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Title: Substitution relationships between fresh oranges and related citrus and noncitrus products
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Title: Substitution relationships between fresh oranges and related citrus and noncitrus products
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Full Text
EPTEMBER 1963


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AGRICULTURAL ECONOMICS REPORT NO. EC 64-2


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I




K- I At


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Substitutio:n Relcoionships Zetween Fresh; Oranges

and VReatec Ci'rus and Noncitrus Prdcucts


I MARSHALL r .:')ULWIP
BILLIE 5. LLO'. D


r--

* -


THE DEPARTMENT OF AGRICULTURAL ECONOMICS, UNIVERSITY OF FLORIDA
IN COOPERATION WITH THE FLORIDA CITRUS COMMISSION, LAKELAND, FLORIDA


a7


i.__.























Substitution Relationships Between Fresh Oranges and Related
Citrus and Noncitrus Products



















by

Marshall R. Godwin

and


Billie S. Lloyd















CONTENTS


INTRODUCTION


METHOD OF STUDY


EXAMINATION OF SUBSTITUTION RELATIONSHIPS


EVALUATION OF FINDINGS


APPENDIX


Acknowledgments


The data on which this study is based were obtained as a part of
a broader study conducted cooperatively by the Department of Agricultural
Economics of the University of Florida, the Florida Citrus Commission,
and the Marketing Economics Division of the Economics Research Service,
United States Department of Agriculture.

The authors are grateful for the advice, assistance, and, above all,
the complete cooperation of Dr. W. T. Manley and Mr. W. F. Chapman, Jr.
of the United States Department of Agriculture.

The retail facilities for the study were made available by Eberhards
Foods, Inc. of Grand Rapids, Michigan. To Mr. L. V. Eberhard, his mana-
gerial staff, and the personnel of the company of which he is President,
the authors offer their most sincere thanks for their understanding,
patience and unreserved assistance.

Supply problems were handled admirably by the Grand Rapids Produce
Company. For their consistently high-caliber performance much credit
is due Mr. Gordon Klieman, Mr. Gene Kutchenski, and Mr. Robert Davenport.


-?s! i !, ". !'!s ll-!-?L_-1111












INTRODUCTION


The interrelationship between the several forms in which the

Florida citrus crop is marketed is a major consideration in the devel-

opment of programs which have the objective of market expansion. Ef-

forts which result in an increase in the consumption of one type of

citrus product may or may not represent a net gain for the industry

as a whole. The increase may, to some degree, result from an internal

shift in the consumption pattern of the population whereby a part of

the gain for one citrus product may be offset by declines in the use

rates for others.

The possibilities of substitution in consumption among products

have important implications to the Florida citrus industry. In the past,

the industry has engaged in an intensive effort to expand the market for

its products. Future production outlook suggests that market expansion

activities may occupy a major role in the collective actions of the

citrus industry in the years ahead.

Market expansion activities, regardless of their specific char-

acteristics, must be focused upon the individual products which are de-

rived primarily from the production of oranges and grapefruit in Florida.

Since there are a number of products involved, decisions must be made

regarding how such effort is to be distributed among them. An under-

standing of the degree of substitution between citrus products is an

important element of the information needed to allocate market expansion

effort among products with maximum effectiveness. The most advantageous









application of such effort would be to those products for which the

maximum net gain in consumption could be accomplished with the minimum

effect upon the use levels of other citrus items.



METHOD OF STUDY

In a study conducted during the spring of 1962 in Grand Rapids,

Michigan, data were obtained which provided an opportunity to examine

a part of the total question of the tendency of consumers to shift from

the purchase of one citrus product to another. The data also provided

a means of exploring the linkage between citrus and noncitrus products.

In this study customers were offered Valencia oranges from the Interior

and Indian River districts of Florida and from California at a rather

wide range of prices, and their purchase responses to these price levels

were carefully measured. The price combinations at which fruit from the

three producing regions was sold during this market test are shown in

Table 1.


