth noting, that if fishers are

heterogeneous then this tax will differ among them. That is, a uniform tax rate on effort will not

lead to an optimal fishery. Low cost fishers should use more effort than high cost fishers (see page 13),

imptying a lower hei for low cost fishers. Thus, they will face a lower tax rate than high cost fishers,

if the fishery is to be optimal. By substituting t5, into equation 3.2, it becomes

which is identical to the sociaily optimal marginal effort condition, as given by equation 2.19. Thus,

if the stock size is correctly chosen, each fisher will use the socially optimal effort level.

In order to analyse the effects from a change in the tax, write the tax as

where r is a coefficient that measures tax changes and t' can be thought of as a basic ta.. rate on

fisher i. If r = 1 then the tax rate of each fisher simply equals the basic tax rate, while r = 1.1

indicates that the basic tax rate has been increased by 10% for everyone. Rewriting the tax in this

form dlows straightforward comparative statics of tax changes even with diiTering ta . rates among

fishers. This changes the marginal effort condition, as given by equation 3.4, slightly as the last

t e m now becomes di. To analyse the effect of a change in r the adjusted marginal effort conditions

for al1 n fishers need to be considered, dong with the overall stock constraint. The relevant n + 1

equations are therefore

R: = phci (ei; X) - ci, (e', y') - ce, (e', yi)h,i (ei; X) - rt' = O V i (3-6) n

0(e1 ,...,en,=) = F(x) - x h ( e i ; z ) = O (3.7) i=l

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DISCARDiNG

Differentiating these equations with respect to the effort of al1 fishers, the stock six, z, and the tax

coefficient, T, the resulting equation system can be written in matrix form as

where

and

In order to satisfy the second order sufficient conditions for a maximum, n:,,, must be l e s than zero

for al1 fishers.

The coefficient matrix of equation 3.8 is nothing but A from quation 2.32 above, whose deter-

minant was found to be negative if n is an even number, but positive il n is odd. Denoting the matrix when the last column of A has been replaced with the RHS vector, as A,,

its determinant can be shown to be

< O if n even

i= 1

Using Cramer's rule,

which indicates that stock size will increase as the tau is r a i d . Introducing an effort tax into an

open access Fishery will therefore lead to better conservation of the stock.

Above, it was said that the eilort level of the individual fisher would decrease following an

introduction of an effort tax. This can be verified formaily. Replacing one of the first n columns of

A with the RHs vector, the resulting determinant is2

> O if n even

< O if n odd

Again using Cramer's d e ,

*III the caiculations multiplicative separabiiity of the harvesting Function (see page 10) is invoked to get

t'&, - ti<,= = Ah,,h,i -Ah,.h,j = O

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DlSCARDING

implying that the effort level of the individual fisher is reduced as the tax is raised.

However, for the stock to reach the socidy optimal size, not only must each fisher be using the

optimal effort level, but also the number of fishers must be correct. The condition that determines

the number of fishers is to find the fisher that has minimum average cost equal to the marginal

benefit of fishing. If the tau is chosen according to equation 3.3, this condition can now be shown to

be

i c n 5 p - A < icn+' (3.15)

which is exactly the sarne as the condition for the socidy optimal case, as given by equation 2.24.

The implication is that a correctly chosen effort tax leads to an optimal fishcry. When compared to

the open access equilibrium, the tax leads to the exit of some high cost fishers, while at the same

tirne reducing the effort of each individual fisher that rernains in the fishery. The end result is that

effort is reduced to its efficient level, while the stock size increases to its optimal level, as well.

Obviously, fishers that exit the fishery due to the tax are worse off from the introduction of the

tax. However, it is of interest to analyse whethet the fishers that remain in the fishery are better or

worse off as a consequence of the tau. Keeping in mind equation 3.5, the effect the tau has on the

profits of the individual fisher can be found by diflerentiating equation 3.1 with respect to effort, the

stock size, and the tax coefficient. Alter some rearranging, it is found that

but from the first order conditions ( p - 7)hc. - cl, - rti = O, so the impact a tau increase has on

profits is given by

This equation States that when the tax is increased, two effects need to be considered. The first is

the 105s in profits due to the i~crease in tax payments for each unit of effort. The effort effect will

aiways be negative, lowering the profits of the fisher. The second effect is the stock effect, due to

the increase in stock size that lollows the tax rise. Since (JI -y), h,, and ûzlâr are ail positive, the

stock effect is always positive. Since the two effects counter each other, it is not possible to Say, in

general, what the overall effect on profits is. However, it is possible to use a graphical anaiysis to

understand better the effects a tax will have on the profits of fishers.

As was argued above, the tax leads to a decrease in the number of fishers. Looking at the new

marginal fisher, it is clear that that individual is worseoff than before. Prior to the tax increase, this

fisher was making some intramargind profits, but in the new equilibrium he is making zero profits,

since he is now the marginal fisher. This is shown in figure 3.1, where fishers are ranked fiom the

highliner, making the largest profits, to the marginal fisher, making zero profits. For illustrative

purposes, the profit curve is assumeci linear. The profit curve prior to the tau increase is r(f'ti),

where no indicates the marginal fisher making zero profits. Total profits are given by the area Onor0.


When the tax coefficient is increased fiom r0 to r1 the number of fishers falls to ni and a new profit

curve resdts. Two possible curves are shown in the figure. Firstly, rH(r'ti) shows the case of high

profits, where the marginal fisher is clearly worse off than before. However, fisher n . ~ is just as well

off as before; the tax has not affected his profits. Every &her to the left of nz is better off, while

every fisher to the right of nz is worse off. Whether the total profits are higher or lower depends

on the relative size of the profits in the two goups. The second possible profit curve is given by

rL(rLt'). In that case the new profit curve is everywhere below the old profit curve and al1 fisbers

are worse off than before. As stated above, this second will apply whenever stock siza is geater than

W S Y .

Fishers

Figure 3.1: The effect on profits from a tax

If the stock is biologically overexploited, some fishers may experience positive profits. However,

the more fishers participate in the fishery, the smaller is the stock effect, h,, for the individual fisher.

Thus, it can be specuiated that in cases where there are many fishen, overaii profits wiIl fdl when

taxes are introduced. In that case the effort tax makes remaining fishers worse off than in an open

access situation with no t a , by reducing their producer's surplus. Even if the stock effect is high

enough to increase profits of some fishers, it will take some time before that effect cornes into action.

Depending on the fish species, increases in the size of the stock may take considerable tirne, while

tax payrnents will be felt immediately by fishers.

The end result is that a tax on effort can lead fishers to use the optimal level of effort. The

size of the fish stock will increase to the optimal biomass size, as effort falls from the open access

level to the optimal level. Rent is generated in the tishery, however, the government collects it and

unIess transfer payments are introduced, ikhers wiii not benefit fiom the collection of thii resource

rent. In fact, many, or even dl, fishers will be worse off, with a reduction in profits resulting from

the ta.. In order to address this problem, it would be possible to introduce lump sum payments

where each fisher is compensated for his tax payments. This would not have any impact on the

k t order conditions or the entry condition, leaving the fishery optimal and the fishers as well off as

before. However, another problem with the tax is that unernployment undoubtedly increases when

effort is reduced. Once the tax is introduced, high cost fishers will find it unprofitable to continue

fishiig and will withdraw €tom the fishery. This is represented by no - nl in figure 3.1. From an

economic point of view, this is beneficial, since the least efficient fishers are removed from the fishery

and more efficient fishers rernain. Rom a political standpoint, on the other hand, it now becornes

critical whether other labour markets are present that can absorb the reclundant fishers.

Even if in theory effort taxes may seem promising in terms of rationalising an open access fishery,

there are serious practical problems with these types of taxes. Effort has many different dimensions

and it is practically impossible to tax them dl. If only some dimensions of effort are taxed and if any substitution is possible among the different effort dimensions, then fishers will substitute away

from the taxed dimensions, thus lowering their tax payments and increasing effort.

Another diffculty arises in a fishery with heterogenêous fishers. From equation 3.3 it can be

seen that fishers should be taved at different rates when heterogeneous. If the optimal tau can be

determined for each kher-a difficult exercise, indeed-this is likely to create an administrative

nightmare, apart from the political difiiculty of justifying diflerent taxes on different fishers. High

cost fishers have lower profits than low cost fishers to begin with, and a differential tax rate will be seen to be very unfair toward fishers that are already facing difficulties.

3.3.2 Taxes on landings

Since the common pool problem of fisheries is driven by the fart that one input, the fish resource, is

not priced in a market, a possible option is to generate such a price by tming the amount of catch

harvested by khers. The tax is effectively the unit input price that a fisher must pay to use the

resource. From a practical point of view, monitoring the actual harvest of fish may be very costly,

since it requires on-board monitoring, while, in most cases, monitoring the landings of fish wiil be

a cheaper alternative. Of course, if fishers discard at sea, landings will differ from actual harvest,

but more on that later in the thesis. The management authority sets a tax, t,, on each unit of fish

landed, and for the time being landings are assurned to qua i harvest. The individual fisher will now

want to maximise the following profit function:

The effective price of fish to the ûsher is now (p - t,). The fisher chooses the effort level that

maximises profits. The first order condition for maximisation is

. . . x:, = ( p - tg)he . (e i ;x) - c:.(et, y') - cii (e', y ' ) h , i ( e ' ; ~ ) = O V i (3.19)

When this condition is compared to the comparable first order condition in the €ree market situation,

it is plain to see that if the individual M e r is operating at his free market equilibrium effort level

when the tax is introduced, marginat benefit of effort will no longer be equd to marginal cost. Since

the Esher receives a price for the 6sb that is efktively tower, marginal benefits have fallen, and

profits cari be increased by lowering effort. When effort is reduced, the marginal l o s in terms of

revenue from foregone effort will be less than the cost savings of reducing effort. Each h h e r will

therefore reduce efiort as a consequence of the landings tax.

To analyse the effect on stock size, a similar mercise as with the effort tax can be undertaken.

For equilibrium, the first order conditions for al1 n fishers must hold simultaneously, and it must

also be true that hrtrvest from the stock equals net gowth. Differentiating al1 these equations with

respect to al1 e's, 2, and t,, results in

where

which rnust be negative for dl i to satisfy the second order suficient conditions for maximisation,

and

T : , ~ = ( p - Y - ty)h,i , V i (3.22)

which, from the first order conditions, must be positive.

The coefficient rnatrix is bemming familias, yet again being the matrix A from equation 2.32.

Its determinant has a negative sign if n is even, and a positive sign if n is odd. The determinant of

A,, in this case, can be shown to equal

and Cramer's rule can be used to show that

which impiies that an increase in the landings tax leads to a higher stock size. That means that a

landing tax will dways have a conservatory effect.

Cornparison of the sociaiiy optimal marginal effort condition for each fisher and the componding

condition with a tau, reveals an optimal tax rate of

CHAPTER 3. MANAGEMENT LN THE ABSENCE OF DISCARDING 35

If the tax is set equal to the shadow value of the stock, corresponding to an optimaily operating

fishery, then the marginal effort condition of each individual fisher is identical to the socially optimal

conditions. One notable difierence from the effort tax is that, even with heterogeneous bhers, the

landings tax should be equal across fishers. This reduces much of the administrative nightmare of

effort taxes.

However, it is not sufficient that each fisher behaves optimally. The total number of 6shers is

also important. Looking a t the effect of an optimally chosen landings tax, once the tax is introduced,

the number of fishers wiil fall to the optimal number. Some high cost fishers will incur losses and

subsequently exit the fishery. The condition that determines the number of fishers is the same as

with the effort tax, i.e.,

,Ccn sP-x < ,\cn+' (3.26)

which is identical with the socially optimal condition as given by equation 2.24. The correct number of

fishers, each choosing the socially optimal amount of effort, will lead to a stock lcvei that corresponds

to the social optimum. Notice, however, that some unemployment will be c a d , since the number

of fishers is reduced. It is also likely that the remainirig fishers will be worse off than without the

taxation. Differentiating the profit function with respect to effort, stock size, and the tax, resuits in3

where the effect on profits, of one dollar's increase in the tax, cornes from two sources. The first, is

the reduction in profits due to the actual increase in tax payments, which could be called the payment

effect. The second effect arises from the stock increase that wiil result from the higher tau. That

leads to each effort unit being more productive and consequently the stock effect is positive. Since

the two effects counter each other, it is an empirical question for the fishery in question, whether

the stock effect is large enough to outweigh the payment effect. As was the case with effort tax, the

more fishers there are, the smaller will h, be for the individual fisher, reducing the weight of the

latter effect, and the more likely it is that profits fall with increased taxation.

'Differentiatir~~ the profit function and rearranging gives

Rom the first order conditions, @ - cui - t ,)h,, - c:, = O, so the equation collapses to

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DISCARDING

3.3.3 Overview of taxes

It is rare to see taxes used in fishery management with the purpose to collect resource cent. One

reason is that to find the optimal tax, considerable information is needed (Xrnason, 1990). The

management authority needs to know benefits and costs functions for al1 6shers participating in the

fishery, in addition to biological growth functions of the k h stock. However, Cunningham (1994)

argues that objective hinctions, such as social welfare functions, are ohen flat-topped, which means

that the difference between a socialiy optimal situation, and a close approximation will be very

small. if this is correct, then a tax that is approximately optimal may well yield social benefits very

close to the optimal ones. However, in a fisheries situation, one qualification must be made to that

argument. Even if a flat-topped function leads to only small changes in benefits, changes in effort

may be considerable. Thus, a tax that is slightly below the optimal one might lead to an effort level

much higher than the optimal effort level. In this case, it must be evaluated whether high monetary

benefits outweigh the conservation objective.

Another, and probably more important, reason why taxes are rarely used, is that often an

objective of the management authority is to improve incomes of fishers. in that case it may be

very difficult to justify added taxation on the people whose income the aim is to improve. Also, an

extra tax on one sector of the economy, whiie not txcing other sectors similarly, may be politically

unjustifiable.

Even if the two methods of taxation presented here, can in theory both lcad to optimal resulu,

there is one important difference in case of heterogeneous fishers. While fishers will be taxed a

uniform landings tau rate, the effort tax will differ among fishers. As discussed earlier, this gives rise

to various difiiculties of implementing an effort tau. In addition, a landings tax is much casier to

monitor than an effort tax. Landings records are collected in rnost fisheries, while eflort is a much

more difficult concept to measure and monitor.

One final thought on taxes, arising from the effect that h, has on profits. In a fishery that is

severeIy ovefished, from a biological point of view, some form of taxation might be a very effectix

tool to rationalise the fishery. Imagine a fishery where the management authority wants to cut effort

ievels significantly. One of the difficuit questions is what fishers should be aliowed to continue in

the hhery. A tax would assist in making that decision for the management authority. Let's assume

that a landings tax is imposed and licenses are issued to al1 the incumbent hhers. With the new

tax many fishers wiii undoubtedly find it unprofitable to fish and would like to leave the fishery.

Most likely these will exactly be the high cost fishers that the management authority would Iike

to remove in the first place. The authority could, dong with the tax, offer an attractive buy-back

scheme and permanently retire the Licenses bought back. The benefit of such a plan is that Gshers

that retire could accept leaving the fishery if compensated through the buy-back. The tax revenue

could be used to fund the buy-back sche~ue so that other sectors of the economy are not burdened

with extra payments. Fihen that remain, d l benefit if the stock is productive enough to outweigh

the loss due to effort reductions. However, as will be discussed below there are various pitfalls that

can undermine the success of such a scheme.

3.4 Restrictions on catches and entry

The most widely used tools in fisheries management are to restrict catches and to limit entry of

fishers into a fishery. It is, in fact, hard to find examples of commercially important fisheries that

do not have either or both of these restrictions. Usually catch restrictions take the form of a total

allowable catch (TAC) set by the management authonty. Once total harvest reaches the TAC, fishing

must stop. The level of the TAC is usually based on advice from fishery biologists. Traditionally, the

aim has been to maximise sustainable harvest from the fishery and thus the TAC is set at a level that

brings the fishery to the MSY stock size. However, it is important to see what setting a TAC does in

terms of efficiency and for the collection of resource rent.

Limiting entry is an effort restriction. The idea is to set the number of fishers at a level that

corresponds to the optimal effort level in the fishery, and prevent increases in effort through inflow

of fishers. Other effort restrictions are often used in conjunction with limited entry and will be

discussed below. First, however, the attention turns to catch restrictions.

3.4.1 Total allowable catch

Since overexploitation of fish stocks is the result of harvest rates that are too high, restricting harvest

is a potential remedy. If the reason for overexploitation is seen to be fishers not recognising the impact

on harvesting on stocks, then by restricting harvest, fishers are forced to take the stock into account.

For this purpose a TAC is imposed. When a fishery is controlled by a TAC, the management authority wants to set the TAC in the

fishery that is consistent with maximisation of the value of the Bshery to society. The problem can

Here, the role of the constraint is to ensure that total harvest does not exceed the TAC. The management authority wants to set TAC = F ( I ) , where ? is the sociaiiy optimal stock level. Substituting

in for TAC, the Lagrangian to be maximised is

CHUTER 3. MANAGEMENT IN THE ABSENCE OF DISCAROlNG

and the corresponding tirst order conditions for maximisation are

It is clear, that if the TAC is, in fact, chosen equal to F(%) in equation 2.18 then the first order

conditions here are identical to the ones given by the socidy optimal situation (equations 2.16-

2.18). Consequently, the eflort level, stock size, and shadow d u e tbat maximise the value function

are the socially optimal ones. However, if the TAC is chosen incorrectly, then the values of e l , . . . ,en,

2, and A that maximise equation 3.28 will not be socially optimal.

if the TAC is enbrceable, then any womes about conservation should disappear. However, even il the TAC is chosen correctly, the management authority faces a problem regarding economic efficiency.

If the fisher is operating at the effort lewl that maximises the d u e of the fishery to society, the

individual marginal effort condition will not hold. That is to Say,

phci (el; X) > c:,(ei, y') + CL, (e', IJ')~,, (ei; z) (3.34

because X = O for the individual fisher. Each fisher will now have an incentive to increase effort,

because the individual benefits of doing so outweigh the costs. But, if the TAC is al1 being taken

at the current effort levei, how can an individual hher increase effort? if it is kept in mind that

management by a TAC sets no restrictions on the harvest of an individuai fisher, it is clear that by

being ahead of the other Mers, one individual fisher can increase his share in the total harvest in

the fishery. This can be done, for instance, by increasing the hold capacity of a vessel, in order

ta catch more each trip. Altematively, the fisher could instdi a more powerful engine to be able

to make, Say, four trips to the iïshing gounds, while other hhers only make three trips. What is

being described here has been called capital or input stusng. The fisher is increasing the capacitg of

hi vessel in an unproductive manner, since resources are used to increase capacity beyond what is

needed to harvest the TAC. Consequently, costs in the fishery are increasing, dissipating any resource

rent that is created by the catch restrictions. Any fisher that decides not to participate in capital

stuffing, wiIl be left out in the cold with an ever decreasing share of the TAC.

In addition to the individual increase in eftort, more fishers d l be attracted to the fishery than

is sociaiiy optimal. Remember, h m equation 2.24 that the optimal number of fishers is determined

by the condition

i i n 5 - x < icn+' (3.35)

which says that the marginal ûsher has minium average cost equal to marginal revenue. However,

fishers do not consider the shadow value of the stock. Hence, fishers will enter until the minimum


average cost of the marginal fisher is given by ph,i which is higher than the minimum average cost

in equation 3.35. As a result, more fishers, than is socially optimal, will find it profitable to enter the

fishery. Clark (1980) gets to the same conclusion and, additionally, in his analysis he uses a seasonal

mode1 which suggests that the fishing season ni11 become shorter through increased entry of fishers.

To summarise, if a TAC can be enforced properly, then it will meet any conservation objective that

might be set. However, from an efficiency standpoint, any potential resource cent wili be dissipated

through increases in cost arising from the excessive competitiveness in the fishery.

3.4.2 Effort control

A management authority looking at the benefits and costs of a TAC control, might decide that since

effort is the variable that goes out of control, effort shouid be the focus of management restrictions.

In fact, this is a very common management instrument. However, effort can be restricted in many

ways. Common measures are to restrict the number of fishers, the number of days fishing is allowed,

length of vessels, hold capacity of vessels, engine size, gear type, minimum mesh size of nets, and so

on and so forth. The complexity of effort is, as a matter of fact, the main reason why effort control

typically fails to work. The attempt by Smith and Hanna (1990) to measure fleet capacity in the

Oregoii bottom trawl fishery highlights some of the difficulties of measuring effort.

