Bioeconomic evaluation of mixed penaeid shrimp in Pamlico Sound

[From the U.S. Government Printing Office, www.gpo.gov]

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1977 . .

BIOECONOMIC EVALUATION OF
't.
MIXED PENAEID SHRIMP IN

PAMLICO SOUND

Connell E. Purvis
2
James R. Waters
Leon S. Danielson2
James E. Easley, Jr.2

10 June 1977

Completion Report for State-Federal Fisheries Management
Program Contract No. 03-5-042-263

'North Carolina Division of Natural and Economic Resources, Division of Marine
Fisheries, Morehead City, North Carolina 28557
2Department of Economics and Business, North Carolina State University, Raleigh
North Carolina 27607

This report should not be considered as a publication. Data contained herein
are subject to further analyses and interpretation.

TABLE OF CONTENTS

INTRODUCTION --- - ------ - ---- - - ---- - ------ - 1

BIOLOGICAL STUDIES ---- - -- - - - - --------- 3

Study Area ---- - ------------------ ---- 3
Collection of shrimp---- 5

Results and Discussion ----- ------- 5

ECONOMIC -- - -------- 11

Introduction - - - ------------ - ----- - --------- -

The Benefit-Cost Equation --------
Application of the Model --------------------- ------- 20

Simulations --- - ------------ -- - -- - --- - ------ 23

MANAGEMENT IMPLICATIONS ----- ---------------- 29

ACKNOWLEDGEMENTS --------------- - ------- -------- -- --- - --- -30

LITERATURE CITED - ----------------- ---------- - -- - - - ----- - ----- - ------ 31

INTRODUCTION

In many estuarine areas of North Carolina, two species of penaeid shrimp
are present simultaneously in commercially significant numbers, but with only
one species of commercial size. The smaller pre-commercial sizes are usually
discarded overboard during shrimping activities for the commercial sizes. Ap-
plication of management techniques resulting from shrimp research has reduced
the discard or loss of small, pre-commercial shrimp in most of the smaller
estuarine areas (Purvis and McCoy, 1972). This loss still occurs, however,
primarily in the larger Pamlico and Core Sound estuaries during late st-er
and fall when pre-commercial size pink shrimp enter the catches during the
brown shrimp season.
The annual loss of pre-commercial shrimp discarded or otherwise destroyed
under the above conditions is not known. It is reported that, at times, as much
as 50 percent (by weight) of catches in Pamlico Sound may consist of precommercial
size pink shrimp that are usually discarded overboard during late August to Nov-
ember. Many of the pink shrimp reach commercial size during the late fall season

and are utilized.

It has been determined that pink shrimp overwinter in North Carolina
estuaries, with major commercial concentrations remaining in Core, Bogue, and
southern Pamlico Sound the following spring (Purvis and McCoy, 1972). The entire
spring pink shrimp fishery is dependent on the overwintering survivors.
Shrimp management objectives held by the North Carolina Division of Marine
Fisheries have been 'to (1) protect the resources, (2) optimize utilization, and
(3) maximize economic yield when possible. The first of these objectives has
been achieved by regulating the harvest and by regulating the alteration of
the coastal zone, The second and third objectives have been more difficult.
However, biologists have attempted to attain these goals by regulating the size
of shrimp harvested. Unstable economic conditions locally and nationally have
created a greater need to economically evaluate shrimp resources.
The management problem is to time the harvest of the shrimp resource so as
to maximize economic yield to the fishery. The simultaneous presence of two
shrimp species, only one of which has attained marketable size, requires that a

-2-

choice must be made between present and future income. Harvesting brown shrimp
when pre-commercial sized pinks are destroyed and discarded in the harvesting
process represents a sacrifice of future income because the number of pink shrimp
potentially available for capture later in the fall or next spring has been re-
duced. However, restricting shrimping activity in an effort to reduce pink
shrimp discard represents a loss in present income if the restrictions result
in a reduction in brown shrimp landings. Thus, in selecting the "best" manage-
ment policy, the decision-maker must weigh the reduction in present income
against the potential increase in future income that would result from adopting
that management strategy.
The objective of the biological phase of the study was to document the
effects of harvesting commercial-sized brown shrimp on sub-commercial pink shrimp
during late fall, and to determine survival of overwintering pink shrimp during
the following spring.
The purpose of the economics study was to specify a framework within which
alternative public policy actions concerning pink shrimp discard can be evaluated.
The emphasis was on: (I) developing an economic model by which management decisions
can be guided; (II) identifying the relevant biologic and economic information
required to estimate the value of pink shrimp discarded during the brown shrimp
season, and the value of reduced brown shrimp landings that would result from
implementing selected management policies; and (III) estimating the net economic
gains to be realized by the North Carolina shrimp fishery due to adoption of
selected management strategies designed to reduce the level of discard.

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I. Biological STUDY AREA

Pamlico Sound, North Carolina's largest estuary, is the most important pink
shrimp area in the state (Figure 1). It is bordered by the mainland and its
tributary rivers (Pamlico, Pungo, and Neuse Rivers) on the western side. The
eastern side is formed by the outer banks with their three inlets: Oregon,
Hatteras, and Ocracoke. At the northern end it connects with Albemarle Sound
via Croatan and Roanoke Sounds which are separated by Roanoke Island. At the

southern end Pamlico Sound is continuous with Core Sound.