TABLE l.--Price combinations at which Valencia oranges were sold,
Grand Rapids, Michigan, spring 1962

Price Florida Prices California Deviations from
Combination Int. Ind. R. Price Base Price

(cents per dozen)
I 33 33 43 -16
11 37 37 47 -12
111 41 41 51 8
IV 45 45 55 4
V 49 49 59 Base
VI 53 53 63 + 4
VII 57 57 67 + 8
VIII 61 61 71 +12
IX 65 65 75 +16










In order to insure that some customer purchase response would

be obtained, the fresh fruit prices employed in the study were varied

over a comparatively wide range. Under each of the price combinations

shown in Table 1, customers could purchase any of the three types of

oranges in any quantity they desired. California prices were deliber-

ately set 10 cents per dozen above Florida prices under all circum-

stances in order ;o approximate the normal market relationship between

fresh fruit from he two areas. Prices were varied equal amounts above

and below a base rice reflecting the approximate market level for fresh

oranges at the ti e the study was conducted. Florida fruit employed in

the tests consisted of a mixture of 165 and 200 sizes from both the

Indian River and Interior districts, while California oranges were all

size 138. Only U.S. No. 1 fruit was used.

The fundamental elements of economic theory would suggest that

the aggregate sales of the three types of fresh oranges included in

this test should vary inversely with the price level at which they were

offered to customers in the retail test situations. Successive in-

creases in price might be expected to result in a decline in the amount

of fruit purchased. Conversely, the logical result of price reductions

would be higher total sales of the three types of oranges. The basic

data obtained in the study indicate that customers did, in fact, behave

in a fashion that was generally consistent with economic theory (Fig-

ure 1).

At the base price of 49 cents per dozen for the two types of

Florida fruit and 59 cents for the California product, the aggregate





















Purchase rates
in pounds per
100 customers
50 -


I I I l I l I
33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price per dozen


Fig. l.--Aggregate Customer Response to Varying Price Levels for
Florida and California Valencia Oranges.










sales of oranges averaged 23.6 pounds per 100 customers passing through

the test stores. As prices at lower levels were introduced, customers

responded by increasing their purchase rates. Sales at the lowest test

price of 33 and 43 cents for Florida and California fruit, respectively,

amounted to 41.1 pounds per 100 customers. This was about 90 per cent

more than the volume of fruit bought at the base price level. As prices

were moved to higher levels, customers consistently reduced their pur-

chase rates. At the highest test price of 65 cents per dozen for

Florida fruit and 75 cents for California fruit, aggregate orange sales

amounted to only 13.3 pounds per 100 customers.

Considering the entire range of prices at which fruit was sold

during the tests, it is evident that customers varied their purchase

rates to a considerable degree in response to the various price levels

with which they were confronted. Sales of oranges at the highest test

price were only about one-third of the quantities purchased at the low-

est test price.

Since customers varied their purchase of fresh oranges sub-

stantially in response to the prices at which fresh fruit was avail-

able to them, this study afforded an opportunity to examine the ques-

tion of the existence of substitution relationships between oranges

and other products found in retail food stores. With this objective

in mind, detailed sales records were kept during the field investi-

gation on the customer purchases of an assortment of both citrus and

noncitrus items which are usually regarded as competitive with fresh

citrus fruit. These were:










Citrus Products

Frozen orange concentrate
Fresh grapefruit
Canned single-strength orange juice
Canned single-strength grapefruit juice
Canned single-strength lemon juice
Canned single-strength orange-grapefruit blends
Frozen concentrated orange-grapefruit blends
Frozen concentrated lemon-lime blends
Other frozen concentrated citrus blends
Citrus hot packs
Frozen limeade concentrate
Frozen lemonade concentrate

Noncitrus Products

Frozen grape concentrate
Single-strength grape juice
Single-strength pineapple juice
Apple juice
Prune juice
Tomato juice
Orange and grapefruit flavored synthetic products