Setting aside any problems that may arise, the idea behind effort controls is very simple. The

management authority sets a maximum effort level in the fishery equal to the sum of the individual

effort leveb that solves the social maximisation problem as given in equation 2.13. If this total effort

level can be enforced, then net benefits from fishing should be maximised. However, even if this

optimal total effort level can be determined, difficult problems face the manager of the fishery. The

first one is how to divide effort among fishers. If al1 fishers are identical this is not a major problem,

as each fisher will be allowed the same amount of effort. If fishers are heterogeneous, on the other

hand, the problem is much more difiicult to handle. As was explained in Section 2.2.1, effort should

be divided in such a way that marginal costs from effort are equal across fishers. With many fishers,

determining the optimal individual effort level requires substantial information, and enforcement

and monitoring is l iely to create a considerable headache for the management authority. Even with

identical fishers, there is still one difficulty that may arise. If fishers have the traditional Ci-shaped

average cost function, then the number of fishers is important, even if they are al1 the same. This

means that some fishers must be rernoved fiom the fishery. But which ones? From an efficiency point

of view, it does not make any difference, since they are di identical. However, in a real life situation

this decision may be very difficult to make. This may be possible through a buy-back scherne where

fishers are awarded compensation for leaving the fishery. It is likely that the least efficient fishers

wilI be the ones that accept the buy-back offer. However, for the buy-back to be successful, the

government must make sure that the retired effort is not brought back into the hhery-

A second problern arises hom perverse incentives for fishers. Assume that the optimal effort


has been calculated for each hher. -4s in the case of TACS, a t the socially optimal effort level,

marginal revenue will be greater than marginal cost for the individual fisher (see equation 3.34).

As a consequence, fishers will want to increase their effort levels, if a t ail possible. if the effort

restrictions are simple, such as restricting the nurnber of vessels, they may be easy to monitor, but

in al1 Likelihood simple restrictions are ineffective in restraining effort. AS has been said above,

fishing effort is a variable with many dimensions. As long as the marginal revenue of effort is

greater than marginal cost of effort, fishers will look for ways to increase effort dong dimensions

that are not restricted by the government. For instance, iE the number of vessels is restricted, fishers

may circurnvent that by increasing the size of their vessels or by increasing the nurnber of fishing

trips, In this way the effective capacity of the fleet is increasing, i.e., effort is rising. Consequently,

harvest becomes too high and stock size fails often leading to shorter seasons (Clark, 1980). Pearse

and Wilen (1979) explains how this exact behaviour contributed to the failure of the limited entry

licensing system in the Pacific sdmon fisheries off the West Coast of Canada. Another contributing

factor to the failure of this management system was that the buy-back that was to accompany the

effort restriction did not work as planned. Transferability of licenses dong with expectations of high

profitability in the future lead to increasing value of licenses which eventually lead the government

to cancel the buy-back programme because the government could not pay the nigh prices demanded

for licenses (Copes, 1990).

The difficulties in restricting effort can hardly be overstated. As long as substitution is possible

among effort dimensions, effort controls are likely to fail, both Gom a conservation and an economic

perspective. To model this properly an explicil knowledge of the cost functions in the fishery is

needed (Clark, 1980). The worst consequence of effort restrictions is that fishers often increase

capacity in cost ineffective ways! For instance, where length restrictions have been imposed, vessels

have been made much wider, at a considerable cost and often compromising the safety of the vessel.

Monitoring effort restrictions is often difficult, and complicated evcn more by the fact that effort

changes that are cost reducing should be allowed, since they will decrease the social cost of fishing.

However, this requires that the management authority can diitinguish between effort changes that

are cost efficient, and effort changes that are ody capacity improving. The fact that most cost

efficient effort changes are also capacity improving magnifies the monitoring difficulties.

3.5 Individual quotas

Controlling harvest and restricting effort are both part of what have been called command-and-

control instruments. Such instruments are restrictions set by the management authority that must

be foilowed. With command-and-control instmments no incentive exists for the fisher to adhere

"Casual browsing through publications such as Fishing News International will support this assertion.

to the instrument; it is a restriction supported by legislation. In fact, in most cases of command-

and-control instruments, the fisher has an incentive to cheat. As seen above, harvest and effort

restrictions lead to situations in which the marginal benefit for the individual fisher to harvest more

6sh is greater than the marginal cost. Thus, the fisher has an economic incentive to circumvent the

regdation, if possible. The alternative to command-and-control are market based instruments, of

which taxes are a subset. Market based instruments aim to change the economic incentives faced by

fishers in such a way that they behave in a manner that is consistent with the social optimum. The

objective is to intemalise the edemality caused by the missing market price of the fish stock. The

difficulty with taxes is that their level needs to be determined exogenously by a government agency,

and they do not change automatically with changes in market conditions. Aiso, with heterogenous

fishers, different tax levels may be needed to ensure efficiency. This requires much information, and

monitoring and enforcement costs are likely to be high. Over the last 15-20 years management

systems based on individuai quotas have been developed and introduced in a number of countries

(NRC, 1999). This management system is seen by many as a promising candidate to rationalise

many fisheries, both in terms of conservation and efficiency.

Individual quotas (10s) are an attempt to create property rights over a common property resource.

X two stage process is involved. First, a TAC is determined for the fishery in question for a given

scason (usually one year), and then the TAC is divided among fishers. Total harvest may not exceed

the TAC which is equal to the sum of the individual quotas. The overall constraint given by the

quotas is

where Q' is the quota allocation of the i-th fisher. Each fisher can harvest his own allocation as

he pleases, as long as it is done within the relemnt time period. Once the fisher has finished the

allocation, be must stop fishing, even if other fishen have not begun harvesting their quotas. Each

fisher bas ownership over his quota in the sense that no other fisher can harvest his ailocation.

This new property right should reduce significantly the incentive that a fisher may have for capital

stufing. There is no reason for the fisher to harvest the quota in any way that is not cost efficient.

The individuai fisher has a fked arnount of fish that can be harvested and consequently he will want

to land that quota at the lowest cost possible. Of course, a fisher wiii also try to get as high a price

as possible for the quota resulting in the fisher landiig fish of the highest quality possible. 'Ik-ying

to reduce costs and increase value is possible due to the assurance that the fisher has regarding the

quantity to be harvested. It must, however, be kept in mind that fish harvesting is a complicated

operation and the profitabiity often depends on the behaviour of fish stocks. The fact that fish are

not evenly distributed in the ocean may result in certain fishing grounds being more productive than

others. In such cases, fishers will try to fish in the most productive grounds and this wiii lead &hem to engage in capital stuffing, for instance to ensure that they are able to reach the fishing grounds

ahead of others. Such behaviour will not disappear under an IQ system (e.g. Boyce, 1992).

Notice, that as long as the TAC is enforceable, sustainability is assured. The IQS, per se, are not

a conservation management tool, but a tool to generate resource rent in the fishery. Even so, there

are instances where an IQ system will lead to improwments in conservation. For instance, Casey,

Dewees, ïùrris, and Wilen (1995) document how the derby style halibut fishery in British Columbia

resulted in significant quantities of long l i e gear being left or lost on the fishing grounds leading

to unmeasurable amounts of ghost fi~hing.~ Apart from the adverse effects on the fish stock, this

wasted economic resources since valuable fishing gear was lost to the fishing operators. Once an rQ

system had been introduced in 1991 there was no incentive to rush the fishing and consequently the

practice of leaving fishing gear behind has ceased.

One of the more controversial aspects of ip systems is whether quotas should be freely transferable

or not. Most economists tend to support transferabity (e.g., Hannesson, 1993). If quotas are

transferable, then more efficient fishen can buy quotas of less efficient fishers, resulting in Pareto

improvements. However, some concern has been expressed over the consequences of transferability.

Firstly, when a new IQ system is put in place, quotas are usually allocated to incumbent khers

without payments. This first generation of quota fishers can therefore gain considerably by selling

the quotas; a gain that subsequent generations can not achieve (Copes, 1986). Secondly, there are

worries about concentration of quotas. The argument is that if only very few people own quotas

they can take advantage of that, by renting out quotas at a very high price (Anderson, 1991).

The concentration argument is also a more general concern of a situation where a monopoiy or

monopsony situations may result from an increased market share. Thirdly, concerns have been

raised regarding the effects of quota transfers on small fishing communities, in particular, what will

happen in instances where fishing communities are left without any quota (Eyth6rsson, 1996). The

opportunity costs of fishers in small khing communities rnay often be very low and at the snme time

they may not have access to funding to purchase quotas. Because of these concerns, the analysis of

IQ systems will be twofold in this thesis; first the case of non-transferable quotas will be investigated,

and then quotas will be made transferable to analyse the difference.

Like any other fishery management system, tqs are not without problems. One of them is

discarding which is the focus of this thesis. These problems are discussed further below.

3.5.1 Non-transferable quotas

The management authority sets a TAC in the fishery and each fisher receives an ailocation of 4'. Given his allocation, each fisher maximises profits as given by

'Ghost fishing refers to the fact that lost fishing gear di continue to catch fish, inaeasing the mortality of the fish stock.

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DlSCARDING 43

The fisher is assumed to behave as the fisher from above, not recognising the impact harvesting has

on the fish stock. However, the fisher now faces a quota constraint that limits his harvest possibilities.

The Lagrangian of the constrained maximisation problem is

where pi is the Lagrangian multiplier associated with the quota restriction. It measures the shadow

value of quota, i.e., how much the profit of the fishers would increase if given an additional unit of

quota. The first order conditions for a representative fisher are

Cf, = phci (ei;z) - cf,(ei, y') - c:,(eil yi)hem (ei;z) - pih,.(ei;z) = O (3.40)

c:, = ,ji - h(ei;z) = O (3.41)

If the TAC is set to equal the optimal harvest level, then it is possible to allocate quotas such that

pi = A. In that case, this fishery will be operating a t the efficient level, provided the optimal number

of fishers has been allocated their optimal amount of quota. If dl fishers are identical, then, if the

optimal TAC is known, it is easy to find the optinial allocation of quotas, once the correct number of

fishers is known; simply give every participating fisher the siune quota, Le., 4' = ~Ac/ri. However,

if fishers are heterogeneous, the optimal allocation becomes more complex. If everyone receives the

sarne amount of quota, the shadow values of quotas will be different among fishers. This implies

that the fishery is inefficient, as it would be possible to increase profits by reallocating quotas. This,

again, is the farniliar condition of marginal costs having to bc equal across al1 fishers for efficiency

to be achieved. For efficiency, in a heterogeneous fishery, it is necessary that different fishers receive

different allocations from the TAC. Determining optimal allocations d l undoubtedly be difficult and

costly, and the cost increases with the number of fishers. An additional problem is that the number

of fishers must also be reduced to reach an optimal fishery. Deciding which hhers are to be left out

in the cold is a very hard decision indeed.

However, even if quotas are not allocated optimally, some resource cent will be generated. This

can be seen from the marginal effort condition (equation 3.40). As long as p' has a positive value,

marginal benefits faIl from ph,. to @ - pi)h,i. As a consequence, the fisher will reduce effort. Now,

fishers value the fish stock, through their quota holding. At the open access effort level the marginal

cost of effort is higher than the marginal benefit. Reducing effort will lead to a l o s in revenue, but

these wiii be more than outweighed by cost savings, giving rise to the generation of resource rents.

Different from the t a situation, the fishers wiii capture these rents, as long as quotas are handed

out for free. Notice howewr, that the fishery may not be efficient fiom a social point of view, since

marginal casts rnay M e r across fishers and further efficiency gains could be made by re-allocating

quotas.

The number of fishers is determined endogenously in a transferable i~ system. The initial

allocation is unlikely to create an equiiibrium situation and thus room from gains from trade exists.

In a fully transferable iq system there are no restrictions on quota transactions; some fishers with

quota aliocation may want to leave the iishery, and consequently sel1 al1 their quota, whiie some

people outside the hhery may want to enter and buy quota. The nurnber of participating fishers

is determined in the sarne rnanner as in the previous discussion, Fishers will enter as long as their

marginal benefit is a t least equal to their minimum average mit. in a transferable IQ system, fishers

will enter until

icn 5 p - a < icn+' (3.48)

Whether the optimal number of fishers participates in the fishery, depends on the TAC setting of

the government. If TAC = F(Z) , then a will equal the optimal shadow value of the stock and

equation 3.48 then is identical to the optimal condition for entry, as given by equation 2.24. If, on

the other hand, the TAC differs from F ( f ) , then the number of fishers will not be correct, and the

tishery will not operate in the socially efficient manner.

It is, however, worth noting that a transferable IQ system will lead to an economic efficient solu-

tion given the size of the biomass. Regardles of which TAC the government sets, the transferability

of quotas will lead to a fishery where marginal cost of effort is equal across fishers. Once equilibriuni

is reached, each fisher will have the same shadow value of quota (equal to the quota price), so

This irnplies cost cffectiveness in the fishery, where quotas are allocated in such a way that niinimises

the cost of fishing, given the TAC. This is the most significant difference between a non-transferabie IQ

system and a transferable one. With non-transferable quotas, the initial allocation must be efficient,

if efficiency is to be reached, while the initial allocation is irrelevant from an eficiency standpoint

when quotas are ttansferable.

3.5.3 Criticisms of individual quotas

Economists tend to like individual quotas, for various reasons. First of d l , 10s are an attempt at

creating a market, where one is rnissing. [TQS generate rights for access to a common pool resource,

and create market signals, through a new price for the property, that fishers respond to. As a

consequence, resource rent tends to be generated. This property right approach is considered more

desirable than setting taxes, whece the governent must constantly monitor the industry in order

to set the correct tax level. Secondly, a system of rqs can theoreticaüy support any allocation of

weaith that is deemed desirable (.bason, 1995a). This can be done through the initial allocation.

\Vhoever it is decided shodd gain h m the 6shery, can do so if diocated a quota. in theory, quotas

can be given to anyone, who then must decide whether to harwst fish or sel1 the quota. in practice,

CHAPTER 3. MANAGEMENT IN THE ABSENCE OF DlSCARDlNG 46

however, it will be difficult to allocate quotas to people that are not actively fishing and subsequent

generations will almost certainly be left out. Thirdly, studies have shown that fishers tend to take

better care of the catch once an IQ system is implementeà, in order to fetch a higher price for the

catch (Dewees, 1989). Fourthly, safety seems to improve in rq fisheries. When a certain harvest is

guaranteed, there is less rush and haste. For instance, if the weather is bad, fishers will wait until

the weather gets better, rather than compromising the safety of vesse1 and crew (Casey, Dewees,

Turris, and Wilen, 1995). However, safety might be comprornised if owners of fishing vessels try to

cut costs, for instance by overloading vessels.

Notwithstanding these benefits, it must be realised that iqs are no panacea in fisheries manage-

ment. Various problems can arise, ofhtting any efficiency gains. It is possible to categorise these

problems into two types. The fint type occurs because of characteristics of the fish stock which are

incompatible with an iQ system. The second type of problems is due to adverse incentives that such

systems create for fishers. ut addition, many claim that management systems such as individual

quotas cause a major redistribution of weaith, usually from small scale fishers, to large fishing com-

panies. Examples of this literatuce are Duncan (1995) and Péüsson and Helgason (1995). However,

this problem is not unique to rqs, but rather a consequence of the transferability and the traditional

free initial allocation of quotas. For instance, wealth redistribution was observed with the iirnited

entry scheme in salmon fisheries in British Columbia. That scheme allowed licenses to be transferred,

and the initial licenses were ailotteci without charge to the incumbent fishers. This lead to a large

redistribution of wealth, where the losers were the second generation of fishers, who bought licenses

of the first generation at great cost, anticipating an improvement in the economic conditions of the

fishery; improvement that never rnaterialised (Copes, 19W). However, dile to the easier divisibility of

quotas, rather than licenses, there is a greater possibility of concentration of wealth than in fisheries

that have transferable licenses, in particular if the licenses hme some effort restrictions attached to

them. Some of the social impacts of rq systems are discussed in the papers presented in Palsson and

Pétursdbttir (1997). It is of interest to see the effects of government intervention in response to one

or more of the social issues has on the eficiency of an rq system. For instance, Matthiasson (1997)

looks at the impact of subsidiiing vessels from a particular region in an rTp fishery, the underlying

rationale being willingness to prevent quota from being sold from the region. Matthiasson find that

such a subsidy scheme wiii lead to suboptimal results. However, this brings up the question of the

price that a country is willing to pay for ensuring that iife in a particular region of the country is

viable. If that price is higher than the loss in efficiency from the subsidy, then the subsidy scherne

must be considered an improvement over an [TQ system without the subsidy.

The adverse stock effects are dîfEcuit to deal with. These occur because the nature of the 6sh

stock does not allow for the implementation of an IQ system. One example are multispecies fisheries,

where fish stocks are mixed on the fishing grounds. Usudy in such fisheries, it is impossible to

target a particular species, because other species wiil always get caught in the fishing gear as weU.

If a fisher has a quota only for Mme of these species, what is he to do with the catch of species for

which he has no quota? If he lands the catch, he is violating the quota regdation; if he discards the

catch, he is wasting valuable resources. In both cases he may be breaking the law, leaving him in an

impossible situation.

Fisheries that require residual catch management are an example of fisheries where the nature of

the h h species makes quota setting impossible. Pacific salmon are a good example. When managing

salmon, it is important that the correct number of fish be allowed to escape upriver to the spawning

grounds. if too Eew fish manage to get to the spawning grounds, then too lew salmon will be boro;

il too many fish get to the grounds, then they begin to destroy each other's spawning beds. The

management of salmon thus requires setting the appropriate escapement target for 6sh to get to

the spawning grounds, and let fishers harvest whatever is Ieft over. Therefore, a TAC cannot be

determined prior to the season and quotas cannot be allocated to fishers. hny uncertainty about

the quota allocation rneans that fishers will begin to race for fish, in case their allocation might be

decreased at sorne stage during the season. In fact, any hhery where the TAC setting is problematic,

and may need to be adjusted in the rniddle of a season, is not a good candidate for an iq system.

Various other characteristics of fish stocks can lead to a failure of an rq system. However, discussing

these in detail is beyond the scope of this thesis. Copes (1986) gives a good discussion of sorne of

these problems.

Apart from the stock problems, [QS may create some adverse incentives for fishers. klostly, these

arise from the fact that igs do not generate property rights over the fish stocks themselcrs, but only

over the harvest of fish. In fact, for most tq fisheries, the property right is applied to fbh landings,

not fish harvest. Copes (1998) compares fishers to farmers, where a farmer owns and controls his

specific livestock and production facilities. Consequently, the farmer can manage his farm any way

he sees fit. For a fisher to have the same contml over fish wuld entail being able to identify a set

of fish and the environment that these h h live in, and give the fisher full property rights over both

the fish and the environment, It is rather obvious, that for a fugitive resource such as fish, living far below the ocean's surface, such property rights cannot be specified, let alone enforced.

Vatious perverse behaviour can result from the misspecification of property rights. IQ schemes

are regulations that restrict the freedom of fishers. As with any government legislation, an incentive

exists to circumvent the rules and regulations. Trying to exceed the quota, without being caught, is

the most obvious problem. This can take various forms, such as faisifying landings records, trying

to trick fisheries inspectors by putting a layer of less d u a b l e species on top of more valuable quota

species in fish boxes when landing, etc. Any suspicion that such quota busting is taking place,

creates havoc for stock assessrnent. hmong other t h g s , biologists rely on accurate landings figures

to assess the size of a h h stock. Even the slightest suspicion that landings records are systematically

falsified, has serious effects on the work of biologists. -4s an example, Holden (1994, p. 126) desmbes

how biologists assessing fish stocks fot the European Union have generated estimates of "unofficial

CHAPTER 3. MANAGEMENT M THE ABSENCE OF DISCARDtNG 48

catchesn to correct the official statistics, which are known to be very unreliable. The "unofficialn

statistics are, of course, nothing but guesswork, and the resulting stock estimates are understandably

very unreliable as well.