Pamlico Sound is approximately 60 miles long and 15 to 20 miles wide, being
narrowest at the northern end (9 miles) and widest opposite Hatteras Island (26
miles). Pamlico Sound and its tributaries total more than 1.25 million acres.
The maximum water depth of the main body of the Sound is about 22 feet, al-
though because of the extensive shoals around the margin and projecting into the
sound, the mean depth is not more than 15 feet.
Brant Island Shoal and Middle Ground Shoal extend parallel from the mouth
of Pamlico River approximately 16 miles in a southeasterly direction, reaching
mid-sound. Bluff Shoal (approximately 13 miles long) completely divides the
sound extending from the mainland on the north to marginal shoals located around
Ocracoke Inlet. Extensive shoal areas are found bordering the shoreline; the
water depth over the shoals ranges from 2 to 10 feet. The bottom type in the
shoal areas is generally sand and sand-mud combinations. Bottom sediments in
the deeper areas are composed of sand., clay, mud, or various combinations of

these base materials.
The salinity in Pamlico Sound is usually between 15 to 24 ppt, and will
normally not vary more than plus or minus 5 ppt for any given area. There is
little lunar tide within the Sound; the periodic tide range is less than one
half a foot (Parsons, Brickerhoff, Hall and Macdonald, 1954). Therefore, dif-
ferences in salinity, resulting from tidal action are usually small except near

the inlets.

HYDE COUNTY
'po.

........ PA ML ICO ........
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B Point
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Goose Creek Island

0 PAMLICO
COUNTY
JONE..s
PAMLICO SOUND

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Ma@v Point
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Point of Marsh
G'vmThicket
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A TERE

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The wind driven tides in Pamlico Sound seldom vary more than two f eet above
and below the normal water level (U.S. Dept. of Commerce, 1973). Prevailing
winds are from the southwest and produce a lower tide than a northeast wind.
Cedar Island Beach and the Middle Ground area of Pamlico Sound posed the
greatest problem with mixed catches and were therefore selected for concentrated
sampling (Figure 1).

COLLECTION OF SHRIMP

Data were obtained aboard the Division vessel RALEIGH BAY captained by
personnel with commercial f ishing backgrounds and considerable shrimping ex-
perience. The vessel was equipped with a single 50-foot otter trawl constructed
of 3/4 inch bar mesh.
Species composition and length-frequency distribution data were obtained
from samples. Salinity and water temperature data were also recorded. All tows
were timed to permit determination of catch/effort values.
Samples were taken at night and during daylight hours in order to compare
catch/effort data for management scheme considerations.

RESULTS AND DISCUSSION

This report includes pink and brown shrimp discard data obtained during fall,
1976 and spring, 1977 in Pamlico Sound. Shrimp were not available during November
due to early cold fronts which forced water temperature into the low teens ( 0 C).
Winter shrimping observations in Pamlico Sound reveal that water temperatures of
150C or higher are necessary for the shrimp to be out of the substrate; active,
feeding, and available to fishing gear.
Shrimp remaining at the end of the fall season spend the winter burrowed in
the substrate, and this overwintering segment supports the spring pink shrimp
fishery in Pamlico Sound. Movement is not stimulated until rising water temperatures

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occur in the spring. The severe cold weather which gripped the United States
this winter had a damaging effect on stocks of overwintering pink shrimp in
Pamlico Sound. Sampling effort in excess of 15 hours during April and May pro-
duced only three individual pink shrimp. There were no commercial catches of
pink shrimp reported from Pamlico Sound during the spring, 1977. It is apparent
that the near-total mortality of the spring segment of the pink shrimp popu-
lation may be attributed to extreme winter conditions.
Length-frequency distribution of pink and brown shrimp and a summary of
catch composition, number per pound, pink-brown ratio, and percent discard are
presented in Tables 1-3.
Length-frequency distribution modes of pink shrimp remained in the 95 mm and
105 mm total length groups throughout the sampling period (Table 1). Apparently
this condition of modal equilibrium is caused by constant recruitment of juvenile
shrimp, a continuing fishing effort on the larger individuals within the population,
and no migration from Pamlico Sound. Catch-effort data presented in Table 2 further
supports evidence of continuous recruitment. Catch-per-unit-of-effort (CPUE)'did
not decrease with time, but instead, a slight increase was observed. Results of
sampling during the fall of 1975 indicated this same condition of modal equili-

brium and an increased CPUE.

Daylight samples contained insignificant numbers of pink shrimp, even under
turbid water conditions, indicating that pink shrimp are indeed nocturnal and avail-
able to the fishery only during the hours of darkness. Catches of brown shrimp were
also considerably less during hours of daylight. The highest CPUE recorded for brown
shrimp during day sampling was 2.88 lbs per hour, which occurred under rough sea
conditions and very turbid water. On the other hand, night catches of brown shrimp
reached a high of 10.92 lbs per hour and were consistently higher than day samples.
Data presented in Table 2 provide evidence that both pink and brown shrimp were more
readily available to the fishery during hours of darkness.
Length-frequency distribution of brown shrimp presented in Table 1 reveals
that this was a mature population ranging from 95 mm to 185 mm. Peaks in the
length-frequency range give evidence to continuous recruitment of the early
juveniles of this population rather than a single period of recruitment. Brown
shrimp were available in significant numbers throughout the fall and catch-per-
unit-of-effort remained relatively constant. By early October, 31 percent of the
total catch still consisted of brown shrimp. Shrimp landings data show that this
late fall concentration of large brown shrimp has not been available for several

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years in Pamlico Sound. When graded, the brown shrimp of 165 to 175 mm total
length were 16-20 per pound, headless. Pamlico Sound is unique in that this
body of "inside" water is capable of producing such large shrimp.
Discard of total catch varied in Pamlico Sound from 31.59 percent in early
September to 25.43 percent late in the month. During the same period, percent
discard of pink shrimp (only) varied from 78.78 percent to 51.24 percent (Table
3). It should be noted that pink shrimp length-frequency modal groups shifted
from a 95 = total length group to a 105 mm group by late September giving
evidence of growth, thus reducing discards. The lower discard ratios appear to
have been caused by the presence of significant numbers of mature brown shrimp
and pink shrimp growth. These discard percentages are considerably lower than
those reported for fall, 1975.

