AN ABSTRACT OF THE THESIS OF
William Robert Wood
(Name)
in
Title:
for the
Agricultural Economics
(Major)
Master of Science
(Degree)
presented on ■/)/,#';/{■ . ■^/-, 16f{/> I
/'(Date)'
A DEMAND ANALYSIS OF PROCESSED SALMON FROM
THE WEST COAST
Abstract approved:
\
. _ .
,
, . ^
Richard S. Johnston
The primary purpose of the study was to identify the demand
for processed salmon from the West Coast.
The basic approach in
the demand analysis was to identify those variables that determine
the supply and demand for processed salmon.
An econometric model
was established containing the supply and demand equations from
which estimates for the parameters in each equation were obtained.
The main source of data for salmon was obtained from publications
printed by the Bureau of Commercial Fisheries, and the Pacific
Fisherman.
Ordinary least squares using the wholesale price as
the dependent variable in the demand equation was the principal
method of analysis.
Coefficients for the demand expressed flexibilities with respect
to the price.
Price flexibilities calculated at the mean values for all
processed salmon indicated that a ten percent increase in volume
would reduce price by a lesser percentage.
For increases in the
supply of processed salmon, total revenues would increase, where
decreases in supply would cause total revenues to decline.
The results of the study also indicated that for a small percentage
increase in disposable income, prices would increase but by a
lesser percentage.
Inverse relationships were noted between the
price of salmon and the quantity of canned meat and meat products.
Effects of population changes on the price of processed salmon were
inconclusive.
A Demand Analysis of Processed
Salmon from the West Coast
by
William Robert Wood
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
June 197 0
APPROVED:
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Assistant Professo^r of Agricultural Economics
in charge of major
Head of Department of Agricultural Economics
Dean of Graduate School
Date thesis is presented
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Typed by Cheryl E. Curb for
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William Robert Wood
ACKNOWLEDGEMENTS
I wish to express my most sincere appreciation to my Major
Professor, Dr. Richard S. Johnston, Assistant Professor of Agriculture Economics, for assistance received in the preparation done
for this thesis.
His guidance, suggestions, and criticisms have been
extremely valuable.
Appreciation is also extended to those members of the Bureau
of Commercial Fisheries and the National Canners Association who
furnished data and information that was useful in the thesis - in
particular Darrel A. Nash, Chief, Branch of Demand and Marketing
Research, B.C.F., and Stanford R. Beebe, Director, Division of
Industry Statistics, N. C.A.
I also want to thank my wife, Judy, for her time and suggestions
in preparing the final manuscript.
TABLE OF CONTENTS
Page
INTRODUCTION
Statement of the Problem
Objectives of the Study
Comments on Salmon and Salmon Products
Methodology of the Study'
Hypotheses for the Demand
THE SUPPLY-DEMAND MODEL
1
2
3
7
12
13
General Discussion
Limitations and Assumptions
Equations of the Econometric Model
Explanation of the Variables and Justification
for their Classification
Quantity Supplied
Imports
Exports
Stocks or Inventories
Prices
Quantity Demanded
Income
Substitutes
Population
Summary
26
28
31
31
33
35
37
38
41
42
STATISTICAL RESULTS AND INTERPRETATIONS
44
Supply
Demand
All Salmon
Individual Species
Quantity as the Dependent Variable
CONCLUSIONS AND RECOMMENDATIONS
13
16
23
26
44
45
45
49
51
54
TABLE OF CONTENTS (Cont. )
gage
BIBLIOGRAPHY
59
APPENDIX A
61
APPENDIX B
67
APPENDIX C
70
LIST OF FIGURES
Figure
Page
1
Salmon landing for the Pacific Coast fisheries,
1936-1967.
6
2
Quantity of landings for each species of salmon
from 1947-1967.
8
3
The supply and demand model for processed
salmon.
14
4
The imports of canned salmon for the United
States, 1947-1967.
30
5
The pack of salmon for the United States,
1947-1967.
30
6
The relationship between the price and quantity
of processed salmon at the wholesale and retail
market levels.
36
7
The affects of population on prices of processed
salmon.
41
LIST OF TABLES
Table
Pa ££
The annual average wholesale and retail prices
for a 16 ounce, tall, can of Pink salmon.
20
Average monthly wholesale and retail prices
for a 16 ounce, tall, can of Pink salmon.
22
Regression results for canned salmon with price
as the dependent variable.
46
LIST OF APPENDIX TABLES
Table
.
..
Appendix A
Page
B
—
1
The proportion of total salmon landings that were
marketed in the canned form for the period
1960-1968.
62
2
Opening and annual average wholesale prices for a
standard case of canned Pink, Sockeye, and Chum
. salmon for the period 1947-1967.
63
3
Deflated wholesale and retail prices for a 16 ounce
can of salmon, 1947 to 1967.
64
4
The quantity of landings, pack, foreign trade, and
per capita consumption of canned salmon for the
period 1947-1967.
65
5
Factors that are instrumental in the supply-demand
model.
66
Appendix B
1
Comparison of actual with predicted stock level
changes for canned salmon as of July 1 for 19 65
through 1967.
69
Appendix C
1
The correlation between the variables of the demand
equation for canned salmon -- equation b, Table 3.
71
2
The correlation between the variables of the demand
equation for canned salmon, per capita data Equation d. Table 3.
72
3
The correlation between the variables of the demand
equation for canned salmon - Equation c, Table 3.
73
4
The correlation between the variables of the demand
equation for Chum salmon - Equation f, Table 3.
74
LIST OF APPENDIX TABLES (Cont. )
Table
Page
5
The correlation between the variables of the demand
equation for Chum and Pink salmon - Equation g,
Table 3.
75
6
The correlation between the variables of the demand
equation for Sockeye salmon - Equation h. Table 3.
76
7
The correlation between the variables of the demand
equation for Sockeye salmon - Equation i. Table 3.
77
8
The correlation between the variables of the demand
equation for canned salmon - Equation (2. 1).
78
A DEMAND ANALYSIS FOR PROCESSED
SALMON FROM THE WEST COAST
INTRODUCTION
Statement of the Problem
Objective information as to the nature of demand for fisheryproducts amomg consumers in the United States is limited.
As noted
by Waugh and SSTorton:
It £s a curious contrast that agriculture and
fisheries;, though closely related in the market, have
been at ©pposite ends of the spectrum with respect to
the amasant of price and demand analysis applied to the
industry, A tremendous inventory of research on the
prices esff, and demand for, agricultural commodities
has be em built since 1920. In comparison, research
on prices of fishery products has been meager (24, p. 9).
Since tite late ISOO's salmon from the West Coast has been an
important somarcepf seafood; however, little objective information
is known as to the nature of the demand for salmon in the processed
form.
Knowledge of the nature of demand would be useful to mem-
bers of the industry for determining the effects on total revenues as
a result of vaxious levels of output and prices for processed salmon.
Identifying thte demand for processed salmon could be beneficial to
members of £3ae Bureau of Commercial Fisheries as an aid for indicating the possible effects on total revenues in the salmon industry
as a result of changes in programs and policies of fishery management.
Objectives of the Study
The primary objective of the study will be to identify the demand for processed salmon from the West Coast.
The study is pri-
marily directed towards the wholesale level of the salmon market,
although the results will also be applicable to the retail or consumer
level.
The wholesale and processor market level will be identified
as one and the same.
as follows:
The objectives of the research are identified
(1) develop a model of the salmon industry which will
identify the factors that are responsible for influencing the supply
and demand for processed salmon, (2) identify the price, income,
and cross-flexibilities of processed salmon, and (3) predict the results that certain marketing policies would have on total revenues of
the industry.
Canned salmon is the primary form in which processed
salmon is marketed.
The pack of salmon* currently averages about
82 percent of total domestic landings (see Table 1, Appendix A).
The pack of salmon refers to the amount of salmon that is processed
into the canned form each year. It is generally referred to as the
"annual pack". The annual pack would provide the source from
which canned salmon is exported. It would appear possible for imports of fresh salmon to be canned and included as part of the domestic pack; however, the change in the total pack figures used
would be insignificant if fresh imports were, in fact, domestically
canned.
Therefore, concentration of the study will be to identify the demand
for canned salmon.
The words processed and canned salmon will be
used interchangeably to mean the same product.
Comments on Salmon and Salmon Products
Salmon from the Pacific Coast fisheries
accounts for a signi-
ficant portion of the total landings and ex-vessel value for all marine
life caught in these fisheries.
From 1957 to 1967 the salmon catch
represents an average of 25. 1 percent of the total pounds of fish,
shellfish, and whale species caught in the Pacific Coast fisheries.
For the same period, the average annual ex-vessel value for salmon
was 51.5 nnillion dollars which represented 39. 6 percent of the value
paid to Pacific Coast fishermen for all fish.
In 1966, the salmon
catch from the Pacific Coast fisheries represented 8. 9 percent of
the United States catch of fishery products, second only to menhaden
which accounted for 30. 0 percent of the total landing weight (2 3, p.. 14).
Data published by the Bueau of Commercial Fisheries indicate that
only minute quantities of salmon are registered as commercially
caught in areas such as the Atlantic Coast fisheries and the Great
Lakes.
2
Therefore, it can be assumed that the domestic supply of
For the purposes of the study the Pacific Coast fisheries pertain
to the United States. Only landings of fish in the states of Alaska,
Washington, Oregon and California will be considered.
landings for salmon in the United States are furnished from the fisheries of the Pacific Coast.
The manner in which salmon has been marketed has not changed
significantly since it became an important source of food in the late
1800's.
Canned salmon has been the primary form in which this
food resource has been marketed, although salmon is also marketed
fresh or frozen, smoked, and salted or pickled.
There are five species that are important in supplying the
quantity of salmon available for consumption.
for these five are:
The common names
(1) Chinook or King, (2) Chum or Keta, (3) Coho
or Silver, (4) Pink or Humpback, and (5) Sockeye or Red.
When the
word salmon is used in this paper it will refer collectively to the
five species.
When one or more species is discussed, the name or
names will be specified.
Each species exhibits different characteristics in appearance.
For example, the Sockeye salmon has red meat where the meat of
Chum salmon is more pale in color.
These characteristics become
noticeable in pricing arrangements depending on the desirability to
the consumer of the product.
The red meat of the Sockeye salmon
appears to be more desirable to the consumer, and has historically
commanded higher prices than Chum.
Pink salmon is generally the
most abundant of the five species and comprises a large part of
salmon that is used for canning.
Usually Pink; Chum, and Sockeye
salmon account for a majority of the annual pack.
3
Chinook and Coho
salmon are important in the fresh and frozen markets.
4
The per capita consumption of canned salmon in the United
States has been decreasing since the 1930's when the catch, and
resulting production of salmon products, was at its highest.
In 1936
the per capita consumption of canned salmon was 3. 0 pounds; however, in recent years the annual per capita consumption has decreased to less than one pound.