It has been argued, that rqs lead to excessive discarding of fish. The reasoning is simple. Once

fishen are facing a limit on their harvest, in the fonn of a quota, each fisher wants to maximise

the value Gom the quota. Therefore, fishers discard low value fish and keep high value fish, even to

such an extent that no low value fish is landed. Muse and Schelle (1989) and Muse (1991) survey a

number of IQ systems from variou places in the world. In terms of discarding they find no general

result; discarding is in some cases believed to be a serious problem but not in other cases. This

indicates that undetstanding the factors underlying diarding behaviour is very important when it

cornes to evaluating whether a fishery is a suitable candidate for an IQ system or not. This is, in

fact , the purpose of this thesis.

Chapter 4

A mode1 of discarding

As mentioned in the previous chapter, excessive discarding is a potential problem in an individ-

uai quota fishery. It is now time to extend the anaiysis to include discarding in order to evaluate

the effects management policies, includiig individual quota fisheries, have on discarding behaviour.

However, before looking at management policies, it is necessary to look at fisheries without man-

agement. First, the sociaily optimal solution in the presence of discarding will be derived, and then

the focus will be on fisheries operating in the open access situation. This sets the stage onto which

management policies will be introduced in the next chapter of the thesis. Before al1 this, however, a

brief literature overview on discarding is in order.

4.1 Brief literat ure review

Before continuing, it is important to understand chat there are different kinds of discarding. The

first could be called basic discarding and refers to discarding that is sociaily optimal. It may be

difficult to accept that some discarding may be optimal, but as will be seen and further discuçsed

below, this may well be the case. The reason is that the cost of landing and processing the fish, even

if aiready harvested, is simply too high so that the market price does not cover this cost. Discardiig

in excess of basic discarding can be categorised into the following three types.' The first is due to

bycatch. In this case a fisher who is in a multispecies fishery, discards fish catches that are of other

species than the target species. The second type of discards has been labelled quota discards. An

example of this would again be a mdtispecies fishery where the fisher has no quota for some of the

species he catches and consequently throws that catch overboard. The last type of diicards is due to

'Discards can be classified in various ways. Exampks are Alverson, Reeberg, hIurawski, and Pope (1994), Cillis, Peterman, and Pikitch (1995), and Crean and Symes ( l m ) who al1 d e h e discards slightiy dSerently. However, the difference is normally in terms of how dwggregated the analysis needs to be, and the definition here could easily fit with these other definitions

highpding. Being limited by their quota allocation, fishers have an incentive to increase the value

of their catches. As long as this takes the form of better handling of the catch, this is not a problem.

This may, however, lead them to become selective and discard excessively fish deemed less valuable

than other fish. Usuaiiy quota systems disregard the fact that some fish are more valuable than

others. Taking cod as an exarnple, one tonne of low vaiue cod reduces one's quota by exactly the

same amount as one tonne of high value cod. Since fishers would like to maximise the value from their

quota, they may discard fish of low market vaiue to make room for fish of higher market value. Some

fish, highgraded for this purpose, might not have been discarded under a system without quotas. In

this thesis the focus wiii be on highgrading, not bycatch or quota discards. Much of the analysis can

be applied to the other two types oidiscards, in particular in the short run, but there are a number

of additional complications that need consideration when anaiysing multi-species fisheries, such as

biological interactions arnong the relevant fish species. Also, a bycatch problem does not necessarily

mean that fish is discarded. It may be that a bycatch species is more valuable than the target species

and is therefore not discarded. However, bycatch may be a significant problem if the bycatch species

is heavily exploited but the target species is oot. In that case, conservatory nieasures for the bycatch

species will affect the fishery for the target species, perhaps significantly. Boyce (1996) gives an

account of sorne of the problerns facing fisheries managers deaiing with bycatch fisheries.

The literature on discarding is rather scarce. Giiiis, Peterman, and Pikitch (1995) look at

the effects that trip regulations have on highgrading. In another work, the same authors (Gillis,

Pikitch, and Peterman, 1995) take a rather unusual approach by arguing that when fishers face

hold constraints, the decision to discard is similar to diet choice problems faced by natural foragers.

Both these papers show that factors such as vessel's capacity and limiting regulations rnay cause

fishers to discard low value fish in the hope of replacing it with high value fish. However, neither

of these papers looks at any economic variables; there are no cost functions in their models, and

they do not consider the effects of price changes. This is a common deficiency in the discussion

on discarding and highgrading. As wilI be argued in this chapter, discarding takes place solely for

economic reasons. Wre it not for the hope of catching fish that fetch higher prices than the current

catch, no highgrading would ever take place, regardless of how small the hold of a fishing vesse1 is.

Crean and Symes (199.1) use the CFP of the EU as an example when looking for ways to reduce

discards. The authors ofier some general ideas on how discarding can be reduced and argue that

there is just as geat a need to change the attitude and behaviour of the resource users as to

change management reguiations. However, they claim that the discards problem is a "symptom of

a dysfunctional fisheries poliq* (p. 433). This is not necessariiy the case. It is true that policies

may dec t discarding, but, as wii i be seen later, discards may also take place in the absence of any

management policy.

Empirical evidence on discardimg is alrnost n o n d i n g . It is difficult to find data on discarding,

since it is usuaiiy an iliegal activity, and 6shers are not wiUing to admit to it. As mentioned in the

CHAPTER 4. A MODEL OF DISCARDING 5 1

previous chapter, Muse and ScheUe (1989) and Muse (1991) look at barious quota fisheries in the

world, and find that discarding is believed to be a problem in half of the fisheries surveyed. However,

they do not attempt to explain why discarding is present only in some fisheries and not others. In his assesment of New Zeaiand's IQ system, Dewees (1989) reports that 66% of the 62 fishers he

interviewed consider discarding to be the most serious problem with the rq system. It is not clear

whether these fishers base this on their own behaviour or the perceived behaviour of other fishers.

To highlight discarding issues as perceived by fishers, Breeze (1998) sutveys 23 hhers and industry

representatives in the Smtia-Fundy groundfishery. Most fishers said they did not discard themselves,

but that they knew it took place among other fishers. Some blamed discarding on large companies

and some blamed it on the ITQ system in the fishery. .4 few general observations can be made from

these surveys. Firstly, discarding may take place in IQ fisheries, but not necessarily so. Secondly,

discarding seems to be considered non-acceptable behaviour as most fishers do not admit discarding

themselves even if they daim diicarding takes place. Finally, many seem to consider diicarding, or

highgading, a serious problem in IQ fisheries.

In terms of theoretical economic analysis of discarding and highgrading behaviour the field is

not large. During the mid 1990s there appeared a few papers analysing dicarding formally, but the

interest seems to have faded since then. Arnason (1994) develops a mode1 to analyse the economics of

discarding. Some of his findings are that discarding may bc optimal in a fishery with different grades

of fish. Fishen in open access have the same incentive to discard, for a given effort level, as fishers

behaving optimally. He finds that IQS tend to generate an excessive incentive for discarding catch

as compared to a socially optimal fishery. Anderson (1994), focusing on hold constraints, reaches a

similar conclusion, namely that in the optimal situation discarding may be profitable and that ITQS

incrense the incentive to discard. Anderson however clairns in contrast to Arnason that the incentive

to discard in open access is lower than in an optimal fishery. This issue will be addressed below.

Turner (1996,1997) uses a sirnilar approach to Anderson to argue for a system of vaiue-based I T Q ~

rather than weight-based 1 ~ ~ s . His findings are that a weight-based ITQ system leads to excessive

discarding but if the quotas are based on the value of the catch rather than weight the discarding

incentive diiappears. Turner must be given credit for looking for a solution to the discards problem

and analysing in a formal way. However, from a practical point of view, a valuebased system brings

in problems that complicate matters, for instance how to deai with relative price changes within a

season. The practicaiity of Turner's analysis suffers from the fact that the Icelandic relative quota

method, that he uses as an example to argue that the value based approach can work, collapsed many

years ago due exactly to price fluctuations within seasons. As explained in Skarphédinsson (1993),

Icelandic fishers could exchange quotas of one demersal species for another without restrictions

based on value factors determined by the Icelandic Ministry of Fisheries. However, in 1989 the

price of Greenland halibut increased much more than the price of cod, with "...the results that

the value factors which the M i t r y had determined at the beginning of the 6shing year no longer

CHAPTER 4. A MODEL OF DISCARDING 52

reflected the proportional dgerence in value between these species."(Skarphédinsson, 1993, p. 183).

Fishers responded in a predictable manner by increasing their halibut quota by using the exchange

mechanism. As a result the Ministry restricted such quota exchanges to 5% of the landed value of

the quota for a particular species, and exchanges cannot be used to increase the cod quota, which

is by far the most important fishery in Iceland. The problems expetienced in Eeland are Iiely the

biggest sturnbling block of a value baseci quota system, as changes in the value factors during the

course of a season will undermine the credibility of the quota system.

Vestergaard (1996) looks at a shrimp fishery in Greenland and uses data from that hhery in a

model similar to the one of Anderson (1994) ta see if discarding behaviour will result. Like the other

authors he finds that discaràiig may exist without any management of the fishery. When looking

at different management measures the conclusion is that individual non-transferable quotas increase

the incentive to discard. interestingly, in the transferable quota case, Vestergaard finds that the

incentive depends on the quota price. If the price is below the shadow value of the quota in the

non-transferable case then the incentiw to highgrade falls. However, there is no attempt to try to

include the quota price in the mode].

Arnason (1995b) is the only work so far that finds that the relation between discards and the

management system may not be characterised in one simple way. In this tvork the harvesting

technology is endogenous, Le., a Iisher can control the selectivity of the fishing gear, but at a cost.

There a hher may choose to make the gear more seleetive, rather than discard fish in order to

avoid unwanted fish. Which method a fisher uses depends on the relative costs of selectivity and

àiscarding.

There are a number of drawbacks with the literature thus far. Firstly, al1 the above analyses

assume a short run fishery, i.e., the biomass is hed in their models. This is unfortunate because

one of the biggest concerns of discarding, among both fishers and the general public, is the negative

effect it may have on fish stocks. The argument is that excessive discarding and highgrading will

lead to increased fishing mortality, perhaps to such an extent that the fish stock in question may

come under threat of depletion. This is such an important concem that models looking at discarding

shouid be capable of analysing the stock effect.

Secondly, the short run nature of these papers will only give a partial analysis of what happens

to the effort level in the hhery. Effort changes come not only from the change in behaviour of the

individual fisher, but also through the entry and exit of fishers. It it conceivable that an individual

fisher increases his effort whiie the number of fishers faüs to such an extent that overall effort is

decreased.

Thiidly, there is no attempt made in these papers-most of which aim to analyse individual

transferable quotas and discardiig-to explicitly model the quota market and the interaction between

the price of quota and discarding. There have been suggestions, notably by Vestergaard (1996), that

the price of quota may be hked to the incentive to discard, and therefore it seems a worthwhiie

exercise to bring the determination of quota prices into the models.

Finally, the work thus far, with the exception of Turner (1996, 1997), does not formally analyse

possible solutions to reduce the excessive discarding incentive of ITQ systems. A number of remedies

are suggested, but not properly anaiysed.

One of the purpose of this thesis is to address these problems to see if and how that will change

the conclusions of previous work on discaràiig, and what additional insights can be gained regarding

discarding behaviour. A h , Chapter 6 looks in detail at some of the solutions that have been offered

to reduce the level of discarding in ITQ systems.

4.2 Adding discarding to the model

Discarding, in the current model, can occur because the fish stock is differentiated; there are high

qudity fish and low quaiity fish. The difference between high and low quality fish is that catches of

high quality fish fetch a price, pl , which is higher than the price that catches from the low quaiity pan

of the fish stock fetch, pz. Fishers sel1 their catches to fish markets that have substitutes available,

thus prices are not influenced by the supply from this particular fish stock. Why the price diflerential

exists is not important for the purposes of the ciirrent analysis. For a curious reader, one possibility

is that some fish are larger than other fish and that the market is willing to pay a premium for large

fish. What is important, however, is that this differential exists, that fishers are aware of it, and it

is crucial that fishers are able to recognise high quaiity fish from low quality fish while at sea.

As in Chapter 2, fish can be harvested according to

In the mode1 as presented now, part of the harvest is high quality fish, while the other part is Iow

quality. The catch of high quality fish is a certain Eraction, o, of the total harvest and the remainder,

(1 - a), is the catch of low quality Rsh. -4s in other work analysing the economics of discarding,

this production function restricts fishen to harvest a fixed composition of the stock.2 In a model

such as the one developed in this thesis, where the focus is on comparing long run equilibria, this

restriction may not be very serious. The determination of a comes lrom the fishers thernselves.

They experiment with different fishig techniques in order to find the one that maximises their

profits. This experimentation includes gear type, mesh size, tow tirne, distance of gear lrom bottom

etc. As discussed in Arnason (1995b) by varying these techniques fishers can change the selectivity

of their harvesting operations. It is only reasonable to expect that in the long run fishers choose

fishing techniques that maximise their return, i.e., the techniques that equate the marginal benefit

'Bath .Anderson (1994) and Turner (1996), hoarever, point out that this allows a focus on the essentials of discarding in a relatively straightforward manner.


and marginal cost of improving selectivity. It is assumed that this decision is not afkted in any

significant way by the choice of management policy and therefore a is considered k e d in the analysis.

In this model fishers may not necessarily land their full harvest of low quality fish. Fishers might

throw overboard less valuable fish, in either the hope of exchanging it for more valuable fish or simply

because the fisher judges the price not sufficient to cover the landings cost of the fish. Landings of

an individual fisher are given by

Total landings in the fishery are the sum of the landings of individual fishers, i.e.,

It is assumed that discardeù fish do not survive. if al1 discarded fish would survive, then discarding

is not a problem as discarded fish would grow to become bigger and more valuable and could be

harvested at a later stage. The problem with discarding arises because fish that are discarded will

not contnbute to the productivity of the fish stock. How much of discarded fish survives depends

on many factors (see, e.g., Alverson, Freeberg, Murawski, and Pope, 199.1) and some sp ies , lobster

being one, may survive quite well. However, in this thesis complete mortality of discarded fish

will be assumed. It would not be difficult to include a parameter in the model that would reflect

the survival rate of discarded fish (Arnason, 1994). However, it will not add significantly to the

qualitative analysis undertaken here and is therefore not pursued.

The cost in this fishery coma from three sources. The first two are the same as in Chapter 2,

i.e., the cost of effort and the cost of landing the catch. In addition, is the cost of discarding. For

instance, in order to discard fish of lower quality, someone has to keep an eye out for such kh, gab

them and throw them over the side. This may use up time and energy that could be used for other

activities. The total cost of the individual fisher is expressed as

indicating that cost depends on effort, discardiig and landings. The following assumptions are made

regarding the cost function

These are sirniiar to the conditions without discarding (equation 2.11). It is assumed that the costs

of discarding are increasing at an increasing rate as more is discarded. The last condition impiies


that the cost function is additively separable in its arguments. For instance, if the price of fuel

increases, raising the cost of effort, that does not affect the marginal cost of discarding. Also, since

effort, discarding, and landings do not occur at the same time, they do not affect each other's unit

cost. As before, fishers are heterogeneous, so harvesting cost may differ among them in terms of

effort and discarding. Therefore, this mode1 allows for some fishers to earn a producer's surplus.

Now the stage has been set and ail the ingredients needed to analyse discarding have been

introduced. Next it is time to look at the socially optimal situation.

4.3 Maximising value to society

In order to maximise the value of the fishery to society, the management authonty chooses the level

of effort, discarding, and stock six, taking into account that it is not possible to discard more than

is harvested of low quality

max V = Vc'.vd'.+

s.t.

fish. This maximisation problem can be expressed forrnally as

where the role of the first n constraints is to ascertain that only low quality fish are discarded,

while the Iast constraint assures a sustainable fishery. As a side issue, if the analysis was looking at

bycatches in a multispecies fishery, then a stock constraint, such as equation 4.8, must be present

for every fish stock in the fishery, increasing the cornplexity of the equation systern.

The Lagrangian of the maximisation problem is the following

As before, A represents the shadow value of the fish stock. The other Lagrangian multipliers, gi ,

are the shadow values of discarding for individual fishers, and will be funher discussed below. By

differentiating the Lagrangian with respect to the choice variables, the Kuhn-Tucker conditions for

maximisation are found to be

Cfi = piahea(ei,x) +p?(l- a)hCi(ei,x) - c:;(ei,S, y') - ~ji(e' ,d' ,~')h,~(e', X)

+$(l- a)hei (ei,z) - Ahci (ei,x) 5 0, ei 2 O, eiLSi = O, V i (4.10)

cdi = -h - cii (e', 6 , y') + cii (e', S , - r)' 5 0, à' 2 0, d'Cdi = 0, V i (4.11)

CHAPTER 4. A MODEL OF DISCARDING

These 3n + 2 conditions solve for the optimal effort, discardiig, and shadow values of discarding for

the n fishers, in addition to the optimal biomass level and the shadow value of the stock.

Assuming that fishing actually takes place, indicating a positive level of effort, equation 4.10 can

be rewritten to express the marginal effort condition for the i-th fisher as

+ (fi + rf)(l - a ) - h,,(ei,z) = cZ.(ei,d', y') f yhcl(e',z) (4.15)

As in the mode1 without discarding, this simply states that marginal benefits from changing effort

must equal marginal costs of the effort change. The marginal cost, as before, has two components, . .

first the direct cost from the effort increase, cfi(ei,d', y'), and second the increased cost in landing

the additional catch, Le., the cost of landing the marginal harvest, 7, inultiplied with the additional

harvest arising from the effort increase. The marginal benefit reflects that the fish stock consists of

two types of fish, high quality and low quality. Each additional effort unit will bring in a certain

quantity of high quality fish, ah,,(ei,x), which are priced at p l . In addition, some low quality fish

are caught, (1 - a)hcb(ei,x), which are valued at plus whatever shadow value is associated with

discarding. As in Chapter 2, account must be taken of the fact that the fish input does not cary

a market price and therefore the marginal benefit is reduced by the shadow d u e of the additional

harvest, A. The second first order condition, equation 4.11, is the marginal discading condition for a rep-

resentative fisher. It states that the optimal amount of discarding is where marginal benefits from

discarding an additional fish equal the marginal costs from thii action. The Lagangian multiplier,

q', is the shadow value of discarding. It shows how much Society values a marginal increase in the

harvest of low quality fish for fisher i , keeping everything else constant. This increase in profits

results from being able to discard the marginal catch as will be discussed hrther below. Xotice, that

when cost functions differ among fishers, the shadow value of discarding zill differ arnong them.

Since discarding is expressed as an inequality constraint, there are some cases to be analysed,

depending on whether the constraint is binding or not. In figure 4.1 the discardiig constraint is

drawn in (e', d) space. The area above d' = (1 - a)h(ei, z) is non-feasible since there a hher would

be discardiig more than was caught of low quaiity fish. The feasible set is anywhere on or below

the curve. if located on the cuve the fisher is discarding ail the low value catch, while points below

the curve indicate that some low value catch is retained and landeci. Three cases need consideration.

CHAPTER 4. A MODEL OF DISCARDiNG

Figure 4.1: The discarding constraint of an individual fisher

The first i s when profit maximisation leads fishers to operate on the horizontal auis, e.g., point A.

In tliat case, ei > O and d' = O. The second case is when the optimum is somewhere along the

constraint, e.g., point C. The constraint is binding in that case, and e' > O and cf' = (1 - a)h(ei,r).

The third case is when the optimum is somewhere inside the feasible set, cg., point B. There, ei > O

and O < d < (1 - a)h(ef x) .

There is a founh caseo namely when ei = O. However, this is not an interesting case, because

the fishery is not operating. In the discussion to follow, effort is always assumed positive. Let's now

take a closer look at each of the tliree cases of interest.

in Case A, = O and from equation 4.13 it foliows that the shadow value of discarding, q', must

also be equal to zero. The marginal effort condition (equation 4.15) now becomes

where p is the average price of high and Iow d u e tish, weighted with their respective proportion of

the total harvest, Le., p = op1 + (1 - a ) ~ . ~ Since d' = O, it foiiows that = h(eilz).

The first order condition with respect to discarding (equation 4.11) is now

Bq' rearranging, this c m be written as

'This notation will oken be used for the weighted average price throughout the thesis.


and the marginal condition for discarding can be expressed as

In this case, some low quality fish will be returned to sea, but some are retained and landed.