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Table l.--Length-frequency distribution of pink and brown shrimp obtained during
night hours in Pamlico Sound, North Carolina, 1976

PINK SHRIMP
Midpoint of 10 mm size groups 1

Date 35 45 55 65 75 85 95 105 115 125 135 145

9/1 .4 1.3 4.6 8.4 26.3 37.8 18.9 2.1 .2
9/7 1.2 3.0 10.6 23.9 32.3 23.5 4.7 .7 .1
9/12 2.1 5.7 13.7 30.2 33.8 12.8 1.5 .3
9/20 .2 1.5 1.5 6.7 16.4 24.9 32.3 14.2 2.2
10/4 .1 1.1 4.5 16.7 23.0 26.2 20.0 7.2 1.3 .1
10/26 1.1 3.9 11.3 19.3 31.1 19.0 10.3 3.6 .4

BROWN SHRINP

Midpoint of 10 mm size groups

Date 75 85 95 105 115 125 135 145 155 165 175 185

9/1 .3 4.5 24.3 27.7 9.8 22.9 9.1 1.3
9/7 .1 3.8 17.7 21.7 17.0 22.2 15.9 1.4 .1
9/12 .6 4.7 20.9 22.2 16.5 18.9 12.9 3.3
9/20 2.7 26.2 23.3 18.4 18.9 8.3 2.0 .2
10/4 4.4 23.7 21.6 18.5 18.9 10.5 2.4

10/26 .7 5.2 12.4 22.9 15.9 15.9 11.8 4.6 6.5 2.6 2.0

percent of total number of size groups (total length mm). All shrimp in size groups
less than 105 mm (70-per-pound, headless) are considered pre-commercial.

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Table 2.--Comparison of day/night catch effort of pink and brown shrimp in Pamlico Sound,
North Carolina, 1976
DAY PINK SHRIKP NIGHT

-Mean water Total Number Mean water Total Number
Temp. Sal. number shrimp CPUE Temp. Sal. number shrimp CPUE
Date 0C) (PPT) caught sampled (lb/hr) 1 (OC) (PPT) caught sampled (lb/hr)

9/1 23 22 110 110 .22 23 22 579 476 1.17
9/7 23 19 23 23 .09 23 19 1,455 765 2.36
9/12 23 19 94 94 .37 23 19 1,304 752 2.24
9/20 22 19 101 101 .53 22 19 1,509 402 5.86
10/4 23 22 73 73 .37 23 22 2,526 921 4.48
10/26 16 18 0 16 18 1,289 700 3.10

BROWN SHR3MP

DAY NIGHT

Mean water, Total Number Mean water Total Number
TSmp. Sal. number shrimp CPUE Temp. Sal. number shrimp CPUE
Date C) (PPT) caught sampled (lb/hr) 0 C) (PPT) caught sampled (lb/hr)

9/1 23 22 435 282 2.77 23 22 1,266 711 8.03
9/7 23 19 162 162 2.88 23 19 1,639 869 10.92
9/12 23 19 208 136 2.51 23 19 1,294 814 6.96
9/20 22 19 71 71 1.07 22 19 926 408 10.57
10/4 23 22 29 29 .53 23 22 1,156 742 6.84
10/26 16 18 0 16 18 153 153 .62

lHeads on

Table 3.--Summary of catch composition, count, pink-brown ratio, percent discard and catch per unit of effort,
data obtained in Pamlico Sound, North Carolina 1976

Percent Compo-
sition of catch Count (no/lb Pink- Percent discard by number CPUE (lb/hr)
by s2ecies headless) brown ratio pink-brown Total
Date pink brown pink brown (number) catch. pink only catch pink brown

9/1 31.4 68.6 113 36 1:2.2 31.59 78.78 9.20 1.17 8.03

9/7 47.0 53.0 123 30 1:1.1 33.29 70.98 13.28 2.36 10.92

9/12 50.2 49.8 103 33 1:1.0 24.84 51.72 9.20 2.24 6.96

9/20 62.0 38.0 103 35 1:0.6 25.43 51.24 16.43 5.86 10.57

10/4 69.0 31.0 100 30 1:0.5 25.07 45.27 11.32 4.48 6.84

10/26 89.4 10.6 95 56 1:0.1 32.47 35.57 3.72 3.10 .62

Economic

Introduction

The essence of the pink shrimp discard problem is a choice between

present and future income. Harvesting brown shrimp when pre-commercially

sized pink shrimp are destroyed and discarded in the harvesting process

reduces the stock of pink shrimp available for capture in the late fall

and spring fishing seasons. This reduction in sto ck size implies a lower

expected quantity of future pink shrimp landings than would occur if

discard did not exist. Hence, discarding juvenile pink shrimp represents

a sacrifice of future income. However, a management strategy designed to

protect immature pink shrimp from being discarded implies a loss of present

income if adoption of the policy results in a reduction in commercially

sized brown shrimp landings. Clearly, the decision maker must weigh the

reduction in present income against the potential increase in future income

that would result from adopting a particular management strategy.

