SYSTPMS A.NALYSIS OF U.S. I-I/u^AGEMENT STRATEGIES
IN TKE GULF OF MEXICO SHRIl-iP INDUSTRY

By

PAUL JEROME HOOKER

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILU-IENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
1972

UNIVERSITY OF FLORIDA

3 1262 08552 4485

Copyright by

Paul Jerome Hooker

1972

FOR KERRY

ACKITOVTLEDGMEIH'G

My debt of gra^.itud£ for assistance during my graduate career
exceeds my ability to provide acltnowledgment . I tru.tit that my many
unrecognised benefactors will forgive vie fc-i ciLiug ori].y a fe\': of the
debts that I perceive to be the greatest.

The greatest debt should be acknov;ledged first. Mine is duo ray
wife, Martha, for her moral support during my graduate career and uiy
young daughter, Kerry, for making that career vrorthwhile,

Leo Polopolus has served as Chairman of my Supervisory Conmittee,
academic and professional advisor, and friend. Max II. Lar.gham has pro-
vided good advice during my graduate career and liis thorough reviews of
my dissertation research materials have been invaluable. W. W. McPherscn
has provided a X'/ellspring of experience from v/hich I have freely drawn
as a student and as author of this dissertation. C . C. Osteibind
brought the expertise of an economist with experience in the Gulf of
Mexico shrimp industry to bear in his revicvj of the dissertation manu-
script. For these contributions, as well as many left unmenticned, I
wish to thank the members of my Supervisory Comnuttee.

I wish to thank K. R. Tefertiller, Chairman of the Department of
Food and Resource Economics of the University of Florida, for providing
financial assistance during the course of research on this project. In
addition, I wish to acknowledge departmental support of the project
which allowed use of the facilities of the University of Florida
Computing Center.

iv

Mrs. Cindy Bass, with the picLovinl aid oi= Mrs. Pntti Fesmlre, has
accomplished the transrorm^tion of: this dissertation from a longhand
manuscript into its present form. For this feat she has earned my
gratitude and admiration of her considGrable ability.

TABLE OF CONTENTS

Page

ACKNOWLEDGl-IENTS iv

LIST OF TABLES viii

LIST OF FIGURES . . . .' x

ABSTRACT xi

CHAPTER I

INTRODUCTION 1

CHAPTER II

BIOECONOMIC THEORY 3

Fish Population Theory 3

A Theory of Open Access and Common Property

Resource Exploitation 17

Bioeconomic Theory of a Fishery 33

CHAPTER III

GULF OF MEXICO SHRIMP INDUSTRY: DESCRIPTION AND MODEL ... 38

Description of the Industry 38

The Gulf Shrimp Resource 38

The Gulf Shrimp Fleet 46

Processing and Marketing the Gulf Shrimp Catch . . 56

A Model of the Gulf Shrimp Industry 58

A Model of the Gulf Shrimp Resource 59

A Model of the Gulf Shrimp Fleet 62

A Model of the Marketing and Demand Sector of

the Gulf Shrimp Industry 69

CHAPTER IV

METHODOLOGY AND DATA 73

Simulation as a Tool for Model Building and Policy

Evaluation 74

Data 84

The Computer Program 95

vi

TABLE OF C01;TEvyi'S--Con!:irnied

r?.ge

CllArTKR V

RESULTS OBTAINED WITH THE SIi-lLlLATIOi>I MODEL Ai'i) POLICY

IMPLICATIONS '^''

Model Validation -^^

Simulated P.csults for the Policies Con:;.ldf:rv-f] 11'';

Policy Implications -'-^^

CHAPTER VI

RECAPITULATION OF THE PPESENT STUDY WITH SUGGESTIONS FOR

Iffl'ROVEMENTS /Mv'D FURTHER WOPvK 130

APPENDIX I

APPENDIX II

LIST OF REFERENCES .
ADDITIONAL REFERENCES
BIOGRAPHICAL SKETCH .

15!

Recapitulation of Objectives and Evaluation of

Achievements • •

Improvements Needed in the Present Model snd Suggest ionb

for Further Work ^^^

134
1^)8
180
183
185

vli

LIST UF TABLES

Table Page

3.1. Landings of Gulf slirimp by area and specicF! for the years

1967, 1968, and 1969 *. 41

3.2. Percentage distribution of Gulf shritnp landings by area

and species for the years 1967, 1968, and 1969 ... 43

3.3. Average landings and percentage distribution of average

landings of Gulf shrirap by area and species over the
years 1967, 1968, and 1969 44

3.4. Summary of shrimp otter trawl boats, vessels, fishermen,

and gear in the Gulf states, 1966 47

3.5. Summary of shrimp otter travel vessels of the Gulf states,

by tonnage groups, 1966 51

3.6. Marine economics data - 65 foot Gulf of Mexico shrimp

vessels 53

4.1. Age (in months of 4.33 weeks each) distribution by size

and sex of brown, pink, and white shrimp in the Gulf

of Mexico 86

4.2. Coefficients to convert 24-hour days fished to fishing

mortality and estimated square nautical miles fished

by area 87

4.3. Vessel size classes and sweep capacity of nets along

headrope in hundreds of feet 89

4.4. Mean 24-hour days fished per month by a vessel in each

size class 90

4.5. Factors to adjust days fished by a vessel in a size

class to reflect variations in average days fished

by vessels in different areas 91

4.6. Number of vessels in each size class estimated to have

home ports in each area and number of vessels in

each size class assumed to be fishing in each area

in December of a typical year 93

4.7. Reduced form coefficients for quarterly shrimp model,

1956-1967 94

viix

LIST OF TABLES— Contiriued

Table Page

5.1. Adjusted coefficients to convert 24--hour days fished to

fishing mortality and factor? (APFACJ's) by which
initial estimates of the mean number of shrimp
recruits were multiplied for final use in the
model 99

5.2. Size composition of actual shrimp catches in the Gulf

and South Atlantic states for the years 196A-1970

and average size composition of thirty years catch

data generated by the computer model 101

5.3. Simple correlation coefficients between selected vari-

ables based on values generated by the computer

model 3 06

5.4. Comparison of percentage distribution of effort by area

in each month of the year of sample vessels with the
percentage allocation generated by the computer
model in the 30th year for vessels (vessel size
classes 2-5) 109

5.5. Comparison of percentage distribution of effort among

aggregated areas in eacli month of samiple vessels

with the allocation geiierated by the model 110

5.6. Annual fixed cost charges per vessel employed by the

computer model and the capitalized values that

these sums represent 113

5.7. Value of the fleet under different assumptions about

average life of vessel and gear and using values

given in [1] 115

5.8. Average annual returns from the Gulf shrimp catch, costs

to the industry and fixed investment in the industry
assuming a five year investment life under various
settings of the policy variables 118

5.9. Rate of return to fixed investment in the Gulf shrimp

fleet under various settings of the policy

variables 119

5.10. Changes in average annual returns, costs, and investment

occasioned by the imposition of controls 120

5.11. Average annual total production costs incurred by the

Gulf of Mexico shrimp fleet per pound of shrimp
produced and average annual wholesale price of shrimp
produced and average annual wholesale price under
alternative policies 124

ix

LIST or FIGURES i

Page

Curves Describing the Population DyaainicG of a Single

Year-Class Within a Fishery -•

Major Shrimp Fishing Areas in the Gulf of Mexico .... AO

Shrimp Vessel with Otter Traul Nets Deployed . 49

Shrimp Processing and Marketing Channels 57

Schematic Representation of a Framework for Validation

of Simulation Models ""^

4.2. Flow Diagram of the Computer Model of the Gu!! f of

Mexico Shrimp Industry ■ ^6

5.1. Annual Values Generated by the Computer Model for

Wholesale and Ex-vessel Prices, Total Landings,

Imports, and Effort in Adjusted Days Fislied 104

5.2. Annual Values Generated by the Computer Model for Total

Production Costs, Adjusted Days Fished, Value of
the Fleet Assuming a Fixed Year Investment Life and
Net Return

Figure

2.1.

3.1.

3.2.

3.3.

4.1.

5.3.

Simple Correlation Coefficients Between Selected

Variables Based on Values Generated by tha Computer
Model

105

108

Abstract of Dissertation Presented to th?
Grfjdu;,>te Council of the University of Florida in Partial fulf i.llr.cnt
of the Raquireincnts for the Degree of Doctor of Philosophy

SYSTEMS /J\ALYSIS OF U.S. MAIvlAGEi-IENT STRATEGIES
IN THE GULF OF MEXICO RHRBIP IOTjUSTRY

By

Paul Jerome Hooker

March, 1972

Chairman: Leo Polopolus

Major Department: Food and Resource Economics

The shrimp resource is an open access resource. Except for r.itua--
tions attributable to territorial waters, the shrimp resource is open
to exploitation by anyone possessing the physical capability to exploit
it. A priori theoretical reasoning suggests that the economic return
attributable to the shrimp resource as a productive input will be dis-
sipated so long as it retains an open access status. A problem of
immediate practical importance is to determine the extent of dissipa-
tion of the returns to the shrimp resource in its open access status
and the relative efficiency of different institutional schemes in
capturing this return.

The first objective of this study was to determine the responses
of individual fishing firms in the Gulf of Mexico shrimp industry and
the resultant aggregate effect for the industry to changes in the shrimp
population in the Gulf of Mexico, technological conditions of harvesting

xl

and processing, and demand coiiditj.ons . A second ob3Cc!.i\e was to
deteriiiine whether a] tP) native nanageraent strcitegies exist which will
improve industry effiiciency in a social sense, reducing overinve.stiv.ent
and/or the extent of non-optimal husbandry practices that occur as a
result of the free use of a;i open access resource.

A theory of the basic resource was developed to describe tlie behav-
ior of a particular year-c]ass in a fishery ovor time in teims of growth
in Vi'eight, recruitment patterns, and natural and fishing mortality
rates. An economic theory of exploitation of an open r.ccess resource
was developed and the divergency between behavior that is optimal for
the industry as a whole and the behavior resulting from uncoordinated
individual actions was derived. The basic resource and economic theo-
ries were then synthesized into a bioeconomic theory cf an exploited
fishery and the on-vessel entry and fish landings charges needed to
manage the fishery in an efficient m^anner were specified as theoretical
aggregates.

An abstract model of the Gulf shrimp industrj' V7as constructed based
on the developed theory. The industry model took the form of three
sub-models, one each for the basic resource, harvesting, and demand
sectors. The interface between the basic resource and harvesting sector
models was composed of the availability of shrimp by size and area and
the amount of effort applied by the shrimp fleet to capturing the basic
resource. The interface between the harvesting and demand sector models
encompassed the catch produced by the fleet and the ex-vessel price paid
for this catch by the demand sector. The model provided policy vari-
ables in the age (size) at which shrimp first become subject to capture,
the barriers to vessel entry into the fleet as expressed in annual

Xll

license fees, and per pound taxes ciiarged the fleet members on the
shrimp landed as expressed in reduced ex-vessel prices.

The first objective was satisfied and the abstract model trans-
formed into ^n cinpirir.al model by drawing, en published research results
as well as estimating model parameters from primary secondary' data.
The empirical model of the Gulf shrimp industry was developed as a
simulation model and a computer program was developed to generate model
behavior over time. Information generated by the simulation model on
selected indicators of industry performance was used to satisfy the
second objective by establishing tentative conclusions, subject to the
limitations of the model, as to the relative effectiveness of the poli-
cies considered in attaining alternative objectives.

xiii

CHAPTER I

INTRODUCTION

niere are both academic and practical reasons for this particiilar
studj'. Tlic shrimp resource is an open access resource. E>;cc'pL for
situations attributable to territorial waters, the shrimp resource is
open to exploitation by anyone possessing the physical capabllit}/ to
exploit it. The problems involved in creating instjtutions for effec-
tive public or private ownership of open access resources and in
determining the relative efficiency of exploitation of the resource
under various institutional forms are particularly intriguing from the
academic point of view.

These problems are not without practical importance. For example,
the annual value of the Gulf shrimp resource at point of first sale has
been in the neighborhood of $100 millioii in recent years. A priori
theoretical reasoning suggests that all the return attributable to the
shrimp resource as a productive input will be dissipated so long as it
retains an open access status. Thus, a problem of immediate practical
importance is to determine the extent of the potential return available
from the resource and the relative efficiency of different institutional
schemes in capturing this return.

The objectives of this study are to:

1. Determine the responses of individual fishing firms in the
Gulf of Mexico shrimp industry and the resultant aggregate
effect for the industry to changes in:

1

2

a. The shrimp population In the Gulf of Mer.ico;

b. Technologic;il coijditlcias of harvesting and processing; and

c. Demand condiiions.

2. Determine whether alternative management strategies exist whicli
will improve industry efficiency in a social sense, reducing
overinvestment and/or the extent of non-optimal huirbandry prac-
tices that occur as a result of the free use of an open access
resource.
The plan of attack for fulfilling the above objectives Is briefly
as follows. Chapter II presents some theoretical considerations with
respect to open access resources, especially fishery resources. (The
term "fishery resources," as used here, includes the crustaceans.)
These considerations involve economic, as well as biological, theories
of the fishery resources. Chapter III presents a description and
abstract model of the Gulf shrimp resource involving both economic and
biological considerations — thus, it is a bioeconomic m.odel. Chapter IV
discusses the methodology used and data limitations. Chapter V contains
the results of the application of the model to the available data,
simulated results from operating the system under alternative management
strategies, and a discussion of policy implications. Chapter VI, the
concluding chapter, is devoted to a review of the study and a critical
evaluation of the analysis with suggestions for improvement and further
research.

CHAPTER II

BIOECONOMIC THEORY

A fishery is a prime example of a system involving man as an ecc-
nomically viable predator on a natural population. To adequately
describe such a system, biological theory describing the behavior of
the natural population must be meshed with economic theory describing
the behavior of man as the predator. The result of this synthesis may
best be called "biocconomic theory." The biological stock enters into
the economic model as an input. Consequently, when dealing with bioeco-
nomic theory, biological theory is appropriately treated first. After
a discussion of fishery population theory, the economic theory of
exploitation of open access resources is presented. The chapter con-
cludes with a combination of the two theories into a bioeconomic theory
of a fishery.

Fish Population Theory

This section draws heavily on som.e recent work in fish population
analysis by J. A. Gulland [20], although generalized functional forms
are used in place of Gulland 's specific functional notation.

Considering a closed stock subject to exploitation, the factors
(rates) determining changes in the stock over time are [see also 20,
p. 3]:

1. Recruitment or the rate at which young fish reach a size and/or
age at which they are considered to become part of the stock

3

subject to exploitation; e.g., larv:'! shrimp and pelagic
flounder are not considered ))art of the conmercially exploited
stocks of shrimp and flounder. If tliere is no clear-cut
natural recruitment size, then the recruitment size may be
arbitrarily set.

2. Growth of individuals or the time rate of gain in length and/or
weight or some other measure of growth.

3. Deaths due to fishing or the catch rate; these V7ill be roughly
correlated with landings and will be ascertained by "fishing
effort" which is determined outside the biological frame^TOrk
of the fishery.

4. Deaths due to other causes or the natural mortality rate.
Figure 2.1, corresponding roughly to Gulland's Figure 1.1 [20,

p. A], depicts the behavior over time of the length, weight, and number

of individuals in a particular year-class (the progeny of the stock in

a given year) and the behavior over time of the total weight of the

year-class.

The ordinate of Figure 2.1 is assumed to be arranged in units

appropriate to the particular curve of interest. The abscissa measures

time. The reproductive process is assumed to be essentially complete

at t ; t is the time at which the individuals are recruited to the
o r

stock while t is the point in time at which they become subject to
mortality from fishing. Beyond t , the solid portion of the line repre-
senting number of individuals is drawn under the assumption of zero
fishing mortality, while the dashed portion represents numbers of indi-
viduals when the year-class is subjected to some constant level of
fishing mortality.

VJeight ,
Length,
or Number

W maxiraum

or
L maximum

1

^^ individual length

individual veit^ht

f;otal vcight of
year-class

number of individuals

-Bl

Time

Figure 2.1. Curves Describing the Population Dynamics of a
Single Year-Class Within a Fishery

6

The total weight curve is calculated under the assumption of an
uncxploited stock. The total weight of t.ie year-class in the absence
of fishing is assumed to increase, at first at an increasing rate until
time t , and thcr at a decreasing rate until some maximum weight is
reached at time t • Then total weight declines, more and more rapidly
at first but eventually at an algebraically increasing rate, until the
year-class is eliminated from the stock. Individual fish are assumed
to grow in length throughout their lives at a decreasing rate. Indi-
vidual fish gain in weight throughout their lives at an increasing rate
during the first part and at a decreasing rate during the latter part
of their lives. The number of individuals in a year-class decreases
over time, slowly approaching and finally reaching zero, implying that
the natural mortality rate is positive and decreases over time; i.e.,
the rate of survival is negative but increasing algebraically at any
point in time. The individual weight and number factors combine to
produce the aggregate weight behavior described above.

The recruitment and fishing mortality factors do not lend them-
selves to straightf on^/ard description so vjell as the otlier factors. If
the population has a well-defined and short spavrning season and homoge-
neous development of young so that all members of each year-class are
essentially the same size, then the recruitment function will take the
form of a series of points, zero at all times other than the instant of
time in which year-classes enter the exploitable stock, at which time
the function takes on the value of the size of the year-class in ques-
tion. However, if, as is more likely, the spawning period occupies a
more or less significant portion of the year and subsequent development
is not homogeneous, then recruitment will not occur at an instant of
time. Rather, it will be spread over an interval of time during which

7

the proportion of the year-class being recruited into the stocV increases
at first at an increasing and later at a decreasing rate. Given that
the juveniles are in the sairie area as is the exploited stock, the time
pattern of recruitment is of interest wi*"h respect to determining opti-
mal time patterns of fishing and gear selectivities. An alternative
situation is one in vhich juveniles are segregated from the exploited
stock by location and recruitment occurs by migration. In this situa-
tion, the proportions of the year-class of different length (size) being
recruited are of interest. Until a mean recruitment length is reached,
the proportion of the year-class entering the exploited stock increases
at an increasing rate while it increases at a decreasing rate beyond
this mean length. To place the appropriate emphasis on the recruitment
rate and to relate it to an aspect of fishing effort — gear selection —
the following quote from Gulland is helpful:

Recruitment is, by its nature, much less easy to express
in quantitative terms than mesh selection. As the main
interest is in the combined effect of recruitment and
selection — i.e., the pattern of entry into the catch — the
recruitment pattern is very important when it is above,
or overlaps, the range of gear selection, but not when it
is complete before gear selection starts. If, therefore,
all fish have been recruited at a size below the selection
range of any likely mesh size, then the precise pattern of
recruitment may be ignored, and it can be taken arbitrar-
ily as occurring at some convenient length or age below
the selection range ... [20, p. 86].

The importance of the recruitment rate seems to lie in its relationship
to gear selectivity. The interaction of these two factors produce the
commercially important result: the rate of entry of juveniles into the
catch.

Gear appears to fall into three general groups: completely non-
selective gear; e.g., a fine-mesh purse seine; gear that is non-selective
above some size of fish; e.g., certain trawls; and gear that is selective

8
over a certain range of fish sii,e, allov;ing those smaller and larger to
escape; e.g., gill-nets. There is little to say about the completely
non-selective gear except to point out that if legal size restrictions
on landings are placed on a fishery (thus arbitrarily defining the size
at which juveniles are recruited into the exploited stock) and juveniles
are subjected to the non-selective gear, then a certain portion of the
catch will be discarded at sea. If part or all of this discarded catch
dies, the various year-classes will be reduced by the extra mortality
not reflected in landings. Thus, the stock will be reduced beyond what
would be expected from measured fishing mortality (landings). The
implication is that in order to properly assess the population, measured
fishing mortality (landings) must be adjusted to allow for the mortality
experienced by the juveniles.

Gear that is selective to the extent that escapement of individuals
below some size is allox'/ed is of particular interest in this study.
Shrimp trawls allow small individuals to pass through the netting while
larger individuals are retained. The selectivity is not perfect,
however, and over some size range, the proportion of individuals retained
increases with size and varies from zero to one. It seems reasonable
to assume that the proportion of individuals retained (recruited into
the catch) increases at first at an increasing and then at a decreasing
rate over the relevant size range, producing a sigmoid curve in a plot
of fraction retained against size. If a size limitation is placed on
landings at a size falling within this selection range and if all or
part of the resultant discarded catch dies, the yield curves estimated
from recorded landings data will underestimate the potential yield by
not taking into account the fishing mortality experienced by the
juveniles. In this situation restrictions on gear selectivity, if

9

feasible, restrictions on time of fishing, if the recruitment pattern
is time-oriented, and/or restrictions on location of fishing, if
recruitment is by migration, may present superior alternatives from the
standpoint of maximizing yield for a given amornt of effort Jn that
simultaneously the year-classes being recruited are strengthened and a
larger proportion of the catch handled is actually landed.

Gear that is selective over a certain si?.e range is probably t)ie
most effective as far as selection is concerned. Gill-net selectivity
typifies this type of gear, having a selectivity curve (plot of propor-
tion retained on size) that is normal in shape. Size limitations are,
apparently, seldom used in conjunction with restrictions on mesh size
as gill-net selectivity curves appear to be sufficiently sharp so as
to cause size of fish retained and mesh size to be closely related. It
is apparently easier to regulate mesh size than to enforce minim.um size
limits on fish in the catch, thus the former course of action is taken.
This action usually serves to eliminate the problems involved in
estimating "true" selectivity or yield curves when legally defined
recruitment sizes and gear selectivity ranges overlap. Gear that is
selective only below some certain size (so that proportion of fish
retained varies from zero to one over the selection range) is the gear
considered below.

Deaths due to fishing are determined in large part by the amount
of fishing effort expended and are thus determined by forces exogenous
to the biological system. However, a constant level of fishing effort
per unit area and per unit time produces mortality behavior similar to
natural mortality. A constant fishing mortality coefficient (defined
as an increasing linear function of a measure of fishing effort such as

10

number o£ trav;l tov/s per unit area per unit tiii.u) implies that tlie
number of fish surviving over time from a given recruited year-class
decreases but 3t an algebraically increasing rate.

The above discussion of factors affecting a particular year-class
of a fisli stock, and the stock itself by extension to all year-classes
making up the stock, is conveniently summarized by presenting the theory
in generalized notational form. The expressions that follow represent
a modification and extension of CuJ.land's derivation of a simple yield
curve for a single year-class [2.0, section 9]. The variables of
interest are:

N = number of fish surviving at age (t - t ) during a unit time

interval t.
N = number of fish considered to be recruited during t, either by
migrating to a different area or by reaching a particular
size.
N = number of fish retained by gear during t.

C = number of fish caught during t.

Y = the weight of the catch, C , during t.
L = average length at age (t - t ) .
W = average v/eight at age (t - t ) .