The third first order condition, equation 4.12, is the marginal stock condition, which says that

the stock size must be kept at a level where the marginal benefit from increasing the stock size

equals the marginal cost from doing so. Comparison with equation 2.17 reveals that when discarding

is introduced to the analysis, a distinction must be made between the two types of fish. Also, if

the shadow value of discarding is positive, low quality fish become more valuable and that must be

included in the marginal valuations.

The n first order conditions represented by equation 4.13 simply state that no fisher can discard

more than his harvest of low quality fish, and the final first order condition (equation 4.14) ensures

the sustahability of the fishery, since according to that condition equilibrium harvest must equal the

surplus growth of the fis11 stock.

As stated above, the 3n + 2 first order conditions detcrmine the optimum levels of effort, dis-

carding and stock size, as well as the shadow values of discarding and the stock. in addition to

these variables, the number of fishen is endogenous to the model and needs to be determined. The

marginal fisher wiH earn zero profits and his profit function looks like

indicating that fishers enter tliis fishery until

where, as before, ici is the minimum average cost for fisher i. This condition shows that the level of

discarding will affect the number of fishers. If the marginal fisher does not discard, à" = 0, then his

average c a t is equal to a weighted average of the prices minus the shadow value of the fish stock,

which is basically identical to the situation where there was no discarding in section 2.2.1. If, on

the other hand, aii low quality fish are discarded, the average cost of the marginal fisher is equal

to p ~ a - A. These two situations cannot be compared, since the level of discarding depends on the

functions in the optimisation problem of the social planner, and therefore X will undoubtedly differ in

the two situations. What is clear, from equation 4.26, is that the optimal nurnber of fishers depends

on the average revenue of the marginal fisher, includiig loss from discarding and adjusted for the

shadow value of the stock.

4.3.1 What to discard?

Where a fisher actually chooses to operate-at point A, B, or C in figure 4.1-depends on the

particulam of each situation. The prices and the parameters of the cost function are the primary


Discarding

t Discarding

t

Y , A - - Effort

Figure 4.2: Profit maximising situations of an individual fisher

factors to consider. It is useful, for a diagrammatical analysis, to make use of the concept of isoprofit

curves. In the cunent context, an isoprofit curve shows ail combinations of effort and discarding that

give the same level of profit. At the global profit maximum this curve is but one point. Figure 4.2

shows two possible scenarios. In panel (a) point B shows the combination of effort and discarding

which maximises profits; the global maximum. Two isoprofit curves are drawn in the diagam, Io and li, where a higher subscript refers to an isoprofit curve giving higher profits. It is clear, as the

curves are drawn, that points A and B are both on isoprofit curves with lower profits than at point

B and therefore a fisher would never choose to operate there. Panel (b) of figure 4.2 shows another

possibility. Now the global maximum is outside the feasible set and is therefore not attainable. In

this case a fisher maximises profits where an isoprofit curve is tangent to the discarding constraint,

in this case at point C. Now, points A and B give lower profits than C. At C, the fisher is discarding

d l catches of low value fish. Retaining some of that catch, given the effort level, would move the

fisher towards point B and ont0 a lower isoprofit curve.

4.4 Open access

The previous sections analyseci the optimal situation in a lisheu where discarding may take place.

However, most fisheries in the world are characterised by a common pool externality, and are believed

to be far away frorn the optimal situation. Before analysing how management policies affect discarci-

h g it is therefore appropriate to look at the open access situation. As above, it will be assumed that

fishers do not recognise the impact of their harvesting activities on the fish stock.

Each 6sher chooses the level of eflort and discarding that maximises his individual profits, while

not being able to discard more than is caught of low quality fish. Formally this is eupressed as

Since the fisher does not recognise the impact harvesting has on the fish stocks, there is no stock

constraint. The Lagrangian is

where pi is the shadow value of discarding for the individual fisher. By differentiating the Lagrangian

with respect to the choice variables the Kuhn-Tucker conditions for maximisation are found to be

As was the case before discarding was introduced into the mode1 (see section 2.2.2) the fisher uses

too niuch effort. If the fisher was operiiting at the optimal effort level, as given from equation 4.15,

the marginal effort condition for the individual fisher (equation 4.30) would be violated because the

fisher does not recognise the shadow vaiue of the fish stock. At the socially optimal effort level? the

marginal effort condition is

As marginal benefits are greater than marginal costs, the fisher h a an incentive to increase effort.

The discarding first order condition (equation 4.31) looks identical to the optimal condition from

the previous section. Therefore it can be argued that the incentiw to discard in open access is the

same as in the optimal situation (Amason, 1994). Anderson (1994), on the other hand: argues that

the incentive to discard may well be lower in open access than in the socially optimal situation. An

analysis of this issue will be postponed until the comparative static section below.

Looking briefly at the situation where aii catches of low quality fish are discarded (case C from

above) then the shadow value of dicardimg is positive and from equations 4.30 and 4.31 can be

shown to equal

When compared to the socially optimal shadow value, rli from equation 4.22, is it clear that for any

given level of effort, pi > $. This is because the shadow value of the fish stock enters the social

shadow value, $, but not the private shadow value, pi. Since the individual fisher does not take into

account the negative effect discarding has on stock size, his value of additional discarding exceeds

society's value.

In addition to the increased effort of the individual fisher in open access as compared to the

optimal situation, more fishers will enter the fishery. This is for exactly the same reason as in the

mode1 without discarding. Fishers do not recognise the shadow value of the fish stock, increasing

the marginal benefit from fishing. Fishers will enter the fishery until

This is very similar to equation 4.26 which shows the socially optimal entry condition. The only

difference is that now X is missing, increasing the average cost at which the marginal fisher enters,

indicating that more fishers will be operating in the fishery than is socially optimal. This can also

be looked at from the revenue side. Since fishers do not recognise the shadow value, their private

landed value of the catch is higher than the social landed value. Therefore the marginal fisher can

enter at a higher average cost than if the shadow value is included.

To compare the stock size between the socially optimal situation and the lree market guilibrium,

rewrite the socially optimal marginal stock condition (equation 4.12) as

The LHS of this equation measures the marginal benefits from reducing the size of the fish stock,

while the RHS is the marginal cost of the reduction. Since in open access the landed value is higher

than is optimal, it implies that the marginal benefit of reducing the stock, for any given effort level,

is higher in open access than in the socially optimal situation. As a result, at the optimal stock size

fishers in open access will have marginal benefits from reducing the stock geater than the marginal

cost. They will fish the stock further down and consequently the stock size in open access will be

lower than is socially optimal.

4.4.1 Comparative statics

In this section the focus will be on the effects changes in the exogenous variables have on the decisions

of fishen operating in a free market situation. The situation analysed is one where some discarding

takes place, but stüi some low quality catches are retained. In that case, fishers are not dected

by the discarding constraint and cm choose new combinations of effort and discarding without

restrictions when exogenous variables change. Analysing tbis situation, which corresponds to point

B in figure 4.1 and panel (a) in figure 4.2, gives the best understanding of how discarding behaviour

of fishers reacts to outside changes.

The unconstrained maximisation problem of the individual fisher is simply

where y' = h(e i ; z ) - d. The first order conditions are

Equation 4.38 states that at the maximum marginal benefits of effort must quai marginal costs,

and equation 4.39 is the marginal condition for discarding.

Equilibrium in open access is given by solving together equations 4.38 and 4.39 for al1 n fishers,

in addition to the stock constraint

which ensures the sustainability of the resource. By totally diflerentiating these 2n + 1 equations,

the following equation system can be obtained

where

This equation system can be written in matrix notation as foliows

where the coefficient matrix, denoted B, has been partitioned into smaller matrices. The b o l M elements of B refer to n x n diagonal matrices. For instance, the diagonal of nui consists of the

CHAPTER 4. A MODEL OF DISCAIUIING 64

second derivatives of each profit functions with respect to the effort level of the corresponding fisber.

That is

IId, is the same except the cliagonal elements are differentiated with respect to d'. The matrix O is

n x n matrix where ail elements are zero, and fi is a 1 x n vector of zeros, and C r is the transpose

of 6. The vectors, in general, are 1 x n, containing the elements indicated. For instance,

This notation will be utiliseci throughout the thesis as it simplifies considerably sorne of the matrix

equations that need to be anaiysed.

Turning the focus back to B, its determinant can be shown to be

To use Cramer's rule in the comparative statics exercise, the appropriate column from the matrix

on the RHS of equation 4.43 must be substituted in for the appropriate colurnn in B. If e is an

exogenous variable that is changing, and r is the endogenous variable of interest, then IB,,I ir!dicates

the determinant where the column corresponding to r has been replaced by the column corresponding

to 2.

Changes in the price of high quality fish

The fint effect to be analysed is the impact caused by increases in the price of high quality tkh.

Firstly, look at the size of the fish stock. By using Cramer's rule?

Since the numerator is positive and the denorninator negative, the whole expression is negative. This

says that as pl increases, the stock size n a fall. lntuitively this is sensible. Landed fish has become

'To calculate t h i determinant, and the many that follow in this thesis, use was made of the mathematical computer programme, Maple V, Release 3, aeated by the University of Waterloo. The number of tishers was set to t h e and bfaple asked to calculate the determinant. Once the outcome had been simplifieci, it was expandeci to the case of n fisbers.


more valuable, increasing the benefits from harvesting the stock. This implies that overall effort

must have increased, since otherwise the stock could not be fished down to a lower size.

The change in the effort decision of the the individual fisher is given by

which is positive since both the numerator and denominatm are negative. This indicates that the

effort of individual fishers increases as the price of high value fish increases.'

Next, discarding can be analysed. That t u m out to be a simple exercise as IBdip, 1 = O and

t herefore, ad' - = O PI

So an increase in the price of high value fish has no impact on the discarding decision of the fisher.

The reason for this is the assumption of constant marginal cost of landings. As previously stated,

that cost represents the marginal benefit from discarding. Since that is not dected by the price

change, the individual fisher wiil discard the same amount as before the price change.

To finish the analysis of the increase in pi , the effect on the number of fishers needs to be

determined. It is after al1 possible that even if individual fishers increase effort, total effort falls if

enough fishen leave the fishery. The change in minimum average cost of the marginal fisher is

which implies that since the minimum average cost of the n-th fisher increases there will be more

fishers in this fishery. That more fishers enter the fishery gives rise to the possibility that discarding

may increase. The new fishers may find it optimal to discard sorne fish, leading to an increase in

total discarding even if the incumbent Gshers niaintain their level of discarding.

Now a complete story can be told of the impact of an increase in the value of high value fish.

Once the price rises, the retums from landing more high value fish become higher. Consequently,

incumbent fishers increase effort in order to land more fish. It is noteworthy that because the

marginal benefit of discarding does not change, fishers do not have any incentive to change their

discarding behaviour for any given effort level. in addition to the increase in incumbent effort, more

fishers will be attracted to the fishery since returns from fishing have increased. These fishers may

'In the derivation of equation 4.48 the term

appears as a part of aei/i3pr. invoking multiplicative separability of the harvesting function (see page 10) in e' and z as done in Terrebonne (1935) reduces the tenu to zero.


have lead to an increase in the overall discarding level. The increase in effort, both from incumbent

and new fishers, results in a smaller biomass than before the price increase. However, depending on

the relative locations on the yield effort curve, before and after the price change, total harvest in the

new equilibrium may be higher or lower than before.

Changes in the price of low quality b h

It was seen above that discarding was aot dected by a change in the price of high value fish. Now

it is t h e to see if the same applies to changes in the price of low quality fish. -4s before, start by

looking at the impact on stock size. That is given by

As was the case when pi increased, stock size falls when pl rises. Keeping in mind that fishers are

landing some of the low value catch, the reason is basically the same as before. The value of landing

fish has increased, and as a consequence fishers are willing to add effort to catch more fish. As

before, the fall in biomass indicates that overall effort rnust have risen. That is partially confirmed

by looking at the effect on the effort of the individual fisher, which is

implying that the individual effort rises! By comparing this last equation with equation 4.48 it is

observed that the portion of high and low value fish in the harvest affects the impact on effort. This,

of course, comes as no surprise. The bigger is the share of the catch that receives a price increase,

the bigger increase in the revenues of the fisher results from each additional effort unit.

The effect on discarding is

x:iei IIT i f i

which indicates that as the price of the iow value fish goes up, the incentive to discard falls. This is

to be expected as the opportunity cost of discarding has now risen. M e n one fish is discarded the

revenue lost because the fish is not sold in the market has increased.

This last finding is of considerable interest when comparing the open access to an optimal fishery.

As has be stated a number of times above, fishers do not take into account the shadow value of the

'As in equation 4.48 it is necessary to invoke multipticative separabiity of the harvesting hinction in e' and 2.


fish stock when in open access. Effectively that mems that the price in open access is higher than

the price in the optimal situation. if that is true, then the open access price of low value fish is

higher than the price in the optimal fishery. According to the last comparative static result, this

implies that fishers will discard less in open access than in the optimal situation for any given effort

level. This is in contrast with Arnason (1994), but agrees with the arguments presented in Anderson

(1994). Finally, the number of fishers needs to be analyseci. Differentiating the minimum average cost

of the marginal fisher as given in equation 4.35 results in

This is slightly problematic to differentiate since the effect on total harvest depends on the position

on the yield effort curve. However, it is not too difficult to see that

which says that if no discarding takes place, the increase in average minimum cost equals (1 - a ) ,

while if d l the low quality fish is discarded, then the fisher will receive no increase in revenue and

his minimum average cost is unchanged. For discarding levels in between O and h(ei; x) there will be

increase in the minimum average cost of the marginal fisher, but it will be less than (1 -a). This is

reasonable, as when some low value fish is discarded, the increase in revenue resulting from the price

increase only cornes from the part of the low value catch that is actually landed. The conclusion is

thus that, unless the discarding constraint is binding, the number of fishers will increase, exacerbating

the effort increase from the incumbent fishers.

To conclude, the impact of a increase in the price of low d u e fish has very similar effects as the

increase in the price of high d u e fish. Total effort increases, both due to current fishers increasing

effort and to entry of new fishers. The result of the effort rise is a reduction in the biomass of h h . The only difference is that the incentive to discard falls when pl increases, while it was unaîTected

£rom a change in pl .

Changes in the proportion of high quality fish

The last exogenous variable that needs analysis is a , the proportion of high quality fish. By looking

at equation 4.43 it may be observed that in the matrk on the RHS the column for a is very simiIar

to the column for pl . As a consequence, the result from changing a will be very similar to the result

from changing pi . In fact, the formulae for for a wiii be the same as those for pl if the a s in the


latter are replaced by pl - pr. Firstly, the stock impact wiil be negative as seen from

which says that the biomass level will fall as the proportion of high value fish in the catch increases.

This is logical. The more high value fish in the harvest, the more valuable wiU the landed value frorn

each tonne of fish be. That increases the marginal benefit of landing fish and subsequently each

fisher will want to land more fish. As always, lower biomass implies a higher total effort level. That

can be partially confirmed by

As was the case with the price increases, increasing a will lead to more effort being used. A higher

a means that more high value fish is now resulting from each effort unit used in the fishery. in other

words, the marginal benefit from effort has increased. That of course leads fishers to use more effort

in order to equate the marginal benefit of effort with the marginal cost.

As was the case with the change in pl , a change in a has no impact on the level of discarding

for the individual fisher. Namely,

The reason for this finding is that the decision to discard is taken after the fish is caught, and

therefore whether there is more or l e s low value fish in the net does not directly affect this decision.

Remember, though, that if al1 low value fish was being discarded, a obviously will impact the quantity

discarded, but in the discussion here, the discarding constraint is assumed not binding. In reality, it

is likely that the cost of discarding may depend on a , at least when looking at large changes in this

parameter. For instance, finding one small fish among one thousand may be very hard, whereas if

there are 500 of each type, finding low quality fish will be much easier. This kind of a relationship

is not explicitly modelled in the cost function used here, but would not be very hard to indude.

However, it is not easy to imagine large changes in a as a frequent occurrence. As was argued in the

beginning of this chapter, a is a function of the fishing techniques used by fishers. Changes in those

are Iikely to corne slowly over time and not in large jumps, in which case, the impact on discarding

costs are likely to be minimal.

The impact of a change in a on the minimum average cost of the marginal fisher can be derived

indicating that the minimum average cost of the marginal fisher wiil increase and therefore more

fishers will enter the fishery, pushing up the effort level.

By looking at al1 of the comparative statics of a change in a , is can be observed that al1 of them

depend on the price differentiai. The smaller is the pnce differential, the less impact a change in a

will have. This is reasonable as the smaller is the price differential the less the fisher will care about

whether the fish is high or low value. Therefore, dight changes in the proportion of high value of

the total will become les important to the fisher.

4.5 Discarding and dumping frontiers

The incentive to discard can be analyseci by looking at the price differential between the two types

of fish. Without this price differential, discarding will not take place at ail, since nothing is gained

by throwing away low quaiity fish. Think about highgading; why replace low quality fish with high

quality fish if the price per pound is the same. Therefore, it is of interests to examine exactly how

much price differential is needed for discarding to take place. To address this, the concepts of a

discarding fronbieq and a dumping b n t i e r ni11 be developed.

A discarding frontier shows the pnce combinations at which the fisher is not discarding, but is

at the same time indifferent between holding on to the marginal low quality fish or discarding it. To

show this concept, use the case of a fisher in open access. As was shown in section 4.4, the individual

fisher seeks to maximise his profits as given by

The discarding frontier is found from the first order conditions of this maximisation problem. How-

ever, since the fisher is not discarding, the discarding constraint is not binding, d' = 0, and pi must

also be equal to zero. This implies that al1 catches are landed, i.e., y' = h(ei;z). The first order

conditions for maximisation are

R:, (ei,O) = plah,i (ei;z) + ~ ( l - a)h,, (ei;x) - c:, (ei,O, h(ei; z)) - 7h,,(ei;z) = O (4.62)

ri, (ei, O) = -fi - ci, (e', O, h(ei; t)) + 7 = 0 (-1.63)

By solving for y in equation 4.63, substituting into equation 4.62, and rearranging, the following

ecpation can be derived

cCi (ei,O, h(ei; 2)) + c i i (ei10, h(ei;z))h,i (e'; x ) P2=p1- ah,, (e'; x) (4.6.1)

This equation shows the combination of prices at which the fisher does not discard, but is indifferent

between discarding the last low quality h h caught, or keeping it. This is the discarding frontier. If the price ratio changes sfghtly in favour of the high quality fishl then some low quality fish will be


Figure 4.3: Discarding frontier

discarded. The Frontier is shown in figure 4.3. If no pria differentiai exists, then the fishery is located

on the 45O line. The discarding Frontier intersects the horizontal avis to the right of the vertical axis,

because the last term in equation 4.64 is negative. If the price ratio is such that it fails somewhere

between the 45' line and the discarding frontier, e.g., point (l), then marginal benefits of discarding

will be less than marginal costs and no discarding will take place. It is plain to see from figure 4.3

that a positive price differential is not a sufficient condition for discarding. hnother interesting

feature is that even if f i is zero, discaràiig will not necessarily happen. At point (la), pl = 0, but

al1 catches of low quality fish wiil nonetheless be landed. Again, marginal costs of discarding exceed

marginal benefits and the fisher will not bother sorting through the catch seaching for low quality

fish. If, on the other hand, the price ratio is such that it falls to the right of the discarding frontier,

e.g., point (2), then discarding will taiœ place. Marginal benefits from discarding will be at hast

as high, maybe higher, thm marginal costs of discarding. In that situation, some or al1 of the low

quaiity catches will be discarded.

It is passible to extend the malysis with the use of the dumping frontier. The dumping frontier

shows the combination of prices at which the discarding constraint becornes binding, and the fisher

begins to dump all low quality catches. The 6sher is, however, indinerent between throwing out the

last low quality fish, or retaining it. Here, the term dumping is used to refer to a situation where al1 low quality catches are discarded and ody high quality catches are landed.