The objectives of the economic portion of the pink shrimp discard

study are:

(1) to specify an economic framework within which alternative public

policy actions concerning pink shrimp discard can be evaluated; and

(2) to estimate the expected net economic gains to be realized by the

North Carolina shrimp fishery if selected management strategies

were to be adopted.

The basic bioeconomic model was proposed in the last report. The method

of analysis was to establish an accounting equation that can be easily used

to evaluate the benefits and costs of any discard policy considered for

implementation.

_12-

The focus of this report is on objective (2). In general, it was

found that the values of several parameters (e.g. the natural mortality

rate and the reduction in brown shrimp landings) in the cost-benefit equation

may fluctuate from year to year due to variations in uncontrolled factors,

especially weather conditions. Hence, the approach adopted here is to

simulate various states of nature, and then compute the benefits and costs

associated with.each situation.

The Benefit-Cost Equation

A complete evaluation of alternative discard strategies requires the

management agency to specify the set of policies and/or combinations of

policies to be considered. Then, for each policy, it must identify and

quantify the costs imposed upon and the benefits received by the fishery

relative to the situation that would prevail if no policy was adopted.

Finally, the preferred policy is that for which the difference between total

benefits and total costs is greatest. If costs exceed benefits for each

policy, the best management strategy is to permit the discard of pre-

commercially sized pink shrimp.
The benefit-cost decision rule is to choose the i th policy from among

the T (i = 1,2,...,T) policies being considered that maximizes the

difference between benefits, Bi. and costs, C i*
.MaximizeI B. C. for B. - C. > 0
1 1

where
B. = (Q K Bd Q KB d.)(W P + (Q KB d Q KB d W X P + As. + AV.B
1 0 0 i 1 KF)(ZF) 0 0 i i KS ZS.
and C = (PAQ - PA ) + AE. + AV C
i 0 0 iQi .1 i

The variables used in the equations are defined:
o denotes the "no policy" alternative
i = 1,2,...,T represents the values of variables when the i th
policy is in effect.

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There are three sources of costs to be considered before implementing

a discard policy. These include the value of foregone landings of

commercially sized shrimp, administrative and enforcement costs, and any

increase in vessel operating costs as a result of the policy's regulations.

The primary cost component is the value of the reduction in landings

forces upon the fishery by the policy's restrictions on shrimping activity,
PAQ - P A It is important to note that the relevant co st is the value
0 0 iQi*
Of COL ercially sized shrimp not landed during the discard period that would

have been landed had the policy not been adopted. Since value is the

product of price and quantity landed, changes in both of these terms should

be considered.

Quantity landed can be viewed as a technical relationship between the

fish stock and the amounts of economic inputs employed by the industry. For

a given population size, factors such as the number and size of vessels in

the fleet, the type of gear used, the number of hours fished per day, and

weather all influence industry landings.

d =discard rate = number of juvenile shrimp number of marketable
sized shrimp.
Q =quantity of commercially sized shrimp landed at the time of
discard.

K number per pound of brown shrimp landed
W a composite term, representing the effects of growth and
mortality on the juvenile pink shrimp saved from discard. It
is used to determine the expe t d landings in each future period
= fall, W = spring
and the number per pound (@f
KF,KS represent the size of pink shrimp landed in the fall and spring.
A F S
P ,P P represent the average price Rer pound of brown shrimp landed
during the fiscard period, P , the price of pink shrimp in
tte fall, P , and the price of pink shrimp in the spring,
P
F S =
Z ,Z discount factor indicating that $1,00 of present income is
preferred to $1.00 of future income.

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Each discard policy will affect this technical relationship so as to

reduce the quantities of both commercially and pre-commercially sized

shrimp that are landed. For example, increasing the minimum legal mesh

size may reduce the quantity of juvenile pink shrimp landed and discarded,

but it will also permit more commercially sized shrimp to escape. Prohibiting

night shrimping would virtually elimin ate the discard problem except at

sunrise and sunset. However, if the environmental factors are such that

brown shrimp are also feeding at night, this policy would virtually

eliminate the brown shrimp fishery as well as the pink shrimp discard.

The impact that particular policies will have on brown shrimp landings

is not known. However, this study examines its importance in the benefit-

cost equation by assuming several levels for the reduction in brown shrimp

landings.

It has already been stated that the value of the reduction in brown

shrimp landings can be decomposed into a change in landings and a change

in the price per pound received by fishermen. A well-known economic

phenomenon asserts that a decrease in the quantity landed can be expected

to cause an increase in price per pound. Thus, changes in price vary

inversely with changes in landings, and tend to minimize the cost of

adopting a discard policy.

In general, the greater is the increase in price per pound, for a

given reduction in landings, the.lower will be the total cost of any

policy. This results because, although fewer pounds of brown shrimp are

landed, each pound landed receives a higher price. Alternatively, the

smaller is the unit price increase, for a given reduction in landings,

the greater will be the cost of adopting a discard policy.