Table 4, Appendix A, shows the
per capita consumption of canned salmon for the years 1947 to 1967.
The results of decreases in per capita consumption would appear to
be the results of a decline in the natural supply of salmon, and an
increase in the population of the United States.
Figure 1 shows how
the landings of salmon have decreased substantially since 1936.
Factors noted as contributing to reduced landings over the years
have been over-fishing, dams, and destruction of spawning grounds
(13).
Since I960 the general level of landings has increased above
the low landing levels experienced in the late 1950's.
However, with
increases in population, the annual per capita consumption of canned
salmon has remained relatively constant during these more recent
3
4
For the period from I9 60 to 1967, the three species accounted for an
annual average of 91. 9 percent of the total salmon pack.
For more information as to the physical characteristics of these
five species an article by Idyll (13) should be consulted.
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Figure 2, page 8, is included to show the relative importance
of landings for each species of salmon.
It should be noted that Alaska
produces about five times the catch of salmon as do the other three
Pacific Coast states, Washington, Oregon, and California, combined
(13).
Methodology of the Study
The basic approach in this demand analysis will be to identify
those variables that determine the supply and demand for salmon.
An econometric model will be established containing the supply and
demand equations for which estimates for the parameters in each
equation will be calculated.
The main source of data for salmon will
be obtained from publications printed by the Bureau of Commercial
Fisheries, and from the Pacific Fisherman. ^ Data from these sources will consist mainly of landing quantities, imports and exports,
the annual salmon pack, and the prices for canned salmon.
The concept of ex post demand will be used in this study.
Sos-
nick (20) noted that two kinds of functions relating price paid to quantity purchased must be distinguished.
5
One is ex ante demand - a
The Pacific Fisherman can be considered the official magazine of
the fish processing industry. (Since 1967 it has been combined with
other publications to form the National Fisherman. )
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hypothetical relation that summarizes buyers' preferences or intentions.
The other is ex post demand - a historical relation obtained by
analysis of a time series.
Ex post demand expresses the average of the
average prices that historically were associated with
various quantities sold, after allowing for the effect
of changes in various shift variables.
Ex ante and ex post demands do not converge as
statistical problems are resolved. In general they will
differ if prices have varied within the time periods
considered.
When price variation has occurred systematically,
the average quantities historically associated with various average prices will differ from the ex ante demand
that prevailed. As a result, the ex post function will
not reproduce the ex ante function. Instead, the parameters of the ex post function will incorporate the
effects of the historic pattern of intraperiod price
variations (20, pp. 729-730).
The use of annual data for this analysis would appear to incorporate the intraperiod price variation and parameters to estimate
an ex post function.
This will have to be kept in mind when interpret-
ing the results of the analysis.
The wholesale price of canned salmon will be used as the dependent variable in the demand equation .
The conventional approach
to a demand analysis identifies the quantity consumed as the dependent
Retail prices of canned salmon are not available in sufficient quantities to be used in this analysis. The role of prices will be discussed in more detail under the subheading, Limitations and
Assumptions of the Model.
10
or endogenous variable.
This is based on the principle that the price
of a commodity will determine how much of it is consumed.
For pro-
cessed salmon the quantity consumed will be treated as a predetermined variable in the demand equation.
"7
A single demand equation
will then be used to estimate coefficients for the variables in the equation.
The production of canned salmon is felt to be predetermined in
the model allowing consumption to be classified as predetermined.
Fox outlines some considerations for farm supply which are relevant
to the supply of salmon.
Suppose the supply of a given commodity entering
the marketing system is not affected by the current market price. Suppose further that the marketing system
passes on this supply in a routine way, so that, except
for normal wastes and lostes in the marketing process,
the supply that reaches the consumers is exactly equal
to that marketed by farmers. In this case, consumption
is not determined by prices during the marketing period;
it can be used as a predetermined variable (10, pp. 12-13).
The concept from the above quotation can be applied to the
supply of salmon.
The supply of processed salmon is hypothesized
to be independent of current prices, and directly dependent upon the
quantity of landings of salmon.
Because canned salmon accounts for
a large percentage of total landings, it will be classified as
7
Other variables affecting demand will also be classified as exogenous
or predetermined. These variables are discussed in the subheading
entiled, "The Supply-Demand Model".
11
predetermined in the equation.
Ordinary least squares (O.L.S.) using the step-wise procedure
for introducing variables into the equation will be the principal statistical method of analysis.
are:
The principal reasons for using this method
(1) the availability of a high speed computer to analyze
the time
series data in the equations, (2) partial derivatives taken on each
variable in the demand equation will show marginal rates of change
for each explanatory variable with respect to the dependent variable.
The basic time period under consideration will be the 21 year
period from 1947 through 1967.
The time series data for the vari-
ables in the equations of the formulated model will be within this
time frame.
The main reason for using this period of time is that
no serious price restrictions were imposed by the United States
government which would detract from price determination in the
market place.
There were maximum prices imposed on canned sal-
mon for a short period during the Korean War; however, ceilings
were high enough so that prices were determined within the set
limits (1).
»
12
Hypotheses for the Demand
A review of popular articles, books, and research studies of
salmon and other fish suggested the following hypotheses about the
demand for canned salmon: (1) the elasticity of demand for all species
of canned salmon would be near -1.0, butnothighly elastic, and (2)
the elasticity of demand for individual species of canned salmon
would exceed in absolute values the elasticities of the -1.0 and approach elasticities of -3.0 to -5.0.
With price as the dependent
variable, price flexibilities may be calculated; however, estimates
for the magnitudes of the price elasticities will be made from price
g
flexibilities.
It is hoped that the results of this research will reveal
information that will form a basis for substantiating or rejecting the
above hypotheses.
8
Price flexibility is the percentage change in the price of a commodity
associated with a small change in the quantity demanded of the
commodity or related variable, all else remaining constant. For
Q price elasticity
example, price flexibility is defined as 3P . (—);
is defined as _£Q . /£\
ap VQ
13
THE SUPPLY-DEMAND MODEL
General Discussion
In analyzing the supply and demand for canned salmon, the
approach will be to explain the general nature of the relationship of
the supply and demand as postulated in Figure 3.
the economic model.
This will constitute
Limitations and assumptions pertaining to the
analysis will be made for the variables affecting both supply and
demand before developing the system of equations to be used in the
econometric model.
Landings of salmon, imports and exports of canned salmon
will be treated as exogenous variables in the supply portion of the
econometric model.
pack.
Landings directly affect the quantity of salmon
Changes in stock levels of canned salmon will be treated as
a function of landings in year t-1, the expected landings in year t,
and be classified as predetermined.
Therefore, the salmon pack,
imports, exports, and changes in stock levels of canned salmon are
the variables that determine the domestic supply available in a
specific year or time period, t.
The quantity supplied will be equal
to the quantity demanded, and will :be identified as a predetermined
variable in the demand equation.
14
Quantity of
Salmon
Landings (L
)
Domestic Supply of
Processed Salmon
/
Quantity of
Salmon Landings (L )
Stocks of
Processed Salmon
(S)
Imports of
Processed Salmon
(I)
v^..
Exports of
Processed Salmon
(E)
/
/
/I
' |
/ |
Marketing
Margin
|
I
I
Disposable Per
Capita Income
(Y/N)
U.S.
Population
Quantity of
Substitutes
(M)
Figure 3.
The supply and demand model for processed salmon. Arrows show direction of
influence. Heavy arrows indicate major paths of influence which account for the
bulk of the variation in current prices. Light solid arrows indicate definite but less
important paths; dashed arrows indicate paths of negligible, doubtful, or occassional importance.
15
Factors which affect the quantity demanded for a commodity
are the price of the commodity, consumers' income, the price of
related commodities, and consumers' tastes and preferences (8,.
pp. 73-74).
However, in this model for canned salmon, changes in
tastes and preferences are not considered explicitly.
The price of
the commodity is treated as the dependent variable for statistical
reasons and is determined by the remaining three determinants of
demand.
Since aggregate quantities rather than per capita quantities
will be used in the demand equation, population will be included as a
variable.
Further discussion of population will be given on page 41.
Since quantity supplied is being treated as a predetermined
variable (i. e., independent of price) then it appears reasonable to
specify an estimating equation in which price, the only variable
endogenous to the system, is dependent.
Single equation ordinary
least squares procedures are then appropriate for estimating demand
parameters.
With the wholesale price of canned salmon as the depen-
dent variable, direct estimates for price flexibilities rather than
price elasticities will be obtained.
It is assumed that a marketing margin would exist between the
prices for canned salmon.
This margin would account for such items
as the cost of. transportation from primary to retail points of distribution, marketing expenses such as labor, advertising, administrative
costs, and ah allowance for a profit at the retail level.
16
iJlmitations and Assumptions of the Model
There are two main limitations which may hinder the demand
analysis.
First, retail prices for only canned Pink salmon are avail-
able, and collection of these prices was discontinued in 1964.
9
Second, records of stock levels have not been available for enough
years to be used in the supply equation of the model.
The original
intent was to include actual stock levels of canned salmon as a variable in the equation to aid in determining the quantity of canned salmon available for consumption.
What effects will these two limitations have on the demand
analysis?
To measure the effects of the demand for canned salmon
on prices at the consumer level, using wholesale prices, may inject
unnecessary bias into the results.
An assumption will be made that
fluctuations in wholesale and retail prices of canned salmon are of
the same magnitude which will allow the results of the research to be
applicable to the consumer level.
9
With the wholesale price, the
Retail prices for Pink salmon were collected by the Bureau of Labor
Statistics until 1964.
17
estimated price flexibility would be larger than estimated with retail
prices.
10
It will be assumed that the change in stock levels between two
consecutive years is a function of the landings in the previous year
and the expected landings in the current year.
This assumption can
be stated as an hypothesis and tested against those data on changes in
actual stock levels that have been published.
This test should
give some indication of the validity of the hypothesis; however,
a complete test to substantiate or reject the hypothesis cannot be
made because only three observations are available.
The following list of assumptions are made to aid in the development of this demand study with explanations to follow those subjects
that require further detail.
1.
The individual demand by each final consumer or household
for canned salmon is the same, and the aggregate demand
is a summation of the individual demands.
If the marginal rate of change of price with respect to quantity, -— ,
is the same for both prices in the demand equation, then by
definition of the flexibility at a specific quantity and price, 9_P .Q.,
the ratio of quantity to the wholesale price will be larger than 9Q P
for the same quantity with the retail price. This would cause the
absolute value of the flexibility to be larger at the wholesale price
level, given a constant per unit marketing margin.
Since December 1964, the National Canners Association has published stocks of sold and unsold canned salmon held by packers.
18
2.
Consumers1 tastes and preferences have not changed during
the period of the analysis,
3.
Canned salmon has no restrictions as to areas of distribution and consumption in the United States.
4.
Fluctuations and trends in wholesale and retail prices of
canned salmon are equal over time.