To find the dumping frontier, f is set equal to (1 - a)h(ei ;z) , but since the attention is on

the exact switching point where dumping begins, it follows that = O. Since all is discarded,

y' = ah(ei; 2). The two relevant first order conditions are

n:i e', (1 - a )h = plahei + ~ ( l - a)hei - cf, (e', (1 - a)h, ah) - yhei = O (4.65) t )

The dumping frontier can be derived by the same method as the discarding frontier. Its equation is

c:i (e', (1 - a)h,ah) + ci,(ei, (1 - a)h,ah)h,. P2=P1- (4.67) ohei

To compare the two frontiers, as given by equations 4.64 and 4.67, make use of the fact that for any

effort level,

c:, (e', (1 - a)h,ah) + ci, (el, (1 - a)h,ah)h,,

> cf, (ei, 0, h(ei; z)) + ch, (ei, O, h(ei; z))h,, (4.68)

Thus, it follows, that the dumping frontier must everywhere lie below the discarding frontier, as

shown in figure 4.1. In the area between the two frontiers, e.g., point (2), the fisher has an incentive to

discard, but does not dump al1 harvest of the low quality fish. That is to say, O < d < (1 - a)h(ei;x)

and = O. However, once the dumping frontier is reached, the fisher dumps al1 low quality catches,

i.e., d' = (1 - a)h(ei;z) and as soon as the fisher moves beyond the dumping frontier, pi greater

than zero.

The slope of the discarding frontier can be found by differentiating equation 4.64 with respect

to p l , p?, and ei. After some manipulation the slope can be expressed as7

The second term of the right hand side of the equation is negative. From the first order conditions,

(P-7) is positive, but heie,/h,i is negative. Since ceie,/ahe, is positive, with a minus sign, the whole

bracketed term is negative. From equation 4.48, 8ei/8pi > O. The second term is thus negative,

indicating that the slope of the discarding frontier is l e s than one.

This last 6nàing has one interesting interpretation. imagine a fisher located somewhere dong

the discarding frontier, not discarding, but indifferent between throwing away the marginal fish or - - - -

%ote that h m the first order conditions


Discarding frontier

Dumping frontier

Figure 4.4: Discarding and dumping frontiers

not. if the price of low quality fish increases by one dollar, the price of high quality fish must increase

by more than one dollar for the fisher to again be indifferent about what to do with the marginal

fish. In other words, the price differential must increase for the fisher to be as willing as before to

keep the marginal fish.

.An interesting implication is that the absolute level of prices influences the decision to discard.

This rneans that fishers are much leçs likely to d i a r d valuable fish, such as orange roughy, than

species that fetch lower prices, such as hake. This is a consideration that rnust be taken into account

when establishing whether discarding is a problem. Importantly, it also implies that discarding is a

dynamic problem that may appear and disappear with price fluctuations.

4.6 Discussion

With the simple mode1 presented here, some interesting results arise. Firstly, when there is a

differeritiated fish stock then it may clearly be optimal to discard some or al1 of the catches of low

quality fish. Since it is costly to discard, it is obvious that fishers would prefer not to catch this fish,

but the technology is such that they cannot avoid it. Using a different terminology; the fishing gear is

not perfectly selective. Nonetheless, it is reaçonable to expect that the leml of selectivity is optimal

in the sense that selectivity must be such that the marginal benefit of improving selectivity equals

the marginal cost. If that was not the case, some fishers could improve their profits by changing

selectivity, and since the analysis here focuçes on long run equilibria it would not be rational to use

gear that is suboptimally selective.

Secondly, it is important to understand that discarding is an economic problem. It is solely

caused by economic factors, in particular dinerences in prices, and physical factors such as the hold

size of a vesse1 will not result in discarding without the economic factors.

Thirdly, as in the model without discarding, an open access fishery will not operate at effort and

discarding levels that are optimal. Too many &hem will also participate in the hhery. Al1 this leads

to a biomass that is smaller than optimal. The reason for this behaviour is that fishen do not take

into account the shadow value of the fish stock, which effectively raises the landed value they receive

from harvesting.

Finaiiy, the comparative statics of the model suggest that for a given effort level in the open

access case, the individual fisher wilL discard less than is socially optimal, The reason is that the

effective price of fish facing the fisher disregards the shadow vaiue of the fisii stock and therefore is

higher than socially optimal. Therefore the private benefits from landing the fish are higher than

the social benefits and consequently fishers will discard less than is optimal.

Chapter 5

Management policies and

discarding

The discussion now rnoves to the effects that different management policies have on the incentive to

discard, and to see whether discarding affects the optiniality of management policies. In the fisheries

literature this has not received much attention at 811. With the exception of Vestergaard (1996),

who discusses discarding under TAC management, individual quotas are rcally the only policy where

this question has b e n addressed. Even there, the work is somewhat limited; only a handfui of

papers have looked a t this issue, as seen from the literature review in the previous chapter. It is

important for the understanding of discarding to analyse the efïects of other management policies

as well. For instance, if there is a concern that discarding may intensify under an IQ system, the

question needs to be asked whether that will also happen under an alternative management system.

Without proper analysis that question may be hard to answer. The management policies analysed

in this chapter are the policies that were shown in Chapter 3 to have the potential of bringing a

fishery to its optimal situation, namely the two taxes, effort and landings, and the two individual

quota schemes, non-transferable and transferable.

5.1 Taxes

in Chapter 3 it was shown that in a situation where there is no discarding, a tau on landings and

a tax on effort are quivalent in the sense that either one can lead to the socially optimal situation.

Now the tirne has corne to see whether that is also the case in the presence of discarding. As in

the previous discussion, an effort tax will ûrst be analysed and then the attention tums to a t u on

landimgs.

CHAPTER 5. MANAGEMENT POLICIES AND DISCARDING

5.1.1 Taxes on effort

The government or management agency imposes a tax on the effort of fishers, such that each fisher

has to pay t f i for every unit of effort used. The maximisation problem of a representative fisher is

where a new tem, t5,ei, harr been added to the cost of the individual fisher. As before, the fisher

can at most discard the total catch of low quality fish. The Lagrangian of this optimisation problem

is

The first order conditions for hher i are

By inserting the optimal Ievels of the choice variables from the socially optimal solution from the

previous chapter, a candidate for an optimal tax can be found as

t:, = Ah,. (5.7)

where A and h,. are evaluated at the socially optimal levels. This tax rate is the sarne as the optimal

tax on effort derived in equation 3.3, It is ~ r t h recaliiig that in the case of heterogeneous fishers

the effort tax will differ amang fishers. Low cost fishers will be operating at effort levels with a lower

marginal product of effort, hei, than hi& cost fishers and will thus be taxed at a lower rate.

The next step is to look at the marginal condition for discarding to see how that is afïected by

the introduction of the tax. Cornparing that to the optimal condition as given by equation 4.11,

the only difierence is that the shadow value of discarding is pi in the current condition, but rj' in

the optimal one. If these are identical once the tax has been imposed, then the marginal discardiig

condition will equal the optimal one. First, solve for 7 in the marginal effort condition to get

Next substitute y into the marginal discarding condition, and rearrange to get

CHAPTER 5. MANAGEMENT POLICIES AND DISCARDING 76

which, if evaluated at the optimal values for the choice variables, is identicai to the optimal shadow

value for discarding, qi. Therefore, the marginal discarding condition with the tax equais the

marginal discarding condition in the socially optimal case.

Next look at the entry condition into the fishery with the effort tax. In the mode1 before

dicarding was introduced a correctly chosen effort tax leads to the optimal number of fishers. It can

be shown that when discarding is present and the effort tax from equation 5.7 is introduced, fishers

will enter the fishery until

Since the harvesting function is concave in effort, its average product (AP) of effort decreases with

increasing effort, implying that marginal product (MP) of effort is less than average product. Thus,

for the marginal fisher enhen -- h p MPn --- -- = n , < l

h(en,z) "ce".+, r\pn en

The entry condition can now be rewritten as

Since A > An,, a comparison with the optimal entry condition as given by equation 4.26, reveds that

the ,CC is higher for the marginal fisher in the tax case and there will be too many fishers operating

in the fishery if discarding is present. Therefore, the effort tax will not lead to an optimal situation;

effort will be too high through the excessive number of fishers.

The final anaiysis of the effort tax is to look at the comparative statics of increasing the ta.. For

tbat purpose, it Ml1 be assumed that some low quaiity fish is discarded, but not ail. Like before,

this assumption allows fishers to react in an unconstrained manner to any exogenous changes.

As in section 3.3.1, tf, is rewritten as rt'. Since the discarding constraint is not binding, the

relevant first order conditions are

In addition, the stock constraint must hoid in equilibrium

TotaUy differentiating these 2n + 1 equations with respect to al1 effort and discarding levels, the tax


rate and stock size yields the foiiowing equation system

where the coefficient matrix here is identical to B in equation 4.43, whose determinant was found to

be negative.

Looking first at the effect on stock size, it can be shown to eclual

which says that increases in the effort tax will lead to an increase in stock size. Even if the tax rate

is not optimal, a more stringent tax on effort will have a conservatory effect. Since the only way to

increase the stock size is to reduce effort, the overall effort level must be reduced.

To confirm, the effect that a change in the effort tax has on the effort of the individual fisher is

given byl

(F'(~) - 2 h z ) aei -- i=I j#i - a7 IBI < O V i

AS expected, an increase in the effort tax lowers the effort used by each individual fisher.

Finally, the incentive to discard is not afkcted by the effort ta^, as seen by

ad' O - = - = O V i IBI

The tax depends on the amount of effort used, regardlm of the quantity discarded. Therefore, the

incentive to discard is unchanged Erom before as tax payments cannot be avoided by changing the

discarding decision for any given effort level.

The final conclusion is that an effort tax will not lead to an optimal fishery. The first order

conditions for the individuai fisher are the same as in the optimal case, but too many fishers operate

in the fishery. However, an effort tau WU Lead to a larger biomass than the open access situation

and d l therefore improve conservation, ewn in the preçence of discarding. The incentive to discard,

given the effort level, is not dected by changes in the effort tau. That is, the incentive to discard

for the individual fisher is optimai.

'For this result it is necessary to invoke multiplicative separability of the harvest hnction as was done in section 3.3.1 above.

CHAPTER 5. MANAGEMENT POLICIES AND DlSGARDlNG

5.1.2 Taxes on landings

The other tax explored in Chapter 3 was a tax on landings. In many respects, a tax on landings

is a more practical choice of tax, since measuring landings is much easier than measuring effort. In fact, most countries do keep statistics on fish landings. In the discussion in Chapter 3 it was found

that if the optimal tax could be cdculated and implemented, then the fishery would move to its

optimal level. The question is whether that will also occur when discarding has been introduced to

the niodel.

Now, a landings tax, t,, is introduced in the fishery, and in the hee market situation the max-

imisation problem of an individual fisher is

It must be kept in mind that the tax is charged on landings of fish, not catches of fish, for instance

because the cost of monitoring catches is much higher than the cost of monitoring landings. The

fisher chooses the levels of effort and discarding that maximise profit, which can be found from the

Lagrangian

The first order conditions are

Ct, = p1ah,i(ei;x) + pr(1 - a)heB (ei;s) - ~ : , ( e ' , d , ~ ' ) - c~,(ei,ri ' , y')hea(ei;x)

-tYh,i(ei; z) + pi(l - a)h,, (ei;z) 1 0, ei 2 O? eiC$ = O (5.23)

C i = - P L - ~ ~ i ( e i , d ' , y i ) + ~ ~ , ( e ' , d ' , y ' ) + t , - P i ~ ~ , ri' 2 O, d'Cg, = O (5.24)

C = (1 - a)h(ei;x) - â' 2 O, pi 2 O, = O (5.25)

which, by now, are becoming quite farniliar. -4 candidate for an optimal tax is

where X is the optimal shadow value of the fish stock. -4s in the case of the effort tax, the candidate

for the optimal Iandings tax is equal to the optimal tax in the absence of discarding (equation 3.25).

In this case, the tax should equal the shadow value that society puts on the fish stock.

Imposing the tax on landings as given in equation 5.26 leads to a marginal effort condition equal

to the optimal one. However, for the optimal effort decision to be made, the marginal discarding

condition must also equal the optimal one, and the number of fishers must be correct. First look at

the discarding condition and substitute in for t, . That results in


This diffen from the optimal discarding conditions, because the marginal benefit from discarding,

which optimally is y, has now become y + A. In other words, the marginal benefit of discarding has

increased by the amount of the tax. The reason is simple, Now that a tax must be paid on every fish

that is landed, that tax can be reduced by discarding 6sh. rilternatively, if a tax ne& to be paid,

the bher may decide that it is better to pay the tax on high value fish, tather than low value fish,

to minimise the impact of the tax. Therefore, the marginal benefit of discarding has risen, leading

to an increase in tbe incentive to throw away fish.

As before, the number of fishem operating in the fishety is an important aspect that needs to be

anaiysed. By setting the profits of the n-th fisher equal to zero, and manipulating that equation, it

can be seen that new fishers will enter untii

If t h last equation is compareci to equation 4.26, which detemineà the optimal number of fishers,

it can be seen that an extra term is included in the cunent equation, namelp Ad"/h(e", x), Since this

term is positive, representing the savings in tax from discarding fish, the average cost at which the

marginal fisher enters is higher than optimal, indicating that there will be too many fishers operating

in the fishery.

Let's use comparative statics analysis to see the effects that a landings t u has on the behaviour

of the individual fisher. This can be done by looking at the maximisation problern of an individual

fisher, that is not restricted by the discarding constraint. His maximisation problem is

The first order conditions are

a:, = piah,. (ei ;s) + p2(l - ~ ) h , i (e'; z) - c:, (e i ,d , ?li) - cb, (ei,&, y')h, i (ei; x)

-t,h,i(ei; X ) = O V i (5.30)

nii = - ~ - ~ ~ , ( e ~ , & , ~ ~ ) + c ~ ~ ( e ~ , d i , ~ ~ ) + t ~ = O V i (5.31)

These 2n equations along with the stock constraint

solve for the effort and discarding levels of aii the n hshers, and for the size of the biomass. In order

to undenake the comparative statics, differentiate these equations with respect to dl effort and

discarding levels, the stock size and the tau rate. The resulting equation system can be e-ressed as

As in the case of effort tax, the coefficient matriu here is identical to B in equation 4.43, and its

determinant is negative.

Using Cramer's rule, the impact that a change in the landings tau has on the fish stock is given

Thus, as with an effort tax, an increase in the landings tau will lead to an increase in the biomass.

Again note that a tax has the effect of conserving fish, even if the tax is not chosen a t its optimal

level. This was the case with the effort tau, and is also true in the case of a landings tau. increased

biomass in turn means that overall effort must be reduced.

The effect that the change in landings tau has on the enort of an individual fisher is'

which indicates that as the landings tax increases? effort of the individual fisher falls. This is per-

fectly logical, as laiidecl fish has become more expensive, increasing the marginal cost of effort.

Coriseqiiently, the fisher will reduce the effort level in order to equate marginal benefit and rnargind

cost of effort.

Finally, is the effect on discarding. When the tax is increased, the effect on discarding is

In other words, discarding will increase with an increase in the kmdings tau. Discarding gives the

fisher a way to avoid the tax, and be l e s affecteci by the tau since the more of the low value fish is

discarded, the more of the landed catch is being sold at high price. However, keep in mind that even

if discaràing is on the rise as a consequence of the tax, the biomass is increasing.

5.2 Individual quotas

Individual quotas are the final management tool to be analysed. -4s before, the analysis is in two

parts, fkst looking at the case of non-transferable quotas and then extending the discussion to

transferable ones.

2~ultiplicative separability of the harvest huiaion is needed for this result.


5.2.1 Non-transferable quotas

In this case, the management authority sets a TAC which is then divided into individual shares

and ditributed among the fishers. Remember, that the TAC applies to landings but not the catch.

Therefore, the possibility exists that the harvest exceeds the TAC. The maximisation problem of the

individual fisher is now

s.t. (1 - a)h(ei;z) - d' 2 O rji - = rji - h(ei;z) +d' > O

where the lùst constraint is the discarding constraint a s before, and the second constraint specifies

that the fisher cannot land more fish than his individual quota allocation, rji.

The Lagrangian for the individual fisher is

where pi is the shadow value of the quota, measuring how much profits would increase were the fisher

to receive one more quota unit. The first order conditions are given by

Cf, = piahei(ei;z) +p?(l - a)he8(ei;z) - c:,(ei,d',y') - ~g,(e' ,d ' ,~')h,,(e ' ;z)

-pihe, (ei;z) + jii(l - a)hei(ei;z) < O, ei > O, eiC,, = O (5.41)

, = -p? - cd, (e', ri ' , y') + cg, (et, d', y') + - ji' 5 0, d' 2 O, d'Cd' = O (5.42)

Cl, = (1 - a)h(ei;z) - d' > 0, jii 1 0 , jiiL,, = O (5.43)

Cii = 4' - h(ei;z) + d' > O, pi 2 O, p i l o i = O (5.44)

The only new condition here is the last one. That condition reproduces the quota constraint, speci-

fying that the fisher cannot land more than his quota docation. For the purposes of this thesis the

analysis is only of interest when the constraint is bindiig, and for the remainder of the discussion it

will be assurneci that Li. = O and pi > 0.

Looking quickly at the marginal effort condition (equation 5.41) and comparing with the open

access condition as given in equation 4.30, a new term now appears in this condition, namely

-$h,, (ei;x). This terrn represents the value of the quota to the fisher, reducing the marginal

benefit h m effort. This is an opportunity cost bom using effort, as the remaining quota gets

srnalier when effort is used. Comparing this with the optimal effort condition (equation 4.10) shows

that if pi in the current equation was replaced by A, the current equation wouid be identical to

the optimal condition. Therefore, by looking at the marginal effort condition, imposing individual


quotas will rnove the effort level in the fishery away from the open access equiiibrium towards the

optimal equiiibrium.

Tuming to the marginal discarding condition (equation 5.42) and comparing with the corre-

sponding open access condition, a new term also appears. With the introduction of an individual

quota, the marginal benefit of discarding increases by the shadow d u e of the quota, p'. The reason

is that a low value fish reduces the quota, and discarding that fish not only saves on landings cost

but also increases the quota that is unused. Therefore, at any given effort level, a fisher has a geater

incentive to discard than before the quota was introduced. Comparing the marginal discarding con-

dition with the optimal condition (equation 4.10) shows the same effect. The marginal benefit of

discardimg has risen, increasing the incentive to discard fish for any given effort level. This is true

whether or not the discarding constraint is binding, since even if p' = 0, the shadow value of the

quota pushes up the marginal benefit of discarding. The increased incentive to discard, caused by pi,

should be called highgrading. In this instance, the fisher is discarding fish, not because the market

price is not sufficiently high, but rather because he wants to fil1 as much as possible of his quota

with high value fish. This is perfectly rational as one kilogramme of low value fish reduces the quota

by exactly the sarne amount as one kilogramme of high d u e fish. The opportunity cost in terrns

of foregone quota is therefore the same while the revenue from landing high value fish is of course

higher than the revenue from landing low value fish. This is the basic rationale behind highgrading.

In the case of non-transferable quotas, the nurnber of fishers will be exogenous, determined by the

management authority. Assuming that the authority knows al1 relevant information, it will choose

the optimal number of fishers and also give quotas to low cost fishers. However, in real life this may

be very difficult to determine. One possible option is to auction off the quotas to the highest bidder.

In theory that should lead to the low cost fishers acquiring the quotas as they will be the ones that

can pay the highest price for quotas. The issue of how to allocate quotas is beyond the scope of this

thesis, but for an interested reader Morgan (1995) discusses allocation issues under quota ~ystems.~

Comparative statics

To look at the comparative statics of the individual quota system the discarding constraint is yet

again assumed nonbinding. However, the quota constraint is bindiig and the shadow d u e of quotas

is assumed positive. Taking this into account, the appropriate h s t order conditions are now

Cf, = ~ , a h , i ( e ' ; ~ ) +p_(l - a)het(ei;z) - ~ f , ( e ' , d ' , ~ ' )

-cli(ei,d', y')h,.(e'; x) - pih,i(e'; X) = O V i (5.45)

Lii = - p ; ! - ~ ~ ~ ( e ' , f , ~ ' ) + c ~ , ( e ' , d ' , y ' ) + ~ ' = O Y i (5 -46)

Lii = q'-h(e';x)+d'=O V i (5.47)

'Is is of general interest that Morgan argues that the auction process can be designeci to meet virtuaily any policy and economic goals for the îkhery in question, including goals relating to social equity.