B = biomass (total weight of year-class) at age (t - t^) .
M = instantaneous natural mortality coefficient.
F = instantaneous fishing mortality coefficient defined to be a

linear function of fishing effort per unit area per unit time.
The time index, t, ranges from time of completion of reproductive
process, t , to infinite time, t^ and thus, (t - t^) is the age of an
average member of the year-class. Two ages of interest are (t^ - t^) ,

11

the mean recruitment age of the year-clasR at vjhlch all individuals may
be assumed recruited, and (t -• t ), tlie mean age at which the year-
class becomes subject to fishing mortality. These ages may be the same
in time-varying recruitment or, especially in location- varying recruit-
ment, they may be different. In any event, they are defined to represent
the ages in the interva.ls during which recruitment and selectivity occur
at which one half of the year-class is considered recruited and/or is
retained by gear when contacted. It is oftentimes convenient to assume
that the full year-class is recruited or becomes subject to fishing
mortality at the relevant mean age.

The theoretical relationships with directions of change are:

1. Number of fish and total mortality rate v^7ith direction of
change:

(2.1) N = N(M, F, t - t )

t

(2.2) dN /dt = N (N^) < 0

(2.3) d^Nj./dt^ = N (Nj.) > 0

(2.2) and (2.3) also hold when F = 0 or M = 0.

2. Length

(2.4)

L^ = L(t)

(2.5)

dL^/dt > 0

(2.6)

d^Lj./dt^ < 0

3.

Weight

(2.7)

W^ = W(t)

(2.8)

dW^/dt > 0

(2.9)

d\^/dt^ > 0

12
(2.9a) d^v/j./dr.^ < 0 , ' ^ ^r

where t is such that d W /dt . =0.
w t. t - t^

4. Bioraass

(2.10) B^ = N^W^

(2.11) dB^/dt = W^ dN^/dt + N^ dW^/dt
(2.11a) dB^/dt > 0 , t < tg
(2.11b) dB^/dt < 0 , t > tg
(2.11c) dB^/dL =0 , t = tg

dW dN 2 2

(2.12) d^B^/dt^ = W^ d\^^/dt^ + 2 J~ dT" "^ ^\ "^ "t'''^^

(2.12a) d^B^^/dt^ > 0 , t < tj^^ , t > t^2

(2.12b) d^B^/dt^ < 0 , tg^ < t < tg^

(2.12c) d^B^/dt^ = 0 , t = tg^ , ^^ = '^B2

Conditions (2.11a), (2.11b), and (2.11c) describe the relative offsetting
effects of decreases in biomass due to reduction in numbers of indivi-
duals versus increases in biomass due to increase in individual weight.
Equation (2.12) expresses the variation in rate of change in biomass in
terms of rates of change and direction of rates of change of numbers of
individuals and individual weight. Conditions (2.12a), (2.12b), and
(2.12c) state the direction of rate of change over different periods of

time and are consistent with (2.2), (2.3), (2.8), (2.9), and (2.9a).

*
5. Recruitment with proportion of year-class recruited (R^ = Nj./N^)

expressed as a function of age, (2.13), and length, (2.16).

13
(2.13) R^ = n' (M, F, t. - l:^)/N(K, F, t - t^^

* *

t^ < t < t^

(2.13a) R,^ = 0 , t 5 tj^

(2.13b) P^ ^ -^ ' ^ - *^3

(2.1A) dR /dt > 0 , t < t < t

(2.15) d^R /dt^ > 0 , t^ < t < t2
(2.15a) d^R^/dt^ < 0 , t^ < t < t^

(2.15b) d^R /dt^ =0 , '^ " ^2

In equations (2.16) - (2.18), L must bs considered a length measure,
not an average, and N (L ) is the number of fish of length less than L
that are considered to be recruited.

(2.16) R^ = N*(L^)/N(M, F, t - t^) , L^.^ < ^^ < Lp^

(2.16a) Rj. = 0 , L^ < L^^

(2.16b) R^ = 1 , L^ > Lj,3

(2.17) dR^/dL^ > 0 , L^i < L^ < L^3

(2.18) d^R^/dL^^ ^ Q ^ ^^^^ ^ ^^ ^ ^^^^

(2.18a) d^R^/dL^^ < 0 , ^^2 '^ ^t ^ ^R3
(2.18b) d^R^/dLj_^ = 0 , L^ = Lr2

6. Selectivity (travel-type) with proportion of fish retained by

+
gear (S = N /N ) expressed as a function of length (a measure

of size proportional to the positive square root of surface

area and to the cube root of volume or weight). In equations

14
(2.19) - (2.21), as in (2.16) - (2.18), L^ liUould be inter-
preted as a measure of length, not an average related to the
population.

(2.19) S^. -- 4(L^)/N(M, F, t - t^) , Lg^ < L^
(2.19a) Sj. - 0 , L^ < Lg^

(2.19b) S^ = 1 , Lj. > Lg3

(2.20) dS^/dLj. > 0 , I^si '^ -^t ^ ■^SS

(2.21) d2Sj./dL^^ > 0 , Lgi < Lt '^ ^S2
(2.21a) d^S^/dL^_^ < 0 , Lg2 < L^ ^ -"^SS

(2.21b) d^S^/dLj.^ = 0 , L^ = Lg2

7. Catch in numbers of fish

(2.22) C^ = C(F, N^)

(2.23) 9C^/8F > 0

(2.24) 8^Cj./3F^ > 0 , 0 < F < F^

(2.24a) a^C^/3F^ < 0 , F^ < F < ~

(2.25) 9C^/3N^ > 0

(2.26) 3^C^./3N^^ > 0 , 0 < N^ < N^
(2.26a) 3^C^/3N^^ < 0 , N^ < N^ < «>

(2.27) 3^C^/3F3Nj. > 0

(2.28) dC = ^ dF + ^ dN

^ 3F SN^

< Lr,^

s:j

15

') 2

(2.29) d C - ^t dF + 2 _ t_ d.-^dN + D^_C_ dN "

t
Conditions (2.23), (2. 24). and (2.24a) state that the Earginal return
to effort, assuiiiing numbers of fish constant, is everywhere positive
but declines after some level of effort is reached. Conditions (2.25),
(2.26), and (2.26a) describe a different type of marginal behavior,
namely that as numbers increase, assuming effort constant, catch
increases but at a decreasing rate beyond some population level.
Condition (2.27) states that as numbers increase, the return to marginal
units of effort increases or, conversely, as effort increases, the
marginal increment due to increasing numbers increases. Equation (2.28),
expressing the total change in catch for changes in effort and numbers,
is especially interesting when divided through by the incremental change
in fishing mortality, dF, a proxy for effort. Recalling that number of
fish is a declining function of fishing mortality, it becomes apparent
that the change in catch due to a change in effort is not readily pre-
dictable as to sign or direction of change — given by equation (2.2y) —
when allowance is made for the negative effect of increasing effort on
fish numbers.

8. Weight of catch

(2.30) Y^ = Y(F, N^, W^)

or
(2.30a) Y^ = Y(F, B^)

(2.31) 8Y^/3F > 0

(2.32) 3^Y /3F^ > 0 , 0 < F < F^

(2.32a) 3^Y^/3F^ < 0 , F^ < F <

CO

(2.33) ?A'^/9Nj. > 0

(2.3M 9^Y^/3N^^ > 0 , 0 < N^ < N^

(2.34a) 9^Y /3N ^ < C , N^ < N^ < «>

(2.35) 8Y /3w > 0

(2.36) 3^Y^/3W^^ > 0 , 0 < W^ < VJ^
(2.36a) 3^Y /3VJ "*' < 0 , W^ < W^ < ^

(2.37) 3^Y /3F3N > 0

(2.38) d^'-Y /3F3W > 0

(2.39) 3^Y /3N 3W > 0

3Y 3Y 3Y

(2.40) dY^ = -3^ dF + 3^ dN^ + 3^ dW^

2 ^'^ 2 ^^\ 2 ^\ 2 ^^\

dF oN oW t

3^Y 3^Y

+ 2 ^^^f, dFdW^ + 2 ^-. ^f. dN^ dW^
3F3W t 3N 3W t t

Equations and conditions (2.30) - (2.39) describe the weight of the
catch and the partial effects of changes in effort, numbers of fish,
and average weight of fish. Equations (2.40) and (2.41) describe the
total effect on weight of catch of simultaneous changes in effort,
numbers, and individual weight and are most interesting when divided
through by the incremental change in effort. As is the case in (2.28),
the change in weight of catch due to a change in effort is not predict-
able a priori when the decreasing effect on numbers of increases in

17
eitort; is taken into account, A consideration of (2.41) indicates that
the direction of rate of change in v/eight of catch due to changes in
fishing mortality is as unpredictable as the rate of change itself.

Equations and conditions (2.22) - (2.41), especially those dealing
v;ith changes in fishing mortality, represent that part of fish popula-
tion theory that may provide a liiik witli an econouiic theory of coiiimoa
property resource exploitation.

A Theory of Open Access and Common
Property Resource Exploitation

In the opening chapter, a distinction between open access resources
and common property was implied. Before erecting a theory of exploita-
tion, more explicit definitions of the resources are needed. Open
access resources are those that arc open to exploitation by any who
possess, or may ever possess, the physical ability to exploit the
resource. In terras of ownership, the resource is not owned by djiy
group comprising fewer people than the world population. The effec-
tiveness of world ownership as an institution to implement management
goals is sufficiently limited to permit acceptance of "open access" as
synonjTuous with "no ownership" when applied to resources.

The terra "cormion property," when applied to resources, implies that
ovsmership exists by use of the word "property" but that ownership is
exercised by a group of people in "common," for example, the citizens
of a state or country. Institutions for attaining optimal exploitation
rates may or may not exist but the implication is that the "common"
group is not so large as to make their creation impossible. The key
difference between "common" and "private" property resources lies in
the behavior of the individual exploiter. In the common property
situation, each individual, playing an unrestrained profit-seeking role.

18
will follow a course of action that is inconsistent vzilh an optimal use
rate for tlie resource as a v;hole anrl that does not maximize profit for
the group exercising the common property rights. In the cnse of private
property, the expectation is that the individual, in pursuing a profit
maximizing course, will act in a manner consistent V7ith optimal use of
the resource as a whole assuming no technical externalities. Examples
illustrating these essential differences exist in the form of land and
oil pools in common and private property situations and fish in open
access (high seas) and regulated common property (territorial waters)
situations. Wlien arraying resources on a scale denoting then to be
open access, common property, or private property, a continuum forms
with no sharp demarcation between the various classes. A different and
helpful classification of resources by their reaction to time-varying
use rates is presented by S. V. Ciriacy-Wantrup [12, pp. 42, 43].

Some relevant literature on fisheries economics j.ncludes the seminal
articles by H. Scott Gordon [19] and Anthony Scott [28], as well as the
work of Christy and Scott [11], Crutchfield and Pontecorvo [14],
Crutchfield and Zellner [15], and Daniel Bromley [9]. The paper by
Bromley presents a provocative literature review. A comprehensive
review of the work just cited would be redundant in view of Bromley's
[9] work. However, acknowledgment must be made of the significant
contributions to fishery theory of these authors. The theory developed
here undoubtedly owes much to these authors but the debt is in the form
of general knowledge rather than specific contributions.

The resource to be exploited is assumed to be a flow resource in
that it provides an exploitable flow of goods or services — fish, wild-
life, scenic beauty, water, or capacity to absorb man-made effluent —
from a given area over time. The resource may or may not be affected

.19
by exploitation rates, but aome exploitation I'ate must, at sorae time,
be positive in order for the resource to be of interest and maintain
its resource character. In addition, the marginal utility derived from
exploiting the resource must be positive in the absence of externalities.
That is, the resource must not be a "free good." This qualification
leaves the definition broader than may be inmiediately apparent. For
example, stars of the seventh order of magnitude provide a flow of star-
shine that is exploited at a positive rate by astronomers who delight in
viewing seventh order stars. The qualification does state that for
something to attain resource character, it must somehow affect humans.
In this sense, orbital bodies under the direct gravitational influence
of seventh order stars do not qualify as resources at the present tim^e.

The resources of interest are those that require human effort to
maintain a positive exploitation rate and thus have positive costs asso-
ciated with their exploitation. The effort required for positive
resource exploitation will vary over resources and is considered to be
composed of inputs combined in constant proportions (linear expansion
path) and treated as a single input. Physical returns to effort are
assumed to increase but at a decreasing rate beyond some level of input.
The condition of the resource, including qualitative factors, is assumed
to be expressed by a single quantity index at any point in time. This
assumption is, admittedly, heroic, but does much to facilitate the
following exposition and, for a fishery, may not be so unreasonable as
it first sounds. Demand for the product and factor supply curves are
assumed to be less than perfectly elastic to the industry but perfectly
elastic as viewed by the individual firm.

The variables involved in open access or common property resource
exploitation are:

20

Y. = output of producer i clvriiig a unit interval ot tine, t; e.g.,

a week, moath, year, decade, etc.

Y = total output for the industry during unit time interval t.

X. = input or effort of producer i durincr t.
xt

X = total industry input during t.

P = price of the output during t, arisumed constant over producers.

P = input price, identical foi" all producers, during t.

R = a quantity index reflecting the condition of the resource

during t.

n = number of producers involved in the resource industry during

t.

TR.^ = total revenue for producer i during t.
xt

TR = industry total revenue during t.

TC . = total cost to producer i during unit time interval t including
It '

a "normal" return to "ii:ced" resources.

TC = industry total cost during t.

NR.^ = TR. - TC.^, net revenue of producer i during t or "pure
xt It It' " ■

profits. "

NR = TR - TC , industry net revenue (pure profits) during t.

In generalized functional notation, the relationships of interest,
their rates of change, and the directions of rates of change are as
follows :

9. Individual output

(2.42) Y.^ = Y.(X.^, R^)
It X xt' t

(2. A3) 9Y^^/3X^^ > 0

(2.44) 3^Y^j./3X.^^ > 0 , X.J. < X.^

21
(2. /,4a) 3\j./9\/ < 0 , X.^^ > X.^

(2.45) 9Y.^/3R^ > 0

(2.46) S'^'Y. /SR ^ > 0 , R < R""^
(2.46a) d^Y. /[)R ^ < 0 , R > R"'"

(2.47) 8^Y.^/8X.^3r^ > 0

xt It t

9Y. SY

(2.48) dY.^ = ^;^ dX.+ -^r^ 6R

it dX. It dR t

it t

9 9^.. , 8^Y 9^Y

(2.49) d^Y.^ = ^ dX./ + 2 x^— ^-^ dX. dR^ + z- dR^

It 9^_ 2 It 9X.^9R^ It t 3j^ 2 t

it t

10. Individual effort and numbers of individual producers

(2.50) X.^ = X.(NR^^_^) , r = 1, ..., k , 0 1 X. (NR. ^..„) < X.^

(2.50a) X^j. = X^^, X. (NR.^_^) > X^^

(2.51) ^\t^^^\t-T ^ ° ' "^ " ^' •••' ^ ' ° -h^^\t-r^ ^ \^

(2.52) 9^X.^/9NR.^ 9NR.^ >0 , l<r<s , s=l, ...,k
^ ' it it-r it-s ' — — '

X.(NR.^ ) < X.-*"
1 it-r^ 1

(2.53) n^ = n(NR^_^) , r = l, ...,k , 0 < n(NRj._^) < n"^

(2.53a) n^. = n^, n(NR^_^) > n^

(2.54) 9nj./9NRj._j. > 0 , r = 1, ..., k

(2.55) 9^n^/9NR 9NR^ >0 , l<r<s , s=l, ...,k

t t-r t-s — —

11. Total effort

(2.56) X^ = Z. "t X.^

t 1=1 It

11

(A definition)

(2.57) 8Xj./:)X.^ = 1

(2.58) 3X^/?n^ ^^ l.^^ X., /n^

12. Resource condition

(2.59) Rj. = R(X^)

(2.60) dRj./dX^ < 0

(2.61) d^R^/dX^^ > 0

13. Total output

(2.62) Y^ = S.^t Y.^

(2.63) 3Yj./8Y^^_ = 1

(2.64) 8Y^/3n^ ~ S.^^^t Y.^/n^ + ^.^t SY.^/9n^

where, from (2.49), (2.66), and (2.64),

8Y. /5n = OY. /9R JOR /3X )(9X /Sn ) < 0

it t it t t t L L

9Y ^ 3Y^

(2.65) dY =9^dn +i:.^^t3Y-d^'it . ._.

Equation (2.42) describes individual output (harvest in pounds,
numbers, board feet, acre feet, etc., per time unit) as a function of
individual effort expended and the condition of the resource. Equations
(2.43), (2.44), and (2.44a) describe the return to an increment of
effort, assuming resource condition constant, as increasing at first at
an increasing rate but eventually (beyond input level X^ ) increasing
at a declining rate. In more technical economic terms, equation (2.42)
is a production function which exhibits diminishing marginal returns to
effort beyond input level X^^. Further, given constant input (effort)
and product prices, the profit-maximizing producer will operate at or

23
beyond input level X. if at all. Equations (2.A5), (2.46), and (2.46a)
indicate that increases in the resource condition (effort constant)
increase individual output along a sigmoid path, at an increasing rate
at first but evertually at a decreasing rate. Viewed another V7ay,
equations (2.45) - (2.46a) indicate that the efficiency of a given
amount of effort increases as it is applied to increasingly dense
resource stocks but at a decreasing rate throughout. In fisheries,
effort may be divided into search time, actual harvest time, and on-board
processing time. For a given amount of effort, increases in density of
fish will at first add to catch at an increasing rate as both search time
and actual harvest time are large in relation to on-board processing
time and are decreasing while processing time increases. As processing
time, V7hich is independent of stock density, comes to dominate in the
total effort, increases in stock density will increase catch at a
decreasing rate. Equation (2.47) says that effort and resource condi-
tion are complementary in their effect on output, increases in resource
condition increasing the rate of increase in product due to increases
in effort and vice versa.

Equation (2.48) expresses the unconstrained ("total") change in
individual output in tenns of partial rates of change and unconstrained
increments of effort and resource condition. The direction of change
in output is predictable from (2.48) alone only when effort and resource
condition move in the same direction in which case output will move in
the same direction as effort and resource condition. The direction of
change in the rate at which output is changing, as given by (2.49),
depends upon the relative directions of change in effort and resource
conditions as well as the level of effort and resource conditions. For

similar movements in effort and resource condition below X. and R ,

1

24

output will increase at an increasing rate. The direction of rate of

change above iiiput levels X." and R' for movements of effort and resource

condition in the same direction will depend on the relative magnitudes

of (2.44n) and (2.46a) versus (2.47) and t)ie relative size of the changes

in inputs. Equation (2.48) is particularly interesting when divided

through by the increment in effort, dX , and written as (2.66) in which

form it expresses the unconstrained change in output resulting from a

change in effort (numbers of firms constant).

3Y. dR
(2.66) dY. /dX. = 3Y. /9X. + ^*^ ^

it it it it 3r dX.

t xt

To the individual member of an industry with many producers, the term
dR /dX is zero. That is, he neglects changes in the resource condi-
tion that result from changes in the effort he expends. This may be
rational for the individual since the cost of considering this small
change in his decision process probably outweighs the benefits to be
obtained from considering it. However, for the industry as a whole,
the effect of changes in effort on the resource condition is not negli-
gible. This discrepancy leads to the difference between the sum of
changes in output expected by individuals from individual changes in
effort and the change in output for the industry as a whole resulting
from the sum of individual changes in effort. The sum of changes
expected by individuals is:

(2.67) E. "t dY. /dX_ = I. "t dY.^/dX.^

1=1 It it 1=1 it It

while the actual change for the industry is:

9Y. dR

(2.68) Z. "t dY. /dX.^ = E. "t dY./dX.^ + Z. "t ^^ ^

1=1 It It 1=1 It It 1=1

9R^ dX.
t it

25

Since dR /dX. is negative (it is the product of (2.60) and the total

derivative of (2.56) assuming u constant and dX. /dX. = 0 for i ^ i)

t J t It

the actual change in total output from an increase in effort is smaller

dY^ dR
by the positive amount -Z._ t ,," -jri — than is the sum of changes

t XL

expected by individuals. This discrepancy, derived assuming the number
of producers in the industry constant, is part of the reason that indi-
vidual producers, following profit-maximizing courses of action, will
not behave in a manner consistent with maximizing industry profits.
Equations (2.50) and (2.50a) describe the effort of individual
firms as a function of past net revenues up to a ceiling (X. ) beyond
which individual firms find themselves incapable of increasing effort.
Condition (2.51) says that higher past net revenues increase current
effort, and condition (2.52) (for r = s) describes the rate of increase
as constant or increasing for the range over which the function is
defined on past net revenues. The sign of (2.52) (for r = s) is inter-
preted to mean that, when hypothetical sets of past net revenues are
compared, the increment in effort called forth by an increment in net
revenue at a higher level of net revenue is at least as large as the
increment of effort called forth at lower levels of net revenue. Such
behavior is taken to be typical up to the ceiling (X. ) at which the
individual cannot effectively increase effort. The plausibility of
(2.52) (for r = s) rests on the assumption that individuals are more
sensitive to changes in net revenue at high levels of net revenue
(their adjustments are larger) than they are at low levels of net
revenue. Equation (2.52) (for r < s) states that higher levels of net
revenue in a given period reinforce the effects of net revenues from
subsequent periods. Equations (2.53) - (2.55) describe numbers of

26
producers in any time interval as a function, similar to individual
effort, of past net revenues of the industry. That is, entrants are
seen to increase at a constant or increasing rate as a function of past
levels of in'.lustry net revenue with levels in previous periods having
a reinforcing effect on those in subsequent periods.

Equation (2.56) states that total effort during any time interval
is the sum of individual effort over the number of producers in the
Industry during that interval. Equation (2.57) indicates that aggregate
effort is measured in the same units as individual effort. Equation
(2.58) defines the effort level of new entrants as being at the average
for the industry. Were equations (2.53) - (2.55) to be developed for
different size classes of producers, then (2.58) would be modified to
reflect the effect of entry into each size class. Definition (2.58) is
a sort of "minimum knowledge" relation and should be replaced if more
information is known about entrants.

Equation (2.59) describes the condition of the resource as an
instantaneously adjusted function of effort. Conditions (2.60) and
(2,61) state that the resource condition declines as a function of
effort but at an algebraically increasing rate. While the particular
form of (2.59) will depend upon the theory of the behavior of the
resource under study, there are probably few exceptions to the limits
imposed by (2.60) and (2.61). A resource may be depleted as effort
Increases but it will be depleted less and less efficiently so that very
large amounts of effort are required to finally destroy the resource.
Equation (2.10) in the section on fish population theory, after modifi-
cation to represent the biomass of all year-classes comprising the fish
stock, may be substituted for (2.59) in a bioeconomic model of a fishery.

