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Full text of "Systems analysis of U. S. management strategies in the Gulf of Mexico shrimp industry"

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^) < 

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

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

2. Length 



(2.4) 


L^ = L(t) 


(2.5) 


dL^/dt > 


(2.6) 


d^Lj./dt^ < 


3. 


Weight 


(2.7) 


W^ = W(t) 


(2.8) 


dW^/dt > 


(2.9) 


d\^/dt^ > 



12 
(2.9a) d^v/j./dr.^ < , ' ^ ^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 > , t < tg 
(2.11b) dB^/dt < , 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^ > , t < tj^^ , t > t^2 

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

(2.12c) d^B^/dt^ = , 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,^ = , t 5 tj^ 

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

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

(2.15) d^R /dt^ > , t^ < t < t2 
(2.15a) d^R^/dt^ < , 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. = , L^ < L^^ 

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

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

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

(2.18a) d^R^/dL^^ < , ^^2 '^ ^t ^ ^R3 
(2.18b) d^R^/dLj_^ = , 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. - , L^ < Lg^ 

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

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

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

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

7. Catch in numbers of fish 

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

(2.23) 9C^/8F > 

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

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

(2.25) 9C^/3N^ > 

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

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

(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 > 

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



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



CO 



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



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

(2.34a) 9^Y /3N ^ < C , N^ < N^ < «> 

(2.35) 8Y /3w > 

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

(2.37) 3^Y /3F3N > 

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

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

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 Th eory 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^^ > 

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



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

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

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

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

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 , 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 , < n(NRj._^) < n"^ 

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

(2.54) 9nj./9NRj._j. > , 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^ < 

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

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 ) < 

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. = 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 Fishe ry 

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 = 

xt \ 1=1 It n t / 

(2.80) Z/, dB. = 

(2.81) Z/. dN. = 

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. s etiferu s. In addition, small numbers 
of a smaller shrimp called seabob , Xiphoponaeus kroveri , are taken near 
the outlets of Louisiana rivers. The royal red shrimp, Hy menopenaeu s 
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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/<2 

Table 3.2 transforms the aci.'j;-il landings of Tdble 3.1 into percent- 
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 $. 6 9'4/ pound . 

Shrimp 
Variable Costs Sea son 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 

P roc essin g an d M ai']'.rtin.o, Ilia Gull" Sl irimp 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-ti ng__3nj_U&mam l Sector 
"o£~t"he Gu"lf~Sh r3.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_ 
Ec onometric Analysis of th e U. S. Shr imp 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_ Mode l 
Euild i n g and Policy Ev aluation 

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 M ind , 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/poun d) 

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 S weep 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 









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 









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 



















100 




10 


VII 
























75 



94 



o 



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95 

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

The Computer Progra m 

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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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 


$ 







$-19,435,148 


$237,633,000 


2 


114,826,800 









-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 


lbs. 


$ 




$ 


$ 


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 


$ 


$ 


$ 





$ 


2 


28 










-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 Wholesal e 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 



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in 



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CO 



(Mr*-0'-<in-*'^mcor\jorM'-« 
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CMCMfOCMoOvi-inu'XvtinrOCMl^ 



O O O O O O LH 

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in 

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ino(^'-<'N.''^-4-ins0r^ 
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r-(>-)f-Hr-<'-<<-<<--<t-<>— *•-' 



in'-fojro^inor^ 
co 



--icM'<\«i-Ln>or>-coCT< 



CvJ CO 



APPENDIX II 



Simulation program, BIGOKE, and initialization data 



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LIST OF REFERENCES 



1. Anonymous, B asic Economic Indicatoi's; S hri mp, Atlan t ic and Gu lf, 
Working Paper No. 57, Division of Economic Research, National 
Marine Fisheries Service, College Park, Maryland, May 1970. 

2. Anonymous, Gul f C oas t Sh rimp 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 Econo mics 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," Fish ing 
News Inter, ational 10, No. 1, 34, 37 (vTanuary 1971) as abstracted 
in Coiiuierci al Fisher ies Abstracts, National Marine Fisheries 
Service, United States Department of Comnercc, July .1971, pp. 7-8. 

5. Arnold, V. , An Ana ly sis to Determine Optim um Shrin 'i' Fishing Effor t 
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 Comm on Property Natural 
Resource Use: A Case Stud y 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," Journ al of Poli ticaJJEconom^, 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 For tran IV Language , IBM Corporation, Prograinming 
Syster.-£ Publications, New York, New York, 1966. 

22. Lassiter, Roy L., Ut ilization 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 Shri mp and an Estimation of Its Iconomic ^^ 
Adapta bility 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 A meric an 
Econoiuic Review , Vol. 50, No. 5, December 1960, pp. 893--907. 

26. Osborn, Kenneth W. , Bruce W. Maghan, and Shelby 15. Drumraond, Gul f 
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, Econo mic Study of the Shrimp 
Industry in t he Gulf and South A tlantic States, Bureau of Economic 
and Business Research, University of Florida, GainesviDlej Florida, 
1965. 

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

pp. 116-124. 

29. Smith, V. L., "Economics of Production from Natural Resources," 
The Ameri c an Economic ll cview, Vol. LXIII, No. 3, Part 1, June 1968, 
pp. 409-A31. 

30. Surdi, Richard W. and Donald R. Wiittaker, principal contributors, 
S hellfish: S ituation and Outlo ok: 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 Fisher ies ... So me 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 . , Esti ma t ion of the Economic Benefits to F ishermen, Vessels 
and Society From Lin ited Entry to the Inshore U. S. Northern Lob ste r 
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, R ecent Developments and Resea rch in 
Fis he ries Econo mics , published for The New England Economic Research 
Foundation by Oceana Publications, Inc.. Dobba Ferry, New York, 1967. 

Carlson, E., Bio-Economic Model of a Fi shery ( Pri marily De mers al) , 
Working Paper No. 12, Division of Economic Research, Bureau of Commer- 
cial Fisheries, College Park, Maryland, March 1969. 

Cleary, Donald P.. De mand and P rice Str uct ure 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, Yearboo k of 
Fi sh er y Stati stics, Vols. 26 and 27, FAO, Rome, Italy, 1968. 

Nash, D. and F. Bell, An Inv entory o f Demand Equati on s for Fishery 
Prod ucts , 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 
Popula tions , 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 E l ements of an Evaluation of the Effects of Legal 
Facto rs 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 Ec onomics of Fisherie s, 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 th e International Statistical Inst i tute , 
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 



9 

9110