5.
Opening wholesale prices for canned salmon are representative of the annual average wholesale prices.
6.
Stock levels of canned salmon are a function of the landings
in the previous year and the expected landings in the
current year.
Assumptions one and two are made for ease of analysis in interpreting the results of the demand analysis.
Using aggregate quan-
tities to identify the demand for processed salmon is associated with
a macro-relationship, assuming that the macro-relationship is a
summation of each individual or micro-relationships.
Coefficients of
demand for the macro-relationship are further assumed to be structurally significant.
As noted by Fox:
If all the elements of an aggregate can be depended upon
to change by the same arithmetic or logarithmic amounts,
the regression coefficient we obtain in arithmetic or logarithmic formulations, respectively, has structural significance (11, p. 525).
19
Using price as the dependent variable may not be in accordance with
a definition for a true structural equation set forth by Fox (11, p. 87).
"A structural relationship is to be distinguished from a purely empirical relationship not supported by any theory. " Traditional demand
theory identifies the quantity demanded of a commodity as the dependent variable; however, the argument that quantity supplies of processed salmon is independent of current price in the study does establish a theory for empirical testing.
Therefore, the assumption
is made that the coefficients of the variables in the equation with price
as the dependent variable are assumed to be structurally significant.
As specified in assumption three, the distribution of canned
salmon would not be limited to certain areas of the United States.
Canned salmon is not highly perishable and can be easily transported
and stored.
The results of a study of large urban areas by the Bureau
of Commercial Fisheries (21) indicated that canned salmon was consumed in all regions of the United States.
Therefore, the results of
this demand analysis should be applicable to consumers and household
units in the nation as a whole.
National income and consumption data
for substitute products can be used without injecting an undue amount
of bias into the analysis, unless regional influences are large.
The relative fluctuations and trends of wholesale and retail
prices of canned salmon are assumed to be the same as noted in
assumption four.
Table 1 shows the average annual wholesale and
20
Table 1.
The annual average wholesale and retail prices for a
16 ounce, tall, can of Pink salmon.
Wholesale
Price
Retail
Price
Difference
Dollars per Pound
1948
$0,454
$0,549
$0,095
1949
0.409
0.567
0.158
1950
0.382
0.476
0.094
0.475
0.618
0.143
1952
0.386
0.558
0.172
1953
0.394
0.528
0.134
1954
0.395
0.521
0.126
1955
0.436
0.559
0.123
1956
0.472
0.608
0.131
1957
0.472
0.625
0.153
1958
0.468
0.625
0.160
1959
0.486
0.620
0.134
1960
0.527
0.663
0.136
1961
0.583
0.743
0.160
1962
0.572
0.765
0.193
1963
0.502
0.710
0.208
1951
Note:
So\irce:
'
The retail price is an average of 46 cities. The wholesale
pricing point is based on one pricing point, Seattle, Washington.
Bureau of Labor Statistics and the Bureau of Commercial
Fisheries.
21
retail prices for Pink salmon. 12
There is some variation between
prices, especially in recent years where the price differential appears to have increased.
Wholesale and retail prices for Pink sal-
mon appear to move up and down together.
The correlation coeffi-
cient, r, between wholesale and retail prices, is equal to 0. 95 which
means that a high association exists between the two sets of prices.
For shorter periods of time, a time lag of adjustment would be expected for the retail price, but it is doubtful that any lags would exist
between the wholesale and retail prices on an annual basis.
Monthly
price data are shown for three years in Table 2.
Opening wholesale prices
for canned salmon are assumed to
be representative of the annual average wholesale prices as indicated
by assumption five.
Table 2, Appendix A, shows that both sets of
prices follow similar trends in annual variation.
The weighted aver-
age opening prices for salmon will be used as the price variable when
the demand equation for all five species of canned salmon is analyzed.
12
13
Pink salmon is used as an illustration because retail prices were
published for this species until 19 64. Pink salmon also accounts
for the largest percentage of the total pack, and is representative
of the total amount of salmon canned.
Opening prices are announced each year by the large fish processing firms that can salmon. The companies that announce these
opening prices for the pack are usually the ones that are in the top
ten in the production of canned salmon. A paper by Wood (25)
gives further details as to pricing in the salmon industry.
22
Table 2. Average monthly wholesale and retail prices for a 16 ounce, tall, can of Pink salmon
Wholesale
Price
Retail
Price
Difference
Wholesale
Price
Retail
Price
Difference
DOLLARS PER POUND
1961 - Jan.
0.576
0.708
0.132
1962 -July
0.574
0.775
0.181
Feb. 0.583
0.720
0.137
Aug.
0.570
0.775
0.205
Mar. 0.583
0.728
0.145
Sept.
0.531
0.759
0. 228
Apr. 0.583
0.735
0.152
Oct.
0.531
0.751
0.220
May 0.583
0. 739
0.156
Nov.
0.531
0.747
0.216
June 0.583
0.742
0.159
Dec.
0.531
0.741
0.210
July
0.583
0.746
0.163
Aug. 0.583
0.750
0.167
0.517
0.738
0.221
Sept. 0.583
0.755
0.172
Feb.
0.516
0.732
0.216
Oct. 0.583
0.761
0.178
Mar.
0.510
0.722
0.212
Nov. 0.583
0.766
0.183
Apr.
0.505
0.718
0.213
Dec. 0.583
0.769
0.186
May
0.505
0.721
0.216
June
0.500
0.718
0.218
1963 - Jan.
0.589
0.754
0.165
July
0.500
0.699
0.199
Feb. 0.594
0.771
0.177
Aug.
0.500
0.709
0.209
Mar. 0.594
0.772
0.178
Sept.
0.495
0. 696
0.201
Apr. 0.594
0.773
0.179
Oct.
0.488
0.689
0.201
May 0.594
0.773
0.179
Nov.
0.484
0.695
0.211
0.594
0.773
0.179
Dec.
0.488
0.691
0.203
1962 -Jan.
June
Note: The retail price is an average of 46 cities. The wholesale price is based on one pricing
point, Seattle, Washington.
Source: Bureau of Commercial Fisheries, and the Bureau of Labor Statistics.
23
Two primary reasons for using these prices are:
(1) time series
data for opening prices are available for all five species, and (2) a
large portion of the salmon pack is sold at opening wholesale prices
(14).
Assumption six is established with regards to estimating the
change in stock levels of canned salmon between years.
In the
model, stock levels changes will be estimated by the function,
A^t =cil -r—"•> where ^St is the estimated change in the stock level
^t
for year t, L is the quantity of landings, t is the time period. The
symbol aj is the parameter for the ratio of landings in the two time
periods.
Further details as to stock levels will be discussed under
the subheading, Explanation of Variables.
Equations of the Econometric Model
In this section the equations of the model for processed salmon
as depicted in Figure 3 will be formulated, with a detailed explanation of the important variables following the formulation of the equations.
The supply equations indicate the amount of processed salmon
supplied by wholesalers, with the annual salmon pack derived from
the quantity of landings in year t.
The single demand equation with
the wholesale price of processed salmon is formulated in (1. 6).
The
system of equations for processed salmon is formulated as follows:
24
Supply:
Kt = GQ+OJ^ + UJ
Identity:
(1.1)
Qf = K +1 +E,
^St
(1.2)
=
a1^2li
(1.3)
Ij
t
Identity:
QStS= Q^ + ^t
Equilibrium
Condition:
Demand:
.
(1.4)
QStS = QSt
P t - P 0 + P iQ t
(1.5)
+
^2(1.) + P MC
3
*%
'
+
P 4Nt
+ u
6
(1 6)
-
where
Endogenous Variable
ps = Wholesale price for canned salmon. For more than
one species this will be a weighted average price
(dollars per pound of processed salmon, deflated
by the Consumers1 Price Index).
Exogenous or Predetermined Variables
E = Exports of canned salmon (millions of pounds of
processed salmcm)
I = Imports of canned salmon (millions of pounds of
processed salmon)
K = Salmon pack (millions of pounds of processed salmon)
This variable does not include imports of canned
salmon.
L. = Landings of salmon (millions of pounds of fresh
salmon) The value of this variable, it is assumed,
is independent of current price, being largely biologically determined.
25
N
= Populations of the United States. Includes military
personnel and families living in the United States
(millions)
M
= Quantities of canned meat and meat products federally inspected (millions of pounds)
Q
Q
^
Q
g
ss
sd
S
Y
= Quantity of canned salmon supplied, net of changes
in inventories (millions of pounds of processed
salmon)
= Quantity of canned salmon supplied for consunaption
(millions of pounds of processed salmon)
= Quantity of canned salmon demand (millions of
pounds of processed salmon)
= An estimate of the change in stock levels of canned
salmon (millions of pounds of processed salmon)
= Disposable income of the United States (billions of
dollars, deflated by CPI)
The Oj's, (3.'s, and a
denote the parameters for the system.
The u.'s are the error terms for applicable equations.
period is identified by the subscript t.
The time
The p.'.s are the parameters
from which flexibilities with respect to price can be estimated.
The
subscripts r, p, and c will be used to identify variables that apply
to Red, Pink, and Chum salmon when individual species are examined.
Except for the weighted average wholesale price for all canned salmon, annual data will be used for all variables.
Sufficient wholesale
price quotations were not available to calculate annual averages for
canned Chinook and Coho salmon.
Therefore, opening wholesale
prices for each species will be used to calculate the weighted average
wholesale price.
26
Equations (1.2) and (1.4) are definitional equations.
Imports
a;nd exports, for purposes of this study, are assumed independent of
current price.
This assumption is discussed further on pages 28-31.
Data on changes in stock levels from year to year are not in sufficient.
quantities to be used in the analysis and must be estimated.
procedure for estimating a
given in Appendix B.
The
in equation (1.3) and calculating AS are
g
With the known quantity, Q , and the estimated
change in the stock level from the previous year, AS , the quantity
of processed salmon available for consumption, Q
ss
, can be obtained.
Ordinary least squares (O. L. S. ) will be used to calculate estimates for the parameters of equations (1. 1) and (1.6).
The following
pages give a more detailed explanation of the variables included in
the above model.
Explanations of Variables and Justification
for their Classification
Quantity Supplied (Q
ss
)
The main source for canned salmon is the domestic landings
taken each year.
On p a g e 2 it was noted that canned salmon accounted
for approximately 82 percent of the salmon landings.
Therefore, it
can be hypothesized that the amount of salmon canned is directly
proportional to the quantity of salmon landed, and independent of the
current price.
Other forms by which salmon is marketed are fresh
27
and frozen, salted and cured, and smoked.
Salmon entering these
markets are usually caught by trolling gear as opposed to the net-type
gear used for salmon to be canned.
The primary fishing season for salmon extends from the months
of May through October.
The time and length of the season will vary
from region to region, and also in accordance with existing government regulations regarding the number of days it is legal to catch
salmon in each of the Pacific Coast fisheries.