27

Equation (2.62) expresses total output as the sum of individual
outputs over producers in the industry during time interval t. Equation
(2,63) states that individuals make contributions to total output in the
same magnitude in which individual output 5s measured. Definition (2.64)
gives the change in total output resulting from nev? entry (or exit) as
the sum of changes in individual output due to the additional depletion
of the resource by the entrant, plus the product of the new entrant
which is defined to be the average product of all producers in the
industry. Definition (2.6A) could be improved by reflecting productivity
of entrants by size class or incorporating more complete information on
the productivity of entrants when such inform.ation is available.

Equation (2.65) adds to the sum over producers of the behavior
indicated by equation (2.48), the change in total output resulting from
a change in the number of producers. That is, (2.65) takes into account
the effect on total output of changes in established producer output
(the sum over producers of the product of (2.48) and (2.63) as well as
the effect on total output of new entrants (2.64)). Rewriting (2.65)
as (2.69) using the rules of differential calculus and equation (2.66)
helps to delineate these effects and to point out the discrepancy in
situations arising from individual behavior as opposed to industry-
oriented behavior.
(2.69) dY^ = E.^^t (3Y.j./SR^)(8R^/3X^.)(3x^/9n^) dn^.

+ ^i=l^ (^it/\) '\

+ Z.^-t (9Y^/8Y.^)OY.^/3X.^) dX.^

+ ^1=1^ (3\/3Y.^)(3Y^^/3R^)(dR^/dX.j.) dX.^

23
The first and fourth terms on the riglit-hand side, of (2.69) are negative
while the second and third terms are positive.

Assume, for the moment, constant product and input prices and past
net revenues high enough to encourage increases in effort by individual
firms as well as entry by new firms. Individual producers believe that
they affect only the elements of term three from the right-hand side of

(2.69) and will, individually, increase effort so long as that direct
increment in value of output is greater than the increment in value of
input required for its production, halting further increases when the
two are equal. The ex ante equilibrium position for all producers
together, when each pursues his selfish interests in an unregulated
manner, is given by:

(2.70) P ^ E "t 0Y_/3X. J dX.^ = P ^ Z. !^t dX_

yt 1=1 It It It xt 1=1 It

or, if l^J^t dX^j. = 1

(2.70a) ? I. '^t (8Y. /9X. J dX.^ = P ^
yt 1=1 It It It xt

or, if dX. =1
It

(2.70b) E. "t P ,(8y. /3X.J = n P ^
1=1 yt It It t xt

or

(2.70c) Z..;t Py,0Y^,/3X,,)/n^ - P,,

Equations (2.70) - (2.70c) state an ex ante condition that individuals
attempt to attain, namely to equate, on an individual basis, the value
of the marginal product of the input with its price. This translates,
on an industry-wide basis, to equating the value of the marginal product
of a one-unit Increase in industry-wide effort to the price of the
input (2.70a) or to equating the value of marginal product averaged
over members of the industry to the price of the input (2.70c). These

29
conditions cannot obtain ex post and the left-hand side of (2.70) viil
(assuming numbers of firms constant) be reduced by the product of P
and the fourth teiin on the right-hand side of (2.69) so that the average
for the industry of the actual value of marginal product of effort is
less than the price of that effort as indicated in (2.71).

(2- 71) ^t h=l' t^^^it/^^it) ■' (9Y,,/9\)(dR^/c^X.^)] dX.^/n^ < P^^
This is not the final situation for the industry as a ichole. Past net
revenues were assumed to be high enough to entice new entrants. New
entrants have a mixed effect on output: they tend to reduce it by
depleting the resource through increases in effort (term one on the
right-hand side of (2.69)) but they increase it by the average produc-
tivity for the industry (term two of (2.69)). Thus, new entrants may
have a positive, negative, or nei\tral effect on total output. However,
new entrants will expect to receive the average revenue for the industry
as a whole and will plan to enter, ex ante, so long as industry net
revenue (or average net revenue) is positive, stopping when average
industry revenue (marginal revenue to entrant) equals average industry
cost (marginal cost to entrant). However, all the entrants together
affect the resource by depleting it so that, ex post, the increment to
industry revenue from entry will be less than average factor cost by
the value of the marginal depletion caused by the new entrants (P
times term one of (2.69)). Thus, the increment in value of total output
(all prices constant) is made up of the increment due to entrants and
the increment due to expansion of effort by established members of the
industry. For both increments, ex post value of marginal product for
the industry is less than cost of the marginal input although individ-
uals seek ex ante to equate apparent value of marginal product and cost

30
of marginal input. Sinco cogIg must equal revenues ex 2ps_t, the nega-
tive net marginal revenues must he home hy the indiviJ.ial J'inus in the
industry and may be evident as lov; incomes or less than "noriiial" returns.
Thus, high past net revenues lead to lov7 net revenues In the current
time period and the unstable nature of the situation is apparent.

A stable situation may prevail only if firms continuously accept
less than "normal" returns or if all firms in the industry luckilj'
discover that proper ratio of privately expected value of marginal
product to marginal factor cost that equates the increment in value of
output for the industry to the increment in industry cost. A third
alternative, in which firms learn to reckon all costs (voluntarily take
the viewpoint of the industry) seems unworkable since firms would not
be likely to have the information or incentives to take the viewpoint
of the industry. The first alternative of sustained below "normal"
returns may explain part of the behavior of som.e open access or comriion
property resource industries, especially when "normal" returns origi-
nally are based on acquisition value of inputs and not salvage value
(see [9]). The second alternative may contain some explanatory power
also if the marginal returns indicated do not (as they do not here)
recognize uncertainty. That is, due to uncertainty, firms may attempt
to maintain a ratio of value marginal product to input price that is
consistently greater than one so that the ex post result from uncer-
tainty planning may be closer to the value marginal product expected by
the individual firm than is predicted by theory under certainty.
Although these factors may contribute to a partially stable situation,
they do not lead to an equilibrium in the sense of equating marginal
factor returns with marginal factor cost.

31
This section is best sumTnarized by presenting, as briefly as
possible, the conclusions of the theory of open access resource exploi-
tation under variable prices, i.e., where input and product prices are,
respectively, functions of input and product quantities. A given incre-
ment in total output, dY given by (2.75), is attributable to increments

in the effort of established firms, E. ,t dX. , as well as in effort due

1=1 it

to entry, ^._,t X. /n dn , which sum to give the total increment in
effort, dX . To maximize industry revenue, the increment to total
revenue is equated to the increment in total cost or:

(2.72) (P + Y dP /dY ) dY = (P + X dP /dX ) dX

yt t yt t t ^ xt t xt t^ t

Individual establislied producers see their marginal products as a func-
tion of their effort alone and, taking price as constant, collectively
try to equate marginal revenue product to marginal factor cost as given
by equation (2.70). Entrants, who enter at average levels of produc-
tivity and average effort expenditure, perceive the marginal return to
entry as the average return for the industry or P Y /n and the mar-
ginal cost of entry as the average cost for the industry or P X /n .
(The marginal cost of a unit of effort from expansion by established
firms is assumed to be the same as the marginal cost of a unit of effort
by entry.) The marginal conditions for a static entry situation from
the individuals' point of view, are:

(2.73) Py^ Y^/n^ dn^ = P^^ X^/n^ dn^

The condition that established industry members and entering firms,
acting as individuals, attempt to attain is given by the sum of (2.70)

a

and (2.73) or:

(2.74) P^^ [l.Jlt 0Y,^/8X.^) dX.^ + (Y^/n^) dn^] = P^^ [l.J^t dX.^

32

The riglit-hand side of (2. 74) corresponds to the riylil-hand side ol

(2.72) if input supply is assumed to be infinite at a constant price

(as it is assumed by individuals). The left-hand side of (2.74), :n

addition to considering the effect of a change in output on output price

to be zero (as individual producers consider it) , neglects to take into

account the depleting effect of increased effort on the resource. To

equate the value of the marginal increment in output for the industry

to the cost of the marginal increments in effort required to produce it

involves, ignoring price effects, satisfaction of:

(2.75) P dY = P (E "t dX. + (X /n ) dn )
yt t xt 1=1 It t t t

Theory indicates that for maximum industry profits to be obtained
(monopoly and monopsony profits) equation (2.72) must be satisfied for
the industry. The competitive industry situation (zero profits, normal
returns included as a cost, guaranteed by the satisfaction of (2.73)
under freedom of entry) is realized by satisfaction of (2.75). A con-
dition of chronic below-normal returns is attained when individual
producers and entrants attempt to satisfy (2.74). The crux of the
problem at hand is that individuals involved in exploiting an open access
or unregulated common property resource \>7ill attempt to satisfy equation
(2.74), resulting in chronically low returns in resource industries
involving no, or ineffective, ownership of the resource. The ensuing
chapters will be concerned with determining the extent of possible gains
from institutions (policies) designed to correct the problem of low
returns. Any possible gains must, of course, be weighed against costs
of implementing the policies necessary to attain the gain. The follow-
ing section describes a bioeconomic model of a fishery, necessary for
empirical work, in theoretical terms.

33

Bloecouoinic Theory of a Fishery

Earlier sections of this chapter were concerned with the theoret-
ical behavior of a particular year-class in a closed stock of fish and
with the theory of oiploitation of an open access resource. This sec-
tion combines the efforts of earlier sections into a bioeconomic theory
of a fishery that will be useful in analyzing the shrimp industry. For
a slightly different development, and one that incorporates the effects
of "vessel crowding" — assumed negligible here — see the article by
V. L. Smith [29].

Equation (2.30a) describes the weight of the catch from a partic-
ular year-class as a function of effort and the biomass of the year-
class. In most fisheries, the catch is actually made up of fish from
several year-classes, in general J year-classes, so that (2.30a) should
be rewritten in terms of a year-class j where j = 1, ...» J. Equation
(2.42) gives the output of an individual producer in teinns of individual
effort and resource condition while equation (2.62) defines the output
for the industry. Modifying and combining (2.30a), (2.42), and (2.62),
total industry output is seen to be (2.76), the sum over individuals of
the catches from different year-classes.

(2.76) Y^ = E. ^t Z.-^T Y..(X. . B.J
t 1=1 j=l ij ' It' 2^

The biomass of a particular year-class is (abstracting from the effects

of varying stock density on growth and mortality rates) a function of

the growth and mortality rates natural to the species , the fishing

mortality the year-class has suffered, and the size (in numbers) of the

parent (spawning) population or E._. N where all year-classes at

^ ^1 J o

least as old as j are spawners and t is the "birth" year of the year-
class in question.

34
Total revenue to the industry, t>ie sum uf total revenues to indi-
viduals, involves tlie product of the weight of each year-class in the
catch times the price per unit v.'civ,ht ccr.inianucd hy tlie year-class {for
example, different size shrimp, corresponding; to different ages, hring
different prices per pound). That is:

(2.77) TR = I. !}t Z.^^ P .^ Y.. (X. . B.J
t 1=1 j = l yjt ij It' jt

Total cost is the sum of individual total costs as given by the product
of total effort (2.56) and price per unit effort P

xt

(2.78) TC^ = P X = P Z. ^t X

t xt t xt 1=1 It

Demand price, P . , is taken to be a declining function of output while

yjt'

input price, P , is assumed to be an increasing function of input
quantity. However, individuals, and the industry, are assumed to treat
prices as if there were no quantity effects on prices, thus eliminating
monopoly- and monopsony-type price effects. For equilibrium to occur in
the industry, the value of increases in output due to increases in effort
must exactly offset the increase in costs due to increases in effort (due
to expansion by established firms and entry). Further, the value of an
increase in effort due to expansion by established firms (the "intensive
margin," see [29]) must equal the value of an increase in output due to
entry in order for stability to occur on the "capital" side of the produc-
tion system. Stability of the fish stock requires that decreases in the
stock due to fishing and natural mortality are just offset by the sum of
increases in biomass due to growth in weight and recruitment. In addi-
tion, the number of spawners , Z. . N. , must remain constant if that

number is equal to or less than the number required to produce the maximum
size spawn that the biological system will support. (For example, there
may be some number of eggs above which further egg production is super-
fluous so far as maintaining or adding to the adult stock is concerned.)

33
At some level of net revenue (zero, it net revenue is synonymous
with pure profits and certainty is assumed) equilibrium may occur in
the fisbci-y in the sense that increments to value equal increments to
cost and fish stock is stable (catch equals sustainable yield where
sustainable yield is that yield that may be taken in perpetuity without
affecting the stock). The condition (2.73) applied to the fisheries
assures that the net revenue level at industry equilibrium is zero.
Mathematically, the equilibrium conditions are formed by setting the
total derivative of net revenue, equation (2.77) less equation (2.78),
equal to zero and satisfying the additional constraints that the time
rate of change in biomass is zero as is the change in num.ber of spaw-ners.
The conditions are:

(2.79) Z. "t l.\ P .^
1=1 j = l yjt

^dY.. 8y.. 8b. \

^ It jt It/

8Y.. Y.. 9Y..

j_ iJt . xit J . lit ,^

+ 3 — ^— + — ^- dn^ + ^p ■' dB_

dn^ n^ t oB.^ it

t t jt -J

- P ^ f E "t dX.^ + — dn I = 0

xt \ 1=1 It n t /

(2.80) Z/, dB. = 0

(2.81) Z/. dN. = 0

While (2.79) represents the conditions for competitive industry equilib-
rium (zero profits), individuals do not take into account the indirect
effects of their actions and will, as pointed out in the preceding sec-
tion, attempt to expand output by increasing efforts, thus raising
marginal factor costs (by raising P ^) and lowering value marginal pro-
ducts (by lowering P , through the effect of diminishing returns to
effort and through depletion of the resource) , resulting in the left

36
side of (2.79) being less than zero. If (2.80) and (2.81) are satis-
fied, (2.79) may be persistently below zero, the negative net marginal
value products being absorbed in incomes tc the fisheriaen belovj acqui-
sition cost incomes (but above salvage valr.e ircomes) .

In order to assure equilibrium by satisfaction of (2.79), some
management authority need only levy on the industry a tax on entry
(license fee, L) equal to the value of the reduction in output caused

by entrants or

8Y.. 8B. 9X

(2.82) L = E "t E. . P .^ ~^3-J^^ dn^

1=1 1=1 yit 3B. dX dn t
-* ■^-' jt t t

and a tax on individual landings (landings fee, D) equal to the reduc-
tion in value caused by expansion of effort by established firms or

(2.83) D = Z "t E.^ P _ -^-^^3-1^ dX.^

1=1 J=l yjt 3B dX^^ It

where P . is the prevailing price at contemporaneous industry output.
If tax-incidence problems are solved, this Pareto-ef f icient competitive
industry equilibrium is as optimal as any other Pareto-ef f icient point.
If a social welfare function is devised that acquiesces to the consumer
desires expressed in the demand function, then this equilibrium is
socially optimal.

Although the charges needed (L and D) to manage a fishery in an
efficient zero-profit manner can be specified as theoretical aggregates,
the pattern of license fees for vessels of varying sizes and efficien-
cies and the pattern of landings fees for fish of different sizes and
per unit values are not so readily apparent. For heterogeneous firms
and landings sizes, the charge levied may well influence the pattern of
landings sizes and/or the characteristics of entering firms. The direc-
tion of such influence is not obvious from the static considerations
given here and requires modification and adaptation of the theory, by

37
specific industry, ivit.o a v;orkable dynamic model capable of evaluating
alternative control strategies (policies). The theory presented here
is modified and extended into a dyna:,! i c model capable of analyzing the
Gulf of Mexico shrimp industry in Chapter III.

CHAPTER III

GULF OF MEXICO SHRIMP INDUSTRY;
DESCRIPTION AND MODEL

The Gulf of Mexico shrimp industry may be divided into three seg-
ments. The basic segment is formed by the natural shrimp resource and
the dynamics of its population behavior. A second segment is the fleet
of boats and vessels that is involved in capturing the basic resource.
The third segment consists of the processing and marketing channels that
facilitate the movement of shrimp from the point of first sale at dock-
side to the consumer's table. This chapter presents a brief description
of the Gulf of Mexico shrimp industry and then, in somewhat more detail,
an abstract model that represents the essential workings of the industry.

Description of the Industry

The descriptive portion draws heavily on work done at the University
of Florida by David A. Whittaker, Jr. [33], C. C. Osterbind and R. A.
Pantier [27], and Roy L. Lassiter [22], as well as National Marine
Fisheries Service (formerly Bureau of Commercial Fisheries) publications
by John P. Doll [16] and Kenneth W. Osborn, Bruce W. Maghan, and Shelby
B. Drummond [26] , and a dissertation completed at the University of
Rhode Island by Richard James Berry [7].

The Gulf Shrimp Resource

The commercially important Gulf shrimp resource is comprised largely
of three species of shrimp: brown shrimp, Penaeus aztecus; pink shrimp,

38

39
p. duo r a rum; and white shrimp, P. setiferus. In addition, small numbers
of a smaller shrimp called seabob , Xiphoponaeus kroveri, are taken near
the outlets of Louisiana rivers. The royal red shrimp, Hymenopenaeus
robustus, is harvested in depths of from 200 to 300 fathoms (one fsthom
equals six feet) in the waters off the east and southwest coasts of
Florida and southv^est of the Mississippi River Delta.

The Penaeus species have similar life cycles and habits. The
adult shrimp spawn offshore and the larvae make their way back into the
coastal estuarine systems, V7here they develop into juvenile shrimp.
The juvenile shrimp begin to migrate back to the open sea where, upon
reaching adulthood and spawning, the cycle is completed. Individual
shrimp may live from eighteen months to tvjo years and reach lengths of
170 mm. (6.7 in.) for males and 200 mm. (7.9 in.) for females. Shrimp
are generally considered an annual crop, however, and are harvested
from the time they are juveniles in the estuaries. Brovm and pink
shrimp are nocturnal in habit and burrow during the day into the mud
and coral silt bottoms which they respectively seem to prefer. Wliite
shrimp, on the other hand, are active during daylight hours and burrow
into the mud bottom at night.

Brown shrimp are found in heaviest concentrations along the Texas
coast, white shrimp along the Louisiana coast, and pink shrimp off the
coast of Florida near the Dry Tortugas and Sanibcl Island and in the
Gulf of Campeche off the northwestern coast of the Yucatan Peninsula.
Figure 3.1 (after Lassiter [22, p. 2]) depicts the seven areas of the
Gulf of Mexico that comprise the study area and Table 3.1 gives landings
by area and species for the years 1967, 1968, and 1969 (see also [2]).
Together, these references depict the recent occurrences of shrimp in
commercial harvests and, presumably, the distribution of the various
shrimp species.

AG

t^i^ki^^^

Area I

^/^*

>^'^J!!^

Q'-^-

85°

I

Pensacola, Florida, to the Mississippi River
Mississippi River to Texas

Texas Coast ^

High Seas Off Mexican Coast West of Longitude 94
High Seas Off Obregon and Campeche

Figure 3.1. Major Shrimp Fishing Areas in the Gulf of Mexico

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ages of total landings vhic]i inore rr.<-<dily indicate the importance of
the major species vjithin areas, their relative contribution to tota]
landings, and the relative iripcrtance of tlie seven areas in their con-
tribution to total landings. Differences between years are associated
with 1) differences in total shrimp abundance, 2) differences j'n
relative species abundances, 3) shifts among areas in shrjiup concentra-
tions, and 4) changes in the fishing effort applied by area and among
years. In Table 3.3 the results of Tables 3.1 and 3.2 are averaged
over the three years. Table 3.3 shows brown shrimp to comprise about
62 percent, pink shrimp about 12 percent, and white shrimp about 25
percent of average total landings. Seabobs and royal red shrimp comprise
less than one percent of total landings and are thus net considered
further in this study.

Areas III, IV, and V, where brox-m and white shrimp concentrations
are found, are the most consistent hea\^-producing areas with Area IV
showing the greatest concentration of white shrimp and Area V the
largest concentration of brovm shrimp. Area I follows in importance
and contains pink shrimp almost exclusively. The high seas off the
Mexican coast (Area VI) produces brown shrimp while Obregon and Campeche
(Area VII) produces largely pink shrimp. Area II, contributing the
smallest amount to total catch, contains all three species in roughly
equal numbers although pink shrimp may be slightly more abundant.

A word of caution must be added against interpreting Tables 3.1 -
3.3 as indicators of absolute slirimp abundance. These data reflect
commercial landings and thus, in addition to the availability of shrimp,
they reflect the shrimpers' choice of where to fish. The fishermen's
choice of trawling area is influenced by bottom conditions, i.e., whether

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45
grass is present or the bcttora ic scuddad with coral, large sponges or
other obstructions, and distance from port. Thus, Tables 3.1 -■ 3.3
should be interpreted as indicating conicercia] ly important concentra-
tions of shriap, given current technology and knowledge of bottom
conditions.

In addition to variation by area, shrimp concentrations vary in a
seasonal pattern by species. Osbcrn et al. [26] have summarized five
years of data (1959-63) to indicate shrimp concentrations by area,
species, and month of year. Their findings on density by area are
roughly the same as those presented above. The seasonal patterns of
abundance of the three species are such that shrimp are available in
heav^' concentrations the year round. Brown shrimp concentrations
support a summer and early fall fishery vjith 80 percent of the landings
occurring from June to October and the peak catches occurring in July
and August [26, p. 6], Pink shrimp support a year-round fishery
although landings are somewhat lower during June through September and
peak in December [26, p. 14]. Nearly 80 percent of the white shrimp land-
ings are made in the fall from September to December [26, p. 10].

Although all three species of shrimp are harvested from the time
they are juveniles in the estuarine systems (inshore) until they reach
adulthood offshore, there are some striking differences in the percent-
ages of the various species landed inshore versus offshore and in the
depths of landing. For the study period 1959-63, [26] found that 80
percent of the brown shrimp landed were taken offshore, most of them
in water between 11 and 30 fathoms in depth. Ninety-eight percent of
the pink shrimp landed were taken offshore with the heaviest concentra-
tion (nearly 80 percent) taken in 11 - 20-fathom depths. In contrast
to the brown and pink species, 42 percent of the white shrimp landed

AC)
were taken in inshore waters. By depth, iiliout. 90 percent of tlie white
shrimp landed \,'ere taken In less tVian 10 fatlsoins of vater.

In summary, bro\n shrirp, Penaeus aatecus, are n'.OGt abundant in the
summer and early fall in the offshore waters of Texar. . Louisiana, and,
to a lesser extent, Mississippi and Alabama, Pink sbrjrap are abundant
at all times except the late summer in the olfsliore waters of south-
western Florida (Dry Tortugas and Sanibel Island) and tl;e western Yucatan
Peninsula (Obregon and Gulf of Carapeche) . White shrlii'p are most abundant
during the fall of the year about equally in the inshore and offshore
waters of the coast of Louisiana and, to a lesser extent, Mississippi
and eastern Texas. The concentrations of shrimp reported here doubtless
reflect activity patterns of the shrimp fleet in that they are inferred
from conunercial landings. However, the commercially important ccncen-
trations of shrimp would seem to be fairly v?ell indicated by these data.