While the prices of the foregoing items varied to some extent

during the course of the study, they were generally much more stable

than the price of fresh oranges. Consequently, it was possible to

make a statistical determination of the effect of price and the re-

sulting purchase rate for fresh oranges upon the sales of the other

fruit, juice, and drink items considered. Basically, the analytical

procedure entailed the measurement of the extent to which the sales

of the related products varied directly with the price of fresh oranges

or, to put it another way, the extent of the inverse relationship be-

tween fresh orange sales and the sales of the related products. In


The statistical procedure is outlined in the appendix
statement.










general, this was accomplished by determining whether the quantity pur-

chased of a specific commodity was affected by changes in its own price,

by changes in the price of fresh oranges, or by both forces. If there

was an apparent relationship, statistical tests were made to determine

the significance of each type of price effect, and an analysis was con-

ducted to measure the amount of variation in sales of an individual item

accounted for by changes in its own price and by changes in the price

of fresh oranges.



EXAMINATION OF SUBSTITUTION RELATIONSHIPS

Of all the products considered in the study, it was anticipated

that fresh grapefruit and frozen orange concentrate would be the most

likely to respond to changes in the price of fresh oranges. It appeared

logical that, as the price of oranges increased, consumers might substi-

tute either another fresh citrus product or a closely related orange

product such as frozen concentrate. For this reason, an extensive anal-

ysis was made for these two commodities.

Over all price treatments for fresh oranges, sales of fresh

grapefruit were relatively stable (Figure 2). The statistical analysis

of the data indicates that neither extreme fluctuations in the price of

oranges nor moderate variations in the price of the grapefruit itself

had any significant effect on grapefruit sales. This finding implies

that, within the limits of measurement afforded by this study, con-

sumers are not willing to substitute grapefruit for fresh oranges to

any great extent.










Pounds per
100 customers
35-


30-

25-


'


7


K


41 45 49 53 57
51 55 59 63 67
Price of fresh oranges per dozen


K


61 65 Fla.
71 75 Calif.


K~~


Fig. 2.--Sales of Fresh Grapefruit at Varying Price Levels for
Fresh Oranges.


s


- -


N
N
N
N\
N
N



N
N\
N


I


N










There was, on the other hand, considerable variation in the

sales of frozen orange concentrate at the various price levels for fresh

oranges (Figure 3). Analysis revealed, however, that almost all of this

variation could be attributed to changes in the price of concentrate rather

than to changes in the price of fresh oranges. Furthermore, the relation-

ship between customer purchase rates for concentrate and the prices of

concentrate and fresh oranges, although significant, accounted for only

9 per cent of the total variation in sales of this product. Apparently,

some factor or combination of factors other than prices of the two com-

modities affected concentrate sales considerably.

Foremost among possible factors influencing concentrate sales

were the various promotional programs engaged in by the cooperating re-

tailing organization during the time interval covered by the study. On

several different occasions concentrate was offered at special prices

and featured in the advertisements of the retailer. During the study,

the product was sometimes sold at a discount price with a coupon. On

Wednesday of each week the cooperating retailer gave twice the usual

amount of trading stamps to store customers as an inducement to shop on

this day. The double award of trading stamps applied to frozen orange

concentrate as well as all other products in the test stores. It was

not possible to measure the effect of these programs in any way. How-

ever, the data do show that sales of concentrate increased materially

on those days when the special offers were available to customers, re-

gardless of the price level of fresh oranges and regardless of the price

of frozen orange concentrate itself.











m -


Ounces per 100
customers (not
reconstituted)


360


320


280 -


240 -


200-


160-


71


120 -


80-


40 -
K\\\


7


33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen

Fig. 3.--Sales of Frozen Oranqe Concentrate at Varying Price Levels
for Fresh Oranges.










An analysis of the sales data for the remainder of the products

considered in the study produced results which fell into the same two

categories as grapefruit and frozen orange concentrate. Like fresh

grapefruit, there was one group of products whose sales did not res-

pond to changes in the prices of either the product itself or the price

of fresh oranges. A second group consisted of those whose sales res-

ponded to changes in the price of the product itself but not to changes

in the price of fresh oranges.