14
For example, the
■*
seasonal catch of Red salmon in Bristol Bay, Alaska, may be taken
within a two to three week period in July depending on the magnitude
of the run and seasonal regulations set by government agencies.
The
season for Chinook and Coho in the Columbia River may run in excess
of three months (7, pp. 12-14).
Regardless of the number of fisher-
men, types of gear, and length of the season, the annual run of salmon is the primary determinate of the quantity caught.
Regulations
are established to help insure that a sufficient number of adult salmon escape inland to spawning areas in order to replenish the natural
stock for future years.
Thus, for the combined reasons that (1) the
quantity of salmon landed can b e reasonably assumed to be
14
Important agencies that regulate the fishing seasons and escapement
of salmon in the Pacific Coast fisheries are the International Pacific Salmon Fisheries Commission, the Alaska and Washington
Department of Fisheries, the Oregon Fish Commission, and the
California Department of Fish and Game.
S
28
|
independent of current price, and (2) most salmon is sold in the
canned form, the salmon pack is treated in this model as predetermined..
The quantity supplied of canned salmon, Q
as predetermined in the model.
ss
, will be treated
Imports, exports, and stocks of
canned salmon will be discussed on the following pages.
Imports (I)
Imports of canned salmon do not represent a significant portion
of the total supply in the United States because in recent years imports have declined to relatively insignificant amounts.
During the
late ^SO's imports of canned salmon represented 15-20 percent of
the total canned supply; however, in recent years the percent of the
total supply has been less than one.
15
Column 13, Table 4, Appen-
dix A, shows the quantity of imports for canned salmon,
Imports
for the United States come wholly from Canada and Japan (18).
{
f
i
A
breakdown of imports by species is not available from the Bureau of
f
Commercial Fisheries, but according to the Pacific Fisherman, im-
j
ports of Pink and Red salmon appear to be most prevalent.
15
Calculated from data published by the Bureau ol Commercial
Fisheries (23, p. 47).
29
Possible factors affecting the amount of imports could be the
relative price ratios between countries, domestic tariffs on canned
salmon, and the quantity of domestic and foreign landings.
It can be
postulated that a larger quantity of domestically supplied salmon
would cause prices and imports of canned salmon to be lower than
for a smaller domestic supply.
In the late ^SO's and I960, the
annual packs were low causing prices and imports to be generally
higher than in other years of the 21 year period.
The above relation -
ship can be seen by comparing Figures 4 and 5, and the wholesale
prices in Table 3, Appendix A.
The tariff on canned salmon was re-
duced from 25 to 15 percent in 1952, and has remained at this percentage through 1967.
The reduction in the tariff rate enabled prices
of Canadian imports to compete with prices of American canned salmon (16).
No doubt, the tariff reduction caused imports to increase
considerably after 1952, but the sudden decrease after 1959 cannot
be attributed to a tariff increase on canned salmon.
The postulated
relationship would still appear to be applicable because the general
level of annual packs since 1961 as shown in Figure 4 increased over
those in the late 1950ls.
Since imports of canned salmon have not represented a significant percentage of the total supply for the 21 year period of analysis,
the variable will be assumed independent of current price.
30
a,o
o
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
Year, 19
Figure 4.
The imports of canned salmon for the United States, 1947-1967.
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
Year, 19
Figure 5.
The pack of salmon for the United States, 1947-1967.
Commercial Fisheries.
Source: Bureau of
31
Exports (E)
Exported quantities of canned salmon have shown significant
increases since 1961.
Column 14, Table 4, Appendix A, shows the
amounts of exports since 1947.
Since 1957, the annual average
exports for canned salmon have been only nine percent of the total
canned salmon supply.
16
Increased exports could be influenced by
rising foreign demand caused by increased standards of living.
One
of the biggest foreign buyers of canned salmon is the United Kingdom,
which specializes in purchases of Sockeye salmon.
17
Exports by
species are not available from the Bureau of Commercial Fisheries;
however, it can be assumed that Sockeye and Pink salmon are the two
species that have the largest quantities exported.
Exports will be
treated as independent of the system, their magnitudes being determined largely by conditions in importing countries.
Stock or Inventories (S)
Changes in stocks of canned salmon from year to year influenced
the quantity available for consumption.
This is especially true for
canned salmon since the preparation of the product makes for easy
Calculated from data on canned salmon exports (25, p. 47).
17
It was reported in 19 64 that one particular British firm bought
(from both the United States and Canada) one million cases of Sen 1eye salmon, about one-third of the world supply in that year (-1).
32
storage without the need for refrigeration.
Carryover from season
to season occurs because the product is non-perishable.
18
As previously mentioned, landings in year t-1 and the expected
landings in year t are hypothesized to affect the level of carryover
from year to year.
Carryover stocks at the end of year t-1 are de-
pendent upon prices in year t-1 and expected prices in year t.
These,
in turn, are partly dependent upon landings in years t-1 and t, respectively.
As already explained, data are not available on carry-
over stocks for years prior to 1964.
Equation (1. 3), then, is simply
an attempt to account for changes in carryover stocks in the econometric model.
It is not truly a structural or behavioral equation but,
rather, is included for completeness and ease of analysis.
The cost
of storage is also a consideration, and would be expected to have
some influence on the level of inventories; however, for this analysis
only landings of salmon in the previous and current years will be
used to estimate stock levels.
19
The supply of processed salmon available for consumption can
now be stated as:
18
19
Pack + Imports + Changes in Stocks - Exports =
Carryover as of 1 July marks the theoretical opening of the canning
year. Evidence of carryover from one season to the next is noted
in publications of stock levels by the National Canners Association.
See Appendix B for the estimation procedure for accounting for
changes in stock levels.
33
Quantity Available for Consumption.
This relationship can be adopted
for any species of canned salmon as long as known or estimated quantities are available.
As specified in equation (1.5), in equilibrium,
the quantity supplied equals the quantity demanded.
Prices (Ps)
The reason for using the wholesale price of canned salmon as
the dependent variable was given in the Introduction and the relationship between wholesale and retail prices of canned salmon was discussed under the subheading, Limitations and Assumptions.
In this
section a discussion of the differentials between prices of species,
and the ex-vessel price will be presented.
The basis of price differentials for the species of salmon, Red,
Pink, Chum, Coho, and Chinook, results mainly from consumer
preference.
This is based principally on color and oil content, and
from the natural abundance of the respective varieties
as related to consuming demand, with little or no distinction as to nutritive value or flavor. Thus the lower
priced salmon packs are not inferior or less carefully
prepared fish of the same kind, but are actually
different varieties from the more expensive (17, p. 6).
The higher priced canned salmon are Chinook, Sockeye, and Coho,
with Pink a medium priced variety, and Chum the lowest priced
variety.
Wholesale prices for Sockeye, Pink, and Chum are tabulated
in Table 2, Appendix A.
Deflated wholesale prices for all five species
34
species are given in Table 3, Appendix A.
It is assumed that relative differences in prices of the five
species at the wholesale level are carried forward to the retail level;
however, no complete series of retail prices are available for comparison.
Although the ex-vessel price will not be used for this analysis,
it is noteworthy to briefly explain how it is determined.
Ex-vessel
prices are determined prior to the opening of the season by negotiations between representatives of both fishermen's unions and processors.
Once the price is established, it is the minimum that will
be paid to fishermen for their catch throughout the season.
The
predicted magnitude of the salmon run for the forthcoming season
would be expected to influence the negotiated prices for the season.
Different pricing agreements occur in various coastal areas with
rather complicated agreements being established between fishermen
and processors.
Ex-vessel prices are higher for salmon caught by trolling gear
as opposed to purse seines and gillnets.
Trolling is of some importance as a measure of catching
salmon for the fresh, frozen, and cured markets, but
salmon taken by this method is rarely canned due in
large part to the high cost of this type of fishing
(18, p. 18).
The conclusion can be made that troll-caught fish are excluded from
this analysis because these enter the fresh and cured markets.
35
In summary, the basic characteristics of ex-vessel prices
are:
(1) established prior to the opening of the commercial fishing
season, and (2) the accepted minimum price that will be paid to
fishermen.
The ex-vessel pricing arrangement is contrasted with
wholesale and retail prices of salmon which are not negotiated.
Quantity Demanded (Q
sd
20
)
For the analysis, quantity demanded is that which is supplied
from the wholesale level of the market.
The amount supplied is
treated as a predetermined variable which would also allow the
quantity demanded to be predetermined in the demand equation.
A negatively sloped demand curve for processed salmon can
be assumed which would identify an inverse relationship between
price and quantity of processed salmon.
This is best illustrated by
the graphical relationship in Figure 6.
20
An unpublished paper by the author (25) advanced the hypothesis
that due to the concentration of processors of salmon in the fish
processing industry, wholesale prices may be controlled to some
degree by the large processing firms in the industry. Evidence of
this was noted by the announcement of the same opening prices for
the salmon pack by two or more of the large processing firms. The
wholesale level and processors were treated as one and the same.
36
Price
D-retail
Quantity
Figure 6..
The relationship between the price and quantity of
processed salmon at the wholesale and retail market
levels.
The wholesale and retail demand curves are assumed to be
parallel. For a particular quantity, Q, the wholesale and retail
prices are assumed to be P
and P , separated by a constant margin
as implied by assumption four, page 18.
The demand from the whole-
sale level would be a result of a derived demand at the retail or consumer level.
As implied in Figure 6, increases or decreases in the
quantity of processed salmon would cause both prices to decrease
and increase, respectively.
Other variables affecting demand held
constant.
A statement by McGowan indicates that quantity of salmon
demanded may not be limited by consumer acceptance, but by the
limitation of the salmon resource.
37
The volume of canned salmon consumed in the U.S.
is not limited by lack of acceptance of the product in the
market, but rather by the limitations of the resource and
conservation requirements. Canned salmon has demonstrated that it responds well to retail price features. If
continuing research points the way to improved resource
management, there is no reason that increased quantities
of canned salmon cannot be successfully marketed, provided costs are kept in line with competing seafoods products
and other protein foods (15, p. 217).
The viewpoint of McGowan suggests a similar relationship to quantities and prices for canned salmon as depicted in Figure 6.
Implica-
tions from the above statement seem to indicate that larger quantities
of canned salmon will be accepted by consumers providing prices arc
able to be adjusted to meet the larger quantities and not forced upward by increasing costs.
A negative relationship is expected to
exist between the wholesale price and quantity of canned salmon in
the demand equation, (1. 6).
Income (Y)
Y
Pe:-: capita disposable income, — , and disposable income, Y,
will be used to measure the effects of income on prices.
Equation
Y
(1. 6) shows only — as the income variable; however, Y will be substituted into different variations of the basic demand equation when
regressions are run.
Both approaches should give an indication as
38
to the effects of income on prices of processed salmon.
21
A positive
relation should exist between income and prices unless the wholesale
price of processed salmon is decreasing relative to increases in income.