The Gulf Shrimp Fleet

In 1966 there were 7,739 boats and vessels in tJie Gulf shrimp
industry operated by 13,756 regular and casual fishermen. These 7,739
craft were equipped with 9,969 otter trawl net units having a sweep
capacity of 141,472 yards at mouth [23, p. 645]. Tabic 3.4 contains a
breakdown of these statistics by state and by vessel and boat fisheries
for 1966.

By the definitions followed by the U.S. Department of Interior, a
boat is a craft of less than five net register tons \,7l)ile a vessel is a
craft of at least five net register tons. A register ton is a volume
of 100 cubic feet which displaces 6,242.5 pounds of fresh water of
maximum density. The designation "gross" refers to register tonnage
calculated from the volume between decks below tlie tonnage deck and

Table 3.4

Sumniary of

shrimp otter trav/l

boats, vesse.

Is, fxshe

;rinen ,

and gear in

the Gulf

states, 1

966

Number

Fishermen

Otter

Trawls

Number

Number

Yds. at

State

Boats

Regular

Casual

Number

Mouth

Fla. , W.C.

98

142

24

99

1,281

Alabama

203

311

43

203

3,900

Boat

Mississippi

380

178

285

380

3,680

Fishery

Louisiana

3,261

2,919

1,220

3,305

42,016

Texas

861

772

406

861

9,149

Total, excl.

of dupl.

4,797

4,312

1,978

4,842

59,942

Vessels

Fishermen

Otter

Traxjls

Gross

Yds. at

State

Number

Tonnage

Number

Number

Mouth

Fla. , W.C.

886^

43,686

2,140

1,664

25,912

Alabama

366

14,050

882

598

9,730

Vessel

Mississippi

410

16,835

1,020

665

10,878

Fishery

Louisiana

1,342

59,007

3,524

2,354

37,289

Texas

1,409

77,348

3,787

2,646

41,697

Total, excl.

of dupl.

2,942

132,149

7,466

5,127

81,530

Boats and Vessels

Fishermen

Otter

Trawls

Yds. at

State

Number

Number

Number

Mouth

Total

Fla. , W. C.

984

2,306

1,763

27,193

(Boat

Alabama

569

1,236

801

13,630

and

Mississippi

790

1,483

1,045

14,558

Vessel

Louisiana

4,

,603

7,663

5,659

79,305

Fishery)

Texas

2,

,270

4,965

3,507

50,846

Total, excl.

of dupl.

7

,739

13,756

9,969

141,472

Printed as 386, apparently a misprint.

Source: Fishery Statistics of the United States, 1966, Stat. Dig.
No. 60, U. S. Dept. of the Int., Fish and Wildlife Service, Bureau of
Commercial Fisheries, 1968.

II 4. II

A 8
within permanent structures above the tonnage deck, while the "net'
designation refers to the gross tonnage adjusted for cei^tain allowable
exemptions. A regular fisherman earns more than half his income from
fishing while a casual fisherman earns less than half his income from
fishing. An otter trawl net (see Figure 3.2) is designed to be towed
along the bottom, collecting shrimp at the mouth and funneling them
into the cod end of the net.

Table 3.4 indicates that there are 2,942 vessels in the Gulf shrimp
industry manned by 7,466 regular fishermen. These vessels operate 5,127
otter trawl net units having a combined sv;eep of 81,530 yards at mouth.
Since each vessel operates either one or tv;o net units, there must be
(5,127 - 2,942) = 2,185 double rig vessels operating 4,370 net units and
(2,942 - 2,185) = 757 single rig vessels operating 757 net units.
Assuming single rig net units are twice as large across the mouth as
double rig net units [26, p. 4], there are 4,370 + 2(757) = 5,834 double
rig net unit equivalents operating in the Gulf shrimp industry measuring
81,530 yards at mouth. The average double rig net unit is 13.86 yards
(41.58 feet) across the mouth v/hile a single rig net unit is 27.72 yards
(83.16 feet) across the mouth. The average vessel in the Gulf shrimp
industry tows nets having a sweep capacity of 27.72 yards (83.16 feet)
across the mouth. In addition to the main nets, each vessel usually
carries a ten-foot try-net used to locate profitable shrimp concentra-
tions before the main nets are deployed.

The distribution of vessels by states as shown in Table 3.4 corre-
sponds closely to the distribution of landings by areas. Louisiana and
Texas (Areas IV and V) lead in number of vessels and landings followed
by Florida (Areas I, II, and to a large extent VII so far as vessels are
concerned) and Mississippi and Alabama (Area III). Landings from

49

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50
Area VI are probably largely accounted for by Texfs Vfi.ssels while
landings from Area VII are accounted for by Florida and, to a lesser
extent, Texas vessels. Tabic 3.5 indicates the relative size composi-
tion of the fleets landing shrimp in each state. The vessels landing
catches in Alabama, Mississippi, and Louisiana tend to be relatively
smaller than those landing catches in Texas and Florida.

Tliere are 4,797 boats in the Gulf shrimp industry (Table 3.4) of
which the majority (3,261) arc based in Louisiana. Florida has the
smallest number of boats (98). These 4,797 boats are manned by 4,312
regular and 1,978 casual fishermen and carry 4,842 otter trawl net units
with a sweep capacity of 59,94 2 yards at mouth. Assuming single rig
nets are twice as large as individual double rig nets, there are 530
double-rigged boats equipped to tow tv7o nets having a width at mouth
of 6.25 yards (18.75 feet) each. The majority of boats are single-
rigged, towing one net having a sweep capacity of 12.5 yards (37.5 feet)
at mouth.

Many boats are manned by casual fishermen who, as a primary source
of income, either engage their boats in another fishery or leave their
boats idle and take jobs as shore workers or crew on craft employed
outside the shrimp industry. As Table 3.4 indicates, the largest
numbers of casual fishermen are found in Louisiana and fish the highly
seasonal (late fall) white shrimp resource in the inshore or near off-
shore waters. Alternative maritime employment for the Louisiana casual
fisherman is available on oil company tugboats and service boats [22,
p. 39].

Although boats outnumber vessels in the Gulf shrimp industry,
vessels represent the most important segment of the industry, so far as
fishing capacity is concerned, controlling 51.4 percent of the nets and

51

Table

3

.5.

Summary of
by tonnage

shriir.p
groups.

otter
, 1966

trav/1 vess<

-Is of

tlie

Gulf

states

5

•OSS

mage

Number

by

State

Gi

Tor

11a. ,

W.C. Alabama

Miss:

Lssippi

Lo>

aisinna

T(

ixas

Total,
of d

excl.

up] .

5

-

9

38

30

7

41

22

122

10

-

19

89

88

62

235

138

512

20

-

29

41

42

83

166

83

318

30

-

39

134

56

71

167

124

370

40

-

49

152

45

58

176

161

374

50

-

59

78

29

38

141

154

264

60

-

69

217

28

51

231

392

531

70

-

79

69

24

19

113

191

239

80

-

89

22

3

9

32

52

73

90

-

99

40

9

7

23

66

93

100

-

109

3

—

3

9

16

23

110

-

119

2

3

1

2

5

9

120

-

129

1

6

—

4

4

9

130

-

139

—

3

—

2

—

3

160

-

169

—

—

—

—

1

1

190

-

199

—

—

1

—

—

1

Total

vesse]

.s

886

366

410

L,342

1

,409

2

,942

Total gross

tonnage 43,682 14,050 16,835

59,007 77,348

132,149

Source: Fishery Statistics of the United States, 1966, Statistical
Digest No. 60, United States Department of the Interior, Fish and Wildlife
Service, Bureau of Commercial Fisheries, 1968.

52

57.6 percent of tlie sweep capacity. In terms of utilization, che vessel
fleet probably accounts for a larger percentage, of the catch than the
percent of sweep capacity indicates since nearly all the vessels fish
on a year-round basis. To the extent that the offshore vessel fleet
catch is of larger shrimp than the boat fleet catch, the vessel fleet
accounts for an even larger proportion of the value of the shrimp catch
since larger shrimp are more valuable.

As for profitability of operation of the fleet and of vessels ver-
sus boats, no data are available on boat operations since statistics
are not gathered separately for boats. Table 3.6 presents costs and
returns for a typical offshore Gulf shrimp vessel (see also [3]). The
"return to management (gross return less all costs)" or net return is
negative in this case. As shown in Table 3.6, this negative net return
may serve to reduce owner share as in "return to investment" or operator
share as in "return to labor and management." Caution must be used in
applying these figures to vessels in different size classes or ultra-
modern vessels of different efficiency.

C. C. Osterbind and R. A. Pantier [27] and Roy L. Lassiter [22]
present and analyze data from the 1950 's and early 1960 's on costs and
returns in, and utilization of the Gulf shrimp fleet. These studies
are valuable for a historical review as is the more recent Basic
Economic Indicators: Shrimp, Atlantic and Gulf [1] published by the
National Marine Fisheries Service.

A feature of shrimp vessel operation bearing on costs and returns
and adequately described elsewhere [27, 33] is the "share system." The
"share system" is an arrangement whereby captain (whether or not he is
the vessel owner) and crew share in the proceeds of the catch — and in
part of the variable trip cost — in lieu of guaranteed salaries. Under

t;

3

Table 3.6. Marino economics data - 65-foot GnTi of Mexico shrimp
vessels

Vessel Description; 65 feet, SO gross tons and 3-man crew (1967-1968
data)

Expected Production and Prices; 183 fislnug diys, 100,000 pounds (50
tons) shrimp at $. 69'4/pound .

Shrimp
Variable Costs Season Total

Vessel Repair $ 5,798

Gear Repair 5,450

Fuel 4,655

Galley 2,269

Ice 1,456

Other 1,190

Crewshare 16,553

Operator Share^ 8,276

Total Variable Costs $ 45,647

Fixed Costs

Interest on Investment (8%) $ 9,168

Depreciation^ 8,604

Insurance , 3,791

Interest on Operating Capital (1/2 of 10%) 2,188

Administrative 2 ,597

Total Fixed Costs $ 26,348

Summary

Variable and Fixed Costs $ 71,995

Gross Returns 69,400

Gross Returns Less Variable Costs 23,753
Return to Management (Gross Returns Less

All Costs) -2,595
Return to Investment (Return to Management

Plus 8% of $114,600) 6,573 (5.7%)
Return to Labor and Management (Return to

Management Plus Operator Share) 5,681

Captain's commission and wages actually received.

Interest is charged against all investment and average operating
capital whether or not borrowed. Investment is based upon returns to
the vessel, a 15-year useful life and a 12 percent discount rate as
determined by the National Marine Fisheries Service and for this vessel
is $114,600.

Depreciation is not standardized as in other marine economics data
sheets but is as given in Working Paper No. 57 [1].

Source; Marine Advisory Program, Sea Grant, Oregon State University,
Corvallis, Oregon. Prepared February 1971 from Working Paper No. 57,
[1] Division of Economic Research, National Marine Fisheries Service

[3].

54

the share arrangement, the captain and crew receive a percentage of tb.e
value of the catch, this percentage varying over vesf^els and portG and
according to whether or not the captain is the vessel oumer. The share
of the captain and c.vc\^ in variable codLs usually includes food and gear
(net) repair, these costs being deducted from crew share. The obvious
advantages of this arrangement are that it gives the cre\.' an incentive
to maximize catch while holding down certain variable costs that are
directly dependent on crew performance. The share system also guarantees
short-run profit-maximizing behavior by a captain who is not the vessel
owner and does not encourage loyalty of the crew to their emplo^'er.
Such behavior may be at odds with the longer-run interests of the vessel
owner. Since the share system is widely used, apparently many vessel
owners feel that the advantages outweigh the disadvantages.

Francis J. Captiva in a recent paper on "Changes in Gulf of Mexico
Shrimp Trawler Design" [10] describes the recent shift in the Gulf
shrimp industry to slightly larger vessels (80 to 100 feet) of stee] ,
fiberglass, or aluminum construction in place of the tradition.il wooden
vessel. He describes the newly constructed vessels as being higher
powered (from 400 up to 750 horsepower as compared to 150 - 200 horse-
power on older vessels) with more comfortable crew quarters and more
mechanized gear-handling and processing equipment, as well as design
oriented toward diversification to allow handling various gears with
little or no equipment modification. Modern electronic aids installed
in duplicate, power steering with automatic, hand and remote controls,
powerful remotely controlled trawl winches, and relocation of the con-
trol bridge to provide a better view of the working deck are attributes
of many of the newly constructed vessels. Mr. Captiva envisions in the
future an even larger vessel (150 feet in length) incorporating computer

55
designed hull, the capability Lo handle a v;idp. variety of gears, new
concepts in pi-opulsion and auxiliary pDv;er (specifically, a diesel-
electric or gas turbine-electric syr.ten) and otlior innovations. This
"dream" vessel, \7ith its increased hold and supply space and mechanized
processing and freezing equipment, could serve as a motber-ship-catcher-
ship, towing tour electro-shrimp trawls simultaneously.

While changes in vessel design^ equipnient, and fishing techniques
must meet the test of economic efficiency as well as technical feasi-
bility, there are two recent developments that may be important for the
Gulf shrimp industry. One of these concerns the development of the
electro-shrimp trawl, which uses pulsed electric current to force shrimp
up from their burrows, thus permitting 24-hour per day fishing with an
increase in catching efficiency over the conventional trawl. Adoption
of the electro-shrimp trawl by the Gulf shrimp fleet would have the
effect of greatly increasing the potential effort (measured in 24-hour
periods spent in actual fishing) of the fleet since vessels could,
theoretically, fish continuously once they reached the fishing grounds
and found profitable concentrations of shrimp. The other development
concerns the discovery that royal red shrimp concentrate about the 49°F
thermocline. By locating the 49''F thermocline and fishing at that
depth, improved catches of royal red shrimp can be made [4]. The
Expendable Bathythermograph System, originally developed for use by
the U. S. Navy in locating the thermocline, is currently being used in
experiments. Its cost apparently prohibits commercial adoption. The
development of economically feasible gear with which to locate thermo-
clines should lead to greater utilization of the royal red shrimp
resource, thus expanding the shrimp supply.

56

Processing and Mai']'.rtin.o, Ilia Gull" Slirimp Catch

Shrimp processing begins on hoard tht^. catching vessel v.'he7;e shrimp
arc beheaded (thus losing about 38 percent of their body weight). They
are then packed in ice or, on some of the larger modern vessels, frozen
in five-pound cartons for direct marketing or in blocks for later thaw-
ing and further processing. An exception occurs when heavy shrimp
concentrations are located and/or fishing is close to shore. Under
these conditions, the catch rate may be so high that beheading on board
requires more fishing time than does returning the shrimp to shore. In
this case, shrimp may be iced down whole and beheaded during shoreside
processing.

Once the domestic shrimp catch is ashore, most of it is sold as
raw material to processing plants either directly or through "packing
houses" which assemble shrimp for sale to processors. Figure 3.3
presents a detailed analysis of shrimp processing and marketing channels.
About 80 percent of the U. S. shrimp catch is processed as a frozen
product while the remainder is canned or dried. Much of the Pacific
coast catch, especially Alaska's, as well as part of the New England
catch is processed into canned or dried products. Thus at least 80
percent of the Gulf shrimp landings may be said to enter the frozen
product market. The frozen shrimp are converted into three major prod-
uct forms: raw headless, breaded, and peeled and deveined, in order of
importance, with raw headless accounting for about 40 percent and the
latter categories about 30 percent each of the weight of raw headless
shrimp processed into these products in 1969. According to Miller
et al. [2A, p. 29] trends indicate that breaded and peeled and deveined
products will account for a growing share of the frozen shrimp total at

57

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the expense of raw headless. Thei^e propoi' tj.oDy do not I'nit: i r.lljy liold
for imported shrluip, v;liich u\.\de up aboni; 53 percent of the total of
imported and doicestic landL^igs in recent: years [30]. Upon importation,
about 90 percent of tb.e foreign shriinp are in raw headless or peeled
and deveined form. Part of the imports are further processed in U. S.
plants so that the distribution of iraported shrimp in final product
form is about the same as for domestic shrimp. To the consumer, imported
shrimp are indistinguishable from domestic shrimp other than by designa-
tion of place of origin on branded products.

Shrimp products are readily accepted by consumers. Miller et al.
[24, p. 45] report that the retail demand for shrimp is price inelastic,
a rise in price being associated with a less than proportionate decline
in quantity demanded. The retail demand for shrimp is reported to be
income-elastic [24, pp. 45, 46]; i.e., an increase in income is asso-
ciated with a more than proportionate increase in quantity demanded.

The Gulf shrimp industry falls more or less naturally into the
three segments or subsectors described briefly above. While description
may be interesting and is important in gaining a x-jorking knowledge of
the industry, it does not provide a firm base for management or policy
decisions. The following section outlines an abstract model of the
shrimp industry that may serve as the basis for policy and management
decisions.

A Model of the Gulf Shrimp Industry

Following the precedent set in earlier sections of this chapter,
the model developed here will follow the general subdivisions of "Gulf
shrimp resource," "Gulf shrimp fleet," and "processing and marketing."
The model is designed to be used to provide simulated output of variables

59
of interest over time and, as will be apparent, is designed specif iciilly
for the Gulf shrimp resource v/ith data-imposed restrictions clearly in
mind.

A Model of the Gulf Shrimp Resource

All three shrimp species considered here — brown, pink, and white-
are landed at ports in each of the seven statistical reporting areas
(see Figure 3.1 and Table 3.3) and must be presumed to be found in these
areas. However, each species has different, specific seasonal charac-
teristics with respect to abundance so that each species must be
considered separately. In addition, there are differences in growth
rates betv/een sexes of shrimp [7, p. 93] so that males and females m.ust
be considered separately with respect to their effect on size compcsi-
tion of a particular recruit class. Berry [7, p. 29] indicates that
there is no spawTier-recruit relationship operative on the Tortugas
shrimp grounds and the simplest assumption is that there is no spawner-
recruit relationship operative in other areas of the Gulf as well.
However, Berry [7, p. 5A] does note that apparent fluctuations in shrimp
abundance are similar among species and result from environmental
changes affecting large parts of the Gulf. ,

The problem is to devise a model that will reflect the seasonal
pattern of recruitment of different species in different areas of the
Gulf, as well as allow for inter-period randomness in the size of
recruit classes. In addition, the model must include the effect of
natural and fishing mortality and the differential growth rates between
sexes. The assumption is made that, at any point in time, the shrimp
stock is equally divided in members between the sexes. Drawing on the
theory presented in Chapter II, the following variables are defined:

60

R. = Size, in nuwbcirs, of recruit clatis of species i (i = 1, 2,

3 for brovm, pink, c-md white shrimp, respectively) in area

j (j = I, ..., VII, see Figure 3.1) considered recruited at

the end of time period k (k = ] , . . . , T where T defines an

arbitrary time horizon).

N. = Number of shrimp remaining of species i in area j of recruit

class R. ., at the end of interval t (t = 1, . . . , T) . Then
xjk

t - k is the elapsed time since shrimp in recruit class R...

were "recruited" or t - k represents their "age" in the

fishery.
W. ., = Weight of shrimp of species i and sex m (m = ], 2 for female

and male, respectively) in area j of "age" t - k.
F... = Fishing mortality coefficient measured as a pure number per

time period applying to species i in area j of age t - k

during time period t.
M. ., = Natural mortality coefficient measured as a pure number per

time period applying to species i in area j of age t - k

during time period t.

B.. = Biomass of species i in area i at the end of time interval
ijt *^ -^

t.

X = Standardized units of effort expended in area j during
interval t .
By assuming shrimp numbers to be equally divided between the sexes and
shrimp to survive in the fishery for T^ time periods, B. may be

expressed in terms of N. ., and W. ., as;

ijkt ijkmt

2

B.. = (1/2)Z, ^ ^ Z , N.., W..,
ijt ^ ' ^ k=t-T m=l ijkt ijkmt

61

Tlie important relationships required are tho.je relating (1) the fishing
mortality coefficient and effort, (2) L]ie survival characteristics (in
numbers) of a recruit class, and (3) the £,rox^/th (in x>;eight) character-
istics of a recruit class. The fishin?; rportality coefficient (F. , )
is assumed to be a direct linear function of the effort expended in the
area after shrimp reach some age in the fishery, say V, and zero before
this age.
(3.1) F..^^ =0 , t - k < V

Number of shrimp surviving at the end of interval t is a declining expo-
nential function of the mortality rates and the number present at the
beginning of period t (end of period t - 1), The number surviving when

t = k is the original recruit class, that is N..,, = R. ., .

ij kk J.J K

-<^jkt + "ijkt)

(3.2) N.., = N. ., , e
ijkt ijkt-1

The weight of an individual of age t - k is given by;

(3.3) W.

1 - e

32i

(t-k) + B..,

33i

ijklt 31ij
for females and for males is given by:

P^/,

34i

(3.4) W.

1 - e

^42i(^-^) -*■ \31

3

44i

ijk2t 41ij L

Shrimp are classified commercially according to number of tails per
pound. If individual weight is measured in pounds, then the reciprocal
of W. ., times a factor to arrive at heads-of f weight represents
number of tails per pound.

Given size of recruit classes and effort, equations (3.1) - (3.4)
and aggregations of these equations describe the behavior of the shrimp
population in the Gulf in terras of numbers and weight. In addition, a

62
policy variable is provided by V, tlie ape in tlic-. fishery at v/hich shrimp
begin to be subjected to fishing mortality. The variable V may be
manipulated by, for example, restrictions on mesh size, closed seasons
or areas, or any combination of these uieasures. Variability in the model
comes in the form of inter-period variation in sizes of recruit classes
and varying fishing effort. The effort expended provides a link betvjeen
the basic shrimp resource and the harvesting sector, the Gulf shrimp
fleet.

A Model of the Gulf Shrimp Fleet

The craft in the Gulf shrimp f].eet may be divided into H size
classes, vessels in each size class having a different sv-;eep capacity
and, possibly, different cost characteristics. Larger vessels usually
have greater sweep capacity and a day spent trawling by a vessc] of 2X
yards sweep capacity may be considered as contributing roughly twice as
much to fishing mortality as a day of trawling time by a vessel having
X yards of sweep capacity. Thus, an arbitrarily chosen "standard"
vessel size class having a "standard" sweep capacity may be established
and the days spent trawling by vessels in other size classes may be
adjusted by the ratio of sweep capacity of the vessel size class in ques-
tion to that of the "standard" class. Thus, the model of the harvesting
sector must be able to aggregate effort of diverse vessel size classes
into the single effort index required by the basic resource sector model.
In addition, the harvesting sector model must specify catch and gross
revenue of vessels in each size class. Since prices vary according to

Effort data are available in "days fished" — 24-hour periods spent
in actual fishing activity.

