Citation
Demand and substitution relationships for Florida and California Valencia oranges produced for fresh market

Material Information

Title:
Demand and substitution relationships for Florida and California Valencia oranges produced for fresh market
Creator:
Chapman, William Fred, 1931- ( Dissertant )
Godwin, M. R. ( Thesis advisor )
Blodgett, Ralph H. ( Reviewer )
Hamilton, H. G. ( Reviewer )
Manley, William T. ( Reviewer )
Riggan, Wilson B. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1963
Language:
English
Physical Description:
xiv, 258 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Boxes ( jstor )
Customers ( jstor )
Market prices ( jstor )
Native Americans ( jstor )
Orange fruits ( jstor )
Price elasticity ( jstor )
Price elasticity of demand ( jstor )
Prices ( jstor )
Regression coefficients ( jstor )
Supply ( jstor )
Agricultural Economics thesis Ph. D
Citrus fruits ( lcsh )
Dissertations, Academic -- Agricultural Economics -- UF
Fruit trade ( lcsh )
Indian River ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )
Spatial Coverage:
United States -- Florida

Notes

Abstract:
Abbreviated Introduction: The fresh orange market Is an Important segment of the Florida orange Industry. Cash receipts to Florida growers from the sale of oranges are in excess of $200 million annually. Although the fresh orange segment amounts to only approximately 20 per cent of the total market for oranges, It is of sufficient importance to warrant attention as to maintenance or expansion of its position. To maintain or improve the position of this market, the industry has need of definitive information that describes the demand relationships faced in the fresh orange market....Florida orange production is characterized by six major product differentiations. The first major differentiation encompasses two distinct areas of production: the Indian River district, comprised of four counties along the east coast, and the interior district, made up of the remaining citrus-producing counties in the state. It is an accepted fact at the production and wholesale levels that fruits produced in the two areas are differentiated products, and some price differential does exist between the two areas.
Thesis:
Thesis (Ph. D.)--University of Florida, 1963.
Bibliography:
Includes bibliographical references (leaves 255-258).
General Note:
Vita.
Statement of Responsibility:
by William Fred Chapman.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
029994123 ( AlephBibNum )
ACG2276 ( NOTIS )
37410841 ( OCLC )

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DEMAND AND SUBSTITUTION RELATIONSHIPS

FOR FLORIDA AND CALIFORNIA VALENCIA

ORANGES PRODUCED FOR FRESH MARKET











By
WILLIAM FRED CHAPMAN, JR.











A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY










UNIVERSITY OF FLORIDA
December, 1963










ACKNOWLEDGMENTS


The writer wishes to express sincere appreciation to his super-

visory committee chairman, M. R. Godwin, for his advice, council, and

encouragement throughout all phases of the graduate study program. Pro-

fessor Godwin spent many hours discussing, guiding, and developing the

research philosophy of the author, the culmination of which is expressed

in this thesis. For his honest and sincere concern in the development

of the student to a degree seldom found, an unrepayable debt of grati-

tude is due.

Appreciation is extended to the members of the author's

supervisory committee, composed of R. H. Blodgett, H. G. Hamilton,

W. T. Manley, and W. B. Riggan, whose contributions to the graduate

program have been of material benefit.

An especial note of thanks is also expressed to L. C. Martin

and W. T. Manley of Economic Research Service, United States Department

of Agriculture for providing the essential freedom and favorable

environment for conducting the research from which this thesis evolved.

Much valuable assistance in typing and in making necessary

statistical computations was provided by Mrs. Christine Ward, Mrs.

Irene Jolly, Mrs. Judy Cannington, Mrs. Earline Thompson, and Mr. T. L.

Brooks. The final manuscript was typed by Mrs. Carole Puller. For the

untiring efforts of L.W. Hicks in reproducing the final manuscript, and

to K. E. Ford for preparing the illustrations, the author is grateful.

Finally, the sacrifice, encouragement, and devotion of the

author's wife, Nancy, and children, Tony and Nancy Jean, is gratefully

acknowledged and sincerely appreciated.
ii















TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . . . . . . . . .


LIST OF TABLES


LIST OF ILLUSTRATIONS . . . . . . . . . . .