To illustrate the importance of this conclusion, consider the following

example. For simplicity, assume that during the discard period, 200,000

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pounds of shrimp will be landed if no policy is adopted, and 100,000 pounds

if policy i is implemented. Initially, assume that price per pound rises

from $2.25 to $2.50. Then, assume that price per pound does not rise. The

value of the reduction in shrimp landings is computed from the expression
C = PAQ - .PA
0 0 iQi*

Case 1: Price rises to $2.50/lb. Case 2: Price does not rise

C = (2.25)(200.1000) - (2.50)(100,000) C = (2.25)(200,000) - (2.25)(10.0,000)

C $200,000 C = $225,000

The value of the reduction in shrimp landings is greater in Case 2 (no

price rise) than in Case 1. The rise in price partially offset the

reduction in value. With no price change, the harvest value was reduced by

$225,000. In contrast, if price increases to $2.50 per pound, the reduced

value of harvest is $200,000.

Considerable effort has been devoted to determining the relationship
between changes in quantity landed and changes in price per pound. 2

2As indicated in the text, it is necessary to have an estimate of the
change in exvessel price due to a given change in landings. Economic theory
suggests that this information can be determined by formulating the exve.ssel
demand and estimating the values of its parameters.
In general, the exvessel demand for shrimp is derived from the wholesale
and retail demands for shrimp. In addition, there is a demand for North
Carolina shrimp to be shipped to other producing and/or consuming centers.
It was hypothesized that current price is a function of current landings,
but landings themselves are a function of preceding prices. Hence, the
quantity supplied is unresponsive to current market price, and ordinary
least squares estimation techniques may be employed. However, current price
does influence the willingness of shrimpers to fish in future periods.
The estimated demand equation is
ln Pt = -3.43842 - .00014856Q t 0077915 t-l + -00904Yt
(-3.4335**) (-4.8700***) (2.3343*)

R 75

n 52
.01168Z + .01203B t 00129F

(-2.2608**) (3.2089**) (-.4096)

where P = average exvessel price for size 4150 in North Carolina, deflated
by the CPI ($/lb.)

_16-

To su=narize the results, it was hypothesized that a key feature of shrimp

price determination is that producing regions are interrelated by product

flows. Price differentials between markets provide incentives for dealers

and brokers to move shrimp in search of the highest price. Whenever prices,

less transportation costs, rise above those paid in other states, shrimp will

flow into North Carolina. This tends to negate the original price increase.

A reduction in North Carolina landings due to the adoption of a discard

policy is expected to have a small impact on price as shrimp flows into

North Carolina from other regions. In fact, it is estimated that a 10%
3
reduction in North Carolina landings will increase exvessel prices by .3% .

Q total quantity landed, regardless of size, in North Carolina
(1000 lbs.)
St-1 = beginning stocks of shrimp held in cold storage in the U.S.
(million lbs.)
Y = per capita deflated U.S. income O/Person)
Z = quantiE@_ of shrimp landed in other Southeastern and Gulf states
(million lbs.)

B = Consumer Price Index for beef products
F = Consumer Price Index for food fish
Monthly data (May-November) for the period 1969-1975 were used.
All coefficients, except that of the price of food fish, were signifi-
cantly different from zero at the 5% confidence level and demonstrated the
expected sign. T values are shown within parentheses.
- The e:ctremely small coefficient on the North Carolina landiugs variable
suggests one of two possible explanations. First, North Carolina is a small
producer of shrimp relative to total U.S. production and a given change in
C> 0
landings may be insignificant relative to total shrimp production. Second,
there may be a simultaneity bias in the estimated coefficient if the supply
of shrimp landed is influenced by current market price. Although it may be
true that current price does not influence current quantities landed, the
relevant market period appears to be a week. Since monthly data were used,
each observation includes more than one market period.
3To determine the predicted impact on the price of shrimp in North
Carolina due to a change in quantity landed, one must transform the price
equation. First, let
A = -3.43842 - .007791S t_1 + -00904Y - .01168Z + .01203B - .00129F.
Then, P = e -.00014856QeA.
The change in price due to a 1000 pound reduction in quantity landed is
L
P *00014856Q A
-.00014856e- e
dQ

-17-

Hence, a given policy induced reduction in landings will stimulate a

negligible increase in price per pound. This has the effect of maximizing

total cost for a given quantity reduction, and reduces the chance that

benefits will exceed costs.

Increased enforcement and administrative costs, AEi. include the expense
of employing new enforcement officers and equipment, if needed, and any

additional wage payments to existing officers to compensate them for the

time required to fulfill their additional duties. Another enforcement cost

is the increased value of damage inflicted on other species because officers

devote relatively less of their time to these species, and hence do not

detect violations that they would otherwise have detected.

The effect of discard policies on vessel operating cost in the summer,

AVi31 is not known. In general, the enforcement and operating cost components

are assumed to be small relative to the cost in terms of-foregone landings.

Since A includes the values of all variables included in the equation, it
is easier to work in percentage changes. Thus, the percentage change in
price due to a given percentage change in quantity landed is defined
UP _ dP Q [-.00014856e-' 00014856QeAIQ
%dQ dQ P e -.00014856QeA
dP _q -.00014856Q
dQ P
This percentage change includes the value of Q, and hence will vary over
time as quantity landed varies. In the simulated examples presented later,
the initial level of landinas is assumed to be 200,000 pounds. Hence the
percentagereduction in price is

EP-9 = -.00014856(200) -.0297 = 3%
dQ P

-18-

There are four sources of benefits to be estimated when evaluating a

discard policy. The primary benefit is the increased value of commercially

sized pink shrimp expected to@be landed in the late fall. The remaining

sources of benefits include the increased value of commercially sized

pink shrimp expected to be landed in the spring, the increased value of

commercially sized shrimp expected to be landed in future years, and any

decrease in vessel operating costs in the late fall and spring as a result'

of larger shrimp stocks.