The group showing no discernible response to price changes con-

sisted of frozen concentrated orange-grapefruit blends, frozen concen-

trated lemon-lime blends, frozen limeade concentrate, citrus hot packs,

and canned single-strength orange-grapefruit blends for the citrus prod-

ucts, and frozen grape concentrate, single-strength grape juice, and

prune juice for the noncitrus products. Apparently, consumers are not

affected by slight fluctuations in the prices of these products, nor do

they tend to switch their purchases from fresh oranges to these related

commodities as the price of oranges increases.

As can be seen in Figures 4 through 7, sales per 100 customers

for each of the foregoing products were comparatively stable over all

levels of orange prices. The lack of variation in sales can be attrib-

uted in part to the fact that, in most of these cases, fluctuations in

the related product price were not large enough to cause consumers to

make any significant adjustments in their purchases. Small downward

price changes offered no particular inducement for prospective orange

purchasers to substitute one of these products for fresh oranges.








Ounces per 100
customers (not
reconstituted)
10 ......
10- [:



5-




33 37
43 47


Frozen Limeade Concentrate


..... .... ......
.... .....

41 45 49 53
51 55 59 63
Price of fresh oranges per


57
67
dozen


61 65 Fla.
71 75 Calif.


Ounces per 100 Concentrated Citrus Blends--Lemon and Lime
customers (not
reconstituted)
10-




5-


0


37 41 45 49 53
47 51 55 59 63
-Price of fresh oranges per


57 61 65 Fla.
67 71 75 Calif.
dozen


Concentrated Citrus Blends--Orange and Grapefruit
Ounces per 100
customers (not
reconstituted)
10-


~laH~HI~i~~8


41
51
Price


49 53
59 63
fresh oranges per


57
67
dozen


65 Fla.
75 Calif.


Fig. 4.--Sales of Frozen Limeade Concentrate and Lemon-Lime and
Oranqe-Grapefruit Frozen Blends at Varying Price Levels for Fresh Oranges.


5-



n


0 .. .. .. . . . . .. .








Canned Single Strength Citrus Blends--Orange and Grapefruit
Ounces per
100 customers


41 45 49 53 57
51 55 59 63 67
Price of fresh oranges per dozen


N'


65 Fla.
75 Calif.


Ounces per 100
customers (not
reconstituted)


5 -


II


Citrus Hot Packs


I


41 45 49 53 57
51 55 59 63 67
Price of fresh oranges per dozen


Fig. 5.--Sales of Canned Sinqle Strength Oranqe-Grapefruit Blends and
of Hot Pack Citrus Concentrates at Varying Price Levels for Fresh Oranges.


65 Fla.
75 Calif.


M M


"""'









Ounces per 100
customers (not
reconstituted)


Frozen Grape Concentrate


- Ix\ I I I l I l I l III. l Ix Ix x -,


41
51
Price


45 49 53 57
55 59 63 67
of fresh oranges per dozen


65 Fla.
75 Calif.


Canned Single Strength Grape Juice


Ounces per
100 customers


43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen

Fig. 6.--Sales of Frozen Grape Concentrate and of Canned Single
Strength Grape Juice at Varying Price Levels for Fresh Oranges.


I





Ounces per
100 customers


45-


40-


35-


30-


25 -


20-


15-


10-


M
"IN


N





K

K
I

\


I


\i\\M
7X


7












&


7


i


33 37 41 45 49 53 57 61 65 Fla.
3 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen
Fig. 7.--Sales of Canned and Bottled Prune Juice at Varying Price
Levels for Fresh Oranges.


I


&










Conversely, small upward price adjustments for these products caused very

few customers to shift their purchases to fresh oranges.

For all of the other products in the study, sales responded to

changes in the price of the product itself, but not to changes in the

price of fresh oranges. The citrus products included in this category

were frozen lemonade concentrate, canned single-strength orange juice,

canned single-strength grapefruit juice, and canned single-strength lemon

juice and miscellaneous frozen concentrated citrus blends other than

orange-grapefruit and lemon-lime. The noncitrus products were synthetic

citrus flavored products (both orange and grapefruit), single-strength

pineapple juice, tomato juice and apple juice. Consumers made significant

adjustments in their purchases of each of these commodities in response

to changes in its own price, but changes in the price of fresh oranges

had no measurable effect on the rate at which customers purchased them.