63

size of shrimp (as expressed in tails per pound) the size composition

of the catch must be knovm. In addition, cost per unit of effort is

required to derive a measure of profitability. Profitability must be

related to the intensity of fishing effort and to the entry and exit of

fishing vessels to areas and the industry in order to determine effort

vhich is needed as an input to the basic resource sector. The interface

between the harvesting sector and the marketing and der..and sector is

characterized by the weight and size composition of the catch and the

ex-vessel price, by size class, paid for the catch.

The following variables delineate the factors to be considered in

a model of the Gulf shrimp fleet:

C , = Catch (in numbers) of a craft of size class h (h = 1, ...»
hijkt

H) of species i in area j of recruit class R- -j. (^ge in

fishery t - k) during interval t.

Y = (1/2)2 ^, C, .., W.., = weight of catch C, ... .
hijkt ^ '^ m=l hijkt ijkmt ^ hijkt

P = Price per pound of shrimp in area j of age t - k and sex m
jkmt

and thus of count per pound 1/a W. ., vjhere a is a factor
to convert to headless weight.

^\jt = (^/2^^i=l \=t-T^ Cl ^jkmt Sijkt ^^jkmt

= Gross revenue of a craft of size class h in area j during

period t.
X^. = Effort in 24-hour periods (days fished) spent in actual

fishing activity by a vessel of size class h in area j

during interval t.
n, = Number of craft of size class h fishing in area j during

interval t.

n,. = Number of craft of size class h with home port in area j
Ihjt

during interval t.

64

n„, . = New vessels of si'/.c class h having lioine port in area j
2njt

entering fleet at beginning of time interval t so that

"ihjt = "lhjt-1 '""2hjt

S = Sx.7eep capacity (in yards along footrope of nets) of a

vessel of size class h in area j during interval t.

X.. = ^,^\ n, . fS, .^/S .^)X, .^
jt h=l hjt^ hjt rjt^ Tijt

= Effort in standardized "days fished" in area j during

interval t when vessel size class r is chosen as the

"standard" class.

V, = Cost (variable) of a day fishing by a marginal vessel of
bjt

size class h in area j during time period t.

W, = Per time period value of sunk capital plus interest on
ht

this sum at a competitive rate prorated over the expected
life of the sunk capital.

%t = \jt-\jt\jt- V

= Net revenue of a vessel of size class h in area j during
period t.
The relationships of interest are those leading to Di -^ and the rela-
tionships relating effort and profitability. The number of shrimp of
species i and age t - k caught by a vessel of size class h during period
t is given by:

(3 5) C = Vl^\it/^jt>^jt ^
^^^ 'hijkt F..^^+M..^^ iJkt-1

-(F. ., + M. ., )
^ _ ^ ^ ijkt ijkt'

From (3.5) total catch, weight of catch, gross revenue, and net revenue
per vessel may be calculated from their definitions.

Firms owning vessels in the Gulf shrimp fleet must decide in which
area their vessels will fish and how intensely they should fish. The

65

cost structure of vessels in each size class will depend, in addition to

size characteristics, on the area of hem? port and the port area of

current operation. Vessels fishing an area out of a temporary port may

have higher cos uf. than vessels fishing the same area who are permanently

based in a port in that area. Similarly, vessels of the same size class

fishing the same area but from ports at different distances from the

fishing ground will have different costs due to differences 5.n steaming

time to and from the grounds. Thus, the cost of a unit of effort of a

marginal vessel in an area v;ill appear as a step function vjhen plotted

against the number of vessels fishing in the area. This cost will take

on one value when a marginal vessel has its home port in the area and a

higher value when the marginal vessel has a home port in some other area.

It is probably reasonable to assume that migration patterns are such

that the cost of fishing an area other than the home port area from the

home port area is greater than or equal to the cost of fishing out of a

temporary port in that area. Thus, vessels fishing an area other than

their own may be considered to be fishing out of a temporary port in

that area so that there will be only two values for V for a given

vessel size class in a given area during a given time interval. Since

vessels of a given size class have identical revenue functions but

different cost functions depending on home port area, all vessels of a

given size class based in an area will be fishing in that area before

other vessels of the same size class migrate to the area. Thus, the

cost, by size class, of a unit of effort by a marginal vessel in an area

will depend on the relationship betv/een number of vessels fishing the

area and number of vessels based in the area. Specifically:

(3.6) V, .^ = v., .^ if n. _ < n

hjt Ihjt hjt — Ihjt

V =V >V ifn. >n

\jt 2hjt Ihjt ^jt Ihjt

66
Net revenue by vessel size class may be calculii'red for each area
once number of vessels and effort are determined. Entry into the fleet
by new vessels is baaed on the profitability over a number (t ) of pre-
vious time periods by vessels of the size class and area in question.
Entry and exit are probably asymmetrical so that nev; vessels begin to be
attracted only after cumulative net revenue reaches some positive level
(say D-,, .) but vessels may not begin to exit until cu:nulative net reve-
nue is lower or even negative (say D .). Over the range between these
two values, vessels neither enter nor leave the fishery. That is:

(3-^) "2hjt = ^71hj \l~t\ %T' \ll\ %T ^ ^Ihj
"2hjt = ^72hj ^T=t-t^ %T' \l~t\ %T ^ ^hj

"2h3t = ° ' ^.hj < ^'^-t^ Via- ' °lh3

Movements of vessels between areas from one time period to the next
will occur by moving vessels to the area with highest net revenue in the
previous time period from all other areas. In the event that the area
with highest net return has fewer vessels fishing in it than have their
home port there, so that the lower cost coefficient (V-,, . ) is in effect,
the number of vessels required to bring the higher cost coefficient
(V„, ) into effect will be moved to that area on a prorated basis from
the other areas. In terms of behavioral relations:

7

(3.8)

^jt = "hjt-1 -^ ^r=l ^8hrj %t-l - °hrt-l^ %rt-l + "2hjt

where D, . , = Max D, ^ ,
hit-l hst-1

■^ s

and n, _ ^ > n., .^ ,
Tijt-1 — lhjt-1

67
and:

(3.9) n^^^ = n^.^^_^ - 3g,,^^.. (D^^^ ,__^ - D^.^^^_^) n^^^^_^ + n^^^^^

r=l, ...,j-l, j +],..., 7

except that, if rL < n,, , the fo]lov7ing reallocation is pcr-
113 1-1 injt-1 ° ^

formed.

(3.10) n, _ = n,, . , + n„. .^

hjt lhjt-1 2nj t

and:
(3.11)

Vt = Vt-1 - f^Shri ^^hit - \rt^ Vt-l^

8hr j hj ■

^s=l ^8hsj %3t - \st^ '''hst-l^ ^"lhjt-1 - \jt-l^ ^ ^2hrt

r=^l, ...,j-l, j + 1, ...,7

Equations (3.8) and (3.9) indicate that new vessels begin to fish,
or retiring vessels leave the fishery, in their home port area. These
propositions are not unreasonable since new vessejs V7ill probably make
some test runs near their home port until the vcGccl is deened seav7orthy.
If the time interval used is short these test runs will probably require
most of one time period to complete. Likevjise, vessels retiring from
the fleet will most likely be found fishing in their home port area
since cost conditions are most favorable there.

Once vessels are located on a particular ground, they must decide
how intensely to fish, that is, hov; many days fishing time per time
interval to expend. Variability in fishing days per time interval is
probably not large since, if it is profitable to initiate a trip at all,
it pays to fish as intensely as possible while on the trip. However, to
the extent that profitability affects the attitude of the crew about
length of trip and layover time between trips, effort may vary. In
addition, number of trips per time period may be varied for a particular
vessel by postponing equipment maintenance and thus reducing layover time

60
in port. However, maintenance may be postponed only for a finite ariount
of time so that for the avertige vessel in the area, this is probably an
ineffective method of varying effort. Expected returns below the level
at which average variable cost is covered will preclude fishing alto-
gether. However, data are obtained on ex post results, not a priori
expectations, so that a formulation indicating cessation of fishing
activity is probably not reasonable unless expectations can be discovered
and are homogeneous throughout the vessel size class in the area. The
most reasonable proposition is that effort in days fished per time period
varies between minimum and maximum levels as a linear function of net
revenue in the preceding time period.
(3.12) X^j,=X^^.^ , D^.,_,iD^^.

\jt = ^(12)1 %t-l ' °lhj - %t-l - ^2hj

\jt " "2hjt ' ^2hj -\jt-l
Given the behavior described by equations (3.5) - (3.12), various totals

of interest may be calculated by taking the proper sums. For example:

H 3 7 t
Weight of total catch in period t = E^ ^ E . ^ E . ^ E, ^ Y, ...^
" ^ h=l 1=1 j=l k=t-t hijkt

or:

Total standardized effort in period t = E. , X.

J=l Jt

By combining over vessel size classes, species, and areas, catches of

shrimp of the opposite sex and different age that are of the same size,

total weight of shrimp of a given size count may be obtained. Totals

such as these are necessary input to the model of the shrimp resource

as well as the model of the marketing and demand sector.

A Kodelof the- Marke-ting__3nj_U&maml Sector
"o£~t"he Gu"lf~Shr3.inp_ Industry

Rather than attempt to build an original model of the marketing
and demand sector of the Gulf shrimp industry, the approach follovied
here is to take advantage of the work of John Doll entitled, _Ari_
Econometric Analysis of the U. S. Shrimp Market , [16]. Doll's quar-
terly model [16, Chapter IV] is presented below with modification in
symbols. In addition, a relation is presented to convert the single
ex-vessel price appearing in his model into a range of prices for each
size class of shrimp.

The model is simultaneous, involving four jointly determined (endo-
geneous) variables and nine predetermined variables. The jointly
determined variables are [16, p. 65]:

A = Total consumption, per quarter (t represents one quarter here
and does not necessarily correspond to the time period of the
basic resource or harvesting sector models) in millions of
pounds, heads-off weight.

B = Stocks held in cold storage at the end of the quarter, in
t

millions of pounds, heads-off weight.
D = Wholesale price, frozen processed, 26-30 count, Chicago, BLS

(Bureau of Labor Statistics).
E = Ex-vessel price, weighted average for South Atlantic and

Gulf states.
The predetermined variables are [16, pp. 65-66]:

Y = Landings per quarter in the South Atlantic and Gulf states

in millions of pounds, heads-off weight.
I = Imports per quarter, in millions of pounds, heads-off
weight.

70
E ^^ = Ex-vp.ssel price lai^ged one quarter.

B ^^ = Stocks held in cold storage at the beginning of the
quarter.
G = Quarterly total disposable income.

Qo > Q-ij Qa ~ Quarterly intercept dummies for quarters twoj three, and
four, respectively.
1 = The intercept dummy.
The structural quarterly model for v^^hich Doll estimated parameters
is composed of four equations.

Wholesale demand
(3.13) A^ = 3(^3)^ + 6(,3)2 ^2 + ^13)3 ^3 "^ ^13)4 %

■*■ ^13)5 ^t -^ ^13)6 ^
Price linkage
(3.1A) D^ = B(,,), + E.f^ B(i,). Q. + B^,)3 E^_^

"^ ^(14)6 ^t + ^14)7 \
Ex-vessel demand

^''^'^ h = ^15)1 -^ htl ^15)i '^i ■" ^15)5 \ ^ ^15)6 ^t

+ ^15)7 ^t ■*■ ^15)8 Vl + ^15)9 \
Stock balance
(3.16) B^ = 3(,,), + 3(,,)2 ^t + ^16)3 ^t

"■ ^(16)4 Vl + ^(16)5 \
The difference in length of time interval between Doll's model and
the time interval used in the rest of the model presented here raises
the difficulty of obtaining quarterly landings with a model that requires
prices for all time periods within the quarter except the last. This

71
difficulty may be partly overcome by using tht; prices determined in one
quarter for all time periods occurring during the subsequent quarter.
For example, if the shrimp and fleet models employ monthly time periods,
then the prices determined at the end of the preceding quarter could be
used in each month during the current quarter to generate catch. At the
end of the current quarter, monthly catches may be totaled and used to
generate a set of prices which are used for each month in the subsequent
quarter. Thus, prices are constant for the entire quarter. However, if
the number of tim.e periods per quarter is not large, this procedure nay
give reasonable results. An alternative is to use a month corresponding
to the moving average of prices obtained in a hypothetical quarter
employing data from current, previous, and subsequent months in the
preceding few years. Wiile this would allow shorter lags in the har-
vesting sector and thus more immediate seasonal responses, it builds
into the model an incapacity to react to extremely volatile conditions
resulting from large inter-year price variation. A third alternative
is to use quarterly data in the models of the harvesting sector and
basic shrimp resource. This alternative may prove reasonable also.
Choice of an alternative must rest upon empirical considerations.

The problem of disaggregating the ex-vessel price into prices for
each size class of shrimp is serious but a workable solution can be
more readily proposed than for the time period problem. The price of a
given size class of shrimp most likely depends on the relative abundance
of the various-sized shrimp available in the market. Although imports
and cold storage holdings influence the size composition of available
shrimp, the relationship postulated here is between current landings
and price. The price of a given size class of shrimp is postulated to

72
be a direct function of the aggregate price detenniTicci by equation
(3.15) and an inverse function of the proportion of that size shrimp
in total landings. That is:

(^•1^) ^jnt = ^j = 2 P(17)3 Qj + ^17)8n ^

/\ ^o \

"*" ^(17)9 I y"T ~ Y~ J^t
\ nt no y

where the Q., j - 2, ..., 7 are dummies for areas II - VII; i.e., the

equation is normalized on Area I , Y ., is landings of shrimp of size n

(n = 1, ..., N different sizes) in time period t, Y is landings in time

period t, P is the ex-vessel price derived from the quarterly ex-vessel

price determined in (3.15), Y and Y are landings in some base period,

and the B/-,-,xo are coefficients derived from the price spread between
(17) on

size classes in the base period.

Equations (3.1) - (3.17) arc the relations needed to describe the
dynamic workings of the Gulf of Mexico shrimp industry with the excep-
tion noted in the model of the marketing and demand sector. In addition,
modifications in the variables of the model of this sector to make them
correspond more closely to conditions in the Gulf shrimp industry may
be needed. Further refinement will be dictated by the estimation tech-
niques and programming procedures involved in the application of a
simulation model.

CHAPTER IV

METHODOLOGY AlU) DATA

The objectives of this study, listed In Chapter I, nay be presented
as a set of objectives relating to the behavior of individual firms and
a set of objectives relating to industry behavior. The objectives
relating to firms concern the description of the behavior of firms in
the Gulf of Mexico shrimp industry in response to changes in the shrimp
population, the technological conditions of harvesting and processing,
and demand conditions. The objectives relating to the industry concern
the behavior of the industry in th.e aggregate and particularly its
response to management strategies. The management strategies or poli-
cies to be considered are: (1) varying age of shrimp at first capture;
(2) imposing an annual entry fee (license fee) on vessels in the
industry; and (3) imposing a landings fee or tax per pound on shrimp
landed by vessels in the industry.

The procedure for attaining the objectives relating to industry
behavior involved constructing a simulation model of the Gulf of Mexico
shrimp industry that simulates the behavior of the industry under vari-
ous conditions. The objectives relating to firm behavior were realized
by drawing on published results of research into various phases of the
industry and, where such results were not available, by resorting to
synthesis of needed parameters. The major thrust of this study is to
develop a bioeconomic theory of a fishery, to build an abstract model
of the Gulf of Mexico shrimp industry based on this theory, and to

73

74
develop an empirical model that gives plausible results. Ther.? was v.o
attempt to elaborate upon the objectives relating to indivxdurtl firm
behavior as the emphasis ol" this study is to deteiTnine the effects on
the industry of selected regulatory strategies. This chapter describes
simulation as a tool for policy evaluation, the available data, and
the computer r.odel employed in this simulation study.

Si mujL a ti on as a Tool _f or_ Model
Euildi ng and Policy Evaluation

The dog trots freely in the street

and sees reality

and the things he sees

are bigger than himself

and the things he sees

are his reality

["Dog," from Lawrence Ferlinghetti , A Coney Island
of the Mind , Copyright 1958 by Lawrence
Ferlinghetti, reprinted by permission of New
Directions Publishing Corporation.]

In order to describe simulation as a tool for evaluating manage-
ment strategies, one must first define simulation. Simulation is not
a well-defined technique in the sense that linear programming or regres-
sion analysis are well-defined techniques. As is the case in most
descriptions of simulation, several definitions are given and then a
comprehensive definition is made for the purpose of this study.

Describing simulation as a research method, Fred H. Tyner [31,
p. 13] says: "Simulation Involves the application of logical reasoning
to a scale model of selected real-world phenomena, whether the scale
model be one of equations or the prototype of a physical plant." In a
paper discussing the reasons for using simulation J. E. Creameans [13,
p. 6] writes: "The best that one can say about any simulation model is
that it describes the object process using those characteristics which
are important to the results that the model builder wishes to study."

75

G. H. Orcutt [25, p. 893] furnishes an open-ended definition of siranla-

tion: "Simulation is a general approacli to the study and Lise of models,"

Defining simuDation for the purposes of a paper, Boutwell and McMinimy [8,

p. 1] say: "A matheiTiatical simulation model is defined as a model that

traces a series of events through time and/or space in sucli a manner

that the cost and benefit streams of the resulting time path are

measured," In a Rand Corporation publication, M. A. Geisler [18, p. 1]

gives a hint as to the birthplace of the term simulation:

The study of large and complex systems in recent years,
combined with the development of large-scale computers,
has led to the representation of these systems in mathe-
matical form for programming and calculation on high-speed
computers. Calculations so obtained have been essentially
pseudo-observations of these systems, which accounts to
some extent for applying the term simulation to this
technique.

Jay W. Forrester [17, p. I'^i] j while dealing with industrial dynamics

(which may be thought of as a specific type of simulation technique) ,

states:

The first and most important foundation for industrial
dynamics is the concept of servo-mechanisms (or
information-feedback systems) as evolved during and
after World War II.

An information-feedback system exists whenever the
environment leads to a decision that results in action
which affects the environment and thereby influences
future decisions.

As can be seen from the above definitions, there is no general accord

in defining simulation. However, there are commonalities in nearly all

definitions of simulation.

Most of the definitions indicate that systems with interacting

components are involved and that the systems are dynamic as opposed to

static. Simulation is defined, for the purposes of this study, to be

a technique for studying the performance of dynamic systems whose

76
components intei"act to form an environmental sett-lng vjhich may change
as a result of component interaction tlirougli timt-. A simulation model
is an abstract representation of the system to be studii^d. It is
usually, but not necessarily, formulated ii"i terms such that a coraputer
may be used to trace out the interaction of the mode] components over
time. The model components correspond more or less closely to their
real system counterparts in a degree that serves best the purposes for
which the study is being conducted. Further, as implied above, a system
refers to a set of real-world components whose decisions in reaction to
their environment either wholly or in large part determine their future
environment. Simulation involves building a model of this real-world
system and operating the model over time, observing its behavior which
supposedly reflects that of the real system.

At this point, legitimate questions arise. It is very well to be
able to represent a system symbolically and even to have a machine
manipulate these symbols to simulate the system's behavior, but what is
to be gained from this? Cannot the real system be observed as easily
as its machine-bound counterpart? To answer these questions is to
specify the value of simulation as a research tool. If a system is
relatively simple and well-understood and its behavior predictable
without error, then there is no point in simulating the system since
nothing is to be gained from such a simulation. However, many systems
are not well-understood and/or their behavior not readily predicted.
It is in studying these systems that simulation is of use.

In many large and dynamic systems, the components of the system
and the ways in which these components interact may not be readily
identifiable. Building a simulation model of the system forces the
researcher to (1) identify the various components of the system,

77
(2) specify how they interact, and (3) decide the relative importance
of components and interactions to the behavior of the systeE. The test
of the researcher's skill is the degree to which selected m.odel results
approximate the behavior of the system. (VJhile it is possible that the
model may behave correctly for the v.'rong reasons, this chance must be
taken in lieu of a better validation.) The researcher may use all the
conventional econometric analysis at his coraniand to identify the rela-
tionships betv7een the components and the components themselves. Then,
by fitting these relationships into a simulation framework, the
researcher m.ay discover important areas of omission or misspecif ication.
Thus, a value of the simulation technique is that it provides insight
into the components and interactions of a system, i.e., how the system
actually v/orks .

Given that a system may be readily identified and that an accurate
model may be devised, often the complexity of the system prevents accu-
rate prediction of future behavior, especially if some component or
relation of the system is changed. Using a simulation model, the
system's behavior may be traced out through time under different sets
of conditions (different levels or states of the policy variables).
That is, if an accurate model of the system can be devised, then it
will be possible to experiment on the model, gaining valuable (and often
less costly) information about the probable effect of proposed manage-
ment strategies on the system itself. Thus, a second value of simulation
and the one of primary interest in this study is that it gives the
researcher and his decision-making clientele an opportunity to test new
management strategies on a realistic model without fear of a possibly
disastrous result that could occur from testing on the system itself.

78

Thus, simulation is a research teclmiqiKi that has the. noteiit i al to
provide valuable information about the system being naodeled and pof:sible
effects of proposed policies affecting the system. A drawback to
employing simulction as a research technique is that there currently
exists no standardized method for evaluating, the reliability of the
information provided by a simulation model. Lack of a standardized
validation technique for simulation models may be partly due to the
youth (relative to standard econometric methods) of simulation as a
research technique. In addition, simulation models tend to be unique,
problem-oriented models that m.ay not lend themselves v.-ell to standard-
ized validation techniques. However, simulation has been defined for
this study in a rather general sense and an attempt is made here to
develop a general approach to the problem of model validation.

For purposes of exposition, a situation is assumed involving an
analyst employed by a client to provide information about the possible
effects of proposed policies on selected indicators of the performance
of some system. To provide this information, the analyst employs

The terms "analyst" and "client" are used for convenience' sake.
The "analyst" may actually be a group of investigators which may include
all or a part of a group of individuals represented here by the term
"client." The situation assumed here presupposes a "client" who recog-
nizes a problem in a system for which he has authority to implement
policies designed to correct that problem. In addition, the client is
assumed to possess an array of alternative policies among which he will
choose on the basis of information provided by the analyst. This is an
idealistic situation. More likely, the "client" is likely to have con-
fused and/or conflicting views about the problem and policies designed
to correct it. In addition, as is the case in the present study, there
may not exist a "client" with the ability to implement policies even
after problems have been identified and corrective policies proposed.
Alternatively, the analyst may not be able to conceive of or comprehend
the system and/or the problems involved in a manner that leads to the
generation of meaningful information. These problems are not unique
to studies employing simulation as a research technique and represent
needless complication to the framework to be developed here.