As mentioned above, any policy that protects juvenile pink shrimp from

being landed, killed, and discarded increases the stock of shrimp available

for capture in the future. However, not all of the juvenile pink shrimp

that are saved from discard will be landed in the future. Some will die

due to disease or predation. Others will survive to spawn, thus increasing

the stock of shrimp in future years. It is important to emphasize that

benefits are only derived from those shrimp that are landed, or which

reproduce second or third generation shrimp which are landed.

One cannot directly observe the increase in fall and spring pink

shrimp landings at the time the management decision is made. Rather, one

must first estimate the number of pink shrimp that would be saved from

discard if a particular policy was to be adopted. Then, by incorporating

into the model the biological processes of growth and mortality, one can

estimate the number of these shrimp that can be expected to be landed,

week by week, in the late fall and spring seasons.

-19-

The total number of juvenile pink shrimp that can be saved from discard
by adopting the ith policy is computed as
(Q KBd Q KBd
01 0 i
where the o subscript denotes the "no policy" action
and QO,Qi =pounds of brown shrimp,
KB = number of brown shrimp per pound,
doldi = number of pink shrimp per brown shrimp.
The second term of the expression is necessary if pink shrimp discard is

not completely eliminated.

Pinks that are saved from discard are available later in the fall.

However, early in the fall pink season, landings are concentrated in the

smaller sizes. They mature as the season progresses, and command higher

prices as they achieve larger sizes. However, the stock (in numbers)

available for harvest at any time throughout this season is decl ining due

to both natural -End fishing mortalities. Hence, estimating the proportion

of these shrimp in any time period that will actually be landed introduces

into the analysis the dynamic processes of shrimp growth and mortality. We

have chosen to estimate expected future landings on a week-to-week basis.

Mortality rates are estimated by week from the following equations:
Natural mortality rate = I-e-x
Fishing mortality rate = 1-e-m
Total mortality = 1-e- (X+m)

The total mortality rate is used to determine the number of pink shrimp

that survive from one weekly interval to the next. The fishing mortality

rate determines the number of shrimp that can be expected to be landed in

any particular week.

Over time, the surviving members grow in weight and value. One needs

pink shrimp growth rates before a price can be placed on the expected

-2.0-

increase in landings. Growth rates provide information on when individual

shrimp achieve the next larger size, and hence, when the (higher) price for

that size should be used in the valuation process.

The effects of mortality and growth are summarized with the variables
(fall) and W S (spring) of the benefit-cost equation. For the purposes

of this study, the increase in landings that may be realized in future years

because some pink shrimp may survive and spawn is not evaluated. It is

assumed that the environment is the primary determinant of year-to-year

fluctuations in the stock of shrimp, and that the impact on future landings

of a larger breeding population is negligible and can be ignored.

The effect of discard policies on vessel operating costs in the late

fall and spring is not known. Conceptually, a larger population size

would increase population density and make both locating and landing shrimp

less time consuming, and hence less costly.

r
Application of tMe Model

The purpose of this section is to illustrate the use of the benefit-cost

equation. The method of analysis will be to hypothesize several situations,

and then compute the benefits and costs associated with each case. The

values of the variables used in the computations conform as closely as

possible to those actually observed. However, hypothetical values-are used

when data is not available. The values of all parameters will be varied to

provide information on the sensitivity of the benefit-cost outcome to changes

in the parameters. As we learn more about the sizes of the parameters

involved, simulations can be more narrowly defined to approximate actual

situations. Those costs and benefits not included here might also be

estimated and included.

All of the calculations that follow explicitly consider only the expected

value of increased future pink shrimp landings and the value of reduced brown

-21-

shrimp landings. These are the largest,and most visible (to fishermen)

benefit and cost components. All other sources of benefits and costs are

assumed to be negligible. However, the management agency will want to

keep in mind that these additional benefits and costs do exist, whatever

their magnitude.

As already discussed, the chief cost component of a discard policy is

the value of the reduction of brown shrimp landings due to the enforcement

of a discard policy. Three levels of policy induced brown shrimp landings

are hypothesized. Landings could be slightly diminished, reduced by

approximately one-half, or greatly decreased. Each of these situations

could occur with the prohibition of night shrimping. Sampling during the

fall season, 1976, revealed that nearly 85% (5125 of 6001) of the brown

shrimp were landed at night. Although the implied costs are greater than

would be the case if, say 50%, had been landed at night, the benefits are

also greater since a larger number of pink shrimp will be saved from discard.

Hence one cannot expect a policy solely on information of costs or benefits

alone. Both are required.

The benefits of a discard policy are more difficult to quantify because

of the dynamics of shrimp growth and mortality and because there are several

factors which influence the expected quantity of future landings. The peak

discard period is assumed to occur in early September. Pink shrimp saved

from discard are specified to be 95mm in length and are hypothesized to be

available to the fishery until early November (for about 8 weeks)and then

again in the spring,(for 6 weeks).

Estimating the expected increase in future pink shrimp landings is not

an easy task. For a given quantity of shrimp saved from discard, future

pink landings depend on natural and fishing mortality rates, the size of

pinks at the time of discard, and the length of the fishing season.

-22-

For example, assume that N = 5,000,000 individual pink shrimp saved

from discard survive to be the minimum commercial size of 70 per pound,

headless. Then, if the natural mortality rate, x = -.25, and fishing mortality

rate, m = -.25, are specified,, the expected increase in pink landings in each
successive week can be computed. During the first week, NU - e--m), or

1,105,995 shrimp are expected to be landed. Similarly the number of

individuals expected to be available for capture in the second week is
N [1 - (1 - e- (M + X) )) = (.6065) N = 3,032,655.