In addition the harvest must be at a sustainable level so that

For equilibnum in this case, these 3n + 1 equations must be solved together.

impact of changes in quota docation, these equations must be differentiated

pi, 2, and q', for ail i . The resulting equation system is here expresseci as

in order to assess the

with respect to ei, d',

where L:i,i = (P - c,i - pi)heiei - ceici < 0, Cf i , = (P - c,, - pi)hei, > O, Chtdi = < 0, and

8, = F t ( x ) - C:=, h, < O. Denoting the coefficient matrix as Cl its determinant can be wntten as

Unfortunately, there is some ambiguity regarding the sign of ICI. The last term in the determinant

can be either positive or negative. When negative, the whole determinant is negative, but for positive

values large enough, its size will outweigh F t ( x ) - 1 h,, making ICI > O. However, the determinant

can be slight!y rewritten as

where s = hziL6idi/C:iei > O. in this version, the last term of the determinant is negative, but the

term h, F 1 ( z ) - 5 - (5.52)

i=l 1 + Zi

still poses problems. If F 1 ( z ) 5 O then this term is negative and so is the deteminant. There is

aiso some range of positive F 1 ( x ) for which the term in equation 5.52 is negative as well. Even when

equation 5.52 is positive, for some range the determinant will still be negative because the effect

of C h e i l : i z / L f i e i is stronger. Terrebonne (1995) gets around a sitnilar problem by assuming that

Ft(x) < O. This assumption, he claims, ". . . is reasonable for a tkhery comprised of a large number

of entrepreneurs." (Terrebonne, 1995, fn. 9, p. 74). While his assumption is sdicient, it is somewhat

stronger than necessary for signing ICI. However, following Terrebonne's lead, the sign of ICI will be assurneci negative.

The preceding discussion brings up a problem in using comparative statics to compare open

access and individual quotas. It is conceivable that if the open access equilibnum is such that the


stock is heaviiy overexploited, i.e., the stock size is smaller than z ~ s y , the optimal harvest level

rnay be greater than the harvest level in open access. In that case comparative statics that restrict

harvest through smaller quotas may not allow comparison between the open access equilibriuni and

the optimal level since harvest levels wiU be higher close to the optimum than in open access. This

shows the limitations of static analysis, because in real life fisheries management it may be necessary

to have a transition period where catches are restricted well below the eventual equilibrium harwst

level. An extteme case would be a complete moratorium on harvest as was done in the cod fishery

on the east coast of Canada in 1992. Presumably after a certain period, the length of which will

depend on the characteristics of the fishery in question, catches can be gradually increased until the

optimal level is reached. The current analysis could be interpreted as a fishery relatively close to the

optimal situation. In that case, the new equilibrium harvest level will be lower than the initial levet.

Continuing with the comparative statics analysis, the experiment is now to change the quota

by the same arnount for al1 fishers. Focusing the attention on the effect on discarding, the relevant

determinant is

bel L:i, h:, C ~ J d i -h,i Cf , , ( + h,(ei; z) - hz(e': 2)

- ( j ci , eten

By looking at each of the terms in this determinant, they al1 indicate a positive sign of the determi-

nant, except the last one. For that term there is the possibility of a negative number, if some of the

h , ( e J ; z ) terms are large enough. However, the following part of the determinant can be rewritten

as

where zi = h2,Liidi /C:,ei > O as before. The last term in this equation is clearly positive, and 8

comparison of equation 5.52 and the k t term on the RHS in the current equation reveals

CHAPTER 5. MANAGEMENT POLICIES AND DISCARDINO 85

which implies that the first t e m on the RUS of equation 5.54 is positive, and therefore lCdil is

positive as well. As a consesuence,

which indicates that if the quota allocation is increased, fishers will reduce their discarding. However,

if the quota allocation is reduced, then fishen will discard more. This result corresponds well with

the literature on discarding so far. A quota system wili lead to an increased incentive to discard h h .

The effect of a quota change on the shadow value of quota can also be analysed. Substituting

the vector on the RHS of equation 5.49 in for one of the columns corresponding to the shadow values

results in

Using the samc reasoning as for the determinant for discarding, this determinant will also be positive.

Thcrefore 8pi 1% l < O -=- Bi' ICI

indicating that if the quota allocation is increased, the shadow value of the quota will fall. As quotas

become l e s scarce their value falls. On the other hand, if there is a reduction in the quota, the

shadow value increases. The quota constraint is more restricting to fishers and therefore they vdue

the quota more.

The last impact to be analysed is the one on the biomass. By substituting the vector on the RHS

of equation 5.49 in for the last column of C, and using Cramer's rule, the following can be derived

which States that if more quota is given to hhers, then the biomass wül be reduced. The inverse

of that statement is that a reduction in the quota leads to a targer biomass. Thus, even in the

presence of discarding, the biomass in this model will increase folowing a quota reduction. This is

of considerable interest. It irnplies that a reduction in the TAC, combied with a reduction in the

quotas of all fishers, will always lead to an increase in the biomass, even if discarding is present. This

then further implies that the concem that a quota system may lead to a depletion of a fish stock

through excessive discarding is unfounded.

This Iast hdhg is of such importance that it is worth trying to gain understanding of whether

it is the result of the particular model used here or whether the r d t is of a more general nature.


Imagine a fisher that is maximising his profits given his quota allocation. That, of course, implies

that the marginal bene6t from harvesting more fish is equd to the marginal cost of doing so. Now

this fisher is given the news that his quota is being reduced by one tonne. The fisher bas tbree

choices; not changing his harvesting, increasing his harvesting, or decreasing hi harvesting. First

assume that the fisher uses the same amount of effort as before, thus the harvest level does not

change. Since the quota has been reduced, this means that the fisher must be discarding more than

before. 1s that optimal behaviour? His marginal cost must have increased, since in addition to d l

the costs that were being incurred before cornes the cost of discarding one extra tonne of ikh. At the

same tirne, marginal revenue m u t have failen, since less catch is being landeci and sold. Therefore,

marginal cost oE harvesting one more B h must exceed the marginal benefit. Increasing efiort makes

even less sense since that will increase margind cost even further. The only viable option is thus

to reduce d o r t in order to equate marginal cost and marginal benefit. Notice, that discarding may

increase as effort might not be reduced to such extent as to teduce harvest by the same mount as the quota decrease. Some of that tonne may still be caught for highgrading purposes. Howewr,

effort must be reduced as a result of the drop in quota and consequently the biomass will increase.

If it is profitable to increase eRort with a lower quota-it would also have been profitable with the

higher quota.

This analysis can be used to speculate what wiil happen in a transition from an open access

situation where x < znisy and catch levels are lower than they wiIl be in the eventual optimal

situation. In the beginning, quotas will be restrictive, reducing the harvest of fbhers. Consequentty,

effort will fd and the biomass wiii begin tu grow. Discarding may go either way, however, as was

argued above it does not seem ceasonable to expect discarding to increase to such an extent as to

bring harvest levels up to, or above, the initial harvest level. After the stock has grown sufficiently,

quotas will be increased, perhaps a litt1e bit every year, until they wi1l reach the target level. At

that level equilibrium wiii be reached where x > xh1,isy. However, if discarding is present, the fishery

will not be operating at the optimal level. In the eventual equilibrium, fishers are operating at effort

levels that are tw high, discarding is also tw high and the biomass wiU be smaller than is optimal.

5.2.2 h s f e r a b l e quotas

-4s was discussed in section 3.5.2, transferable individual quotas d o w greater efficiency than non-

transferable quotas through sales and purchases of quotas, relieving the governent of the task of

allocating quotas eaicient ly Gom the beginning.

The problem of the individual tisher is now to

CHAPTER 5. MANAGEMENT POLICIES AND DISCARDlNG 87

The fisher maximises hiç retwns, but is restricted by not being able to discard more that the catch

of the low value fish, and by the fact that not more fish can be landed than the quota allows. The

total quota of the ibher is the sum of his allocation and his purchases of additional quota. If qi is a

positive number, that indicates that the fisher purchased additional quota at the unit pnce of a. If

qi is negative, on the other haad, then the fisher sold some of the initial allocation, also at a price

of a.

The Lagrandan is now

(1 - a)h (e i ; z ) - d' +p i ($ + Q' - h(ei; z ) + d')

and the first order conditions are

Cornparing these equations with the non-transferable case in section 5.2.1, reveals some changes in

the first order condition. There is a new condition, quation 5.66, which states that for equilibrium

the price of quota must quai the shadow value of the quota. That means that quota trading wiil

take place until al1 fishers have the same shadow value, equal to a. if that was not the case, and

two fishen have diierent shadow values, then there are gains from trade to be made between those

fishers since the 6sher with the higher shadow value will be willing to pay a price for the quota that

is higher than the shadow value of the second fisher, resulting in Pareto improvement since both

fishen will be better off tban before.

The other noticeable difference is that the individuai fisher can change the quota constraint

(equation 5.68) either by buying additional quota or seliing some of the initial allocation.

The optimal number of fishers will be reduced when a quota is introduced. Remember, that the

quota is restricting the Fisher h m the open access situation hy giving him a quota that is less than

he would want to harvest. Therefore the quota constraint (equation 5.62) is biding. The profits of

the n-th fisher will now be

where a? is the profit he can make by seiiiig the quota docation and leaving the fishery. The

profit of the marginai iisher of staying in the fishery must be equal to the profit he can make if he

CHAPTER 5. MANAGEMENT POLICLES AND DISCARDING 88

leaves. Rom this equation the entry condition in the individual transferable quota situation can be

As long as a is positive, the minimum average cost of the n-th fisher will be lower than in open

access. Consequently fewer fishers wiil operate in the fishery after individual quotas have been

introduced. This is logical, since low cost fishers that d u e quota more will buy quota from high

cost fishen. Some high cost fishers will opt to seil al1 their quota and leave the fishery for grener

pastures elsewhere. It is worth emphasising that these fishers leave the fishery at their own free will

and receive the value of their quota allocation when they Leave. This is very different from al1 the

other management policies considered in this thesis, since in the other cases fishers leave because

they cannot cover their costs and they receive nothing when they leave.

It is of interest to compare the entry condition with the optimal entry condition as given by

equation 4.26. In section 3.5.2 it was shown that if the TAC is set at the right level in an ITQ fishery

without discarding, then the quota price will qua1 society's shadow value of the stock, and the entry

condition in the ITQ case will be the sarne as in the optimal case. In other words, there will be

the optimal number of fishers, and each will use the optimal effort level. However, when discarding

is present, this is no longer true. Even if a = A, the ITQ entry condition has an extra term that

is not present in the optimal condition, Le., Ad"/h(en; x). This t em rcpresents the fact that the

individual fisher does not recognise the loss to society caused by the reduction in the biomass due

to discarding. Therefore, the minimum average cost of the n-th fisher is higher with ITQS than is

optimal, indicating that more fkhers will operate in the fishery than is optimal.

Comparative statics of an ITQ fishery

To compare the ITQ fishery with the open access situation, let's denve the comparative statics results

of the mode1 with ITQS. As in al1 of the comparative statics exercises in this thesis the discarding

constraint is assumed nonbinding. Also, there is a positive shadow value of quota, indicating a

biding quota constraint. The relevant first order conditions are

Notice, that a has been substituted in for to facilitate the calculations. In addition to these

equations, two more need to be taken into account. The first is


whicL set a Limit on the supply of quota, recognising that fishers cannot buy, or sell, unlimited

amounts of quota. What one buys, another must sell, and equation 5.74 is the market clearing

condition for the quota market.

The 1st equation to bc added to the systein is the ubiquitous stock condition

ensuring that the harvest level is sustainable.

Al! these 3n + 2 equations together solve for the endogenous variables in the system, ei, 8, q',

x, and a for d l i . As before the system can be differentiated with respect to ail the endogenous

variables and the exogenous variables of interest. The resulting equation system can be expressed as

ûenoting the coefficient matrk of the above equation as D, its determinant can be shown to

equd

As in the non-transferable case this determinant is difficult to sign. However, utilising Terrebonne's

assumption regarding F', this whole determinant becomes positive!

Starting witti the quota price, the effects an increase in the quota ailocation has can be found

by utilising the foliowing deteminant

which imdies

If there is a greater supply of quotas, i.e., quota allocations are increased, the price of the quota

falls. If les is supplied, then the price increases. This is not surprising at dl; it sirnply indicates a

downward sloping demand for quotas.

'The discussion on page 83 regardiig transition Erom a heavily overexploited îishery also appües to this section of the thesis.


Looking next at the effect on discarding, it is clear in the model. Since the deteminant

is negative, the implication is that

in other words, if the management authority allocates more quota, the individual hher will reduce

discarding. With a higher allocation the quota constraint is not as restrictive as before. As shown

above, the value of quota falls and with it the marginal benefit of discarding low value fish. if, on

the other hand quotas are reduced, the opposite occurs. Quotas will be in geater demand, and

consequently their value increases. The marginal benefit of discarding rises and each fisher will have

an incentive to increase the amount of fish that is discarded.

Turning the attention to the effect an increase in the quota allocation has on stock size, it can

be shown to equal

which States that as the quota allocation is increased the stock size fds. Reducing the quota

allocation, even in the presence of discarding will have conservatory effects on the fish stock. This

is the same result as in the non-transferable case. This is of interest, of course, since a frequently

heard argument against an ITQ system is the destructive impact that discarding may have on the

stock. This model, on the other hand, predicts that the biomass will always increase following a

reduction in quota levels. The rationale is that it will never pay to increase the effort level when you

are allowed to land less fish. It increases marginal costs whiie marginal revenues are falling. Since

stock size falls when more quota is allocated, overall effort must increase. On the other hand, when

quota allocations are reduced, effort must fall since the biomass becornes larger.

5.3 Discussion

There are a number of important conclusions coming fiom the analysis in this chapter. Firstly, and

perhaps most importantly, when compared to open access, the model always predicts an increase in

the biomass for al1 the management policies presented here. Even in the cases where the incentive

to discard increases, that does not threaten the 6sh stock. The impact of excessive discarding is a

waste of economic resources-fish that should be landed and sold, is discarded. This suggests that if

conservation is the main objective, the management authority should be focusing on reducing effort

and not be so concerned with the level of discarding.


Secondly, the two taxes are no longer identical in terms of efficiency. Neither will tead to an optimal solution when discarding is present. However, the two taxes have dinerent implications, as

the incentive to discard for the individual fisher is unchanged from open access in the case of an effort tax, but the incentive to discard increases with a landings tax. This occurs as fishers can

reduce their tax payments by discarding low value fish.

Thirdly, the prcsence of highgrading means that an ITQ systern will not lead to an optimal

situation, even if the management authority chooses the correct TAC level. There will be too much

discarding and too many hhers. However, an iTQ system will still be an improvement from the open

access situation. The biomass will be larger and rents will be generated in the fishery, represented by

the quota price. Whether the fishers capture these rents depends on how the government allocated

the quotas. if quotas were allocated for free, then the rents accrue to fishers, but if the government

charges for the allocation then the government receives a part or d l of the rents.

Finally, an ITQ system has an important feature that the other management systems are lacking,

namely that those fishers that exit the fishery do so at their own choice and they receive a payment

for their quota. In areas where fishers are a low income group this may be of importance as the

revenues receiveà from selling the quota will assist the fisher in finding a new career.

Chapter 6

Some policy alternat ives for

discarding

Whenevet a fisheries management policy is being developed, a careful study of the interactions

between the objectives and the policy tools must be made. It rather seems to state the obvious to say

that the tool needs to suit the objective, but this simple fact is often overtooked. For instance, if the

ribjective of bheries management is consenation, then setting a TAC, ~ssurning it being enforceable,

is suficieiit to achieve any conservation objective. in that case there is no need to bring in taxes or

effort limitations on top of the TAC, since the objective with the policy is met. If, on the other hand,

the objective of the management policy is to conserve the fish and to achieve economic efficiency,

then the setting ot a TAC will not achieve both objectives. Some other policy tool is needed to achieve

the additional objective of eficiency. Various different tools have b e n tried for that purpose during

the past few decades, with rather dismal results. Individual quotas have been one of these tools,

and amting many economists are thought to be the best option to achieve efficiency. However, the

distributional effects of individuai quatas have been disturbing to many, again lending support to the

notion that one tool is needed for each objective, implying that if social equity is a policy objective a separate tool is needed to meet that objective. In general, it is fair to Say that each poiicy objective

requires its specific tool, o t h e m k the policy will fa11 short. if discarding is believed to be a problem

in a particular fishery, and a policy objective is to reduce discarding, then a separate policy tool is

almost certainly needed. Thus the question is which tool cm be used to counter discardimg. In this thesis it has been argued that discarding is an economic problem, caused by the interplay

of eçonomic factors such as prices and costs. T h e r e k , it seems a logical step CO look for solutions

tbat address discarding through economic incentiws. In the fisheries management literature this has

only been done to a very limited extent. .hason (1994) suggests tbree remedies to the discarding

problem. Fi t ly , to issue quotas for each grade of fish, effectively removing any price differentiai

CHAPTER 6. SOME POLICY ALTERNATIVES FOR DISCARDING 93

that may lead to discarding. While this may work in theory, there are major practical diiculties

with this approach, such as price fluctuations and administrative costs. Secondly, Arnason proposes

taxes and subsidies as a possible solution, and thirdly to set legal limits on discarding that then must

be enforced by the management authority. However, Arnason does not elaborate on any of these

suggestions. Anderson (1994) suggests that taxes on high d u e fish or subsidies on low value fish will

stop the discarding of low value fish. He also suggests landings restrictions, for instance that fishers

may be required to land a certain amount of low d u e 6sh for every unit of high value fish landed.

Anderson acknowledges that even if this method has potential, there are a number of problems that

need to be overcome for this to work, Like Arnason (1994), Anderson does not perfonn rigourous

anaiysis of the proposed solutions.

Vestergaard (19%) uses the Greenland shrimp fishery to test some potential discarding remedies.

Firstly, he uses the landing restriction proposed by Anderson (lm) of requiring certain share of the

low value fish to be landed. This causes various dficulties, in particular that some of the high value

fish may be discarded, a behaviour that Anderson calls low-grading. Vestergaard's analysis shows

that taxing the price of the high value species and subsidising the price of the low value species

can eliminate discarding. However, his mode1 shows that the tax or subsidy needs to be linked

with the price of quota in an ITQ fishery, which may cause problems in implementation. Finally,

Vestergaard (1996) suggests that the length of the fishing season might be adjusted. His result is that

a shorter season reduces diicarding under quota systems, presumably due to difficulties in harvesting

the quota. However, shortening the season may remove some of the benefits of a quota system, and

Vestergaard does not analyse this in any detail.

Turner (1996,1997) proposes a value based quota, as opposed to the conventional weight based

quota. This is effectively Arnason's suggestion of quotas by grade. However, there seem to be

practical difficulties with the implementation of that solution. Turner points to Iceland as an ex-

a m ~ l e where a system similar to the one he proposes is used for trading quotas of different species.

Unfortwiately, this programme did not work weii and had to be abandoned because values of the

different species wete fiuctuating within seasons giving rise to perverse incentives (see the discussion

in section 4.1 above). Nonetheles, Turner is on the right track, looking for economic solutions for

an econornic problem.

Crean and Symes (1994) propose a minimum discards strategy for the fisheries managed by the

European Union, but theù discussion is not very specific regardiig the actuai implementation of the

strategy. While they recognise many potential difficulties, they do not give practical solutions. They

emphasise the social aspect of fishing and stress the need for regional sensitivity in the irnplementation

of measuses to reduce diiarding.

In this chapter, four possible management tools to reduce discardimg will be introduced and

analyseci. The first takes a crime and punishment approach where 6shers are h e d for discarding,

essentially treating discarding as a criminal activity that needs to be punished. The second tool takes


an entuely different approach by offering subsidies for landings of the low value species. Essentially,

this approach rewards fishers for not discardig. So, the first approach slaps fishers on their fingers

when they do the "wrong" thing, while the second gives rewards for "correctn behaviour. The

subsidy option reduces the price differentiai between high and low value fish by effectively increasing

the price of the low value fish. The price dinerential can also be reduced by taxing the price of

the high value fish, and this is the third approach anaiysed in this chapter. The fourth, and final,

approach recognises that the marginal benefit from discarding comes fiom the savings in landings

cost when fish is discardeci. The tool used here is therefore a reduction in the cost of landings, It should be recognised that this iid of tools is by no means exhaustive. There are other possibilities to

reduce discarding, for instance the value based approach of Turner (1996, 1997). A h , it is possible

to combine some of the approaches suggested here. For example, it may well be possible to combine

a tax on the high value fish with a subsidy on the low value h h . Other options undoubtedly exist,

but the analysis here will be limited to the four tools listed above.