Y
Both Y and — will be treated as independent of the system.
With price as the dependent variable, estimates for the income elasticity of processed salmon cannot be calculated with any accuracy.
Previous research for fish products indicated that per capita consumption of fish does not increase with rises in per capita income
(2).
A study by Purcell and Raunikar (19) in Atlanta, Georgia, indi-
cated that the per family consumption of salmon increased as inconae
rose, but after 6000 dollars annual income, the per family consumption of salmon declined.
Substitutes (M)
Salmon in all its forms is essentially a protein food.
As such
it must be marketed as a substitute for certain protein bearing foods
21
Y
Aggregate disposable income is equal to (N« —) or Y. For the
demand equation, the partial derivative of price with respect to
Y would be >£, = b., other variables constant, and where b^ is the
coefficient °*
for Y. For Y , aggregate disposable income,
Y, is deflated by population. The^ partial derivative with respect
to _ would be__9j__ = hi, other variables constant, and where b.
J
J
N
9(Y/N)
is the coefficient for Y/N.
39
common to the diet of the average household (6, p. 108).
Other
canned fish products such as tuna would be expected to serve as
direct substitutes also.
22
Therefore, canned tuna may well be in-
fluential in determining the price of salmon.
Using ordinary least
squares to estimate the parameters in a single demand equation with
the quantity of canned tuna as a substitute would not be justified because the price of canned salmon and the quantity of canned tuna consumed would depend on each other.
as endogenous.
Both would have to be classified
This would then require more than one equation to
specify the demand function for canned salmon.
The following two
equations serve as an illustration.
ps =p0 + ^Q86 + p2Y +p3Mt + p4N + u7
(1.7)
M* = V0 + ^p* + Y2ps + u8
(1.8)
Prices of canned tuna and salmon are p and p8, respectively.
and Q
M1
are the quantities of canned tuna and salmon, and Y and N
are the income and population, respectively.
The (3 .'s and y.'s
are the parameters of the two equations with the u.'s, the error term
associated with each equation.
22
For illustrative purposes, those
If a consumer was not particular as to whether salmon or tuna was
used in a fish loaf, price of the commodity would certainly be a
factor in determining which was purchased.
40
variables other than ps and M* in the equations can be classified as
exogenous or predetermined to the system.
In reality the quantity
demanded of salmon may well depend on the price of tuna; however,
to simplify the demand function to a single equation as specified in
the model, the quantity of canned meat and meat products will be
used to measure the cross-flexibility with respect to the price of
processed salmon.
The relationship between canned meat and pro-
cessed salmon is unknown, whereas processed salmon and canned
tuna are both fish products, it can be hypothesized that each is a
substitute for the other in consumption which is an argument for a
multiple equation demand function rather than a single equation function.
If a positive relationship exists between the price of salmon
and the quantity of canned meat, the meat could be classified as a
substitute for processed salmon.
If a negative relationship occurs,
the two commodities could be complementary to each other.
For
canned tuna, a positive relationship would be expected between the
price of processed salmon and the quantity of canned tuna because
one is hypothesized to be a substitute for the other.
meat, the relationship is unknown at this point.
For canned
The quantity of
canned meat and meat products will be exogenous to the demand
equation.
41
Population j[N)
The population of the United States is included in the demand
equation to note its effects on the price of processed salmon.
The
population of the United States has been steadily increasing for the
period of analysis as noted in Table 4, Appendix A.
Figure 7 is
included.to aid in explaining the expected relationship of population
with population with price and quantity of processed salmon.
Price
Quantity of Processed
Salmon
Figure 7.
The affects of population on prices of processed salmon
For simplicity purposes, assume in Figure 7 that population
consists of one person with a demand function, D .
of processed salmon consumed at P, is Q,.
The quantity
Suppose the population
increases by one person who has a demand function identical to that
of the original person, where OQ.. = Q Q .
Therefore, the demand
function for the population is now D , and the quantity demanded at P
is Q2; however, if quantity available for consumption does not
42
increase and remains at Q , then the price for Q
to increase to P .
would be expected
For salmon, the effects of population on the price
in a specific year will be influenced by the quantity supplied for consumption in that year.
In addition, to using the population as a single
variable in the demand equation, an additional demand equation will
be analyzed with the quantity demanded of processed salmon multiplied by the population, (Qs • N).
The partial derivative of price
with respect to quantity will then allow for the effects of quantity on
price to be evaluated at a specific population.
Results of the equation
are given in Table 3, page 46.
Summary of the Model
Equations (1. 1) through (1. 4) of the model identify those variables that are responsible for determining the supply of processed
salmon from the wholesale level of the market.
The size of the
annual pack is hypothesized to be directly influenced by the landings
of the same year, and is the major factor that contributes to the
domestic supply.
Imports, changes in stock levels, and exports are
the remaining factors that determine the supply available to consumers.
The quantity supplied is then equal to the quantity demanded as
noted by equilibrium conditions in. (1. 5).
The basic demand equation for processed salmon with the
expected signs for the parameters is as follows:
43
pS = p0 -P1Qsd+P2 |- + P3MC+P4N + u
(1.9)
The equation as shown would be expected to maintain the same relationship between parameters when examining individual species as
well as the aggregate quantity of processed salmon.
Prices and
income will be deflated by the Consumers1 Price Index (CPI) to
account for inflationary movements of prices and incomes.
As
noted by Footer
If we have reason to believe that a doubling of all
prices and incomes variables has no effect on consumption, effects of the general price level should be allowed
by deflation, that is, by dividing each price, income, or
marketing margin variable by a variable such as the
Bureau of Labor Statistical Consumers' Price Index
(9, p. 27).
44
STATISTICAL RESULTS AND INTERPRETATIONS
Supply
Equations (1. 1) through (1.4) of the supply-demand model estimate the quantity of canned salmon available for consumption.
Data
for the supply variables were available from printed sources except
stock levels which had to be estimated.
23
Equation (1. 1) implies the hypothesis that the quantity of landings, not the current price of salmon, determines the annual salmon
pack.
To test this hypothesis, the quantity of the annual pack for
Pink, Sockeye, and Chum was regressed against the annual landings
for these three species.
Parameters of (1.9) were estimated by
ordinary least squares.
K
prC
= 15. 046 + 0.579 L
; R2 = 0. 922
(14.571) prC
(1.9)
The annual pack and landings of the three species are noted by K and
L.
The coefficient of determination, R , equals 0. 922 which means
that 92.2 percent of the variation in the salmon pack is explained by
23
Data for canned imports and exports for individual species are hot
available from the Bureau of Commercial Fisheries. It is assumed
that both factors account for only small changes in the amount
available for consumption. In the analysis of the individual species
only the pack and estimated stock levels will be considered as
affecting supply.
45
the quantity of landings.
The large t value in parenthesis indicates
the relationship is statistically significant at the one percent level.
Pink, Sockeye, and Chum averaged 91. 9 percent of the total pack of
salmon from 1960-1967, and can be assumed to have maintained a
similar percentage for the years 1947 to I960.
The result of the
regression analysis substantiates the hypothesis that the pack of
salmon is independent of the current price of salmon, and is directly
influenced by the quantity of landings.
Table 1, Appendix B, shows estimates of the stock levels obtained by the function in equation (1. 3) for the years 19 65-1968.
Demand
All Canned Salmon
Equations a through e in Table 3 show the results of the statistical analysis for all canned salmon with price as the dependent
variable.
Four of the five equations had negative signs for the co-
efficients of Qs and R.
The capital letter R will be used to denote
the ratio Ltt" 1 . This would mean an inverse relationship exists
Lt
between the quantity of canned salmon and the price which is consistent with a priori reasoning.
A negative relationship was still main-
tained between price and quantity by using per capita data as noted
in equation d. For equations a through d, price flexibilities calculated
Table 3.
Equation
Number
Regression results for canned salmon with price as the dependent variable.
Species
Constant
Only. Canned
Salmon
,sd
P.C. Canned
Salmon
Canned
Salmon
w/o R
0Sd/N
T.l.D.
Inc.
»sd
0 -N
Y/N
Agg.D.
Inc.
Y
Qnty.
Canned
Meat
MC
P.C.
Canned
Tuna
MVN
Qnty.
Canned
Tuna
M1
U.S.
Population
All
-0.00072
(-1.355)
-0.243
0.00013
(0.666)
0.443
-0.00004
(-0.365)
-0.163
-0.00039
(-0.095)
-0.230
b
All
-0.00087
(-1.252)
-0. 327*
-0.01856 0.00013
(-0.228) (0.638)
0.444
-0.00007
(-0.597)
-0.287
-0.00005
(-0.077)
-0.017
c
All
-0.00022
-0.00119 9.00066
(-0.020) (2.236)
2.251
-0.00007
(-0.586)
-0.285
(-1.614)
-0.072*
d
All
e
All
f
g
Chum
PinV & Chum
-0.00005
(-0.188)
-0.171
-0.10967
(-0.861)
-0.249
0.54537
0.56974
0.00204
(0. 706)
0.778
-0.00815
0.00055
(0. 773)
0.298
-0.00403
(-3.456)
-0.627*
-0.09337 0.000007
(-3.591) (0.048)
0.031
-0.00013
(-1.381)
-0.691
0.00214
(0.704)
0.892
0.00005
(1.179)
0.115*
0.04267
0.00002
(1.369)
(0.090)
-0.00002
(-0.149)
-0.095
0.0014O
(0. 368)
0.525
-0.05673 -0.00009
(-2.288) (-0.640)
-0.241
0.000009
(0.114)
0.029
0.00251
(0.897)
0.630
0.080
h
Sodteye
-0.00072
(-1.280)
-0.150*
i
Sockeye
-0.00240 0.000013
(-0.587) (0.572)
-0.195
0.182
-0.00039
(-0. 734)
-0.182
Note: The coefficients of the equations show arithmetic relationships.
Price is in dollars per pound. Quantities for Q5", Qs, (Qsc** N), M0, M1 are in millions of pounds.
S(
Q VN', MVN are in pounds. Y/N is in dollars. Y is in billions of dollars. N is in millions, and R is a simple ratio.
t-values are in parentheses. Flexibilities with respect to price are calculated at the mean values and are directly
beneath the t-values in the Table.
* Pcjce flexibilities calculated at the mean values are adjusted for stock levels, where Q
** R is the coefficient of detemiination.
= 0+a R
C = 18
C = 18
-0. 07924
(-2.447)
-0.00903
(-0.534)
-0.01240
(-0.389)
0.01484
(0.628)
-2.606
-0.00300
(-0.026)
-0.009
0.00003
(0.053)
0.018
-0.000017
(-1.034)
-1.159
Cos(ct)0
N
a
(-0. 852)
Sin(ct)0
0.00040
(0. 989)
0.170
^^
47
at the mean values ranged from -0. 072 to -0. 327.