79

simulation modeling as his prii-nary resedrcb technique. Figure 4.1
presents a flow diarriram of a possible frainevork in which tlie sinulation
model, as initially constructed by the analyst, may be subjected to
progressively liio-re rigorous validation procedures. The model is refined
by the analyst as a result cf the validation procedures and as a result
of the assessment by the client and the analyst as to the usefulness of
the information generated by the model. As the model becomes more
refined and capable of providing information v.'orthy of r.iore confidence,
so do the validation procedures become more sophisticated and capable
of detecting less obvious aberrations in model performance.

As represented in Figure 4.1, the validation process begins after
initial construction of a model by the analyst. During the process of

model construction the analyst may gain insights into the system that

2
prove to be valuable information to his client. The analyst and his

client can evaluate this information in terms of its implications for
model revision. In addition, the analyst may select model output quan-
tities that he believes to be reliable indicators of system performance
and compare the means, ranges, and standard deviations over the simula-
tion period of these quantities with the means, ranges, and standard
deviations of their real-world counterparts over some base period.
Since the model parameters are usually estimated with data generated by
the actual system for a period in which the system exhibited enough
stability to survive, the model will likely prove stable if it is
properly specified. Model stability is not a goal within itself,
however. There may be inherent instabilities in the system that are

2

These insights may be the most valuable product of the entxre

research effort.

80

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82
isolated as a result of model construction or that the model must cap-
ture in order to provide information on policies designed to eliminate
the instabilities. The comparisons involved in Phase I of the valida-
tion process are not of the t3'pe that lend credibility to irformation
provided by the model. They merely provide crude indicators of the
performance of the model and, together with the information provided by
the interaction of analyst and client, provide input into the process
of revising the initial model.

Phase II of the validation process involves experimenting with the
model to determine the type of policy information the model provides.
This information, after evaluation by the analyst and his client, may
indicate needed model revisions. In addition, the analyst may compute
simple correlation coefficients between selected indicators of the per-
formance of the model. These coefficients, together with a graphic
analysis of selected model quantities, serve to indicate relative
direction of serial movement between model quantities. The relative
movements of model quantities over time can be compared with expecta-
tions based on theory as well as the relative movements of actual
quantities over time. These comparisons together with the information
provided by analyst-client interaction provide the basis for further
revision of the model and comprise Phase II of the validation process.
The revised model is used to provide information to the client which
the analyst and client assess for implications for further model revi-
sion. In addition, values generated by the model for selected aggregated
(over time or variable subsets) output quantities may be subjected to
spectral analysis. The resultant time path parameters relating to trend
as well as amplititude, frequency, and phase angle of cycles may be

83

compared with those resulting from spectral analysis of actual data.
The information thus provided by Phase III of the validation process
may be used to direct further revision of the model. Phase IV of the
validation process involves considering model- generated values of dis-
aggregated output quantities produced by the model after its revision
at the end of Phase III. These quantities may be analyzed by graphic
methods and calculation of simple correlation coefficients as in Phase
II or by spectral analysis as in Phase III or both. The results of this
procedure, together with the information obtained through analyst-client
interaction may be used to attain a fourth level of revision of the
model.

The framework for model validation presented here may be modified
or extended to meet the needs of a particular situation. At each phase
in the validation process the client receives information from the
model through the analyst. On the completion of any phase (possibly
even before Phase I begins) the client may decide he has enough infor-
mation. The analyst and his client may choose to cease revising the
model after any phase of the validation process, considering any
increase in model reliability not worth the cost of the required model
revision and validation. The analyst may be hindered in his validation
procedures by the absence of actual time series data on variables of
interest with which to compare model results. Thus, it becomes clear
that the process of model construction, revision, validation, and use
remains as much an art as it is a science. Even within the framework
presented here, the analyst must effectively allocate his resources
(presumed to be scarce) between model "validation" and model revision
and maintain a balance between the sophistication of his validation
procedures and the level of development of his model.

Data

Models that represent complex systems make stringent demands on
the data. In the case of the GuJf of Mexico shrimp industry data in the
form of parameter estimates that can be used directly in building a model
of the industry do not exist for many of those needed. Those parameters
that could not be adapted from published literature were synthesized
from available data using basic sLatistical techniques. Estimates of
the parameters describing the behavior of the Gulf shrimp resource were
derived from estimates made by Berry [7]. The work of John Doll [16]
provided most of the parameter estimates for the marketing and demand
sector of the model were synthesized from primary data published in
Osterbind and Pantier [27], Lassiter [22], Lyles [23, for the years
1965 and 1966], Osborn et al. [26], Surdi and Whittaker [30], and Arnold [5]

A model of the Gulf shrimp resource requires an individual growth
equation and a survival equation which incorporates estimates of natural
mortality and mortality due to fishing. Equations (4.1) and (4.1a),
derived from equations given by Berry [7, p. 127] are the growth (in
weight) equations for male and female pink shrimp, respectively, on the
Dry Tortugas grounds utilizing a monthly time period. These equations
are used in this study to represent weight in grams of individual shrimp

of brown, white, and pink species on all grounds.

f/ T^ „ , , . ,„ - r -.1992(t + 1.062)1 3.134

(4.1) W (males) = 42.3 |1 - e J

f, , s ,, fr: 1 X TO o F-, -.2382(t - .2633)1 3.115
(4.1a) W (females) = 73.3 Ll - e J

The time variable, t, is measured in months of 4.33 weeks each from time

of hatching (zero age of shrimp). By multiplying equations (4.1) and

(4.1a) by factors to convert to heads-off weight, convert from grams to

85

pounds, and taking the reciprocals of the results, the number of shrimp
per pound at a given age may be determined. Factors to convert heads-on
to heads-off weight are (as derived from E. J. Barry [6, p. XVL]) for
brown shrimp, C,S21; pink shrimp, 0.625; and white shrimp, 0.649. The
size classification of shrimp considered are: (1) very small, over 55
tails per pound; (2) small, 41-65 tails per pound; (3) medium, 26-40
tails per pound; and (4) large, 25 and under tails per pound. Table 4.1
gives the age, in months, of male and female shrimp in the four size
categories. Shrimp are assumed to become subject to capture at three
months of age. The variation in heads-on to heads-off weight conversion
factors made no difference between species in these gross size
categories.

The survival equation used in this study is of the form specified
in equation (3.2). The natural mortality coefficient, M, is not differ-
entiated by species, time, or area and the initial value used was 0.22
[7, p. 88]. Fishing mortality (F ) was related to effort (in standard-
ized 24-hour days fished -X. ) by area and time as shown by equation
(4.2).
(4.2) F.^ = b.X.^

Initial estimates of the b.'s were derived for each area from the b

J

value given by Berry [7, p. 88] of 11 x 10~ by multiplying by 1125 and
dividing by the square nautical miles fished in the area (as estimated
from maps presented in [26]) to convert to an equivalent area basis and
multiplying by 24 to convert to an equivalent time basis. The initial
estimates of the b.'s and the estimated area fished in square nautical
miles in each area are given in Table 4.2 for each statistical area.
Standardized days fished are derived from reported 24-hour days fished

86

Table 4.1. Age (in inonths o£ 4.33 vje.eks each) distribution by
size and sex of brown, pink, and white shrimp in
the Gulf of Mexico

Size Category
(tails/pound)

1) over 65

2) 41 - 65

3) 26 - 40

4) 25 and under

Males

3 through

4 inonths

5 through

6 months

7 through

9 months

10 months
and over

Age

Females

3 months

4 months

5 through

6 months

7 months
and over

87

Table 4.2. Coefficients to convert 2'-';-hour days fished to
fishing mortality and estimated square nautical
miles fished by area

Estimated
square nautical
Area j b miles fished

'■■■■■ - . - J

I 1.13 X 10"^ 26,185.50

II 2.26 X 10~^ 13,092.75

III 2.50 X 10"^ 11,902.50

IV 1.19 X 10~^ 24,995.25
V 1.25 X 10"^ 23,805.00

VI 3.12 X 10"^ 9,522.00

VII 0.92 X 10"^ 32,136.75

88
per vessel size class by multiplying days fished by each vessel size
class by the estimated sweep capacity per vessel in hundreds of feet.
The vessel size classes used and their sweep capacity in hundreds of
feet are given ia Table 4.3.

The computer model calculates number of recruits each month by
adding to the mean recruits each month the product of a normally dis-
tributed random number with zero mean and variance of one and the
standard deviation of recruits in that month. The estimated means and
standard deviations of recruits for species in each month in each area
are presented in Appendix II in the data required for initialization of
the simulation program. Appendix I presents the computer program and
data required to estimate recruits by species by month and area.

The model of the harvesting sector — the fleet — of the Gulf of Mexico
shrimp Industry is required to generate 24-hour days fished by vessels
in each size class in each area. To do this, the computer program
adjusts average days fished per month by a vessel of a given size class
in a given area by a factor depending on net revenue in the preceding
month. Adjusted average days fished per vessel is then multiplied by
the number of vessels in that size class fishing in the given area.
Adjusted days fished by vessels of all size classes are then standardized
by multiplying by vessel size class sweep capacity in hundreds of feet
and added together to determine 24-hour days fished in that area.
Table 4.4, adapted from tables by Lassiter [22, pp. 40-46], presents
estimates of the average 24-hour days fished by a vessel in each size
class in each month of the year. Table 4.5 gives the adjustment fac-
tors by which the data in Table 4.4 are adjusted to arrive at average
24-hour days fished per month by a vessel in each size class in each
area in each month of the year. These factors are based on the ratio

89

Table 4.3. Vessel size classes and sweep capacity of nets along
headropc in hundreds of feet

Vessel size class Gross register tonnage Sweep capacity

100 feet

1 less than 5 .375

2 5-19 .500

3 20-49 ,800

4 50-79 1.000

5 80 and over 1.250

90

Table 4.4. Mean 24-hour days fished per month by a vessel in each
size class

Vessel

size

class

Month

1^

2

3

4

5

January

1.0

2.9

4.2

5.4

4.9

February

0.5

2.7

3.7

5.9

5.0

March

0.5

3.2

4.6

6.6

7.9

April

0.5

2.7

4.1

6.5

5.2

May

1.0

3.2

4.5

7.2

6.8

June

1.0

4.9

5.4

6.7

6.7

July

0.75

5.8

6.4

7.4

7.1

Augus t

1.5

5.2

6.5

7.7

7.0

September

2.5

4.5

5.3

6.9

7.2

October

3.0

5.5

6.2

7.2

7.3

November

3.0

3.8

5.0

6.3

6.3

December

2.0

2.7

4.2

6.5

6.4

Estimated from closed seasons in 1969, personal knowledge, and
the distribution of white shrimp landings as given in [26].

91

Table 4.5. Factors to adjust days fished by a vessel in a size class
to reflect variations in average days fished by vessels
in different areas

Area Adjustn.ent factor

I 1.15

II .83

III -73

IV .83
V 1.13

VI 1.13

VII 1.15

92
of the average days f i shed per year by vessels in an area to the average
days fished per year by vessels in all areas.

The number of vessels estimated to have hone ports in each area is
given in Table 4.6, along with the number of vassels assumed to be
fishing in each area in December of a typical year. The latter figures
are needed to initialize the simulation model.

The model of the marketing sector employs a quarterly time inter-
val. Given catch for the quarter, this model calculates ex-vessel
price as well as consumption, ending stocks in cold storage, and whole-
sale price. The calculated ex-vessel price is used to determine the
ex-vessel prices used in the model of the harvesting sector for each
month in the succeeding quarter. The model of the marketing sector is
based on the quarterly model estimated by Doll [16] and the reduced
form coefficients of Doll's model are presented in Table 4.7 for the

variables as identified in Chapter III. In addition, Doll [16, p. 104]

3
presents an import equation that is employed here. The equation is

given as (4.3) using the same variable defined as in Chapter III.

(4.3) I^ = -9.212 - 0.1952Y^_^ - 8.4988Q2

In order to be consistent with the model of the harvesting sector, the

ex-vessel price computed with the parameters presented in Table 4.7 is

converted to ex-vessel prices for each size class of shrimp and further

3

There is an exception. Doll [16, p. 104] reports the coefficient

of Q- in equation (4.3) as -88.4988. Use of this value, holding Y

and G at mean values, produced negative imports which did not occur in
the data he reported using. Since imports were nearly the same in the
second and third quarters in this data [16, pp. 98-99], the value of
-8.4988 was used as the coefficient for Q^ , approximating the coeffi-
cient of Q_, and reflecting the assumption of an error in the reported
coefficient.

93

Table 4.6. Number of vessels in each size class estimated to have
home ports in each area and number of vessels in each
size class assumed to be fishing in each area in
December of a typical year

Vessels estimated to have home ports :
each area by vessel size class

Ln

Area

1

2

3

4

5

I

0

7

170

191

41

II

98

101

52

21

3

III

582

158

242

110

29

IV

3

,257

233

347

283

46

V

860

135

251

429

93

Vessels
December

assumed
of a typ

to bf
ical

2 fishing
year by

; in each area in
vessel size class

Area

1

2

3

4

5

I

0

7

170

291

61

II

98

101

52

21

3

III

582

158

242

110

14

IV

3

,257

233

347

283

26

V

860

135

251

229

23

VI

0

0

0

100

10

VII

0

0

0

0

75

94

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95

adjusted to reflect variations in the proportion of total catch that
each size class represents.

The Computer Program

The model was reduced to a computer program using the Fortran IV
Level E language designed for the IBM System/360 [21]. The program and
initialization data are presented in Appendix II. Figure 4.1 is a flow
chart of the essential workings of the program, denoting input and out-
put of the main program and the subroutines.

96

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60

CHAPTER V

RESULTS OBTAINED WITH THE SIMULATION MODEL
AND POLICY IMPLICATIONS

In order to gain credibility for results from simulation under
various levels of the policy variables, a simulation model must be
verified to possess some desired degree of validity. This chapter
describes the phases of the validation framework presented in Chapter
IV that were completed with the present model. The policies considered
and the results obtained with the simulation model for specified policy
levels are presented along with a discussion of the implications of the
policies for the attainment of various objectives.

Model Validation

The validation procedures described in Phases I and II of the
framework for model validation presented in Chapter IV (see Figure 4.1)
were applied to selected annual summary data generated by the present
model. After the comparisons described in Phase I were made, the model,
as originally constructed, was revised and a 30-year period was simu-
lated. The model revision segment of Phase II was not accomplished.

Thirty years was an arbitrarily chosen period that promised to be
sufficiently long to allow any unsuspected cyclical behavior to be dis-
covered and yet allow the required computer storage space for the
program to remain small enough to qualify the program for the lowest
hourly rate for machine time as determined by storage requirements.
Actually, all cycles appeared complete within five years, the "length
of run" chosen for policy experimentation.

97

98
In addition to the comparisons involving annual suiriinary data, montlily
values generated by the model for allocation of effort are presented to
Indicate how the procedures described in Phase II for aggregated quan-
tities might be applied to disaggregated quantities during Phase IV,

The output data describing shrimp landings, prices, and imports
were compared with equivalent summary data found in Shellfish; Situa-
tion and Outlook; 1970 Annual Beview [30] covering most of the decade
of the 1960's. The output data concerning vessel numbers, allocation
of vessels among areas, fishing intensity, and profitability were com-
pared to the figures presented in the tables of Chapters III and IV, as
well as to the data presented in Osterbind and Pantier [27], Lassiter
[22], and Lyles [23]. There was no attempt to determine correlation of
simulated output with actual data through statistical techniques.

Operation of the model using initial parameter estimates indicated
two areas where adjustments were needed. Landings were extremely low,
indicating that either the coefficients used to convert effort into
fishing mortality (the b.'s) were too low or estimates of mean recruits
were too low, or both. In order to maintain a proper ratio of shrimp
in each size class of catch, both sets of estimates were adjusted upward
until catch levels approximating those actually occurring in the indus-
try were obtained. Table 5.1 presents the b. estimates used in the
model as well as the factors by which the initial estimates of the mean
number of shrimp recruited by month and area were multiplied. In addi-
tion to the adjustments required to produce landings similar to those
occurring in the industry, the imports equation presented by Doll [16,
p. lOA] was further adjusted to reduce predicted imports to a level
approximating actual occurrences. The adjustment made was to change

99

Table 5.1. Adjusted coefficiants to convert 24-hour days fished to

fishing mortality and factors (ADFACJ's) by xv/hich initial
estimates of the mean number of shrimp recruits were
multiplied for final use in the model

Area i b .
___! 1.

AD>

'kCJ.

4,

,00

4.

.00

2,

,00

1,

,75

1.

.75

1,

.00

3,

.00

I 4.93 X 10~^

II 9.85 X 10~^

III 7.26 X 10"^

IV 3.31 X 10"^
V 3.49 X 10~^

VI 9.08 X 10"^

VII 5.81 X 10~^

100
the intercept value used from the -9.212 presented in equation (4.3) to
the value -19.212 used in the model as presented in Appendix II. No
further adjustments in the model parameters were made as a result of
Phase I validation procedures. Phase I comparisons based on output
from the model as presented in Appendix II are given below.

Surdi and Whittaker [30, p. 7] report annual Gulf shrimp landings
from 1960 to 1970. During this period landings varied from a low of
79.6 million pounds (heads-off weight) in 1961 to a high of 145.2
million pounds (heads-off weight) in 1970 with average annual landings
for the period 1960-1970 at 119.1 million pounds. The model listed in
Appendix II, using the initialization data listed there, generated
annual landings values ranging from a low of 93.6 million pounds to a
high of 113.9 million pounds with an annual average of 104.4 million
pounds and a standard deviation of 5.0 million pounds. Thus, the model
generates landings in the ranges of actual landings occurring during
the decade of the 1960's; however, model landings show more stability.
Average generated landings were below average actual landings during
the 1960 's by 14.7 million pounds per year for an average percentage
error of 12.3 percent per year. This discrepancy may result from low
estimates of mortality, shrimp recruits, or both. It may also result
from the intra-year cyclical patterns of shrimp abundance by area and
effort allocation being out of phase in the model as compared with the
real world and may be altered during later revision.

Table 5.2 presents information on the size composition of actual
catches in the Gulf and South Atlantic states from 1964 through 1970
and the average composition of 30 years of catches generated by the
computer model. While the size classifications used in the model

101

Table 5.2. Size composition of actual shrimp caiches in the Gu]f and
South Atlantic states for the years 1964-1970 and average
size composition of 30 years catch data generated by the
computer model

Percent of actual catch

Year

Large Medium Small

(30 & under tails/lb.) (31-50 tails/lb.) (over 50 tails /lb.)

1964
1965
1966
1967
1968
1969
1970

39.5
35.3
36.8
37.8
34.7
32.9
36.3

35.8
35.9
31.1
34.8
33.3
31.7
30.3

24.7
28:8
32.1
27.4
32.0
35.4
33.4

Mean

36.2

33.3

30.5

Standard
Deviation

2.15

2.30

3.73

Percent of average catches generated
by the computer model

Large
(25 & over
tails/lb.)

Medium

(26-40

tails/lb.)

Small
(41-65
tails/lb.)

Very small

(over 65
tails/lb.)

Mean

27.9

29.8

21.7

20.6

Standard
Deviation

1.31

1.71

1.48

1.56

Mean

Large Medium Small

(30 & under tails/lb.) (31-50 tails/lb.) (over 50 tails/lb.)

37.9

28.5

33.6

Calculated from catches generated by the model on the assumption that
catches in the medium (26-40) and small (41-65) categories are uniformly
distributed over the five tails/lb. intervals making up these classifi-
cations.

102
am not the same as those reported by Surdi and Wiittaker [30, p. 8],
the data in Table 5.2 indicate that the shrimp catches generated by the
computer model have a similar si?.e composition to that of actual
catches.

Surdi and Whittaker [30, p. 16] report ex-vessel prices occurring
for brown, white, and pink shrimp at Brov^msville-Port Isabel, Texas,
Morgan City, Louisiana, and Tampa, Florida, respectively, for each
month of the years 19G9 and 1970 for three sizes of shrimp. There are
thus 72 observations on prices for each size of shrimp. The ex-vessel
price for 15 - 20 tails per pound count shrimp ranged from a low of
$1.07 per pound to a high of $1.48 per pound. Prices for large shrimp
generated by the computer model fell within this range. The ex-vessel
price for shrimp counting 31 - 35 tails per pound ranged from a low of
$0.75 per pound to a high of $1.10 per pound, a range which contained
the prices generated for medium shrimp as defined in the model. The
prices for shrimp counting 51 - 65 tails per pound ranged from a low of
$0.41 per pound to a high of $0.77 per pound. The prices generated by
the model for small shrimp were generally near the top of this range
while the prices for very small shrimp concentrated near the bottom of
the range. As with landings, model prices showed somewhat more stabil-
ity than real-world prices.

The computer model generated average imports of 180.3 million
pounds (heads-off weight) per year with a standard deviation of 0.8
million pounds. About 23 percent of the imports occurred in the first
quarter, about 20 percent in each of the next two quarters with about
37 percent of the imports entering the country in the last quarter.
Thus, generated imports were slightly lower than the average annual

103

imports of 182.1 million pounds per year reported by Surdi and Whitr.akor
[30, p. 12] for the years 1960-1570.

The above comparisons of means and standard deviations of model
quantities with actual data for the 1950 's indicate that the model as
presented in Appendix II did not explode; it reproduced values within
the ranges established from actual data. The comparisons of Phases II
through IV of the validation framework presented in Chapter IV are
intended to provide indications of the underlying economic relationships
contained in the model. Relative movements in selected model quantities
are presented below.

In the present model total personal disposable income is held con-
stant, thus eliminating shifts in demand due to population and/or
productivity effects. In addition, to the extent that personal dispos-
able income is correlated with time (as it was in Doll's data [16,
pp. 29, 97]), holding this variable constant removes any trend in
demand. Thus, the movements in values generated by the model reflect
variations in shrimp supply resulting from resource availability and
effort variability. Figure 5.1 presents the values generated over a
30-year time period by the model for average wholesale and ex-vessel
prices, total landings, imports, and effort in adjusted days fished.
Figure 5.2 presents the values generated by the model for total produc-
tion costs, adjusted days fished, value of the fleet assuming a five-
year investment life, and net return (ex-vessel value of the catch less
total production costs). Table 5.3 presents simple correlation coeffi-
cients for the variables presented in Figures 5.1 and 5.2 plus ex-vessel
value of the catch. These comparisons correspond to those indicated in
Phase II of the validation framework described in Chapter IV. As indi-
cated in Figure 5.1 and Table 5.3, wholesale and ex-vessel prices

104

185-
180-
175-
170-
165-
160-
155-
150-
145-
140-
135-
130-
125-
120-
115-
110-
105-
lOO-
95'

90-
85

Imports
(mil. of
lb.)