In all cases, however, less than half the variation in sales for a par-

ticular commodity could be attributed to the relationship between sales

rates and changes in its own price. Factors other than price either of

the product or of fresh oranges accounted for over 50 per cent of the

variation in the sales of every item.

Sales per 100 customers at different levels of orange prices

for individual products in the second group are shown in Figure 8

through 15. That sales varied considerably at different price levels

for fresh oranges isespecially noticeable for frozen lemonade concen-

trate, canned single-strength orange juice, canned single-strength

grapefruit juice, and tomato juice. For each of these products, the





Ounces per
100 customers
150 -


140 -
130 -
120 -
lO-
110 -
100 -
90 -


80 -
70 -


50 -


40 -


30 -
20-
10-


N









K


7













K


7








K


7


N





K


I


-- --- -- ::-


33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen
Fig. 8.--Sales of Canned Sinqle Strenqth Oranqe Juice at Varying
Price Levels for Fresh Oranges.


M


I.,-









Ounces per
100 customers
180-


7







K


41 45 49 53 57
51 55 59 63 67
Price of fresh oranges per dozen


65 Fla.
75 Calif.


Fig. 9.--Sales of Canned Sinqle Strenqth Grapefruit Juice at
Varying Price Levels for Fresh Oranges.


160o
140"
120-
100
80o
60-
40-
20-


7


y ~ r~ `-r











Frozen Lemonade Concentrate


Ounces per 100
customers (not
reconstituted)
60-


K


33 37 41
43 47 51
Price


N NN


45 49 53
55 59 63
of fresh oranges per


57
67
dozen


Canned Single Strength Lemon Juice


Ounces per
100 customers


0 M R 0M MI


41 45 49 53 57
51 55 59 63 67
Price of fresh oranges per dozen


I1"


0 rI a.
75 Calif.


Fig. 10.--Sales of Frozen Lemonade Concentrate and Canned Lemon
Juice at Varying Price Levels for Fresh Oranges.


40-


30-


20-


10-


0


65 Fla.
75 Calif.


I


x 1 1 I ..


" i


"`


AAAJ


" 1
















Ounces per 100
customers (not
reconstituted)


7


-7


65 Fla.
75 Calif,


Price of fresh oranges per dozen
L -
Fig. 11.--Sales of Miscellaneous Frozen Concentrated Citrus Blends
at Varying Price Levels for Fresh Oranges.
















Ounces per
100 customers
25"


K


Ni~i


x


N~~ ~ N


33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen

Fig. 12.--Sales of Synthetic Citrus Flavored Products at Varying
Price Levels for Fresh Oranges.


"`













Ounces per
100 customers
30-


N


N











K


K


33 37 L
43 47 5


l 45 49 53 57 61 65 Fla.
1 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen


Fig. 13.--Sales of Canned Pineapple Juice at Varying Price Levels
for Fresh Oranges.


V -


~i~i~i





Ounces per
100 customers
240 -


220
200 -
180-


160 -
140 -
120 -


100-


80-
60-
40-
20-


N


73i


7


33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen
Fig. 14.--Sales of Canned Tomato Juice at Varying Price Levels for
Fresh Oranges.


11





M Im


Ounces per
100 customers
40-


30-


25-


20-


15-


7


7


7ii~


I


33 37 41 45 49 53 57 61 65 Fla.
43 47 51 55 59 63 67 71 75 Calif.
Price of fresh oranges per dozen


Fig. 15.--Sales of Canned Apple Juice at Varying Price Levels for
Fresh Oranges.