For example, the
flexibility of equation Is indicates that a ten percent increase in volume (quantity demanded) would result in only a 3. 3 percent reduction
in price.
Therefore, the results of the analysis would indicate that
gross receipts are greater with increases in the quantity demanded,
or with decreased quantity, gross receipts decline.
As noted in
equation a, with the exclusion of stocks from the equation decreases
in the price of canned salmon would be less with increases in volume.
According to Houck (12) the inverse of the price flexibility establishes
a minimum estimate for the price elasticity.
For equation b, the
estimated price elasticity is -3.4 which would indicate that the demand for canned salmon is elastic.
Four of the five equations for all salmon indicated a positive
relationship between income and price.
Using equation
ID
as an
example, the income flexibility calculated at the means indicates
that a ten percent increase in income would increase the price ot
canned salmon 4. 5 percent for given values of all other variables.
A negative relation exists between the quantity of canned meat
and meat products and the price of canned salmon.
As noted in
equation b, a ten percent increase in the quantity of meat demanded
would be associated with a 2. 9 percent decline in the price of
canned salmon.
However, t-values are too low to preclude the
1i
i
48
rejection of the hypothesis that the coefficients are zero. ^
j
Equations d and e were included to note the effects of the
quantity of canned tuna on the price of canned salmon.
;
A negative
relationship for canned tuna in equation <d existed using per capita
data, and a positive relationship occurred using aggregate quantities
in equation e.
A priori reasoning as discussed on pages 39 and 40
would indicate that a positive relationship should exist between the
i
price of canned salmon and the quantity of canned tuna. . The negative
sign of the coefficient for canned tuna in equation d would not reject
the hypothesis that the two commodities are substitutes because the
I
j
t-value is low which would preclude any conclusions from being made.
i
The inverse relationship of the population with price indicates
that increases in population do not cause the price of canned salmon
to increase.
The variable, (Qs . N) was included in equation e_ to
measure the effects of the quantity of canned salmon on price at a
designated population, N.
The relationship would then allow the
effects of quantity on the salmon price to be evaluated at a specific
population.
24
25
25
From the discussion about population beginning on
With 15 degrees of freedom, t-values have to be at least 1.753
and 1. 341 to be significant at the 10 and 20 percent levels.
The partial derivature of price with respect to quantity for this
expression would be of the form — ^ = bi + b2S(j(N); where b-^ is
the coefficient for Qsd, bz the 9Q coefficient for Qsd. N).
49
page 41, a negative demand curve would be expected.
The results
of equation _e show a negative relation between price and quantity
when the cross-product term is taken into consideration.
The variables in equations b and £ are the same except for the
sine and cosine functions in equation^.
The inclusion of sine and co-
sine functions was designed to account for variables which might
have had a systematic influence on price but which had not been ineluded in the model.
With an increase in the R
2
statistic, the size
of the coefficients and corresponding t-values of all variables
c
except M were changed; however, the signs remained the same.
Individual Species
Three of the four equations in Table 3 show negative relationships between the price and quantity of the individual species.
Only
the coefficient for the quantity of Pink and Chum taken together shov/s
a positive sign.
As shown in equation_f and h> results of the price
flexibilities taken at the mean values indicate that a ten percent
increase in the quantity demanded of Chum and Sockeye would reduce
price only 6.3 and 1.5 percent, respectively.
Therefore, total
revenues would increase for all three species with increases in
quantity demanded.
Both positive and negative relationships occur between prices
and income for the individual species.
In all equations the t-values
50
are such that one cannot reject the hypothesis that the coefficients
are equal to zero.
Conclusions as to the effects of income on prices
of the individual species are not possible.
The cross-price flexibilities with canned meat are negative
in all cases except for Sockeye.
The negative relationship is con-
sistent with that obtained for all canned salmon.
For example, the
cross-price flexibility for Chum calculated at the means, shows that
a ten percent increase in the quantity of canned meat would decrease
the price of canned Chum by 6. 9 percent.
The price of canned Sockeye showed a positive relationship
with the quantity of canned tuna (equation^) which would substantiate
the hypothesis that canned salmon and tuna are substitutes in the
market.
The effects of population on the price of the individual species
are positive, which would be in agreement with the a priori reasoning put forth on pages 41 and 42.
For Sockeye salmon, for example,
a ten percent increase in population would increase price to 6. 3
percent, as noted in equation h.
The t-values for the population
variable of the equations i_ through h are not large enough to reject
the hypothesis that the coefficients are different from zero, which
would allow little confidence to be placed on the results.
The quantity of canned tuna in equations ^andj^ was included
to observe its effect on the R^ statistic.
To treat tuna as independent
51
of the price of canned salmon and maintain a single equation demand
model would be contrary to the argument put forth earlier in this
paper.
The correlation matrices between variables for the important
equations of Table 3 are listed in the tables of Appendix C.
Quantity of Canned Salmon as the Dependent Variable
By using the quantity of canned salmon as the dependent variable in place of price, more significant results occur.
The whole-
sale price of canned salmon now becomes an explanatory variable
with the other variables on the right hand side of the demand equation.
Under the present classification, both the price and quantity
of canned salmon would be endogenous, requiring multiple equations
to be used in the demand model.
For this example, price will be
temporarily assumed to be exogenous so that a single demand equation can be analyzed to illustrate the improved t and R^ statistics
with the quantity of canned salmon as the dependent variable.
(2.1)
Qsd = 477. 105 - 124. 078 ps - 0. 045 (~) + 1. 004 pm
(-1.363)
(-0.590)
(1.293)
-0.325
-0.402
0.481
_
R2
.sd
Q
- 1. 290 N
(-1.270)
-1.083
= 0..747
(2.2)
= 1.513 - 0.442ps - 0. 001 (-^-) + 0. 05 Ipt + 0. 007pmiP
N
(-0.933) (-4.165)
(3.973)
(1.585)
-0.195
-1.173
0.559
0.573
R2 = 0.915
52
The first equation expresses the variables in aggregate quanY
titles, except for the per capita disposable income, — .
The price
index for all meat, Pm, was used in place of the quantity of canned
meat.
Population is identified as N.
Equation (2. 2) expresses per
capita quantities with the wholesale price of canned tuna and the
consumer price index for meat, fish, and poultry, P
, added as
an explanatory variable.
Prices and incomes are deflated by the
Consumer Price Index.
The t-values are noted in parenthesis and
the elasticities calculated at the mean values are directly beneath
the t-values.
Results of both equations are similar indicating
negative results for both price and income coefficients, and positive
relationships with the prices of canned tuna and other meats.
Research-by the Bureau of Commercial Fisheries identified
single demand equations for canned salmon similar to equation
(2.2).
Per capita consumption of canned salmon was used as the
dependent variable with the wholesale price of canned salmon, per
capita income, the wholesale price of canned tuna, and the Consumer
Price Index for meat, poultry, and fish as explanatory variables.
The results of the regression using ordinary least squares were
26
The results of selected canned salmon equations were received
by a letter (dated July 7, 1969) from Darrel A. Nash, Chief,
Branch of Demand and Marketing Research, Bureau of Commer
cial Fisheries, College Park, Maryland.
53
similar to those obtained in equation (2.2).
(2. 2), the quantity of canned salmon Q
estimated change in stock levels, S.
sd
For equations (2. 1) and
is a function of Q
s
and the
This quantity of canned sal-
mon may be different than used for research done by the Bureau.
54
CONCLUSIONS AND RECOMMENDATIONS
In the introduction three objectives were set forth to be accomplished in this research project.
Each will be discussed as to degree
of accomplishment in this research.
A supply-demand model was developed.
First, those factors
that contribute to the supply of canned salmon available for consumption were examined.
The domestic landings of salmon are the most
important source from which the pack is made.
It was determined
that approximately 82 percent of the total landings are processed
into the canned form for marketing to the consumer.
Imports of
canned salmon during the 1947-67 period were never more than 20
percent of the total supply, and in recent years have dropped to
less than one percent.
Exports have increased but amount to only
an average of nine percent of the total supply since 1957.
Since chang-
es in stock levels were not available, a variable to estimate the levels
in year t wa.s postulated to be a function of the ratio of landings in
the previous year, t-1, with the landings for the current year, t.
The quantity of canned salmon available for consumption then becomes
a function of:
(1) the pack, (2) imports, (3) changes in stock levels,
and (4) exports.
In the demand equation the wholesale price for canned salmon
•was used as the dependent variable.
The basic reason for classifying
55.
the price as dependent was that the nature of the supply of salmon
was predetermined and not affected by the current price.
Factors
designated as affecting the price were the quantity of canned salmon
demanded, which in equilibrium equalled the quantity supplied, the
per capita disposable income, the quantity of canned meat and meat
products, and the United States population.
Coefficients for the demand equation expressed flexibilities
with respect to price rather than elasticities as generally associated
with identifying quantity as the dependent variable.
Price flexibili-
ties calculated at the mean values for all canned salmon indicated
that a ten percent increase in volume would reduce price by a lesser
percentage.
Signs of the coefficients for Sockeye and Chum were
also negative which indicated that a quantity increase would cause
total receipts to increase.
Pink and Chum together showed a positive
relationship between price and quantity.
For increases in the supply
of canned salmon, total revenues would appear to increase, and with
decreases in supply, the percentage change in price would be smaller
causing total revenues to decline.
The hypotheses that the demand
for canned salmon is elastic cannot be rejected as a result of the
study.
For all equations except for Sockeye, income showed a positive
effect on the price.
Therefore, it can be concluded that as disposable
income increases, the price of canned salmon will also increase.
1
56
.;
■...■'.
.
Ho\vever, calculated values of the t statistics were low.
t
I
Negative cross-flexibilities of canned salmon with canned
■
i
'
meat would indicate that two products are not substitutes for each
other.
The t-values were not large enough to allow for the rejection
of the hypothesis that the coefficients were different from zero; however, it is possible to put forth the hypothesis that canned salmon
and canned meat and meat products are not substitutes for each other.
For all canned salmon, a negative relationship existed between
the price and population.
j
From this it would appear that population
increases do not cause increases in prices of canned salmon taken in
il
i
i
aggregation.
For individual species, positive relationships existed;
f
however, the t values for the population coefficients were not significant which would allow little confidence to be placed in the results.
The results of this research would indicate that the salmon
industry would benefit by maximizing output.
Increased volume of
canned salmon would cause prices to decrease by a smaller percentage which would cause total revenues to increase.
The conser-
vation and restrictions associated with limiting the exploitation of
the salmon resource would appear to dampen the efforts to increase
the volume of canned salmon produced in the short run.
It would
appear that increases in volume would occur only through the
57
fluctuations in the natural runs of salmon each season; however
if in the long-run conservation leads to increases in the overall
level of catch, then the industry may benefit from the larger output.
McGowen (15) noted in his paper that consumption of canned salmon
responded well to price features which would give further evidence
that larger quantities can be marketed if prices are adjusted accordingly. .