The number expected to be landed in the second week is
(3,032,655)(1 e-m) = 670.1820

If these shrimp are sized 60 per pound, this implies that 11,180 pounds

were landed in the second week.

The value of the natural mortality parameter used in most of the

situations evaluated in this study, X = -.25, approximates the values

4
estimated for pink and brown shrimp in North Carolina.

Throughout the fall, the survivors among the pink shrimp that were saved

from discard grow in length and weight, and hence move into progressively

larger size groups. The expected length of shrimp landed in each weekly

period from September to November was approximated from the equation
males: 1 27 (1 - e-.217(t + 9.82)
females: I 34b,5(l - e-* 188 (t + 6.93)

Although these equations were estimated from spring pink shrimp growth

relationships, they were assumed to be at least approximately correct for

41. McCoy, Edward G., Migration, Growth, Mortality of North Carolina
Pink and Brown Penaeid Shrimps, Special Scientific Report No. 15, June 1968.
2. McCoy, Edward G., Dynamics of North Carolina Commercial Shrimp
Populations, Special Scientific Report No. 21, March 1972.
3. Purvis, Connell E. and Edward G. McCoy, Overwintering Pink Shrimp
Penaeus duorarum, in Core and Pamlico Sounds, N.C., Special Scientific
Report No. 22, April 1972.
4. Purvis, Connell and E. G. McCoy, Population Dynamics of Brown
Shrimp in Pamlico Sound, Special Scientific Report No. 25, January 1974.

-23-

the fall as well. Biologists have not been able to estimate curves for
the fall due to the confounding effects'of water temperature on growth.

Male and female lengths at week t were averaged, and then used to

determine the expected number@of individuals per pound. Expected pounds

of shrimp landed is determined by dividing the number of shrimp landed by

the number per pound. The appropriate price is also determined once the

expected size of shrimp landed is known. Costs and benefits were evaluated

using average prices that prevailed in the fall, 1975.

Simulations

Tables 1-3 present the estimated difference between the expected

benefits and costs under various assumptions about the values of the

natural and fishing parameters, and the reduction in commercially sized

brown shrimp landings brought about by the policy's restrictions on fishing

activity. In each case, interest was focused on whether or not the range

of observed discard rates is sufficiently large to warrant the adoption

of the suggested prohibition of night shrimping.
a 5
The discard rates used in these examples were 8:1, 4:1, and 1:1.

It is assumed that these discard ratios would be reduced to 2:1, 1:1, and

.1:1, respectively. In other words, the policy would reduce, but not

completely eliminate the discard of.pre-commercially sized pink shrimp.

Table I presents the estimated net benefits of the discard policy

assuming alternative levels- of commercially sized shrimp landings. A

one pound-reduction in brown shrimp landed will increase both the expected

costs and benefits-to be realized from this policy. Costs are increased

because fewer brown shrimp are landed. Benefits are increased because

those pink shrimp that would have been discarded are now able to grow, and

perhaps be landed in the future. However, it can be seen that the impact

Discard rate is expressed as the number of pre-commercially sized
shrimp per marketable sized shrimp landed.

-24-

TABLE 1

Estim4ted Net Benefits
for Alternative Brown Shrimp Landings*

Policy Induced Discard Rate**
Reduction in Brown
Shrimp Landings (lbs)
(31-35) 1:1 4:1 8:1
30,000 11,479 $ 88,389 $238,978
(15% reduction)

100*00 $ $ $
1 - 164,582 - 42,677 124,642
(50% reduction)
170,000 -$313,515 -$176,645 $ 7,505
(85% reduction)

*These examples assume that M = -.25, X -.25, and that pink shrimp
are 95 mm in length at time of discard.

**Each column assumes that the discard rate is reduced from 8:1 to
2:1, 4:1 to 1:1, and 1:1 to .1:1.

-25-

TABLE '2

Estimated tet Benefits
for Alternative Fishing Mortality Rates*

Instantaneous Fishing Discard Rate**
Mortality Coefficient 1:1 4:1 8:1
$ $ $
M = -.15 174,821 - 80,400 .. 49,200
M = -.25 164,582 -$42,677 $ 124,642
M = -.50 -$154,358 -$ 5,000 $ 170,446

*These examples assume that X = -.25, that pink shrimp are 95 mm
in length at time of discard and that brown shrimp (31-35)
landings are reduced by 100,000 pounds (50%). .

**Each column assumes that the discard rate is reduced from 8:1
to 2:1, 4:1 to 1:1, and 1:1 to .1:1.

-26-

TABLE 3

Estimated Net Benefits

For Alternative Natural Mortality Rates*

Instantaneous Discard Rate**

Natural

Mortality 1:1 4:1 8:1

Coefficient

X = -.15 -$145,321 $27,910 $266,200

X = -.25 -$164,582 -$42,677 $124,642

X = -.50 -$188,000 -$128,773 -$47,890

These examples assume that M -.25, that pink shrimp are 95 mm in length at
time of discard, and that brown shrimp(31-35) landings are reduced by 100,000
pounds (50%)

Each column assumes that the discard rate is reduced from 8:1 to 2:1, 4:1 to
1:1, and 1:1 to .1:1.

-27-

on costs is greater than that on benefits. In general, the more severe the

reduction in brown shrimp landings, the less likely it is that expected

benefits will exceed costs.