The analysis will focus on the individual transferable quota system. This system is becoming

more and more widespread in the wortd's fisheries and at the same time faces increased criticism

for encouraging excessive discarding. Non-transferable systems are extremely difficult to keep non-

transferable and therefore they are not included in the analysis. Two examples can be given to

support this view. Fintly, when an individuai quota system was introduced in Iceland in 1984 it

was non-transferable. Quotas were allocated to vessels and could not be moved from one vesse1 to

another, except in cases where vessels had the same owner. This proved very ineffective indeed. The

prices of vessels with quotas soared; the quotas obviously being the reason for the price increase.

Then in 1990 it had been realised that non-transferability was not working and consequently quotas

officially became transferable. Secondly, there is current1:r a non-transferable quota system in m a t

of the major fisheries in Namibia. Quotas are allocated to fishing right holders, which cm be either

companies or individuals, but mostly companies. These quotas cannot be bought or sold, but to

get around that problem companies are bought and sold in the market place and it is clear that

part of the price comes from the perceived value of quotas. Due to these enforcement problems

of non-transferable quotas, the remedies pmposed here will only be anaiysed in the context of a

transferable quota system.

6.1 Crime and punishment approach

A number of countries have set a ban on discarding. Norway has a total ban on discards of the

most important species caught within Nomay's exclusive economic zone (Crean and Syrnes, 199.1).

Namibia is another country that bans discarding at sea. It is clear, from the analysis in previous

chapten of this thesis, that a total ban on discards may not be an optimal strategy. The value of

some catches may simply be so low that it is outweighed by the cost of landing the catch. In such

CHAPTER 6. SOME POLICY ALTERNATIVES FOR D I S C M I N G 95

cases, it is socially optimal to discard the catch. However, even if socially optimal, it is important

that any discards be properly reported for stock assesment purposes.

Lf it is socially optimal to discard some low quality catches, then restricting discards to zero

increases the amount of fish landed, for any given effort level. This increases the cost of landings

which makes the hhery less profitable, because of the additional low value landings which reduce

the net benefit from each effort unit, The resource rent and intramacginal profits rediseci in the

fishery will be reduced. As a consequence, some fishers will exit the fishery, reducing the lewl of

employment in the Cshery.

Rather than banning discarding fully, there is the possibility of allowing some predetermined

amount of diicarding. If the optimal level of discarding was known, then that would obviously be

the level aimed for. However, when a ban or restriction of any kind is contemplated, monitoring and enforcement need to be looked at. It is easy to imagine a discardimg ban being dificult to enforce.

One way is to put observers on board every vesse1 in order to prevent discarding. For example, al1

Namibian fishing vessels must carry observers to ensure that the discarding ban is not virilated. This

puts an extra cost on the fishery, which presumably Cishers should pay. To illustrate how fisheries

may differ, in Namibia labour costs are much lower than in Norway, making a Namibian observer

scheme much cheaper to irnplement than a Norwegian one.

Regdations that restrict choices always generate an incentive to cheat, and if the cost of moni-

toring and enforcing a regulation is very high, it is conceivable that any benefits from the regulation

may be dissipated. if the regulation is considered unreasonable, or even ludicrous, cheating rnay

become cornmon practice, undermining the authority of the legislator and the policing system.

One possible way to reduce discarding is to increase its cmt to the 6sher. The idea is that

as diicarding becomes more expensive, the fisher will discard less to avoid this cost increase. The

question is only how to bring the increase about. Prohbly the most obvious way is to introduce a limit on the quantity of fish that can be discarded and regard any discarding in excess of the limit

as a criminal offence accompanied with poiicing and fines. This will be referred to as the crime and

punishment appmach. In this case, a hher that discards, hces some probability of being caught

and having to pay a fine. To represent this in the current model, the ~xpected cost of being caught

discarding must be included in the profit function of the fisher, in addition to the usud cost function.

Sutinen and Andersen (198j) build on the work of k k e r (1968) to analyse the impact law

enforcement cari have on bheries. Foiiowing their approach, if the allowabte discarcihg is 4, the

fine to be paid when caught discarding is f (& - 4) and the probability of being caught is w, then

the expected fine equals wf (d - 4). The allowable discarding, do, codd of course be zero, in which

case there is a total ban on discards. The properties of the fine huiction are

For al1 d' > do, f (d' - do) is assumed continuous and differentiable with ft(d' - do) > O. To keep

CHAPTER 6. SOME POLICY ALTERNATIVES FOR DISCARDING

the analysis simple, f (d - 4) and do are assumeci the same for ail Gshers, and

f' ( d - 4 ) = u = constant (6.2)

To analyse how this approach aEects fishers, an example wiil be taken of an ITQ fishery, as

presenteà in section 5.2.2 above, where fishers are not bound by the discarding constraint. The

profit maximisation problem of the individual fisher is

where the only difference from section 5.2.2 is that the expected fine has been added as a cost to the

profit function. The Lagangian is

( ) L' = plah(ei;z) + p ? (1 - a)h(ei;z) - d' - ci(e',d', y') - aqi

-w f (à' - do) + pi($ + Q' - h(ei; z) + d )


The marginal effort condition (equation 6.6) has not changed from before, and as was argued in sec-

tion 5.2.2, if a = X this condition will be identical to the optimal effort condition from equation 4.15.

The only first order condition that has changed from section 5.2.2 is the marginal discarding

condition, equation 6.7. There is an extra term in that equation, namely uf'(d - do), representing

the expected cost of the fine from discarding one more fish. This term increases the marginal cost

of discarding, and d l therefore tend to lower the incentive to discard.

The optimal marginal condition was presented above in equation 4.24 as

where the marginal benefits from discarding are on the LHS of the equation and the marginal costs

from discardiig are on the RHS. The current condition can be written in similar fashion as

CHAPTER 6. SOME POLICY ALTERNATWES FOR DISCARDING 97

and by mmparirg these two conditions, it is plain to see that if uf'(d - da) is chasen such that it

equds a, then the two conditions are identical. So if

then the marginal eflort condition and the marginal discarding condition for the individual fisher in

the current mode1 both quai the optimal conditions for effort and discarding.

As has been seen in previous chapters, the number of Bshers is an important aspect that needs

to be looked at when deterrnining how close to the optimal solution a management tao1 btings the

fishery. The profit of the n-th fisher, iocluding the expected fine, is

which, by setting wf(d" - 4) = uu(d" - do) = a(d" -do), can be written as

The entry condition into the Gshery can now be derived as

which has interesting implications. Assuming that a is actually qua1 to A, equation 6.15 shows that

unless 41 = O there will be too rnany fishers operating in the fishery. The reason is that the fishers do

not take into account the shadow d u e of the stock when making their discarding decisions. This,

of course, is the reason why they discard too much in the first place. Therefore, their private cost

of discarding 6 will be less than society's cost. In other words, for optimal behaviour, the fine For

discarding should be charged on dl fish that is discarded, not only the fish that is discarded above

the optimal amount. So even if a fisher discards las than is optimal, and is caught, he should have

to pay a fine.

It seems clear from the discussion that if the management authorïty can choose the TAC level

tbat equates a to the optimal shadow value of the stock, and choose a combiiation of a fine and

probability of being caught when discarding such that w j ' ( d - do) also equals A, then the fishery

will end up in the optimal situation. In other words, il the TAC and the expected fine are chosen

appmpriately, the TAC will meet the conservation objective, the ITQS will meet the objective of

economic eficiency, and the expected fine from discarding wili lead to optimal discarding. Three management tmls are used to meet three objectives.

However, there are a few practical difficdties associated with the crime and punishment a p

proach to the discarding problem, First of ail, the fisher may not know exactly the probability of

being caught. Rirlong (1991), for instance, points out that fishers' beliefs of their own abilities to

avoid detection rnay be overestimated. Such incorrect beliefs lead to suboptimal behaviour, suice


underestimating w le& to too many fishers entering the fishety and a reduction in the perceived

marginal cost of discarding.

Secondly, there is a question regardiig the enforcement of very high fines. It may be that a judge, or a jury, finds such fines unreasonable, given the perceived seriousness of the crime. Thus,

offenders may not be convicted, underminhg the credibility of the punishment scheme. This might

particularly be the case, if fishers are seen as low income individuais. For instance, a judge might

not be willing to confiscrite fishing gear if the Iisher can not eam a living as a result. In addition,

legal systerns tend to be much c o n c e d about equity, again &en leading low income indinduals

being treated "gently" if punishments are seen to affect significantly their ability to provide for their

families.

The third concern regarding a crime and punishment approach is the cost of enforcement. It

may be that the cost of operating the monitoring system needeà to determine the level of discarding

exceecis the benefits gaineci by the resulting reduction in discarding. Therefore, before venturing into

a crime and punishment scheme the extent to which discarding is a problem ne& ta be determined,

and an evaiuation of the enforcement costs must be undertaken.

Finally, Crean and Symes (1994) discuss at some h g t h that to reduce discards, a change in

attitudes is needed from fishers. They argue that fishers must regard discarding fish as unacceptable

behaviour. It is questionable that a discarding policy that treats fishers as criminais will be successful

in creating an appropriate change in attitudes. Such a policy is not likely CO make fishers feel that

they are participating in the management of the fishery and may make them more wiiling to rebel

against the policy. What is more likely to be successful, is a plan that creates the incentives for

fishers to reduce discarding at their own initiative.

6.2 Subsidy on low quality landings

As was seen in previous chapters, the price of Low quality fish, and the price differential between

the high and low quality hsh play a major role in the discarding decision. The following anaiysis

explores the effects the use of a subsidy on low value landings has on a fishery, in particular, on

effort, discarding and the biomass. As in the discussion on the crime and punishment approach, this

analysis focus on the ITQ situation.

Tbe individual hhe r maximises his own profit by choosing the lewl of effort and discarding. The

amount of discarding is Limiteci by the catches of low quaIity fish, and landings are restricted by the

quota allocated to the fkher by the management authority. However, since quotas are transierable,

each fisher can change the quota aiiocation by either purchasing or seKing quota. Landings of low

quality h h receive a subsidy of S. If, as before, the quota price is denoted a, and quota purchases

pi, the maximisation problem of the individuai fisher is to choose effort, discaràbg, and the arnount

CHAPTER 6. SOME POLICY ALTERNATiVES FOR DISCARI31NG

of quota to purchase in order to

The subsidy enters the profit function as an addition to pz, eflectively raising the price of the low

value 6sh. The Lagrangian is

The first order conditions for a representative fisher are now

Rom these equations, it is clear, that the subsidy not only afïects the marginal discarding condition,

as desireci, but also the marginal effort condition. in the marginal discarding condition (equa-

tion 6.21) the subsidy enten as an increase in the marginaI cost of discarding. With the subsidy

present the fisher not only gives up p? when discardimg, but also the subsidy. Casual observation

uould suggest that the incentive to discard will therefore fall. However, the subsidy also enters the

marginal effort condition. It increases the m+nd bbenefit of effort, since re tum on landing low

quality catch have increased.

The number of hhers may be affecteci as a result of the subsidy. The entry condition can be

derived as sd"

Kc" I p + ( l - a ) s - - - ad" P2r < icn+l

a+--- h(en; x) h(en; z) h(en;x)

(6.25)

Comparing this with the condition for an rTq fishery without a subsidy (equation 5.70) shows an additional term in the subsidy condition, namely (1 - a)s - sd"/h(en; z). if the discarding constraint

is not bindiig, d"/ h(en; x) < ( 1 - a) and this additional t e m is positive. That increases the average

mst at which the marginal fisher enters, increasing the number of fishers participating in t h i fishery,

as compared to an ITQ fishery without a subsidy. Oniy when al1 the low value fish is discardeci will there be no &ange in this condition. Tben d"/h(en;x) = (1 - a), and


This suggests that the subsidy wiil not bring the fishery to its optimal state since there are already

too many îishers operating in the fishery, as was seen in section 5.2.2 above.

To fully evaluate the effects on effort and discarding, yet again assume a non-binding discardiig

constraint. Remembering that the fishery must be viable, and that the quota market must clear,

the equations deterrnining the equilibrium in the ITQ case are

Totally differentiating these 3n + 2 equations with respect to al1 the endogenous variables and s

The coefficient matrix is nothing but mattix D from section 5.2.2 above, whose determinant was

positive.

By using Cramer's rule, the effects of a change in the subsidy on the endogenous variables can

be found. Let's begin by looking at the effect on the biomass. It niil be

indicating that when the subsidy is increased, the biomass wiil increase. Therefore the subsidy has

conservatory effects on the fish stock, implying that overd effort will decrease.

The effect the subsidy has on discarding is given by

which gives the expected result, namely that discarding wiil be reduced once the subsidy is intro-

duced. With the subsidy, the marginal cost of discarding has risen, and consequently fishers wüi

reduce the level of discarding.

CHAPTER 6. SOME POLICY ALTERNATIVES FOR DISCARDINC

The effort level of the individual fisher will react to the subsidy change as given by

utilising the multiplicatively separable harvesting function. The individuai Gsher wiil reduce effort

in response to an increase in the subsidy on the low value fish. Since discarding falls, the fisher must

reduce his effort level to stay within his quota.

Finally, there is the impact on the price of quota. To evaluate that, the deteminant

needs to be compared with

in order to use Cramer's rule. These two determinants are almost identical. Only the first terms

within the parenthesis differ. In ID, 1 that term includes (1 - a) which is not present in IDI. Since

(1 -a) is a fraction, it can be shown that while ID,I and ID1 are both positive, 1D.I will be smaller.

Therefore,

indicating that when the subsidy is increased, the price of the quota will increase, but by less than

the subsidy. It is worth noting that this rise in the quota price increases the wealth of fishers that

own quotas.

Taking al1 these effects together, the impact of the subsidy can be analysed and underutood.

When the subsidy is increased, fishen begin to reduce their discarding, since the marginal cost of

discarding has increased. However, for any given effort level that irnplies increased landings which

will now exceed the quota. Fishers will therefore need to reduce effort and/or purchase more quota.

This pushes the price of quota up, but since the subsidy only applies to a part of the harvest, the price

rises less than the subsidy payment. Since effort is falling, the biomass must increase. However, the

beneficial impact of the subsidy is decreased by sorne increase in the number of fishers, but, according

to the model, the increase in ûshers wili not outweigh the effort reduction.

Rom the analysis, it is seen that the subsidy will not lead to the optimal situation in the fishery,

ftom an effiaency point of view. The reason is that the subsidy does not tackle discarding per se, but

is attached to the landings of low value fish. That leads to a situation where a ôsher that discarded

only part of his low value catch wili be rewarded for bringing in catches that he landed without the

subsidy.

CHAPTER 6. SOME POLlCY ALTERNATïWlS FOR DISCARDïNG 102

It is not possible from this mode1 to assess which situation is better, ITQS with a subsidy, or

ITQS without a subsidy. One reason why is the cost of the subsidy scheme. Obviously, the money

to make the subsidy payments must come h m somewhere, and that spending needs to be justified.

The two situations are both suboptimal and which one is preferred will depend on the particulan

of the situation and the objectives of the management authority. If conservation is a high priority,

then the subsidy might be considered worth the trouble. Also, if the fishers in question have low

incomes relative to other groups in society, policy makers might like the idea of supporting fishers,

firstly through the subsidy and secondly through a wealth increase due to the higher quota value.

It is of interest to see what rde the parameter a plays in the results that have been presented

above. By fkst looking at equations 6.36 and 6.37 it can be seen that as a gets smaller and approaches

zero, the closer aa/& rnoves towards being q u a i to 1. Of course, when a is zero, there is no high

value fish, only low value fish. in other words, if a equals zero, then the price of quota will increase

by the exact same arnount as the subsidy. By looking at the effects the subsidy has on discarding,

effort and biomass, when a equals zero, the impact will be nonexisting. So for a fishery that bas largely low value fish, the total subsidy payments will be large - rnultiply s with a high number - but the impact on behaviour will be minimal. The subsidy will now purely be transferring wealth

from those who pay the subsidy to the fishers, without little or any reduction in discarding.

Finally, a word of caution is needed regarding the implementation of a subsidy scheme such

as the one described here. The setting of the subsidy needs to be planned carefully and there are

instances where a subsidy scheme like this could have disastrous effects. The management authority

can obviously not constantly change the subsidy, and it is likely that it would be set for a season at

a t h e . In fisheries where there are great price fluctuations the subsidy might lead to undesirable

effects. imagine for instance a sudden Jrop in prices. ü the subsidy is given in dollar terms, it

could actually lead to the price of the high value fish falling below the sum of the price of the low

value fish and the subsidy. In that case, a situation might arise that fishers would actually discard

the high d u e part of the catch! Anderson (1994) calls such behaviour lowgrading. Price stability

is therefore very important if a subsidy approach is being considered. Subsidies are unlikely to be

effective in a situation where catches are brought to a fish auction market, because there may be considerable price fluctuation in such markets. A fishery where fishers make long term contracts with

processors would be a much better candidate for a subsidy scheme. However, even in that case the

authorities must be careful in not announcing the subsidy until after the contracts between fishers

and processors have been made. Otherwise, the processors might offer a price for the low value fish

equal to the price without a subsidy minus the subsidy. Then the subsidy would not benefit the

fishers, but the processors, and there would be no effect on the behaviour of fishers, since they do

not receive the subsidy themselves.


6.3 Taxing high quality landings

It has been argued by Anderson (1994) and Pascoe (1997) that a tax on high quaiity landiigs is

equivalent to a subsidy on low quality landings. This section look at such a tax on high quality

landings and compares to the subsidy scheme presented in the previous section. In this case, the

management authority charges a tax, t, on high quality landings and the maximisation problem of

the individuai fisher thus becomes

The effective price of high quality fbh is pl - t which is obviously lower than p l . The basic idea with

the tax is to reduce the price differential between the high and low quaiity fish, thus reducing the

incentive to discard. The Lagrangian of this problem is

( ) L = (pi - t)crh(ei;z) + p r (1 - a ) h ( e i ; z ) - d' - ci(ei,d', y')

-agi + $ ( ( l - a)h(ei; z) - d') + + qt - h(ei; z) + 8 )


L e = phel - tah,. - ct, - cg# hct + $ ( l - a)h,, - $h,, 5 O , ei 2: 0 , eiC,, = O

Cd* = - f i - C d i + c p - p i + P i < ~ , & ? O , & & = O

Cqi = -a +pl = O

C,, = ( 1 - a ) h ( e i ; z ) - d' 2 O, pi 2 0, = O . .

L,+ = 9' + q' - h(e i ; z ) + d' 2 0 , 2 O, $t,, = O

The tax only enters the marginal effort condition, but not the marginal discardimg condition. At first

glance, it therefore looks as if the tax wîil not affect the discarding decision, only the effort condition,

This is not promising, as the probIem of excess discarding-highgading-in an ITQ system occurs

through the added benefit of quota savings when fish is discardeci.

To understand better the implications of a tax on high quality catches, use a situation where the discarding constraint is not biiding to undertake comparative statics. The procedure is the same as

in section 6.2 except that the exogeaous variable is the tax on high quality landings. This can be


shown to result in the following matrix equation

ose As in the ptevious case, the coefficient matrix is the matrix D irom section 5.2.2 above, wh

determinant was positive.

By using Cramer's rule, the effects of a change in the tax on the endogenous variables can be

found. Let's begin by looking at the effect on the biornass. It will be

indicating that when the tax is increased, the biornass will decrease. Cornparing this equation with

equation 6.33 shows that the effect of the t a is exactly the same as that of the subsidy. Looking

next at the efiect the tax has on discarding, it can be shown to equal

which shows that an increase in the tax leads to a reduction iri discarding. As with the effect on

biornass, this is exactly the same as in the case of a subsidy (compare with equation 6.34).

The effort level of the individual fisher will react to the tax change as given by

utilising the multiplicatively separable harvesting function. Yet again, this effect is equivalent to the

subsidy one (compare with equation 6.35). The fisher will reduce effort in response to the increased

tax.