One might argue that further research on the demand for
salmon should use a multiple equation approach to specify the demand function.
Perhaps a more significant and realistic result
would be obtained with this type of approach.
For example, with
the price of salmon as the dependent variable and the quantity df
tuna as one of the explanatory variables, both would be classified
as endogenous and require at least two equations for the demand
model.
With multiple equations the technique of simultaneous
equation could be used to obtain estimates for the parameters of
the equations.
Intraseasonal analysis would allow variations in demand for
processed salmon to be identified for shorter periods within a year.
As noted in Table 2, page 22, monthly wholesale prices of canned
Pink salmon show some variation which could be assumed to be
attributed in some degree to changes in demand for the commodity.
58
As noted by Purcell and Raunikar (19) in their study, differences
in consumption levels for salmon were observed throughout the year.
The use of an intraseasonal demand approach would appear to be a
step closer to reality.
59
BIBLIOGRAPHY
1.
All canned fish freed of price control.
51(4):59. 1953.
Pacific Fisherman
2.
Bell, Frederick W. Economic and institutional factors affecting the demand for fish and shellfish. In: The future of the
fishing industry of the United States. Seattle, 1968. p. 185190. (University of Washington. Publications in Fisheries,
new ser., vol. 4).
3.
Bell, Frederick W. and Jared E. Hazleton (eds. ). Recent
developments and research in fisheries economics. New York,
Oceana, 1967. 233 p.
4.
Chairman of John West i'oods comments on salmon prices.
Pacific Fisherman 63(9): 24. 1965.
5.
Cooley, Richard A. Politics and conservation.
Harper and Row, 1963. 230 p.
6.
DeLoach, Daniel B. The salmon canning industry.
Oregon State College, 1939. 118 p.
7.
Gregory, Homer E. and Kathleen Barnes. North Pacific
fisheries. New York, Haddon Craftsmen, 1939. 322 p.
8.
Ferguson, C. E. Microeconomic theory.
Richard D. Irwin, 1966. 439 p.
9-
Foote, Richard J. Analytical tools for studying demand and
price structure. Washington, D. C., 1958. 217 p. (U.S.
Dept. of Agriculture. Agriculture Handbook no. 146).
New York,
Corvallis,
Honaewood, Illinois,
10.
The analysis of demand for farm products.
Washington, D. C., 1953. 99 p. (U. S. Dept. of Agriculture.
Technical Bulletin no. 1081).
11.
Fox, Karl A. Intermediate economic statistics.
John Wiley, 1968. 5 68 p.
12.
Houck, James P. The relationship of direct price flexibilities
to direct price elasticities. Journal of Farm Economics
47:789-792. 1965.
New York,
60
13.
Idyll, Clarence P. The incredible salmon.
graphic Magazine 134:195-219. 1968.
14.
Initial prices for canned salmon.
48(13): 155. 1968.
15.
McGowan, John S. Past, present, and future for canned fish.
In: The future of the fishing industry of the United States.
Seattle, 1968. p. 216-220. (University of Washington.
Publications in Fisheries, new ser., vol^ 4).
16.
Markets, salmon.
17.
Pacific fisherman's canned fish hand-i-book.
Fisherman 48(2): 224 (p. 1-32). 1950.
18.
National Geo-
National Fisherman
Pacific Fisherman 51(2): 141.
1953.
In:
Pacific fisherman's canned fish hand-i-book. 3d ed.
Pacific Fisherman 59(10): 24-57 (p. 1-32). 1961.
Pacific
In:
19.
Purcell, J. C. and Robert Raunikar. Analysis of demand for
fish and shellfish. Georgia Station, 1968. 37 p. (University
of Georgia. College of Agriculture Experiment Stations.
Research Bulletin 51).
20.
Sosnick, Stephen H. Orderly marketing for Ca lifornia
avocados. Hilgardia 33:707-772. 1962.
21.
U. S. Fish and Wildlife Service. Bureau of Commercial
Fisheries. Canned fish consumer purchases. Washington,
D.C., Oct., 1958-Sept., 1959. Various paging. (Fishery
Leaflet no. 47 8 a-k).
22.
Fisheries of the United States.
Washington, D. C., 1966. 75 p.
Vol. 4400.
23.
Fisheries of the United States.
Washington, D. C.,1967. 101 p.
Vol. 4700.
24.
Waugh, Frederick V. and Virgil J. Norton. Some analyses
of fish prices. Washington, D.C, 1969. 194 p. (U. S.
Bureau of Commercial Fisheries. Working Paper no. 22).
25.
Wood, William R. The market structure of the salmon industry. Paper presented for a seminar class on industrial organization and antitrust economics, Corvallis, Oregon State
University, May 2 6, 19 69.
APPENDICES
62
Table 1.
The proportion of total salmon landings that were
marketed in the canned form for the period 1960-1968.
Quantity
Quantity
of
of
Landings
Pack
Difference
Percentage
Pack is of
Landings
Millions of pounds
1960
235.5
206.9
28.6
87.9
1961
310.4
269.9
40.5
87.0
1962
314.5
277.5
37.0
88.2
1963
294. 1
240.5
53.6
81.8
1964
352.3
274.4
77.9
77.9
1965
326.9
265.3
61.6
81.2
1966
387.5
318. 1
69.4
82. 1
1967
206.4
151.6
64.8
73.4
303.4
250.5
52.9
82.5
Average
Note:
To convert a pound of canned salmon to a representative
pound of salmon at landing a factor of 1. 522 is used. This
factor was found to be reliable by the Bureau of Commercial
Fisheries.
Source:
Bureau of Commercial Fisheries.
63
Table 2. Opening and annual average wholesale prices for a standard case of canned Pink, Sockeye
and Chum salmon for the period 1947-1967.
____^
Pink
Sockeye
Chum
Opening
Annual
Opening
Annual
Opening
Annual
.
Average
Average
Aversgn
Dollars per Standard Case
18.10
1947
17.39
23.55
25.14
17.50
16.52
1948
22.50
22.08
26.50
26.42
21.00
19.44
1949
16.00
19.98
25.80
25.65
15.00
16.31
1950
23.00
18.25
28.50
28.65
20.55
16.38
1951
21.00
21.00
30.00
30.92
18.00
18.83
1952
19.00
20.25
28.50
30.20
16.00
16.85
1953
18.00
19.25
27.00
27.69
14.00
15.09
1954
20.00
19.39
28.50
27.39
15.00
14.83
1955
22.50
21.90
31.00
30.15
18.00
17.36
1956
23.50
23.06
33.50
33.28
21.00
20.78
1957
23.00
23.36
33.50
33.57
20.00
19.89
1958
21.00
22.48
34.00
33.63
17.00
17.17
1959
24.50
23.04
36.50
35.17
21.00
18.98
1960
. 24.50
25.13
36.50
36.66
22.50
22.38
1961
28.00
27.97
35.50
35.48
25.50
25.14
1962
24.50
27.38
34.00
35.05
23.00
24.87
1963
23.00
24.04
37.00
36.05
21.00
20.28
1964
21.00
22.03
39.00
38. 90
18.00
19.63
1965
27.00
23.40
36.00
38.65
22.50
19.53
1966
28.00
28.33
36.50
36. 20
25.00
24.28
1967
30.50
28.92
39.50
40.31
26.50
25.76
Note: A standard case consists of 48 one-pound cans of canned salmon. Opening prices are
usually announced in August or September of each year by the large processing firms
that can salmon.
Source: Pacific Fisherman ■
64
Table 3. Deflated wholesale and retail prices for a 16 ounce can of salmon, 1947 to 1967.
Wholesale Prices (Seattle Pricing Point)
Weighted
Average
Chinook
Coho
Sockeye
Retail Price
(Avg. of
46 cities)
Chum &
Pink
Chum
Pink
Pink
Dollars per Pound
1947
0.522
0.640
0.563
0.645
0.440
0.423
0.445
0.522
1948
0.567
0.591
0.391
0.624
0.493
0.459
0.521
0.622
1949
0.451
0.566
0.529
0.630
0.475
0.401
0.491
0.669
1950
0.575
0.558
0.498
0.695
0.418
0.398
0.443
0.555
1951
0.499
0.568
0.546
0.675
0.443
0.411
0.459
0.648
1952
0.462
0.537
0.461
0.648
0.396
0.361
0.435
0.575
1953
0.437
0.523
0.436
0.604
0.383
0.328
0.419
0.552
1954
0.468
0.546
0.502
0.599
0.370
0.324
0.423
0.546
1955
0.539
0.620
0.577
0.668
0.464
0.385
0.485
0.595
1956
0.590
0.616
0.627
0.732
0.488
0.457
0.507
0.637
1957
0.550
0.607
0.586
0.715
0.461
0.423
0.498
0.639
1958
0.489
0.583
0.562
0.688
0.420
0.351
0.459
0.616
1959
0.581
0.613
0.633
0.731
0.444
0.394
0.479
0.618
1960
0.618
0.647
0.637
0.753
0.489
0.460
0.517
0.654
1961
0.625
0.630
0.619
0.720
0.555
0.511
0.568
0.724
1962
0.539
0.624
0.624
0.705
0.537
0.500
0.550
0.738
1963
0.513
0.604
0.604
0.715
0. 462
0.402
0.477
0.675
1964
0.480
0.587
0.597.
0.761
0.418
0.384
0.431
1965
0.610
0.584
0.565
0.740
0.429
0.374
0.449
1966
0.555
0.556
0.547
0.660
0.500
0.443
0.517
1967
0.615
0.551
0.597
0.680
0.502
0.466
0.523
Mean
0.535
0.588
0.567
0.685
0.459
0.412
0.480
0.623
Note: Both wholesale and retail prices are deflated by the Consumers' Price Index for food. The
v/eighted average price is obtained from opening prices for the five species. Chinook and
Coho are quoted opening prices, other prices are annual averages.
Source: Pacific Fisherman, Bureau of Labor Statistics
Table 4. The quantity of landings, pack, foreign trade, and per capita consumption of canned salmon for the period 1947-1967.