LIST OF APPENDIX TABLES . . . . . . . . . .


Page
ii

viii

xii

xiv


Chapter
I.


INTRODUCTION . . . . . .


Statement of the General Problem

Florida orange production .
California orange production .
Production potential. . . .
Utilization trends and population


Position of Florida and California in
the fresh orange market . . .
Marketing period . . . .

Alternative Adjustment Available to the
Florida Orange Industry . . . .

The demand situation . . .
The importance of the sector analysis .
Promotional policy . . ...
Pricing policy . . . . .
Product policy . . . . . .
Optimum allocation . . . . ..

II. PREVIOUS RESEARCH RELATING TO CITRUS DEMAND


S. . 2
* . 2


trends


Examination of Data Sources . . . . .

Citrus Demand Work . . . . . . . .


III. PURPOSE OF PRESENT RESEARCH AND SPECIFIC PROBLEM
ORIENTATION . . . . . . .


The Specific Problem . . . ..

Variety . . . . . . . . . .
Fruit sizes . . . . . . . . .
Fruit grades . . . . . . . .


* . .


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


. . . .












* * *













TABLE OF CONTENTS--Continued


Specifications of the Research Problem..


Rationale Underlying Method Selection .

IV RESEARCH METHODOLOGY . . . . .

The Economic Model . . . . .

The Statistical Model . . . . .

Assumptions . . . .. .

The Experimental Model. . . . .

Limitations of the Model Formulation..

The Statistical Model Redefined . .

Specifications of Experimental Test ..

Size limitations . . . . .
Price differentials . . . . .
Experimental design layout. . . .

Requirements and Specifications of Expel

Selection of test site. . . . .
Selection of test stores. . . .
Orange pricing. . . . . .
Display control . . . . . .
Supply quality and storage. . .
Merchandising restrictions. . . .

Informational Requirements. . . .

Cooperative Arrangements. . . . .

V CHARACTERISTICS OF THE TEST STORES

General Description of Test Stores. .
Stores departmentalized . . . .
Degree of self service . . . .
Trading Stamp plan. . . . . .

Sales and Store Traffic . . . .
Customer count and sales. . . .
Daily distribution of store traffic .


Page
. . . 57


. . . . 58

. . . . 62

. . . . 63

. . . 64

. . . . 66

. . . . 68

S. . . 74

. . . . 75

. . . . 76

. . . 76
. . . . 78
. . . . 79

rimental Units 84

. . . . 84
. . . . 87
. . . . 88
S. . . 88
. . . . 95
S. . . 96

S. . . 97

. . 98

100

S. . . 100
S. . . 100
S. . . 101
. . 101

. . . 102
S. . . 102
S . . . 104









TABLE OF CONTENTS--Continued


Page
Daily distribution of store sales. . . . 105
Daily distribution of produce sales . . ... 108
Daily distribution of total sales per customer 110
Daily distribution of produce sales per customer 110

VI AN EXAMINATION OF THE BASIC INPUT DATA--FRESH
ORANGE SALES. . . . . . . . . ... ... 114

Aggregate Sales by Fruit Type . . . . . .. 114

Sales by store . . . . . . . . . 116
Sales by week. . . . . . . ... 117
Sales by day . . . . . . . 117

Sales per 100 Customers by Fruit Types. . . . 120

Sales by store . . . . . . . . . 120
Sales by week . . . . . . . . 122
Sales by day . . . . . . . . . 122

VII CHARACTERISTICS OF THE DEMAND FOR FLORIDA
AND CALIFORNIA VALENCIA ORANGES . . . . . . 126

Generalized Presentation of the Systems of
Demand Equations. . . . . . . 126

Requirements Necessary and Sufficient
for Economic Consistency. . . . . . 129

Method of Analysis. . . . . . . . 130

Coefficient estimation utilizing the method
of least squares . . . . . . . 131
Coefficient testing by students "t" test .... .132

Price and Substitution Effects. . . . .. 133

Tests Involving Florida Size 200 and California
Size 138. . . . . . . . . . 133

Direct price effects . . . . . ... 138
Differences among price elasticity estimates . 142
Cross-price effects. . . . .....145
Differences between cross elasticity estimates . 146
Summary of price effects . . . . . . 148