Adjusted
Days Fished
(2,000 days)

Wholesale
Prices

(cents
per lb.)

T — t—r
5

T— I — r— 1
10

I I I I I I I 1 I I I rill
15 20 25 30

Total
f \ / Landings
V (mil. of
lb.)

Ex-vessel
Prices

(cents
per lb.)

Figure 5.1. Annual Values Generated by the Computer Model for
Wholesale and Ex-vessel Prices, Total Landings,
Imports, and Effort in Adjusted Days Fished

105

255 -

245 I

235
225
205
200 -i
195
185
165 _
155 -
135 -
125
115 _
105-

Value of
the Fleet
(nil. of
dollars)

Adjusted
Days Fished
...xN.^^, (2,000 days)

Total
Production
Costs
(mil. of
dollars)

■15 _
-25-

-35
-45-1

I I I I

1

I I I I I I I

5 10

I I I I I I I I I

15 20

rTT

TT

25

TT

Net
Return
(mil. of
dollars)

m

30 Time in
Years

Figure 5.2.

Annual Values Generated by the Computer Model for
Total Production Costs, Adjusted Days Fished, Value
of the Fleet Assuming a Fixed Year Investment Life
and Net Return (ex-vessel value of the catch less
total production cost).

106

Table 5.3. Simple correlation coefficicnLs between selected variables
based on values generated by the computer model

Net Total Ex-vessel value
return landings of the catch

Total Production Costs -0.923
Value of the Fleet

(5-yr. investment

life)

-0.809

a

Adjusted Days Fished

-0.950

0.847

Wholesale Price

a

-0.093

Ex-vessel Price

a

-0.380

Imports

a

-0.774

Net Return

1.0

-0.689

0.577

Not calculated.

107
generally move in directjons opposite to that for total landings con-
sistent with the predictions of demand theory (increasing quantities
supplied results in lower prices). The relationship betvjeen landings
and prices was moderated somewhat by the negative correlation between
total landings and imports and the dependence, in the model, of prices
on total supplies (landings plus imports). Total landings and adjusted
days fished (effort) are positively correlated. This result is con-
sistent with production theory for stages I and II of the classical
production function. The data presented in Table 5.3 and depicted in
Figure 5.3 indicate that net return is negatively correlated with total
production costs, value of investment in the fleet, and adjusted days
fished. These comparisons indicate that effort and investment in the
fleet are in excess of the levels needed for maximization of net return.
The positive correlation between adjusted days fished and ex-vessel
value of the catch suggests that the point of decreasing total returns
to effort has not been reached.

Tables 5.4 and 5.5 present data on the intra-year cyclical alloca-
tion of vessels among areas by the computer model. Comparisons of these
data with the data presented by Lassiter [22, p. 34] correspond to the
types of comparisons outlined as part of Phase IV of the validation
framework presented in Chapter IV. Lassiter [22, p. 34] presents infor-
mation on the percentage of total monthly activity spent in each area
by a sample of otter trawl shrimp vessels for the years 1959, 1960, and
1961. Since the computer model allows vessels to fish in only one area
per month, the number of vessels fishing in an area expressed as a per-
centage of vessels fishing in all areas is a measure of the effort spent
in that area. Boats (vessel size class one) do not readily migrate
between areas in the real world and were not allowed to migrate in the

108

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rH -t-)

■1 o

CO X)

^ H

> <:

I I I I I I I < I I

II II II

<; pq u

OCTiCJO r~.>^ u-iv3-rocN4

T-HCNm<rmvor^cx3 cyio

I I I I

3U3"pOTJJ303 uoxaBXS^iJOO SJ^^TS

109

Table 5.4. Conparison of percentage disfrlhution of effort by area
in each month of the year of sample vessels with the
percentage allocation generated by the computer model
in the 30th year for vessels (vessel size classes 2-5)

Area

Month^

I

II

III

IV

V

VI

VII

January

S
M

23.5
9.9

1.4
3.9

4.5
60.9

31.5
4.6

17.4
16 . 6

16.6
3.7

4.6
0.3

February

S

M

29.9
38.9

1.0
2.6

2.1
37.4

21.5
4.2

15.8
13.0

15.8
3.7

13.9

0.2

March

S

26.9

2.3

1.8

21.1

18.7

14.5

14.7

M

30.5

2.5

18.9

36.3

8.4

3.4

0.2

April

S

25.7

8.2

2.9

24.1

23.6

6.8

13.0

M

19.7

2.4

8.5

60.6

5.7

3.0

0.0

May

S

15.0

6.2

3.9

31.5

28.8

6.7

7.4

M

15.0

3.5

6.6

64.5

5.4

2.8

2.3

June

S

7.1

1.5

27.4

27.2

21.0

8.3

7.8

M

13.2

6.7

5.5

62.0

5.4

2.8

4.4

July

S

2.8

0.6

21.0

22.9

46.2

2.8

3.6

M

11.9

6.7

4.9

50.4

18.5

2.2

5.4

August

S

2.6

0.7

17.9

23.8

50.2

3.3

1.2

M

9.6

6.5

4.3

28.6

45.7

1.1

4.2

September

S

2.8

1.0

14.0

23.0

52.7

4.9

1.4

M

8.8

5.1

12.2

25.0

44.0

1.1

3.9

October

S

5.8

1.4

11.0

25.5

44.4

8.5

3.1

M

6.2

3.0

54.2

9.0

25.5

1.0

1.0

November

S

11.7

1.3

10.7

28.3

35.7

7.3

5.3

M

5.4

2.1

55.1

7.1

16.7

13.3

0.4

December

S

14.3

1.7

8.0

27.5

25.8

11.1

11.3

M

5.9

3.2

48.6

6.6

12.8

22.7

0.2

^"S" denotes

sample

values

while "M"

denotes

values

generated by

the model

,

110

Table 5.5. Comparison of percentage distribution of effort among
aggregated areas in each month of sample vessels v^7ith
the allocation generated by the model

Area

Month'

I-II-VII

III-IV

V-VI

34.0
20.3

31.6
16.7

33.2
11.8

30.4
8.7

35.5
8.2

29.3
8.2

49.0
20.7

53.5
46.8

57.6
45.1

52.9
26.5

43.0
30.0

36.9
35.5

January

February

March

April

May

June

July

August

September

October

November

December

S

M

S

M

S

M

S

M

S

M

M

S

M

M

S

M

S
M

S

M

S

M

29.5
14.1

44.8
41.7

43.9
33.2

46.9
22.1

28.6
20.8

16.4
24.3

7.0
24.0

3.8
20.3

5.2
17.8

10.3
10.2

18.3
7.9

27.3
9.3

36.0
65.5

23.6

41.6

22.9
55.2

27.0
69.1

35.4
71.1

54.6
67.5

43.9
55.3

41.7
32.9

39.0
37.2

36.5
63.2

39.0
62.2

35.5

55.2

^"S" denotes sample results while "M" denotes model values gener-
ated. Rows may not add to 100% due to rounding.

Ill

model. Since boats presumably V7cre not. presented in Lassiter's figures,
they are not used in calculating mcntlily activity in the model as shown
in Tables 5.4 or 5.5. Table 5.4 compares the three-year average per-
centage of total activity spent in each area in each month by the sairple
vessels with the percentage allocation generated by the model for vessels
(vessel size classes two - five) in the last year of simulated results.
The sample results as reported by Lassiter [22, p. 34] included marked
differences in patterns of effort allocation between years. The most
notable departure of the simulated results from the actual effort allo-
cation occurs in Areas III and IV. This is partially explained by the
fact that the model, over the simulated period, added 689 vessels of
size class four to the fleet in Area IV. The model allows a rapid
migration rate between Areas III and IV and thus , effort becomes concen-
trated in one area very quickly. A second area where agreement between
model results and simulated results is poor is the intra-year cyclical
variation in effort by month. Areas I, II, III, and VII appear to be
completely out of phase. Table 5.5 aggregates the figures presented in
Table 5.4 for areas between which vessels migrate easily. The figures
in Table 5.5 represent percentage allocation of effort to areas which
have relatively low rates of migration between them. Again, the addi-
tional vessels assigned by the model to Area IV affect the results. The
intra-year cyclical variation in effort by the model appears to be
completely out of phase with that reported for the sample in the aggregate
area containing Areas I, II, and VII. The cyclical variation in model
results and sample results is unclear.

The model is capable of adding vessels to or deleting vessels from
the fleet in response to profitability considerations. Over the 30-
year period simulated, the model deleted two vessels of size class two

112
from the fleet in Area I, a ?.8.6 jjercent decrease in that size category
for that area, and added 689 vessels of size class four to the fleet in
Area IV, a 198.6 percent increase in that size category in that area.
After the first five years of simulation, the model had deleted the two
vessels from size class two in Area I and added 448 vessels to size
class four in Area lY. There were no additions to or deletions from
the fleet other than those mentioned for Areas II and IV.

Recent data on the cost structure of the industry are available
only in very aggregated form. Consequently, the following discussion
of cost estimates used in the model does not correspond precisely to
any of the phases of the validation framework presented in Chapter IV.
It is presented to indicate the basis used to estimate the value of the
fleet. Firm cost data may be found in Osterbind and Pantier [27] and
the National Marine Fisheries Service publication Basic Economic Indi-
cators; Shrimp, Atlantic and Gulf [1], The annual fixed cost charges
employed in the model are given for each vessel size class in Table 5.6.
These figures were derived from data presented in Osterbind and Pantier
[27] and in Table 3.6.

If the annual fixed cost charges are assumed to represent some
proportion of the total investment in vessel, gear, and necessary shore
facilities, then dividing the annual fixed cost charge by this propor-
tion would yield the amount of the total investment. The proportion of
total investment charged as annual fixed cost will depend on the average
length of life of the investment. Table 5.6 presents the values of the
total investment in vessels, gear, and necessary shore facilities derived
from the fixed charges used in the model under three assumptions about
the average life of the investment. An investment life of 5.0 years
corresponds to an annual fixed charge of 20 percent of the total

113

Table 5.6. Annual fixed cost charges par vessel employed by the
computer model and tlie capitalized values that these
sums represent

Value

cf

investment

assuming

Vessel
size class

Annual fixed
cost charges

an

average life

of:

5.0 years

6. 7 years

10.0 years

1

$ 1,800

$ 9,000

$ 12,000

$ 18,000

2

3,600

18,000

2A,000

36,000

3

9,600

43,000

64,000

96,000

4

14,400

72,000

96,000

144,000

5

24,400

120,000

160,000

240,000

114
investment while a b.7-ycar lii'e corresponds to ?.n annual charge of 15
percent and a 10.0-year life corresponds to an annual charge of 10 per-
cent. Current acquisition costs for average vessels and gear in each
size class are in the range of investment values derived using average
investment life-spans of 5.0 and 6.7 years. Assuming a fleet size as
given in Table 4.6, the estimated value of the total investment in the
Gulf shrimp fleet is given in Table 5.7 under the three assumptions
about average vessel and gear life employed in constructing Table 5.6.
Table 5.7 also includes the value of the boats and vessels in the fleet
as they were given by the model at the end of five and 30 years of
simulation. Values presented in Table 5.6 were used in calculating
total investment in fleet, gear, and shore installations necessary to
vessel operation presented in Table 5.7. As a check on these figures,
the value of capital and liabilities per vessel of $71,200 as given in
Basic Economic Indicators: Shrimp, Atlantic and Gulf [1, p. 9] was
used along with a value for boats and gear of $9,000 per unit to esti-
mate the total investment in the fleet. Examination of Table 5.7
reveals that the assumptions of average investment life of 5.0 and 6.7
years give total industry investment values that bracket the value
calculated from National Marine Fisheries Service data.

Simulated Results for the Policies Considered

One of the objectives of this study is to determine whether alter-
native management strategies exist which improve industry efficiency
from the point of view of various groups of participants in the industry
as well as reduce overinvestment in the industry. Gordon Tullock [32]
presents a discussion of regulatory measures for a fishery designed to
achieve various objectives. The charges needed to manage a fishery in

115

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116
an efficient, zero-profit manner arc specified as theoretical aggregates
in Chapter II. These charges correspond to the landings fee and vessel
entry charges considered here. In addition, the regulating agencies of
the various states involved in the Gulf shrirap fishery pursue some
management policies, including closed areas, closed seasons, and gear
regulations, designed to increase the age (size) at v/hich shrimp first
became subject to capture. The specific policies considered here (based
on Tullock's discussion, the development in Chapter II, and current
practices) are:

1. No controls;

2. A set of policies possibly including closed seasons, closed
areas, and gear regulations designed to increase the age at
which shrimp begin to enter the catch (called simply, age at
first capture) from three months to four months;

3. An annual vessel entry fee, by vessel size class of:

vessel size class (CRT) less than 5 5-19 20-49 50-79 80 &

over

annual entry fee ($) 750 1,000 1,600 2,000 2,500

4. A per pound landings tax of $0.10 on all shrimp sizes. (Viewed
as a percentage of ex-vessel price, this tax is relatively
higher on the smaller sizes of shrimp which command lower
prices.); and

5. A combination of the vessel entry fee charges in (3.) and the
per pound landings tax described in (4.).

The $0.10 per pound landings tax was arbitrarily chosen. The annual
vessel entry fees were derived from an arbitrarily chosen fee for vessel
size class four of $2,000 per year by multiplying this fee by the
average sweep capacity per vessel. The rationale for this adjustment

117

is that, in order not to discriminate araong vessels on the basis of
productivity, the annual vessel entry fee should be based on a measure
of vessel productivity. The most convenient measure of vessel produc-
tivity available during the present study was vessel sweep capacity by
size class.

The computer model was used to simulate the behavior of the Gulf
shrimp industry over five-year time periods for the five different
settings of the policy variables. Table 5.8 presents the levels of the
policy variables and the associated average annual values generated by
the computer model for the total catch, wholesale value of the catch,
ex-vessel value of the catch, total production costs, revenue to the
control authority (the authority imposing the policies and collecting
the fees), the difference between total production costs and ex-vessel
value of the catch (which may be considered a net return to fixed
investment if all variable costs, specifically labor costs, are consid-
ered to be covered) , and the value of fixed investment in the fleet
under the assumption of a five-year average life of vessels and gear.

Table 5.9 presents the rate of return to investment represented by
the net return and value of investment figures in Table 5.8 for each of
the policy levels. The revenue collected by the control authority may
be considered a return to the shrimp resource. The disposition of this
return and the welfare implications of alternative dispositions of this
return are beyond the scope of the present study. However, the figures
presented in Table 5.10 make possible some interesting comparisons.
Table 5.10 presents the changes, occasioned by instituting the policy
variables, in the quantities listed in Table 5.8 from the situation of
no controls. In addition. Table 5.10 presents the sum of the revenue
to the control authority and the changes in wholesale value and net

118

Table 5.8. Average annual returns from the Gulf shrimp catch, costs
to the industry and fixed investment ?Ln the industry
assuming a five-year investment life under various
settings of the policy variables

Policy
. a
settings

Total catch

Wholesale
value

Ex-vessel
value

1

96,498,298

lbs.

$136,067,890

$95,391,740

2

96,498,224

lbs.

136,067,840

95,391,680

3

94,303,328

lbs.

133,811,552

94,883,072

4

92,724,624

lbs.

132,358,080

88,322,608

5

92,199,424

lbs.

131,798,112

87,940,096

Policy
. ■' a
settings

Total prod,
costs

Rev. to
cont. auth.

Net
return

Value of
investment

1

$114,826,888

$

0

$-19,435,148

$237,633,000

2

114,826,800

0

-19,435,120

237,633,000

3

119,989,504

8,

,694

,105

-25,106,432

217,833,000

4

102,985,264

9,

,272

,454

-14,662,656

205,431,000

5

11,158,576

17,

,748

,080

-23,218,480

205,431,000

Tlefer to text, page 116,

119

Table 5,9. Rate of return to fixed Investment in the Gulf shrimp
fleet under various settings of the policy variables

Policy settings Percentage rate of return

1 - 8.18

2 - 8.18

3 -11.53

4 - 7.14
3 -11.30

a,.

See text, page 116.

120

Table 3.10.

Changes in average annual returns, costs, r.nd investment
occasioned by the imposition of controls

Chang

es

in:

Policy
settings

Total catch

Wholesale
value

Ex-vessel
value

Total prod,
costs

1

0 lbs.

$ 0

$ 0

$ 0

2

-74 lbs.

-50

-60

-88

3

-2,194,970 lbs.

-2,256,338

-508,668

-5,162,616

4

-3,773,600 lbs.

-3,709,810

-7,069,132

-11,841,624

5

-4,298,874 lbs.

-4,269,778

-7,451,644

-3,668,312

Revenue to cont.

Changes

in:

Rev. to
cont. auth.

authority plus
changes in

Policy
settings

Net
return

Value of
investment

wholesale value
and net return

1

$ 0

$ 0

$

0

$ 0

2

28

0

0

-22

3

-5,671,281

-19,800,000

8,694,105

766,486

4

4,772,492

-32,202,000

9,272,454

10,335,136

5

-3,783,332

-32,202,000

17,748,080

9,694,970

^See text, page 116.

121

return (which reflect the difference between changes in ex-vessel value
and production cost). This sum is a measure of what is left over from
revenue to the control authority after adding any changes in wholesale
and ex-vessel values of the catch and deducting any changes in the cost
of producing the catch. Thus, it is a measure of the net money returns
obtained from instituting a particular policy exclusive of the cost of
implementing the policy. It is what is left (after compensating all
losers and taxing away all gains) to apply to the cost of implementing
the policy.

Increasing the age of shrimp at first capture to four months has
essentially no effect on the quantities considered in Tables 5.8 and
5.10. Imposing an annual vessel entry fee, differentiated by size
class as shown in Table 5.8, reduces total catch, the wholesale and ex-
vessel values of the catch, and the net return. This policy increases
total production costs and revenue to the control authority. The vessel
entry fee policy considered produces a surplus after revenue to the
control authority is adjusted for changes in wholesale value and net
return although this surplus is probably not large enough to implement
the policy. Imposing a landings tax on shrimp decreases wholesale value
but increases net return since production costs are decreased more than
the ex-vessel value of the catch. Thus, the revenue to the control
authority, after being adjusted for changes in wholesale value and net
returns, is significant, amounting to 11.7 percent of the ex-vessel
value of the catch. Imposing both a vessel entry fee and a landings
tax produces the greatest gross revenue to the control authority but a
slightly smaller adjusted revenue than a landings tax alone due to the
larger decline in wholesale value of the catch and a decline in net
return rather than an increase. "Both the entry fee and landings tax

122
policies reduce investment in the fleet although when the polirieL; tire
used singly the landings tax policy seems to more effectively reduce
investment.

Policy Implications

Considering the relatively primitive nature of the model used to
obtain the results presented here, caution must be used in drawing
implications about the various regulatory measures considered on the
basis of those results. In addition, different conclusions may be
drawn as to the relative desirability of a proposed regulatory policy
depending on whether one takes the point of view of the consumer, the
vessel owners, the vessel crew, or processors. The benefit to society
of a policy will vary depending upon the segment of society that the
individual estimating the benefit is most closely associated with. Such
conflicts seem to be inevitable and the approach taken here is to rank
the policies on their effectiveness in attaining several alternative
objectives. The assumption is made that all the policies are equally
costly to implement with the exception of the policy of no controls,
which may be implemented at zero administrative cost. No estimates of
implementation costs have been made.

If the revenue to the control authority is considered to be a return
to the resource and the objective of maximizing this return is assumed,
then the results presented in Tables 5.8 and 5.10 indicate that a com-
bination of the entry fee and the landings tax policies is most effective
in obtaining this objective. The landings tax policy ranks second in
effectiveness. The vessel entry fee policy ranks third. The other
policies give no return to the control authority. Since implementation
costs are unknown, the net effects of the landings tax and vessel entry

123
fee policies cannot be determined and they cannot be compared on a ''net"
basis with the costless alternative of no controls. The policy relating
to age at first capture, since it produces no revenue to the control
authority and has positive implementation costs, is clearly inferior to
the alternative of no controls on the basis of maximizing returns to

the resource.

If maximization of net return to investment in the Gulf of Mexico
shrimp fleet is taken as the objective and policy implementation costs
are ignored, then based on the results presented in Table 5.8, a tax on
landings seems to be the most effective means of attaining this objec-
tive. The policy relating to age at first capture ranks second while a
policy of no controls ranks a very close third. A combination of entry
fees and a landings tax ranks fourth in effectiveness. Imposition of
entry fees alone is the least desirable policy for attaining the objec-
tive of maximization of net revenue to the fleet.

If maximization of the total catch is taken as the objective, a
policy of no controls is most effective. Regulating age at first cap-
ture ranks second while an entry fee, landings tax, and combination of
the two rank third, fourth, and fifth, respectively.

If the objective of industry regulation is to reduce the value of
investment in the Gulf of Mexico shrimp fleet, the per pound landings
tax policy and a combination of the landings tax and entry fee policies
are equally effective in reducing total investment. The entry fee used
alone is the next most effective policy while the age at first capture
and no controls policies do not reduce investment in the fleet.

Table 5.11 contains the total production costs incurred by the
fleet per pound of shrimp produced under the different policies. If
the objective of regulation is to minimize per pound product cost by

124

Table 5.11. Average annual total production costs incurred by the

Gulf of Mexico shrir.ip fleet per pound of shrimp produced
and average annual v/holcsaJe price of shrimp produced
and average annual wholesale price under alternative
policies

Per pound
Policy production costs Wholesale price

1 $1.19 $1.41

2 $1.19 $1.41

3 $1.27 $1.42

4 $1.11 $1.43

5 $1.22 $1.43

See text, page 116.

125

the fleet, a per pound landings tax is the most effective policy. No
controls and regulating age at first capture are tied for the second
position. A combination of landings tax and entry fee is the next
most effective while a vessel entry fee alone produces the highest costs
per pound.

The model does not presently provide information that can be used
directly to evaluate the effects of the policies on consumers. However,
if the wholesale value of the catch is accepted as a proxy for retail
value of the catch and some assumptions concerning retail demand are
accepted, then some tentative inferences concerning the effects of the
policies on consumers can be made. Doll [16, pp. 35, 70-71] finds that
the price elasticity of retail demand (in his annual model) at the mean
of price and consumption is -0.63 and that the price elasticity of
wholesale demand (in his quarterly model) is -0.50 at the means of the
variables. Thus, retail and wholesale demands as reported by Doll
appear to be relatively inelastic, a finding corroborated by Miller
et__al. [24, p. 45]. The significance of these results for evaluating
the effect of the policies on consumers lies in the fact that, given a
downward sloping demand curve, changes in quantity taken in the neigh-
borhood of the quantity used to calculate the price elasticity produce

2

The fact that as catch is reduced in Table 5.8 wholesale value of

the catch is reduced also might seem to contradict the assertion that
wholesale demand is price inelastic in this range of landings. However,
as domestic landings decrease in the model, imports increase after a
quarter lag (see equation 4.3). Thus, the effect of decreased domestic
landings on the total annual supplies of shrimp available to meet whole-
sale demand is not readily predictable. It would appear from the results
in Table 5.8 that, as landings decrease, imports increase by enough so
that the increase in the wholesale price is not enough to produce the
increase in wholesale value of the catch that would be expected if
landings were to decrease and imports were to remain constant.