\\\


\\\


\\\~










extreme peaks in purchase rates were examined in detail to determine if

there were other forces operating which might have influenced the quan-

tities purchased. It was found that, in all cases, product advertising,

price discounts, featured displays, special offers such as coupons, or

some combination of these accounted for high levels of sales and conse-

quently for the sales variation which is apparent. The analytical ap-

proach and the characteristics of the basic data precluded the possi-

bility of a quantitative examination of the nature or the exact extent

of such effects on the sales of individual products.



EVALUATION OF FINDINGS

The results obtained in this study do not reveal any close sub-

stitution relationships between fresh oranges and the selected citrus

and noncitrus products which were examined. The quantities of fresh

oranges which consumers purchased varied considerably and in an inverse

relationship to the level of price at which they were offered for sale.

Under these conditions a direct relationship between the sales of a re-

lated product and the price of fresh oranges would have been a mani-

festation of economic linkage between the two goods. Both the basic

data and the analytical technique should have revealed any instances

where there was a high degree of substitution between fresh oranges

and the other products under consideration.

The absence of a measurable degree of substitution between fresh

oranges and products normally regarded as possible substitutes for them

may be explained in three ways. First, the interaction between price and









quantities of fresh oranges purchased resulted in a relatively constant

expenditure for this product. Given this circumstance, and accepting the

proposition that the amount of money which families spend for food is

relatively fixed, it would appear that high or low prices could have

brought about corresponding downward or upward adjustments in the

quantity of oranges purchased and, as a consequence, a parallel adjust-

ment in the absolute quantity of food which was acquired by the home-

makers confronted with the test situations. Second, the effects of com-

paratively wide variations in the amounts of fresh oranges purchased dur-

ing the tests could have been felt on products not subject to consideration

in the study. Clearly, the study included only a limited number of fresh

fruit items, and by no means all of the canned and processed fruits and

juices which are available in a retail store. Moreover, the possibility

exists that consumption adjustments might have occurred for dairy items,

soft drinks, or other products not normally considered close substitutes

for fresh oranges. Finally, it is possible that a substitution relation-

ship did exist between fresh oranges and the aggregate of the specific

products considered in the study, but that the effect on any one product

was so small that it escaped detection in the analytical procedure.

The last two of the foregoing alternatives suggest the need for

a more refined analysis of the problem of substitution between fresh

oranges and products which are regarded as closely related to them.

Considering the importance of the problem to the Florida citrus industry,

and recognizing the inherent limitations of the approach used in this

instance, further investigations in this area would most certainly appear

to be in order.










Given, however, that the findings do suggest an inclination on

the part of consumers to maintain relatively constant expenditure for

fresh oranges and to vary total food consumption as the means of adjust-

ment to changing price levels for these products, there are certain im-

plications of this condition which deserve examination from the stand-

point of the Florida citrus industry. If this condition holds, the most

advantageous strategy for the citrus industry under conditions of short

supplies and consequent high prices for fresh oranges would be to exert

effort to induce consumers to maintain a constant consumption base in

the citrus sector of their purchase patterns. Effort should be concen-

trated on inducing consumers to shift the absolute adjustment to some

other sector of their food purchases. Conversely, low prices for fresh

fruit would afford the industry with an opportunity to emphasize the con-

sumption of fresh oranges without fear of substantial effects on the

purchases of other citrus products. Should high prices for oranges result

in purchase reductions which are not recovered through increased sales of

other citrus products, the industry might further consider the advantages

of deliberate efforts to maintain adequate supplies of fresh oranges in

the marketplace in order to protect its position.

Application of the foregoing techniques in the strategy of mar-

keting Florida citrus serves to emphasize the need for extended studies

of the demand and substitution relationships for the multiplicity of

products which emanate from the basic production of oranges and grape-

fruit. A thorough understanding of the interrelationships between citrus

items in the market and the intrarelationships between citrus and non-






28



citrus food items would considerably facilitate the decision-making

processes in the marketing activities of firms and of the industry as

a whole.












APPENDIX


The data on which this study was based were collected in 9 food

supermarkets over a six-weeks period extending from April 9 through May

19, 1962. During this period, observations were obtained during 12 days

of store operations for each of the price conditions for fresh oranges.