Thus f a , the effect of the tax does not dXer from the subsidy suggesting that the two policy

options are equivalent. However, when looking at the impact of the tax change on the price of quota

the resuit di6ers irom the subsidy. In the subsidy case, the quota price rose with the subsidy, but in

the tax case the impact is the opposite as seen by

CHAPTER 6. SOME POLICY ALTERNATNES FOR DlSCARDiNG 105

As the tax on high quality landings is increased, the quota price falls as l e s profits can now be

made from the available quota. It is through this d i x t that discarding Is affected. It was noted

above that the marginal discarding condition does not change when the tax is introduced, but the

price of quota enters that equation. When the value of quota falls, so does the benefit of discarding

additional fish. The difference the subsidy and tax have on the wealth of fistiers is apparent now. In

the subsidy case the value of quota rises, making fishers wealthier, but in the tax case the value of

quota falls, reducing the wealth of Mers. The wealth effect also impacts the fishery in another way. In the comparative statics exercise

the effect on the individual hher is analysai, holding the number of fishen constant. However, due

to the reduction in wealth, an increased tax on high quality landings results in the exit of fishers

from the fishery, The profit of the marginal kher is

and the consequent entry condition in the fishery can be expressed as

If this is compared to the entry condition in an ITQ fishery without the tax on high qiiality landings,

equation 5.70, an additional term appears now, namely -at. This term has the impact of lowering

the average cost of the marginal fisher, implying that the tax will reduce the number of fishers

operating in the fishery. This is a fundamental difference from the subsidy, which resulted in an

increase in the number of tishers. AS an ITQ system with discarding present attracts too many

fishers to begin with, a policy of taxing high quaiity landings is tfierefore more promising than a

policy of subsidising low quaiity landings. At any rate, the two policies are clearly not equivalent,

contrary to Anderson (1994) and Pascoe (1997).

The question is whether the tax approach cari result in an optimal fishery. That is, whether a tax

can be found that results in the optimal number of fishers and in the optimal first order conditions

as given in equations 4.10-4.14. By comparing the cutrent entry condition with the optimal one,

equation 4.26, the difference lies in the term

If this were to disappear, then the two entry conditions would be the same. Consequently, a candidate

for the optimal tax can be derived as a d"

t = -- a h(en; z)

as this tax would lead to an optimal number of fishers in the ûshery. To analyse the effect on the

effort of the individual fisher, the tax must be substituted into equation 6.43. To facilitate the

analysis, assume that the fisher is operating on the dumping frontier, discarding everything while


the shadow value of discarding is zero. This implies that d/h(ei; z) = 1 - a. Also assume that the

tishery is optimal such that the quota price equals the shadow value of the fish stock, i.e., a = A. In that case, equation 6.43 becomes

which differs from the optimal condition in one respect, namely that the last term on the wrs is

multiplied by a. Since a is a fraction the marginal benefit for the individual fisher from increasing

effort is higher than optimal for any effort level. if the fisher was operating at the optimal effort

level, marginal benefit would exceed marginal cost and the fisher would employ more effort. The

reamn is that the fisher only recognises the shadow value of landed fish, not of discarded b h . The

recognition of the shadow value cornes through the value of quotas, but the quotas only apply to

landed 6sh. The tax on high quality landings does not change this and therefore the fisher stili has an incentive to increase effort above the optimal level.

The cases where fishers àiscard only part of the catch or discard everything and have a positive

shadow value of discarding are siniilar to the case just analysed. In al1 of these cases, it is not posible

to find a tax on high quality landings such that the marginal effort condition and the entry condition

are both optimal at the same time, and therefore such a tax will not be able to bring an ~ T Q fishery

where discarding is present to its optimal state. However, from an efficiency point of view, the tax is

preferred to a subsidy on low quality landings since the subsidy increases the number of fishers even

if there are already too many fishers in the fishery. The tax, even if not optimal, moves the fishery

in the right direction by reducing the number of fishers.

The result of the analysis here differs from Anderson (1994). There it is assumed that taxing

high value catches or subsidising low value catches is equivalent. That is not correct since the tax and

the subsidy enter the first order conditions in different ways. h tax on high value catches would not

enter the marginal discarding condition, but the subsidy does. in addition, Anderson claims that the

goal is to stop discarding and therefore it is not important to find the exact tax or subsidy. There are

two problems with that point of view. Firstly, the optimal level of discarding is not necessarily zero,

so stopping discarding completely may not be the objective at aii. Secondly, since the subsidy will

affect the effort decisions of the fisher it is not correct that the level of the subsidy is unimportant.

6.4 Reducing the cost of landings

The final management tool to be analysed in this thesis is a reduction in the cost of landigs of fish.

From the marginal discarding conditions derived in this thesis it is plain to see that the marginal

cost of lanàîngs is the marginal benefit of discarding fish. It therefore seems plausible that a policy

that lowers the cost of landings, thus lowering the marginal benefit of discarding, could work weU

in reducing discarding. The implementation depends on the particular situation in each country

CHAPTER 6. SOME POLICY ALTERNATIVES FOR DISCARDING 1 07

or fishery. For instance, if harbour fees are linked to the quantity landed, a reduction in landings

cost could be achieved through a regdation that lowers harbour fees that fishing vessels need to pay

when landing fish. For a governrnent this may be a very attractive policy as the cost of the policy

is liely to be low. Port authorities are usually responsible for the collection of harbour fees so the

government could use aiready established mechanisms for this purpose. Fishers, of course, will make

sure that the port authorities do not charge fees that are too high. Therefore the administrative

cost would not be very high for the government. -41~0, even if this policy represents a subsidy to

the fishing industry, the actual implementation would not entail any transfers to the industry, since

the subsidy would be in the form of a rebate on harbour fees. Of course, landiigs costs can also be

reduced by a direct subsidy on the total amount of fish landed.

For the analysis, the mode1 of r ~ q s in section 5.2.2 will be used. The rnodel can be used without

any changes as the analysis will be done through comparative statics. The equations that need to

be used are equations 5.71 to 5.75. For convenience, they are reproduced here

Equation 6.59 is the marginal discarding condition. As discussed in Chapter 5 the presence of a

causes the highgrading problems of an ITQ systern. A reduction in the marginal cost of landings, 7,

will clearly offset some or al1 of the e f k t of a. However, the marginal cost of landings aiso enters

the marginal effort condition, so as with the subsidy discussed in the previous section effort will be

affectecl by the change in the marginal cost of landings.

Al1 the 3n + 2 equations above together solve for the endogenous variables of the system; ei, d', q', x, and a for all i. As before the system can be Merentiated with respect to d l the endogenous

variables and the marginal cmt of landing. The resuiting equation system can be expressed as

The coefficient matrk is identicai to D in equation 5.76 whose determinant is positive.


Utiiising Cramer's rule, it can be shown that

which implies that changing the marginal cost of landings has no effect whatsoever on discarding

and effort decisions of fishen, and consequently there is na effect on the biomass! How can this be?

The answet comes from looking a t the effect on the quota price, which is

which States that if the marginal cost of landings fails by one dollar, then the quota price increases

by one douar. Looking at the marginal conditions for effort and discarding (equations 6.58 and 6.59)

it is clear this latest result means that changes in the marginai cost of landings have no impact at

al1 on the marginal conditions.

Let's now explain what takes place when the margiral cost of landings is reduced. Shce this

reduces the cost of harvesting al1 fish, regardless of value, this increases the marginal benefit that

can be made from fishing by exactly the decrease in the marginal cost of landings. Since everyone's

marginal benefit increases by the same amount, everyone wants more quota, but nobody is willing to

sell. This will push up the quota price until it has increased by exactly the reduction in the landings

cost. .4t that price, the situation is the same as it was before. Once the new equilibrium is reached

each fisher is operating at the same effort and discarding level as before. The only difference is that

the increased quota price has made curent fishers weaithier than before, while future generations

will be Iess wealthy.

in this model, where the marginal cost of landing is assumed fixed, this policy is completely

ineffective in changing the behaviour of fishers. The difference between this policy and the subsidy

analysed in the previous section is that the subsidy only applied to the low value fish, while the

landings cost rebate applies to ail harvest regardless of value. Therefore the subsidy is only partially

reflected in the price of the quota while the rebate is fully incorporated into the quota price.

6.5 Discussion

in t h i chapter, four different policies to reduce discarding of fish have been analysed. One of these

policies has the potential of bringing the fishery to the optimal situation. This is the crime and

punishrnent approach where fishen are h e d when caught throwing fish overboard. The second

policy, subsidy on the landings of low value fish, is not as promising. \IWe it reduces discardiag it

also attracts more fishers. This is undesirable since under an ITQ scheme in the presence oldiscarding

there are too many fishers to begin with. However, the subsidy policy wül lead to an incroase in

the biomass, so it may be considered justified. A tax on high value lanciings has simïiar effects on

discarding, but in contrast to the subsidy, there will be fewer fishen operating Ui the tishery due to

CHAPTER 6. SOME POLlCY ALTERNATIVES FOR DISCARDING 109

increased costs. The fourth policy, reducing the cost of landing fish, is completely ineffective since

it does not focus on the Iow value fish at ail.

Some lessons can be learned fiom the analysis. Firstly, the policy needs to focus on the discarding

behaviour. The subsidy rewards fishen for landing fish that they would land anyway and affects not

only the discarding decision, but also the effort decision and therefore does not achieve its goal. Secondly, it smms that a policy that increases costs is more effective than a policy that reduces

costs. Recall that in a pure ITQ system in the presence of discarding there are too many fishers. Any

policy that reduces costs is bound to attract more khers and will therefore not lead to an optimai

situation. A cost increasing policy will reduce the number of Gshers and is therefore heading in the

right direction, as long as econornic efficiency is an objective of the management of fisheries.

Chapter 7

Summary and conclusions

This thesis has looked at the problem of discarding of fish frorn an econornic perspective. -4 mathe-

matical rnodel of a fishery was developed. This rnodel allows comparisons among various situations,

firstly, what can be cdled the two extremes, narnely an optimal fishery and an open access one,

and then a number of different management policies that al1 aim at moving a fishery from an open

access situation to an optimal one. The analysis focused on two objectives, firstly, conservation of

the fish stock and secondly, economic efficiency. The analysis was undertaken in a number of steps,

starting with a hhery in the absence of discarding. After looking at the optimal and open access

situations a number of management policies were explored, a number of which have the potential

of bringing a fishery to the optimal level. Then discarding was introduced into the model and the

optimal and open access situations analysed again. Having gained understanding of the discarding

behaviour of fishers, a few management policies were explored, and it was seen that in the presence

of discarding only in special cases would any of them lead to an optinial fishery. Of particular in-

terest was the individual transferable quota system which has been under heavy criticism due to

the alleged incentives of excessive discarding and highgrading that such a system creates. The final

step of the analysis was to examine three potential rernedies to deal with the probIem of excessive

discarding. The fist remedy was a cost increasing policy where fishers are punished through fines

if they are caught discardimg, while the other two worked to reduce the costs to fishers aiming to

create economic incentives for fishers to voluntarily reduce the amount of dicardimg.

As stated in the previous paragraph the analysis was undertaken through the use of a mathe-

matical model. This approach has limitations that need to be recognised and kept in mind when

applying the hdings of the thesis. -4 mathematical model can never reffect fuiiy all the compfexities

of a real world situation; it is a simplification of reality. However, the purpose of using a math*

matical model is to isolate the important factors that explain the behaviour at hand with the goal

of understanding better how these factors work together to influence behaviour. If the modeliing

CHAPTER 7. SUMMARY ANI) CONCLUSIONS 111

exercise is successful in developing this understanding, then it can provide a valuable input for policy

makers when developing laws and regulations. However, the modelling input is only one ingredient

to be included in the policy m a h g process. The practicaiities of the different situations must be

kept in mind as well. For instance, imagine a proposal to implement a crime and punishment scheme

as analysed in Chapter 6. It seems rather obvious it will make a big difference whether the hhery at

hand is a fishery with 50 large scale fishers or a fishery with 3 thousand subsistence fishers. With 50

fishers a crime and punishment scheme may well be a viable alternative, while monitoring 3 thousand

fishers may be asking a bit too niuch, even if leaving aside the political difficulty of trying to collect

fines from subsistence fishers. The specifics of the particular fishery must always be put together

with the results of the mathematical model.

While the analysis in this thesis has been kept at a very basic and simple level, it has proven to

be fruitful in gaining better undentanding of the discarding behaviour of fishers and how they rnay

react to policies that aim to reduce the level of discarding. In the remainder of this chapter some of

the results of the anaiysis in the thesis will be reviewed and discussed.

It must be remembered that discarding may not be a problem at dl. A fundamentai issue is that fishers do not want to discard fish, because it is costly to them. If they had the choice they

would prefer not to catch low value fish in the first place. After ail they make their profits by selling

fish, not throwing it away. However, as long as fishing gear is not perfectly selective fishers will

always catch some unwanted h h . One of the findings of the thesis is that in some cases it will be

socially optimal to discard low value fish. If the price that the fish fetches in the market is below the

cost of bringing the fish to the market then it should be discarded. This is a fact that some people

have a difficulty accepting. For instance, many argue that throwing fish overboard is wasting food

resources which should never be condoned. However, fiom an economic point of view the resources

spent in landing this low value fish are better spent on other economic activities, perhaps other food

production.

It is very clear fiom the anaiysis in the thesis that discarding is an economic decision based solely

on economic factors. For instance, without a pnce differentiai between high value and low d u e fish,

fishers would not discard a single fish. Even if there are other restrictions such as limited hold size

of a vesse1 or quotas that limit the quantity that rnay be landed, without a price differential these

restrictions will not cause discarding by themselves. It is true that restrictions of this type may

exacerbate discarding, but on their own they are not sufiicient. It is iiiely that this explains why

various authors have found that individuai quota systems only sometimes seem to lead to discarding

of fish.

While a positive price dinerential is a prerequisite for discardimg, it is not sufficient. The discus-

sion on the diicarding CO-istraint in Chapter 4 illustrates this point well. Discarding of fish is not a

costless activity, and in some cases the cost of discarding will outweigh the gains from discarding.

.4h, if the species in question inherently is of high value then the benefit of landiig the lower value

CHAPTER 7. SUMMARY AND CONCLUSIONS 112

catches of that species may be high enough to outweigh the discarding incentive caused by the dif-

ferentiai. Stating this diEerently, the higher is the value of the low value fish, the geater must the

price Merential be for a 6sher to discard.

The fact that discarding is a function of the various economic factors makes discarding a dynamic

activity in the sen= that the level of discarding will fluctuate with changes in these economic factors.

For instance, if prices of a particular species are very volatile, Say, due to seasonality or the availability

of substitutes, then discarding is likely to fluctuate depending on the season or the availabüity of

substitute species.

With regard to fisheries management the presence of discarding has considerable effects. Most

of the commonly suggested management policies that theoretically are capable of bringing a fishery

to its optimal level no longer wiU do so. Additionaily, these policies have different effects on the

incentive to dicard fish. For instance, the two taxes analysed in this thesis, will only in special

cases be optimal when discarding is present. 00th the individual quota systems-transferable and

non-transferable-giw rise to excessive discarding and neither is therefore optimal. An ~ T Q system

also leads to a greater number of fishers than optimal since fishers do not recognise the full coçt fmm discarding fish and consequently the private average cost is lower than the social average cost. This

implies that private profits are higher than social profits, thus attracting more fkhers to the fishery.

One striking result ftom the analysis in this thesis is that even X dl of the management policies

analyseci are suboptirnal in the presence of discarding, they dl lead to an increase in biomass as

compareci to the open access situation. If either of the tax rates is increased or quotas reduced the

result is a larger biomass, even when allowing discarciing to take place. This is an important finding

as it suggests that even if restrictive management policies such as [TQS increase the incentive to

discard bh, they will not lead to an increase in effort. A fisher whose quota is reduced will reduce

effort even if he dixards more tish. The reduction in effort will be less than if discarding was not

possible, but it will still be a reduction. Since effort is failing, the size of the fish stock will increase.

This suggests that it is not the level of discards that is important from a conservation point of view,

but the overail effort level and the associatecl fishing mortality of the stock. Therebre conservation

policies should focus on effort, aiming to d u c e fishing mortality, rather than a reduction in discards.

This is not to Say that the excessive discarding that may result Gom a management policy is harmless.

However, the harm is on the economic side, not on the biological side. Excessive discarding le& to

a loss for society in terms of wasted economic resources, but according to the mode1 in this thesis it

will not lead to the depletion of iïsh stocks.

Li excessive discardimg is considered a problem the question is what can be done to reduce

discardùig, preferably to the optimal level. In this thesis, four possibie remedies are explored in

the context of an individuai transferable quota system. The first takes a crime and punishrnent

approach, considering discarding as a criminai behaviour that must be punished. The second remedy

is a subsidy on the l a n d i i of low value 6sh taking the approach that fishers that do not discard

should be rewarded. The third remedy is a tax on high value fish, as that will reduce the price

differential between the two types of fish, and the final remedy is a reduction in the cost of landing

fish, but that cost is a major factor in the discarding decision of the fisher as this cost can be reduced

by discarding fish.

Of the four remedies, the crime and punishment policy is the only one that has the potential of

bringing the fishery to the optimal Ievel. The subsidy on low value landings does reduce the incentive

to discard, but by lowering the average cost of fishers, thus increasing profits, it attracts new fishers

into a fishery that aiready has too many fishers. However, the subsidy approach does increase stock

size as less fish is discarded while the same amount is Ianded as before. Therefore overall effort is

reduccd, increasing the biomass. However, fishers are not operating at the optimal effort level; each

fisher uses tao Little effort while there are too many fishers present. The tax on the landings of

high value fish works in many ways similar to the subsidy with one major exception. Since the tax

increases the cost to fishers, reducing their profits, it leads to the exit of some fishers. Nonetheles,

the tax will not lead to an optimal fishery. The fourth remedy which is to reduce landing costs is

found to have absolutely no effect on the effort and discarding behaviour of fishers. The reason is that

the rebate on landings cost does not distinguish between high and low value fish. As a consequence

this rebate will be fully captured in the quota price. That is, if the rebate is a dollar per tonne the

quota price will rise by a dollar per tonne. The only effect of this policy is to increase the wealth of

current fishers through higher quota values without any effect whatsoever on discarding.

Looking in a bit more detail at the crime and punishment option, the reason why that approach

works is that it focuses on the actual discarding behaviour of fishers, while the other options afïect

other aspects of the fishing operations. However, even if the crime and punishment approach has

potentid, there are serious concerns regarding its implication. For instance, as mentioned above, it

matters whether there are fifty fishers operating in the fishery or three thoirsand. When contem-

plating this option, one must look carefulty at the specifics of the situation at hand. For example,

in Narnibia a no discards poIicy is enforced by observers on board each vessel, sometimes even two

observers on the bigger vessels that stay at sea for weeks at a tirne. In Namibia labour costs are

relatively low and the whole fleet only consists of approximately 300 vessels. In that case a complete

observer coverage is possible. In Iceland, on the other hiuid, the fleet consists of aimost 2,000 ves-

sels and labour costs are among the highest in the world. A full observer coverage is therefore out

of the question. However, there are deep concerns over excessive discarding by the Icelandic fleet.

Therefore, the Icelandic Directorate of Fiheries is considering other rneans of enforcing a discards

ban such as on-board cameras and spot checks. The point is that what works in one fishery may not

necessarily work in another . It should be remembered that excessive diiarding, such as highgrading, is an externality since

it is caused by the individual 6sher not recognising the fidl cost of his discarding actions. Using a

difTerent terminology, the social cost of discarding is higher than the private cost. That, in turn,

implies that fishers do not recognise fully the benefits of more selective fishiig gear. Therefore,

efforts from the government in developing more selective fishing gear may be justifieci in cases where

excessive discarding is believed to be a problem.

The enforcement cost of any policy can be considerable, and one must aiways compare the costs

of implementing a policy, such as the crime and punishment policy, with the perceived benefits. If the costs are greater than the benefits, then it may well be better not to implernent the policy at dl. The difficulties with discarding is that very little reliable data eiasts on its level. In countries where

ITQ systerns have been introduced there has aiways been considerable opposition to such systems.

Due to the difficuity of confirming the extent of discarding it is possible that opponents of ITQS

use anecdotal evidence to make discarding seem more serious than it actually is. The other side

of the coin is that proponents of [TQS may downplay the importance of discarding, again because

diicarding behaviour is difficult to measure. This is not rneant to imply that the people involved

purposely bend the truth, but simply to illustrate the importance of, and need for, proper research

into the issue of discarding-otherwise objective anaiysis and proper understanding of the extent of

discarding is difficult to achieve.

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