Sampling results from the fall 1976 season are the only data available

on the effects of a prohibition of night shrimping on brown shrimp landings.

As noted above, nearly 85% of those brown shrimp caught were landed at

night. The third row corresponds to this situation. Although brown shrimp

may feed during the day, depending on weather conditions, prohibiting

night shrimping; when brown shrimp can only be landed at night would most

likely result in a large net loss to the fishery.

Table 2 presents the estimated net benefits o f the discard policy

assuming alternative instantaneous fishing mortality rates. A larger

fishing mortality rate tends to increase benefits (relative to a lower

rate) since a greater proportion of shrimp available for capture at any
instant are landed. Note that as one moves down any col*u'mn in Table 2,

the difference between expected benefits and costs is increased. Thus, the

greater the fishing mortality rate, the greater the likelihood that expected

benefits will exceed costs.

Table 3 presents the estimated net benefits to the fishery assuming

alternative natural mortality rates. In general, the larger the rate of

loss due to disease, predation, adverse weather conditions, or a lack of

food supply, the lower will be the expected benefits of any policy designed

to protect juvenile pink shrimp because relatively fewer of those saved

from discard will be available for capture in the future. Moving down

any column illustrates this point.

Several attempts have been made to estimate fishing and natural
morta lity parameters for Pamlico, Core, and Bogue Sounds in North Carolina. 6

6See Footnote 4.

-28-

Only two of nine fishing mortality estimates exceeded a value of -.25. Most

were less than -.20, of which three were less than -.10. Thus, the North

Carolina shrimp populations appear to exhibit low fishing mortality rates.

The natural mortality estimates range from a low of -.213 to a high

of -.431. Although these are not as high as the greatest value assumed -

Table 3, Row 3 - they are greater, on average, in magnitude than the level

used in the computation of Tables I and 2.

In all three tables, a discard rate of 8:1 was great enough to result

in a positive difference between benefits and costs of adopting a discard

policy. However, it must be emphasized that this is not conclusive evidence

that benefits will in fact exceed costs. First, these figures represent

expected net benefits. They suumarize the net difference between benefits

and costs only if the anticipated increase in future landings is at least

as great as that which was predicted. Any unforeseen factor that alters

the basic premises upon which these predictions were made will result in an

actual net benefit that differs from the estimated figure.

Second, other factors not mentioned here may vary. Specifically,

Tables 1-3 assume that brown shrimp are graded at 31-35 per pound. If

brown shrimp are actually measuring 21-25 per pound, the total costs of

any discard policy will be understated, and hence the net benefit figures

of Tables 1-3 will be overstated. Since larger shrimp command higher

prices, a given reduction in the quantity of brown shrimp landed will

represent a greater level of foregone current income.

Finally, Tables 1-3 assume that the pink shrimp saved from discard

are 95mm in length. If they were 75mm, there would be a greater time

interval between the time of discard and the time when the shrimp saved

from discard actually reached commercial size. Hence, a larger percentage

would suffer from natural mortality before achieving marketable size.

_29-

MANAGEMENT IMPLICATIONS

This study has considered management alternatives directed at a significant
biological, economic and social problem which occurs in Pamlico Sound almost every
year. In the past, discards of pink shrimp are believed to have been sufficiently
high to indicate that considerable future income may have been lost while fishing
for brown shrimp.
The situation appears to have changed during 1975 and 1976 when the shrimp
supply situation dictated that the market would accept pink shrimp at somewhat
smaller sizes than in the past. In addition during 1976, brown shrimp reached
larger sizes than they had during the recent past.
Results of this study indicate that, under current supply and price situations,
discarding pink shrJmp is an acceptable practice up to the level of about eight
pink shrimp discarded for each brown shrimp retained, at the sizes considered in
this report. Whether higher discards would be economically-acceptable would de-
pend upon changes in vessel operating costs and enforcement costs during the time
in question. If market demand were strong, leading to premium prices for large
brown shrimp, then higher discards of pink shrimp would be acceptable. However,
if brown shrimp prices were weak, it might be best in the long run to protect the
small pink shrimp and look for future income from the pink shrimp later in the fall
and during the following spring, depending on the total market situation.
Some additional study of the parameters considered in this report is re-
commended in order to better define the sensitivity of net benefits to these par-

ameters.

-30-

ACKNOWLEDGEMENTS

The authors are greatly indebted to boat captains Bill Biggs and Frank Meadows
and Marine Fisheries Technicians Rudy Dowty and Darrell Mumford for their field
assistance in obtaining the data used in this report.
Special thanks go to Michael W. Street, Chief, Research and Development
Section, Division of Marine Fisheries for ideas and suggestions used throughout
the report. He is also to be credited with the final organization of the report.
Sincere appreciation is expressed to Elizabeth T. Wainwright and Donna Warren
for typing the manuscript.

-31-

LITERATURE CITED

Parsons, Brickerhoff, Hall and Macdonald (Engineers). 1954. Survey and Report
on the Inland Ports and Waterways of North Carolina. N.C. Dept. of
Conservation and Development, Raleigh, NC

Purvis, Connell E. and Edward G. McCoy. 1972. Overwintering Pink Shrimp,
Penaeus duorarzonin Core and Pamlico Sounds, N.C. North Carolina Division
of Commercial and Sports Fisheries, Raleigh, N.C., Spec. Sci. Rep. No. 22,
29 pp.

U.S. Dept. of Commerce. 1973. Tide Tables - East coast of North and South
America, 1973. National Oceanic and Atmospheric Administration, National
Ocean Survey.

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