Tests Involving Florida size 163 and California
Size 138 . . . . . . . . ... . 149









TABLE OF CONTENTS--Continued
Page
Direct price effects. . . . . . . . 154
Differences between price elasticity estimates . 159
Cross-price effects . . . . . . . . 160
Summary of price effects. . . . . . .. 161

Differences in Demand Estimates Due to Size . . .. 161

VIII THE ECONOMIC INTERACTION AMONG THE THREE VALENCIA
ORANGES. . . . . . . . . . . . .. 167

Derivation of Price Estimating Equations from
Demand Equations. . . . . . . . .. 167

Generalized Presentation of Systems of Price
Estimating Equations. . . . . . . .. 169

Economic Consistency Requirements . . . . .. 171

The Effects of Supply Interactions. . . . . .. 172

Tests Involving Florida Size 200 and California
Size 138 . . . . . . . . . . 173

Prime product effect on price . . . . . .. 176
Competing product effects on price. . . . .. 177
Summary of product effects . . . . . ... 178

Tests Involving Florida Size 163 and California
Size 138. . . . . . . . . . . 178

Prime product effect on price .. . . . . 182
Competing product effects on price. . . . .. 182
Summary of product effects. . . . . . .. 183

IX EVALUATION OF FINDINGS . . . . . . . . 185

Effects of Major Changes in Price and Supply
Conditions for Florida Valencia Oranges . . .. 187

Effect of various price conditions on customers
purchases . . . . . . . . . . 188
Effect of various supply conditions on retail
prices. . . . . . . . . . . 193

General Implications to the Florida Orange Industry--
An Overview . . . . . . . . . . 198
vi












TABLE OF CONTENTS--Continued


X SUMMARY. . . . . . . . . . . .

Characteristics of the Test Stores. . . ..

Sales and Store Traffic ...........

Fresh Orange Sales . . . .

Total sales of fresh oranges. . . . .
Sales per 100 customers . .. . . .

Demand Relationships for Florida and California
Valencia Oranges . . . . . .

Component i--Florida size 200 and California
size 138. . . . . . . . . .
Component II--Florlda size 163 and California
size 138 . . . . . . . .
Differences In elasticities due to size .

The Economic interaction Among the Three
Valencia Oranges. . . . . . .
Component I--Florida size 200 and California
size 138 . . . . . . . .
Component Il--Flortda size 163 and California
size 138. . . . . . . . . .

Price and Supply Interactions . . . . .

Effect of price interaction on purchase rates
Effect of supply interaction on prices. . .

APPENDIXES . . . . . . . . . . . . .

BIBLIOGRAPHY . . . . . . . . . . . .


. .


. .





. .




. C



. C


Page
202

203

203

203

204
204


204


204

205
206


206

206

207

207

208
209

210

255


. .














LIST OF TABLES


Table Page
1. Florida orange production, by type and area of production,
1952-53 through 1961-62 . . . . . . . . 4.

2. California orange production, by type, 1952-53 through
1961-62. . . . . . . . . . . 6

3. Florida Early-Midseason, Valencia and all oranges estimated
tree distribution, by age, 1961, 1966, and 1971 . . . 8

4. Estimated yields of orange trees, by orange type, and age
of tree. . . . . . . . . . . . . 11

5. Estimated production, Florida Early-Midseason oranges,
1961, 1966 and 1971. . . . . . . . . . 13

6. Estimated production, Florida Valencia oranges, 1961, 1966,
and 1971. . . . . . . . . . . . .. 15

7. Estimated production, all Florida oranges, 1961, 1966,
and 1971. . . . . . . . . . . . . 17

8. Florida Early-Midseason and Valencia orange utilization,
1951-52 through 1961-62. . . . . . . . ... .19

9. California Valencia and Navel orange utilization, 1951-52
through 1961-62. . . . . . . . .... 20

10. Per capital consumption of fresh, canned, chilled, and
frozen orange products, United States, 1950-60. . . ... 21

11. United States population, by years, 1951-62. . . .. 23

12. Orange unloads in selected U. S. cities, two-year
intervals, 1955-61. . . . . . . . .. . 25

13. Carlot shipments, California and Florida oranges, by
months, 1954 through 1962. . . .. . . . .. 29

14. Size distribution, Florida Indian River, Florida Interior,
and California Valencia oranges, 1960-61 season. . . 56

15. Basic demand relationships, Florida Indian River sizes
200 and 163, Florida Interior sizes 200 and 163, and
size 138 California Valencia oranges. . . . . . 58
viii