Since 9 price conditions were employed, the field operations produced a

maximum of 108 observations for each of the related products under con-

sideration. Owing to the pressure of other research activities conducted

simultaneously in these stores, the maximum number of observations was

not obtained in all instances. The extent to which less than the maxi-

mum number of observations was obtained can be determined by an exami-

nation of Appendix Tables 3 through 21. Notation in the tables that

107 degrees of freedom were involved in the analysis indicates that the

maximum number of observations were obtained. In instances where less

than 107 degrees of freedom were employed, the observations obtained for

an individual product were less than 108 by the difference between 107

and the number indicated. The tests were designed so that sales of re-

lated products were obtained at each price condition for fresh oranges

at least once on each day of the week for all stores. Daily records

were kept on customer traffic as well as on the prices and sales of the

items under consideration.

The analytical technique was based on the assumption that the

sales of a particular product would be functionally related to the weighted

average price of the product and to the weighted average price of fresh

oranges. For reasons of convenience in analysis, and because multipli-









cative relationships are more consistent with the theory of demand than

additive ones, the basic data were transformed into logarithms prior to

analysis.

The statistical model used in the analysis was

Y' + 0 + plX + f2X2

where


Y' = log of sales per 100 customers of substitute product

0' = log of regression constant

pi P2 = regression coefficients
Xj = log of weighted average price per ounce or per pound

of substitute product

X2 = log of weighted average price per dozen of fresh

oranges

Using the method of least squares, a linear equation was fit to

the data for each related product. The "F" test was used to determine if

the calculated equation resulted in a significant reduction in the total

sums of squares. If the reduction was significant, the "t" test was used

to determine the significance of the regression coefficients, b1 and b2,

associated with the price of the related product and the price of fresh

oranges, respectively. In addition, R2 was calculated to ascertain the

proportion of the total variation in sales that was accounted for by the

relationship existing between sales and the two prices tested. The basic

price and quantity data used in the analysis is given in Appendix Tables

1 and 2. A summary of the analytical results and the relevant tests for

each product is given in Tables 3 through 21.









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GROUP I.--Products whose sales did not respond to changes in the prices
of either the product or fresh oranges.



TABLE 3.--Fresh grapefruit

Source of variation d.f. Sums of squares Mean square F


Due to X and X2 2 .034 .017 .24 n.s.

Remainder 105 7.499 .071

Total 107 7.533



TABLE 4.--Frozen concentrated orange-grapefruit blends

Source of variation d.f. Sums of squares Mean square F


Due to XI and X2 2 .096 .048 .24 n.s.

Remainder 105 21.409

Total 107 21.505



TABLE 5.--Frozen concentrated lemon-lime blends

Source of variation d.f. Sums of squares Mean square F


Due to XI and X2 2 .083 .042 .29 n.s.

Remainder 79 11.542 .146

Total 81 11.625










TABLE 6.--Frozen limeade concentrate

Source of variation d.f. Sums of squares Mean square F


Due to Xl and X2 2 .173 .087 .46 n.s.

Remainder 90 17.036 .189

Total 92 17.209



TABLE 7.--Citrus hot packs

Source of variation d.f. Sums of squares Mean square F


Due to XI and X2 2 .489 .244 1.20 n.s.

Remainder 105 21.448 .204

Total 107 21.937



TABLE 8.--Canned single-strength orange-grapefruit blends

Source of variation d.f. Sums of squares Mean square F


Due to Xl and X2 2 .214 .107 .24 n.s.

Remainder 90 39.416 .438

Total 92 39.630



TABLE 9.--Frozen grape concentrate

Source of variation d.f. Sums of squares Mean square F


Due to Xl and X2 2 .468 .234 1.57 n.s.

Remainder 105 15.636 .149

Total 107 16.104









TABLE 10.--Single strength grape juice

Source of variation d.f. Sums of squares Mean square F


Due to Xl and X2 2 .140 .070 .32 n.s.