1
Total
2
3
4
Landings of Salmoi1
Chinook
Coho
Sockeye
5
6
7
8
Chum
Total
Chinook
Pink
498.0
403.9
431.6
328.7
374. 2
352.2
313.0
324.6
289.9
324.3
265.2
307.5
201.6
235.5
310.4
314.5
294.1
352.3
326.9
387.5
206.4
53.2
46.1
39.6
36.6
43.2
40.8
39.2
36.4
42.8
38.2
30.5
27.6
27.4
24.1
27.0
25.1
27.2
28.8
29.3
27.2
27.2
Mean
325.8
34.2
33.1
41.0
40.8
40.2
52.1
44.4
28.7
31.6
28.7
29.7
26.8
23.3
20.2
13.7
23.2
27.8
28.1
38.1
38.5
38.8
34.2
157.0
124.5
78.0
91.5
66.2
110.1
83.3
91.7
57.6
94.2
67.5
67.8
53.8
95.3
103.6
58.0
43.4
57.3
148.1
102.0
64.7
32.8
86.5
Source: Bureau of Commercial Fisheries
Coho
Sockeye
11
12
Pink
Chum
Mi llions of Pounds
M illions of Pounds
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
I960
1961
1962
1963
1964
1965
1966
1967
9
10
-Pack of Salmon-
«■■• — — ••
191.5
113.4
273.2
85.8
147.6
79.5
97.2
88.7
128.2
102.2
71.7
120.8
61.7
52.6
108.5
143.3
156.6
162.3
79.7
163.0
48.3
58.2
78.9
52.7
74.6
65.1
77.4
64.6
76.2
32.6
60.0
68.7
68.0
38.5
49.8
48.1
60.3
38.8
65.8
31.3
56.5
32.0
117.9
57.1
269.6
230.6
264.7
206.6
222.3
213.4
186.7
199.1
157.3
167.9
153.5
178.9
117.8
135.7
177.1
182.3
157.7
180.3
174.3
209.0
99.6
16.9
16.3
10.0
10.0
11.8
7.8
7.6
6.2
8.5
7.9
6.8
6.6
6.0
4.8
5.5
5.6
4.6
4.6
6.3
4.0
4.4
185.0
7.7
14.7
17.3
13.3
18.8
22.4
19.5
9.9
10.3
10.0
9.0
9.8
7.3
9.1
4.4
7.9
7.6
7.9
10.5
9.0
9.9
6.7
92.4
83.4
51.6
61.8
44.9
67.5
55.8
63.5
36.0
56.8
46.2
45.6
35.4
63.2
69.2
40.2
29.1
37.3
98.0
66.5
41.5
112.9
62.8
155.3
52.7
96.1
56.5
67.0
55.3
80.4
57.4
46.3
75.3
39.4
32.9
65.0
92.9
93.9
93.1
45.6
99.3
29.6
11.2
55.7
71.9
14
13
Foreign Trade of
Canned
Salmon
Imports
15
Per Capita Consumption
Canned
Salmon
Exports
Millions of Pounds
Pounds
32.7
50.8
34.5
63.3
47.1
62.1
46.4
63.8
22.4
37.0
44.4
44.1
27.9
30.4
29.5
36.0
22.2
34.8
15.4
29.3
17.4
0.0
0.9
0.9
0.5
0.6
9.5
12.2
11.3
13.0
28.8
24.4
29.2
31.2
19.1
7.2
6.8
1.2
0.2
0.1
0.6
0.1
61.6
2.6
12.8
1.7
2.1
1.4
2.3
7.2
10.4
5.2
6.7
9.2
13.8
11.9
7.2
9.0
10.2
20.9
24.9
20.5
20.5
1.3
1.6
1.6
1.4
1.4
1.4
1.3
1.1
1.0
1.1
1.0
1.1
0.9
0.7
0.8
0.9
0.9
0.7
0.9
0.8
0.5
37.7
9.4
12.5
1.1
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67
APPENDIX B
The Procedure for Estimating the Change in
Stock Levels of Processed Salmon
68
APPENDIX B
The quantity demanded for consumption is equal to the quantity
of canned salmon supplied net of inventories, and the change in the
stock levels as shown in equations (1.4) and (1.5), page
.
The
changes in stock levels are estimated by the following functions:
AS. = a 1
t-1
T—
, denoting / t-l\
by R.,
t then ^S = a 1 Rt
[—)
*
R can be obtained from the known quantity of landings.
The ratio
The para-
meter, a^, is estimated from the demand equation by the following
method.
Estimates for the parameters are denoted by the lower
case English letters.
PS - b
Ps = b
PS = b
o
0
+b1QSd + b.-ir + b_M + b.N + u
1
2 N
3
4
(2.3)
+b1(QS + a.R) + b_—^- +b-M + b.N + u
(2.4)
+b QS +b.a1R + b0 -^- + b_M + b.N + u
(2.5)
1
1
01
1
11
c.
JN
J
2N3
4
4
By dividing the quantity b-.a.. by b1, an estimate a. for a1 is obtained.
By multiplying a., by R , the predicted change in the stock
level for year t can be obtained.
equal to 21. 333.
For equation b. Table 3, a, was
Table 1 shows the actual and predicted change in
stock levels for all canned salmon since 1965.
-*%»
69
Table 1.
Comparison of actual with predicted stock level changes
for canned salmon as of July 1 for 1965 through 1967.
Year
Actual Stock
Levels
Changes in
Stock Levels
Predicted Changes
in Stock Levels
Millions of pounds
1965
35.2
1966
35.7
1967
60. 1
1968
32. 2
Note:
0.5
23.0
+24:4
18.0
-27.9
40.0
The actual stock levels of sold and unsold canned
salmon held by canners have only been available
from the National Canners Association since
late 1964.
The above comparison of the predicted changes in stock levels
does not appear to follow that of the actual changes for the years
since 1965.
Instead of estimating the changes in stocks, the function
may, in fact, provide a better estimate for stock levels.
with so few observations, no conclusions can be made.
However,
70
APPENDIX C
The Correlation Matrices of the Demand Equations
for Canned Salmon
Table 1.
Ql
R
Y/N
Mc
N
The correlation between the. variables of the demand equation for canned salmon -■
equation b, Table 3.
Quantity of
Salmon, Net
of Inventories Changes
The Ratio
Qs
R
1. 000
-0.515
■0.787
■0.695
■0.341
■0.565
1. 000
0.205
■0.032
■0.089
0. 328
1.000
0.938
0.496
0. 459
1.000
0.531
0. 3 64
1.000
0. 168
L
t-i
t
The Per Capita Quantity of
Disposable Canned Meat
Income
and Meat
Products
Y/N
Mc
U.S. Population
N
Weighted Average
Wholesale Price
of Canned
Salmon
ps
ps
1. 000
The above is the upper portion of the correlation matrix between the variables
in the demand equation.
Table 2.
The correlation between the variables of the demand equation for canned salmon,
per capita data - Equation d, Table 3.
Per Capita
Consumption
of Canned
Salmon
Qsd/N
Qsd/N
1.000
Y/N
Mt/N
Sin(ct)
_—_
Per Capita
Disposal
Income
Per Capita
Consumption
of Canned
Sin(ct)0
Cos(ct)0
Tiana
Y/N
MVN
-0.896
-0.927
0.701
-0.055
-0.527
1.000
0.937
0.537
0.322
0.469
—*—
1. 000
0.7 04
0. 136
0.489
1.000
0. 027
-0. 449
1. 000
0. 152
_-_
1.000
Cos(ct)
ps
Weighted Average
Wholesale Price
of Canned Salmon
___
The above is the upper portion of the correlation matrix between the
variables in the demand equation.
Table 3.
The correlation between the variables of the demand equation for canned salmon
Equation e, Table 3.
Quantity of
Canned Salmon
Q
Q sd
QSd-N
M
Aggregate Disposable Income
sd
1. 000
Quantity of
Salmon times
Population
Qsd. N
Quantity of
Canned Tuna
M
Weighted Average
Price of Canned
Salmon
ps
•0.809
0.831
-0.796
-0.559
1.000
•0.387
0.970
0.458
1.000
-0.341
-0.498
1. 000
0.448
PS'
1.000
The above is the upper portion of the correlation matrix between the
variables in the demand equation.
Table 4.
The correlation between the variables of the demand equation for Chum salmon
Equation f, Table 3.
Quantity of
The Ratio
Canned Chum,
/L.
Vl
Net of Inven1^
tory Changes
s
Q
Q'
R
Mv
N
1. 000
The Per Capita
Disposable
Income
Quantity of
Canned Meat
and Meat
Products
MC
R
U.S. Population
Wholesale Price
of Canned
Chum
N
-0. 605
■0. 655
-0.594
-0. 643
■0. 367
1. 000
0. 152
0.031
0. 114
■0.210
1.000
0.938
0.966
0. 264
1.000
0.973
0.243
1. 000
0.271
1.000
The above is the upper portion of the correlation matrix between the
variables in the demand equation.
Table 5.
The correlation between the variables of the demand equation for Chum and Pink salnion
Equation g, Table 3.
Quantity of
Canned Chum
and Pink, Net
of Inventories
Changes
.s
Q c, p
Q c, p
R
Y
Mc
N
1. 000
The Ratio
JL-1
L
The Per Capita
Disposable
Income
Quantity of U. S. Population
Canned Meat
and Meat
Products
M^
N
Wholesale Price
of Canned Chum
and Pink
cp
0.249
•0.559
-0.478
-0.535
0. 106
1.000
0. 068
-0.008
0.535
o. 382
1.000
0.938
0.966
0. 399
1.000
0.973
0. 365
1. 000
0. 403
1. 000
c, P
The above is the upper portion of the correlation matrix between the
variables in the demand equation.
Table 6.
The correlation between the variables of the demand equation for Sockeye salmon
Equation h, Table 3.
Quantity of The Ratio
Canned Sockt-1
eye, Net of
Inventories
Changes
Qf
Qi
R
Y
MC
N
1. 000
The Per Capita
Disposable
Income
Quantity of
U.S. Population
Canned
Meat and
Meat Products
MC
R
Wholesale Price
of Canned
Sockeye
N
-0.525
-0. 156
-0.210
-0.239
-0. 195
1.000
0.059
-0.010
0. 047
-0. 317
1.000
0.938
0.966
0. 529
1. 000
0.97 3
0. 617
1.000
0. 607
pS
r
1. 000
The above is the upper portion of the correlation matrix between the
variables in the demand equation.
-^
<?
Table 7.
The correlation between the variables of the demand equation for Sockeye salmon
Equation i, Table 3.
Quantity of Canned
Sockeye, Net of Inventories
Changes
Q!
Qr
(Q;-N)
Y
1.000
Quantity of Canned
Sockeye Times
Population
Aggregate
Disposable
Income
(Q?-N)
Quantity of
Canned Tuna
Wholesale Price
of Canned Sockeye
M
0.937
-0.167
-0.230
-0. 197
1.000
0. 163
0. 102
0.012
1.000
0.970
0.549
1. 000
0. 600
•__
1.000
Mt
_•_
The above is the upper portion of the correlation matrix between the
variables in demand equation.
-4
Table 8.
The correlation between the variables of the demand equation for canned salmon Equation (2. 1).
Weighted Average
Price of Canned
Salmon
P0
Y/N
Mc
N
Q
1. 000
Per Capita
Disposable
Income
Quantity of
Canned Meat,
and Meat
Products
U. S. Population
Quantity of
Canned Salmon
sd
Y/N
Mc
0.469
0.368
0.427
-0.559
1.000
0.938
0.966
-0.811
1. 000
0.973
-0.751
1.000
-0. 816
N
sd
Q
1.000
The above is the upper portion of the correlation matrix between the
variables in demand equation.
00