LIST OF TABLES--Continued


Table Page
16. Treatment price combinations, in terms of four cent
deviations, used in estimating demand relationships for
Florida and California Valencia oranges for fresh market. 80

17. Component I experimental price design for the study of the
competitive relationships among size 200 Florida Indian
River, size 200 Florida Interior and size 138 California
Valencia oranges, Grand Rapids, Michigan, April-May,
1962. . . . . . . ... .. . . . 81

18. Component II experimental price design for the study of the
competitive relationships among size 163 Florida Indian
River, size 163 Florida Interior, and size 138 California
Valencia oranges, Grand Rapids, Michigan, April-May, 1962. 85

19. Component I price design for the study of the competitive
relationships among size 200 Florida Indian River, size
200 Florida Interior, and size 138 California Valencia
oranges, Grand Rapids, Michigan, April-May, 1962. . . 89

20. Component II price design for the study of the competitive
relationships among size 163 Florida Indian River, size
163 Florida Interior, and size 138 California Valencia
oranges, Grand Rapids, Michigan, April-May,.1962 . 91

21. Arrangement of displays of Florida Indian River, Florida
Interior, and California Valencia oranges, Component I,
in a study of the competitive relationships between Florida
and California oranges.. . . . . . . . 95

22. Arrangement of displays of Florida Indian River, Florida
Interior, and California Valencia oranges, Component II,
in a study of the competitive relationships between
Florida and California oranges. . . . . . . . 96

23. Number of customers, produce sales, total sales, and
proportions of total sales in produce, by component
and store, experimental tests, Grand Rapids, Michigan,
April-May, 1962. . . . . . . . . . . 103

24. Customer traffic, by component, store, and day of week,
and daily percentage distribution by component,
experimental tests, Grand Rapids, Michigan, April-May,
1962. . . . . . . . . . . 106

25. Total sales, by component, store and day of week, and
daily percentage distribution by component, experimental
tests, Grand Rapids, Michigan, April-May, 1962. . . ... 107
ix












LIST OF TABLES--Continued


Table Page
26. Produce sales, by component, store and day of week, and
daily percentage distribution by component, experimental
tests, Grand Rapids, Michigan, April-May, 1962. . . ... 109

27. Total sales per customer, by component, store and day,
experimental tests, Grand Rapids, Michigan, April-May,
1962. . . . . . . . . . . .. . . . Ill

28. Produce sales per customer, by component, store and day,
experimental tests, Grand Rapids, Michigan, April-May,
1962. . . . . . . .. . . . . . . 113

29. Florida Indian River, Florida Interior, California, and
total Valencia orange sales, by component, by store,
experimental test, nine stores, 31 operational days,
Grand Rapids, Michigan, April-May, 1962. . . . ... 115

30. Florida Indian River, Florida Interior, California, and
total Valencia orange sales, by component, by week,
experimental test, 31 operational days, nine stores,
Grand Rapids, Michigan, April-May, 1962. . . . ... 118

31. Florida Indian River, Florida Interior, California, and
total Valencia orange sales, by component, by day,
experimental test, 31 operational days, nine stores,
Grand Rapids, Michigan, April-May, 1962. . . . ... 119

32. Florida Indian River, Florida Interior, California, and
total Valencia orange sales per 100 customers, by
component, by store, experimental test, nine stores,
31 operational days, Grand Rapids, Michigan, April-May,
1962. . . . . . . . . . . . . . 121

33. Florida Indian River, Florida Interior, California, and
total Valencia orange sales per 100 customers, by component,
by week, experimental test, 31 operational days, nine
stores, Grand Rapids, Michigan, April-May, 1962. . . ... 123

34. Florida Indian River, Florida Interior, California, and
total Valencia orange sales, per 100 customers, by com-
ponent, by day, experimental test, 31 operational days,
nine stores, Grand Rapids, Michigan, April-May, 1962.. ... .124