Remainder 105 23.040 .219

Total 107 23.180



TABLE 11.--Prune juice

Source of variation d.f. Sums of squares Mean square F


Due to Xl and X2 2 .018 .009 .06 n.s.

Remainder 105 15.780 .150

Total 107 15.798









GROUP II.-- Products whose sales responded to changes in its own price
but not to changes in the price of fresh oranges.


TABLE 12.--Frozen orange concentrate

Sums of Mean t
Source of variation d.f. us ea F 2
squares square b b R
bI b2

Due to X and X2 2 .981 .491 5.25-* 3.24"* .26 9%
Estimating equation:
Remainder 105 9.810 .093
Y' = 4.21 3.84X' .10X2
Total 107 10.791


TABLE 13.--Frozen concentrated citrus blends other than
orange-qrapefruit and lemon-lime

Sums of Mean
Source of variation d.f. Sus ot 2
squares square F b b R
bI b2

Due to Xl and X2 2 2.261 1.131 7.22** 3.79-* 1.04 12%
Estimating equation:
Remainder 105 16.441 .157
Y' = 3.10 2.92Xi .52X2
Total 107 18.702


TABLE 14.--Frozen lemonade concentrate

Sums of Mean
Source of variation d.f. us t 2M
squares square b b R
Il 2


Due to X1 and X2 2 18.630 9.315 38.75"* 8.71"* .07 43%
Remainder 102 24.522 .240 Estimating equation:
Y' = 4.67 9.45XI + .04X
Total 104 43.152








TABLE 15.--Canned sinqle-strenqth orange juice

Sums of Mean
Source of variation d.f. F t 2
squares square b b R
1 2

Due to X1 and X2 2 6.723 3.362 25.59** 7.15* .34 33%

Remainder 104 13.661 .131 Estimating equation:
Y' = 5.16 3.33X' .07X2
Total 106 20.384


TABLE 16.--Canned sinqle-strenqth grapefruit juice

Sums of Mean
Source of variation d.f. umsF t R2
squares Square b b R


Due to X, and X2 2 10.701 5.351 19.18** 6.19** .04 27%
Remain Estimating equation:
Remainder 105 29.295 .279
Y' = 5.36 4.71Xi + .02X
Total 107 39.996


TABLE 17.--Canned sinqle-strenqth lemon juice excludingq squeeze bottles)

Source of variation d.f. Sums of Mean F t R2
squares square bl b


Due to XI and X2 2 4.318 2.159 12.35** 4.90~* .64 19%
Estimating equation:
Remainder 105 18.358 .175g
Y' = 1.90 4.21X1 + .33X2
Total 107 22.676


TABLE 18.--Synthetic products orangee and grapefruit Tanq)

Sums of Mean
Source of variation d.f. usF t 2
squares square b b R
bI b2

Due to X and X2 2 3.481 1.741 14.97** 5.41*c 1.04 22%

Remainder 105 12.206 .116 Estimating equation:
Y, = 6.94 8.30Xi .44X-
Total 107 15.687









TABLE 19.--Sinqle-strenqth pineapple juice

Sums of Mean
Source of variation d.f. usF t 2
squares square b b R
b1 b2

Due to XI and X2 2 2.359 1.180 4.60** 3.01'* .31 8%
Estimating equation:
Remainder 105 26.930 .256 Eg
Y' = 9.69 9.96X' + .19X'
Total 107 29.289


TABLE 20.--Tomato juice

Sums of Mean
Source of variation d.f. us t 2
squares square b b R
1 2

Due to X1 and X2 2 3.573 1.786 12.22** 4.94-* .23 19%
Estimating equation:
Remainder 105 15.355 .146 tiati equation:
Y' = 5.37 4.26X' + .11X2
Total 107 18.928


TABLE 21.--Apple juice

Sums of Mean
Source of variation d.f. F t
squares square bb R2


Due to Xl and X2 2 14.135 7.067 21.19** 6.44*- .25 29%
3 Estimating equation:
Remainder 104 34.687 .334
Y' = 6.16 5.26X' .18X'
Total 106 48.822




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