126
larger changes in consumer surp3.us (measured as the area under the.
demand curve and above the price liiie) for price inelastic demand curves
than for price elastic demand curves. For example, there is no change
in consumer surplus as defined here in response to quantity changes
when consumer demand is perfectly elastic; there is, in fact, no con-
sumer surplus. For a complete inelastic consumer demand curve, minute
changes in quantity supplied produce infinitely large changes in con-
sumer surplus.

The average annual wholesale prices occurring under each policy
setting are presented in Table 5.11. The policies do not cause large
changes in v/holesale price. If retail price behavior is similar, most
of the effect on consumers of the reduction in domestic landings
resulting from implementation of the policies would seem to be offset
by increases in imports. However, with apparent annual consumption of
fresh and frozen shrimp of 357.3 million pounds in 1970 [30, p. 13,
preliminary estimate] coupled with an inelastic retail demand at that
quantity, even a small increase in retail price resulting from a propor-
tionately smaller decrease in quantity available will result in a
sizeable loss in consumer surplus. Assuming that the increase in
average wholesale prices indicated in Table 5.11 represents the extent
of the price increase at the consumer level, then the annual loss in
consumer surplus occasioned by implementing a vessel entry fee is on
the order of 3.5 million dollars as compared to no controls. The annual
loss in consumer surplus occasioned by imposing a landings tax or a
combination of a landings tax and an entry fee is on the order of 7.0
million dollars. Regulating age at first capture produces no signifi-
cant reduction in consumer surplus. Thus, assuming that consumers do
not pay for implementing the regulatory policies, do not share in the

revenues these policies produce, and desire to minimize less of consumer
surplus, policies of no controls or regulating age at first capture
would seem to be preferabl-'; co cor.suinars. A vessel entry fee ranks
second in minimizing loss of consumer surplus while a per pouud landings
tax and a combination of a per pound landings tax and a vessel entry fee
cause the largest losses in consumer surplus as measured here.

The column in Table 5.10 headed "Revenue to control authority plus
changes in wholesale value and net return" presents an alternative cri-
terion for ranking the policies. Assume that the decreases in wholesale
value represent losses to society while increases in net return to the
fleet (changes in ex-vessel value less changes in total production
costs) and revenue to the control authority represent gains to society
(ignoring costs of policy implementation). Then the sum of changes in
wholesale value of the catch, net return to the fleet, and revenue to
the control authority represents the net gain to society from implement-
ing any one of the policies. Of course, implementation costs cannot be
ignored and in choosing between a policy of no controls and one involving
some regulation, the gain to society from implementing a policy must be
calculated net of the cost of implementation. Assuming that all the
policies involving regulation are equally costly and that the objective
is to maximize net gain (minimize net loss) to society, the policy
involving a per pound tax is most effective based on the information in
Table 5.10. A policy involving both a tax on landings and a vessel
entry fee is a close second while the vessel entry fee alone ranks a
poor third. Regulating age at first capture produces negative gain to
society and thus, is inferior to a policy of no controls even without
considering the costs of regulating age at first capture.

128

As is evident from tlie discussion in this section, no one policy
is clearly superior for attaining all objectives. The ranking of the
effectiveness of the policies depends on the objective to he attained.
The one clear implication to emerge from this discussion is that a
policy designed to increase age at first capture is never preferable to

one involving no controls, especially when costs of implementation are

3
considered. However, even this conclusion must be accepted cautiously,

remembering that many of the parameter estimates used in the model are
initial estimates. The ordering of the remaining policies by effec-
tiveness changes as objectives are changed. It is possible that the
policy types would change ordering for a given objective if the regula-
tory variables were set at different relative levels. Thus, it must
be remembered that the above discussion is specific to stated levels
of the policy variables. It is quite possible that different combina-
tions of values for the annual vessel entry fee and/or landings tax,
for example, would result in different sets of rankings of the policy
alternatives for given objectives. What is really needed is additional
research to vary each policy variable to determine its optimum level
with respect to a given objective or criterion. A comparison of
policies set at their optimum levels with regard to given objectives
would lead to more meaningful rankings .

The implications stated here are meant to describe the relative
effects of different and specific types of policies, not to endorse a
particular policy in a given case. Also, more meaningful policy

3

It is interesting to note that policies designed to increase age

at first capture are the only regulations currently in effect in the
industry and these are enforced by individual states.

129

rankings will he possible: in an environment in which the objectives and

limitations oT the policy-makers are kno\>m and taken into account. In

addition, there are improvements and extensions needed in the model that

will increase the reliability of the information it provides. Some of
these improvements and suggestions for further research are discussed
in Chapter VI.

CHAPTER VI

RECAPITULATION OF THE PRESENT STUDY WITH
SUGGESTIONS FOR IMPROVEMENTS AND FURTHER WORIC

The present study is summarized in this chapter and attainment of
the objectives is assessed. A simulation model is not easily brought
to perfection and certain improvements needed in the present model are
cited. In addition, this study provides the basis for several sugges-
tions that may prove fruitful for further research.

Recapitulation of Objectives and
Evaluation of Achievements

As listed in Chapter I, the objectives of this study were to:

1. Determine the responses of individual fishing firms in the
Gulf of Mexico shrimp industry and the resultant aggregate
effect for the industry to changes in:

a. The shrimp population in the Gulf of Mexico;

b. Technological conditions of harvesting and processing; and

c. Demand conditions.

2. Determine whether alternative management strategies exist
which will improve industry efficiency in a social sense,
reducing overinvestment and/or the extent of non-optimal
husbandry practices that occur as a result of the free use
of an open access resource.

The steps involved in pursuing the objectives involved developing
a bioeconomic theory of a fishery and applying it to the shrimp resource,

130

131

A rather general abstiact model of shrimp resource resulted from this
application. Based on the abstract model, a simulation model of the
Gulf of Mexico shrimp industry was developed. Experimentation with the
simulation model produced empirical results relating to alternative
policies .

Objectives l.a. and I.e. did not emerge as the primary objectives
of the study. They were achieved, however, to the extent that a model
incorporating estimates of the indicated responses was realized. Objec-
tive l.b., relating to responses of firms and the industry to changes
in technology, was not satisfied. The model resulting from this study
could, however, incorporate certain types of technological changes such
as changes in trawling effectiveness or ability of a vessel to fish
more days per month.

Objective 2. emerged as the primary concern of this study. The part
of the second objective relating to non-optimal husbandry practices was
approached only indirectly through the effect of the policies on measures
of the value of the catch. The effects of the specified regulatory
measures on investment in the harvesting sector of the industry were
determined. In addition, the relative effects of the regulatory policies
on several measures of industry performance were discussed. Part of the
objectives set forth at the beginning of this study were attained to a
limited degree. In order to more fully achieve the stated objectives,
there are certain parameter improvements and model extensions that need
to be made.

Improvements Needed in the Present Model
and Suggestions for Further Work

Most of the work that seems to be needed involves obtaining more
complete data to improve parameter estimates within the model. In this

132
regard, sensitivity analysis on the present parameter estimates to
determine which ones are the most critical and thus, need more careful
estimation would seem to be a logical starting place. Model improve-
ments are, however, not without cost, and potential gains from model
improvements must be weighed carefully against the costs of making and
implementing the improvements before research is undertaken to improve
the model.

Improvements are needed of estimates of the frequency distribution
of shrimp recruits by species, area, and month of year. The means and
standard deviations used in the model to generate recruits are very
rough estimates indeed. Other areas for improvement in the basic
resource model include improving the mortality estimates used in the
survival equations, differentiating the growth of shrimp by species and
season, as well as relating the fishing mortality suffered by a size
class of shrimp to the fishing effort of specific size classes of
vessels. As an example of this latter recommendation, it is unlikely
that vessels over 80 gross registered tons contribute very much to the
fishing mortality of the smaller size classes of shrimp that are taken
in relatively shallow water. On the other hand, boats (craft of less
than five net registered tons) do not contribute to the fishing mortal-
ity suffered by the larger size classes of shrimp in the deep-water
grounds away from the coastal areas. This problem may be solved by
considering fishing effort by vessel size class to be specific to parts
of an area by depth or by inshore versus offshore classification. In
addition, more accurate description of the geographic range of shrimp
of different size classes may contribute to more accurate mortality
rates.

133

The model of the harvesting sector of the industry needs refinement
witli respect to the process by vzhich vessels enter and leave the fleet,
allocate fishing effort among areas, and determine degree of fishing
intensity. The improvement in these areas could come in the form of
more complete specification rather than restructuring of the model.

A study that would perhaps add much to the present model involves
identifying the relative magnitudes of the determinants of cost per day
fished by vessels in different size classes fishing in different areas
of the Gulf of Mexico. The vessel costs per day fished obtained from
such a study could be combined with the catch rate and returns figures
of this study to determine net revenue more accurately. Given accurate
data on net revenue and effort by vessel size class and area, a study
to determine the causal relationships between net revenue and effort
should improve the vessel allocation and effort intensity schemes.

The model of the marketing and demand sector is the product of
Doll [16]. If this model were respecified to conform to a monthly time
interval and expanded to provide an estimate of retail demand and ex-
vessel price by size class of shrimp, it would be more conformable to
the data requirements of the simulation model. This extension of the
model would allow development of a more refined measure of consumer
surplus and, consequently, a more complete evaluation of the effects
of proposed regulatory policies on consumers as well as other segments
of the industry.

Meaningful systems analysis projects are evolutionary in that they
require models which are continually updated to keep them relevant from
the point of view of the current physical, biological, and decision
environments. All of the above suggestions for further work would not,
of course, result in a perfect model.

APPENDIX I

Compute!" program, SHRIMP, and data necidcd to
estimate recruits b}' species by mouth and area

135

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LIST OF REFERENCES

1. Anonymous, Basic Economic Indicatoi's; Shrimp, Atlantic and Gulf,
Working Paper No. 57, Division of Economic Research, National
Marine Fisheries Service, College Park, Maryland, May 1970.

2. Anonymous, Gulf Coast Shrimp Data, United States Department of
Coimnerce, National Oceanic and Atmospheric Association, National
Marine Fisheries Service, Washington, D. C. , in cooperation with
Fishery Agencies of Florida, Alabama, Mississippi, Louisiana, and
Texas. Annual SuBimaries for 1967, 1968, and 1969.

3. Anonymous, Marine Economics Data, Oregon State University Sea
Grant, Marine Advisory Program, Oregon State University Coopera-
tive Extension Service, Corvallis, Oregon.

4. Anonymous, "V'ater Teiaperature Guide to ShriDip and Tuna," Fishing
News Inter, ational 10, No. 1, 34, 37 (vTanuary 1971) as abstracted
in Coiiuiercial Fisheries Abstracts, National Marine Fisheries
Service, United States Department of Comnercc, July .1971, pp. 7-8.

5. Arnold, V. , An Analysis to Determine Optimum Shrin'i' Fishing Effort
by Area, Working Paper No. 40, Division of Econom.ic Research,
National Marine Fisheries Service, College Park, Maryland, January
1970, 196 pages.

6. Barry, E. J., "Gulf Fisheries (Selected Areas): 1969," Division
of Statistics and Market News, National Marine Fisheries Service,
New Orleans, Louisiana, February 19/1.

7. Berry, Pdchard James, "Dynamics of Lhe Tortugas (Florida) Pink
Shrimp Population," Doctoral Dissertation, University of Rliode
Island, 1967.

8. Boutwell, Ken and McMinimy, Vernon, "Use of Mathematical Simula-
tion Models in Analyzing Agricultural Policies," draft of an
Unpublished Memorandum, 1967.

9. Bromley, Daniel, Economic Efficiency in Common Property Natural
Resource Use: A Case Study of the Ocean Fishery, V^Jorking Paper
No. 28, Division of Economic Research, Bureau of Conmiercial
Fisheries, College Park, Maryland, July 1969, 162 pages. Also
published as a Doctoral Dissertation in the Department of Agricul-
tural Economics at Oregon State University, Corvallis, Oregon, 1969.

10. Captiva, Francis J., "Changes in Gulf of Mexico Shrimp Trawler

Design," paper presented at Conference on Canadian Shrimp Fishery,
Saint-John, N. B., October 27-29, 1970.

180

181

n fhristv Francis T., Jr. and Anthony Scott, Tjie_Co2moiLWGalthJjl

Ocpan Flshp.-ies: c._^^Pvr,h1 ..^^. of Growth and Economic AUocatxon.
pabli'ibrd1^r"'R^i^rces for the Future, Inc., by The Johns Hopkins
Prej-s, Baltimore, Maryland, 1965.

12. Ciriacy-Wantrup , S. V., Rescu£c_e_Conserva^on_^_Eco^^

Policy, University of California Press, Berkeley, Californxa, IJ^i.

13. Creameans, J. F.., "m.y Simulation," paper origiur.lly giy^n at a
symposium of the Washington, D. C. Chapter of the Assoc.atxon for
Computing Machinery, May 18, 1967.

14 Crutchfield, James P. and Giulio Poatecorvo, The_Jacifi^_Salm.Dn
Fisheries, published for Resources for the Future, Inc., by Ine
J^ns Hopkins Press, Baltimore, Mar>'land, 1969.

15. Crutchfield, James P. and Arnold Zellner, "Economic Aspects of the
Pacific Halibut Fishery," FTc^herv Industrial Research, Vol. 1,

No. 1, Fish and Wildlife Service, April 1962.

16. Doll , John P. , An Econometric Ana3^sj^_^LlJ2^iL-^A^-£J^gELii^rj^^
Working Paper No. 79, Division of Economic Research, !',c.ticnai
Marine°Fisheries SerA'ice, College Park, Maryland, Feb ruary 19/1.

17. Forrester, Jay U. , Industrial Dynamics, 2nd printing. The M.I.T.
Press, Cambridge, Massachusetts, June 1962.

18. Geisler, M. A., Haythorn, W, W. , and Stager, W A. "Simulation
and the Logistics Systems Laboratory," Mem.orandum El-I-32dl-PK
prepared for United States Air Force Project Rand, September 1.62.

19. Gordon, H. Scott, "The Economic Theory' of a Common-Property
Resource: The FisheiT," Journal of PoliticaJJEconom^, Vol. LXli,
No. 2, April 1954, pp. 124-142.

20. Gulland, J. A., Manual^liLethojl^_JorJlslL.St^^^
li_llsh.Po2ulatiirAii^iii, Food and Agriculture Organxzatxon of
the United Nations, Rone, 1969.

21. IBM Svstem/360 Fortran IV Language, IBM Corporation, Prograinming
Syster.-£ Publications, New York, New York, 1966.

22. Lassiter, Roy L., Utilization of U.S. Otter-Trawl Shrimp Vessels
in the Gulf Area, 1959-1961, Bureau of Business and Economic
Research, University of Florida, Gainesville, Florida, 1964.

23. Lyles, Charles H. , ti^ery__Statistics._ol^heJIn^ Bureau
of Commercial Fisheries, Washington, D. C, 1939-1967.

24. Miller, M. , D. Nash, and F. Schuler, Industrx^AnaJ^:sa^_of_Gulf
Area Frozen Processed Shrimp and an Estimation of Its Iconomic ^^
Adaptability to Radiation Processing, Working Paper No. 16, Divi
sion of Economic Research, Bureau of Commercial Fisheries, College
Park, Maryland, October 1969, 100 pages.

182

25. Orcutt, G. H. , "Simulation of Economic Systems," The American
Econoiuic Review, Vol. 50, No. 5, December 1960, pp. 893--907.

26. Osborn, Kenneth W. , Bruce W. Maghan, and Shelby 15. Drumraond, Gulf
of Mexico Shrimp Atlas, United States Department of the Interior,
Bureau of CoirjTjercial Fisheries, Circular 312, VJashington, D. C.,
May 1969.

27. Osterbind, C. C. and R. A. Pantier, Economic Study of the Shrimp
Industry in the Gulf and South Atlantic States, Bureau of Economic
and Business Research, University of Florida, GainesviDlej Florida,
1965.

28. Scott, Anthony, "The Fishery: The Objectives of Sole Ownership,"
Journal of Political Economy, Vol. LXIII, No. 2, April 1955,

pp. 116-124.

29. Smith, V. L., "Economics of Production from Natural Resources,"
The American Economic llcview, Vol. LXIII, No. 3, Part 1, June 1968,
pp. 409-A31.

30. Surdi, Richard W. and Donald R. Wiittaker, principal contributors,
Shellfish: Situation and Outlook: 1970 Annual Review, Current
Economic Analysis S-20, National Marine Fisheries Service, United
States Department of Commerce, Washington, D. C. , March 1971.

31. Tyner, Fred H. , Jr., "A Simulation Analysis of the Economic Struc-
ture of U. S. AgiiculLuie," Doctoial Dissertation, Oklahoma State
University, Stillwater, Oklahoma, May 3 967.

32. Tullock, Cordon, The Fisheries ... Some Radical Proposals, Ecsays
in Economics No. 6, University of South Carolina, Bureau of
Business and Economic Research, School of Business Administration,
Columbia, South Carolina, February 1962., 29 pages.

33. V>Tiittaker, David A., Jr., "Economi.c Effects of Trade Policies on
the Shrimp Fisheries of the United States and the Latin American
Nations," Doctoral Dissertation, University of Florida, Gainesville,
Florida, 1971.

ADDITIONAL REFERENCES

Bator, Francis M. , "The Simple Analytics of Welfare Maximization," Tlie
American Economic Review, Vol. XLVII, No. 1, March 1957, pp. 22-59.

Bell, F . W . , Estima t ion of the Economic Benefits to Fishermen, Vessels
and Society From Linited Entry to the Inshore U. S. Northern Lobster
Fishery, Working Paper ho. 36, Division of Economic Research, Bureau of
Commercial Fisheries, College Park, Mai-yland, March 1970.

Bell, F. W. and J. E. Hazleton, Recent Developments and Research in
Fisheries Economics , published for The New England Economic Research
Foundation by Oceana Publications, Inc.. Dobba Ferry, New York, 1967.

Carlson, E., Bio-Economic Model of a Fishery (Primarily Demersal) ,
Working Paper No. 12, Division of Economic Research, Bureau of Commer-
cial Fisheries, College Park, Maryland, March 1969.

Cleary, Donald P.. Demand and Price Structure for Shrimp > Working Paper
No. 15, Division of Econo'iiic Research, Bureau of Commercial Fisheries,
College Park, Maryland, June 19'J9.

Crulchfield, J. A., "Econor.ic Objectives of Fishery Management, The
Fislieries; Problems j.n Resource Management," University of Washington
Press, Seattle, Washington, 1965, pp. 43-65.

Food and Agricultural Organi?^ation of the United Nations, Yearbook of
Fi sh ery Statistics, Vols. 26 and 27, FAO, Rome, Italy, 1968.

Nash, D. and F. Bell, An Inventory of Demand Equations for Fishery
Products, Working Paper No. 10, Division of Economic Research, Bureau
of Commercial Fisheries, College Park, Maryland, July 1969.

Ricker, William E., Methods of Estimating Vital Statistics of Fish
Populations , Indiana University Publications Science Series No. 15,
Blooinlngton, Indiana, 1948, 101 pages.

Samuelson, Paul A. , "Contrast Between Welfare Conditions for Joint
Supply and for Public Goods," The Review of Economics and Statistics,
Vol. LI, February 1969, pp. 26-30.

Scott, A. D. , Economics of Fisheries Management: A Symposium, Institute
of Animal Resource Ecology, The University of British Colombia, Canada,
1970.

Sokoloski, A., Some Elements of an Evaluation of the Effects of Legal
Factors on the Utilization of Fishery Resources, Working Paper No. 8,
Division of Economic Research, Bureau of Coimnercial Fisheries, College
Park, Maryland, February 1969.

183

Sugiri, G. K. A., "A Description of the Tortugas Shrimp Fisliery and ii.s
Maximum Sustainable Yield," Master's Thesis, University of Miami, Coral
Gables, Florida, January 1971.

Turrey, Ralph, "Optimization and Suboptimization in Fishery Regulation,"
The American Economic Review, Vol, LIV, March 1964, pp. 6A-76.

Turrey, Ralph and Jack Wiseman, The Economics of Fisheries, Food and
Agriculture Organization of the United Nations, Rome, 1957.

Zellner, A., "On Some Aspects of Fishery Conservation Prob] ei.is ,"
reprinted from the bulletin of the International Statistical Institute,
Vol. XXXVIII, Part III, Tokyo, 1961.

BIOGRAPHICAL SKETCH

Paul Jerome Hooker was born on August 29, 1943, at Homestead,
Florida. In August, 1960, he was graduated from North Marion High
School, Reddick, Florida. In August, 1966, he received the degree of
Bachelor of Science V7ith a laajor in zoolog}' from the UnJ.vcrsiLy of
Florida. During the 1966-67 school year, he taught biology and
chemistry at North Marion High School. In 1966 he enrolled in the
Graduate School of the University of Florida. From August, 1967, to
December, 1971, he has held an NDEA Title IV fellowship, worked for
two quarters as a teaching assistant, and has been employed as a
graduate reseat ch a^'sociate in the Department of Food and Pvcsource
Economics v.'hile pursuing the degree of Doctor of Philosophy. He is
currently employed as Iviterim Assistant Professor of Food and Resource
Economics with the University of Florida on assignment to the Ministry
of Agriculture of Guyana.

Paul Jerome Hooker is married to the former Martha Jean Yongue,
and is the father of one child. He is a member of Gamma Sigma Delta,
Omicron Delta Epsilon, and the American Agricultural Econom.ics
Association.

185

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is Cully
adequate, in scope and quality, as a dissertation lor the degree of
Doctor of Philosophy.

:'olopo.'-!' ■ , Lh^r!.i,on
Professor of Food and Resource
Economics

I certify that I have read this study and that in my opinion it
forms to acceptable standards of scholarly presentation and is fully

conf

adequate, in scope and quality, as a

Doctor of Philosophy.

dissertation for the degree of

jr.

Max 'R. Laagiiauij Professo
Food and Resource Economics

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor oi Philosophy.

W. VJ. McPherson, Professor
Food and Resource Economics

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.

Carter C. Osterbind
Professor of Economics

This dissertation was submitted to the Baaii of the College of Agriculture
and to the Graduate Council, and was accepted as partial fulfillment of
the requirements for the degree of Doctor of Philosophy.

March, 1972

D;';::n, Graduate School

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