35. Measures of dispersion and tests of significance for rele-
vant coefficients in the demand equations for Florida
Indian River size 200, Florida Interior size 200, and
California size 138 Valencia oranges. . . . . .. 136
x









LIST OF TABLES--Continued


Table Page
36. Effects of price changes upon purchases of Florida
Indian River size 200, Florida Interior size 200, and
California size 138 Valencia oranges, Component I, ex-
perimental tests, Grand Rapids, Michigan, April-May,
1962. . . . . . . . . . . . . . 149

37. Measures of dispersion and tests of significance for
relevant coefficients in the demand equations for Florida
Indian River size 163, Florida Interior size 163, and
California size 138 Valencia oranges. . . . . ... 152

38. Effects of price changes upon purchases of Florida Indian
River size 163, Florida Interior size 163, and California
size 138 Valencia oranges, Component II, experimental
tests, Grand Rapids, Michigan, April-May, 1962. . . 163

39. Effects of quantity changes upon prices of Florida Indian
River size 200, Florida Interior size 200 and California
size 138 Valencia oranges. . . . . . . . . 179

40. Effects of quantity changes upon price of Florida Indian
River size 163, Florida Interior size 163, and California
size 138 Valencia oranges. . . . . . . . 184

41. Effects of various conditions of increased and decreased re-
tail prices of Florida Indian River and Florida Interior
Valencia oranges upon consumer purchases of Florida Indian
River Valencia oranges. . . . . . . . .. .. 189

42. Effects of various conditions of increased and decreased
retail prices of Florida Interior and Florida Indian River
Valencia oranges upon consumer purchases of Florida In-
terior Valencia oranges. . . . . . . . ... 192

43. Effects of various conditions of increased and decreased
supplies of Florida Indian River and Florida Interior
Valencia oranges upon prices of Florida Indian River Valen-
cia oranges. . . . . . . . . . . . 194

44. Effects of various conditions of increased and decreased
supplies of Florida Indian River and Florida Interior
Valencia oranges upon prices of Florida Interior Valencia
oranges. . . . . . . . . . . . . 197














LIST OF ILLUSTRATIONS


Figure Page
1. Hypothetical demand relationships for Florida fresh
oranges and processed orange products. . . . . ... 33

2. Component cubes of the Triple Cube Design. . . . ... 70

3. The Triple Cube Design. . . . . . . . . ... 72

4. Display and pricing placards used in the study of the
competitive relationships among Florida and California
Valencia oranges, Grand Rapids, Michigan, April-May,
1962. . . . . . . . .. . . . . . 93

5. Valencia orange display location on produce counter, in
the study of competitive relationships among Florida
and California Valencia oranges, Grand Rapids, Michigan,
April-May, 1962. .......... ......... . 94

6. The effect of price changes for Florida Indian River size
200 Valencia oranges upon retail sales of Florida Indian
River size 200 Valencia oranges, Florida 200-California
138 test. . . . . . . . . ... . . . 140

7. The effect of price changes for Florida Interior size
200 Valencia oranges upon retail sales of Florida Interior
size 200 Valencia oranges, Florida 200-California 138 test 141

8. The effect of price changes for California size 138
Valencia oranges upon retail sales of California size
138 Valencia oranges, Florida 200-California 138 test. . 143

9. The effect of price changes for Florida Indian River size
200 Valencia oranges upon retail sales of Florida
Interior size 200 Valencia oranges, and the effect of
price changes for Florida Interior size 200 Valencia
oranges upon retail sales of Florida Indian River size
200 Valencia oranges, Florida 200-California 138 test.. 147

10. The effect of price changes for Florida Indian River size
163 Valencia oranges upon retail sales of Florida
Indian River size 163 Valencia oranges, Florida 163-
California 138 test. . . . . . . . . . 156
xii











LIST OF ILLUSTRATIONS--Continued

Figure Page
11. The effect of price changes for Florida Interior size
163 Valencia oranges upon retail sales of Florida In-
terior size 163 Valencia oranges, Florida 163-
California 138 test. . . . . . . . . . 157

12. The effect of price changes for California size 138
Valencia oranges upon retail sales of California size
138 Valencia oranges, Florida 163-California 138 test. . 158

13. The effect of price changes for Florida Indian River
size 163 Valencia oranges upon retail sales of Florida
Interior size 163 Valencia oranges, Florida 163-
California 138 test. . . . . . . . 162


xii i














LIST OF APPENDIX TABLES


Table Page
1. Quantity of Florida Indian River size 200, Florida Interior
size 200, and California size 138 Valencia oranges sold
per 100 customers, and value of produce sales per 100
customers, by observation number, date, and price combi-
nation, Component I, experimental tests, six stores,
Grand Rapids, Michigan, April-May, 1962. . . .. . .. 219

2. Quantity of Florida Indian River size 163, Florida Interior
size 163, and California size 138 Valencia oranges sold
per 100 customers, and value of produce sales per 100
customers, by observation number, date, and price combi-
nation, Component II, experimental tests, three stores,
Grand Rapids, Michigan, April-May, 1962. ....... 226

3. Coding and transformation instructions for demand analyses,
Florida Indian River, Florida Interior and California
Valencia oranges. ... . .......... .. ... 231













CHAPTER I

INTRODUCTION



The fresh orange market is an important segment of the Florida

orange industry. Cash receipts to Florida growers from the sale of

oranges are in excess of $200 million annually. Although the fresh

orange segment amounts to only approximately 20 per cent of the total

market for oranges, it is of sufficient Importance to warrant attention

as to maintenance or expansion of its position. To maintain or improve

the position of this market, the industry has need of definitive in-

formation that describes the demand relationships faced in the fresh

orange market.

The major source of competition fresh Florida oranges face in the

marketplace is California's orange production. At present little is

known about the relative values consumers attach to oranges produced

in either state nor the magnitude of price change necessary to induce

them to vary or alter purchase habits.

Historically, the price competition between the two areas has

been quite favorable to California. Consumer preference is the only

basis upon which the California product can enter the market with a

price differential over the Florida product. If oranges from the two

states were, in fact, perfect substitutes, retail prices should be the

same. Yet by virtue of an advertiser-created preference, the California

product can command a higher price. Thus, consumer preference allows

California producers to compete effectively with Florida producers and,
I









thereby, defray cost differences resulting frcm the productive process

as well as differences in transportation charges. This retail price

differential has existed for such a long period of time that it is

difficult to determine how much of it arises from consumer preference

and how much stems from an institutional situation developed over the

years at the terminal market level.

SDuring the past two decades, technological changes and innovations

have revolutionized the orange industry, especially in Florida. The

introduction of frozen orange concentrate and chilled orange juice has

altered substantially the relative market outlet volumes for Florida

oranges. The amount of Florida fruit moving to fresh market has de-

clined with a corresponding increase in the amount moving through

processing channels./ This pattern occurred during a period of rapid

expansion in Florida production and a slight decline in California

production. With this succession of technological advances, it is

reasonable to assume a change in the competitive citrus marketing

situation between the two states. Yet comparatively little research

has been directed toward an assessment of the values consumers place

upon these fruits.


Statement of the General Problem


Florida orange production

Florida orange production is characterized by six major product

differentiations. The first major differentiation encompasses two

distinct areas of production: the Indian River district, comprised

of four counties along the east coast, and the interior district, made

up of the remaining citrus-producing counties in the state. It is an









accepted fact at the production and wholesale levels that fruits pro-

duced in the two areas are differentiated products, and some price

differential does exist between the two areas.

Within each of these producing areas three other major differenti-

ations result from a type-varietal complex. The fruits produced in

each area are generally classified as Early, Midseason, and Late. The

principal varieties of Early fruit are Hamlin and Parson Brown; Mid-

season fruit varieties are Pineapple, Homosassa, and Temple; and the

Late oranges are exclusively Valencias.

In the crop seasons 1952-53 through 1961-62, total Florida pro-

duction averaged 89.6 million boxes of oranges annually (Table 1).

Production of oranges in the Interior district averaged 79.9 million

boxes, or slightly over 89 per cent of the state total, while the

Indian River district produced an annual average of 9.7 million boxes.

Early and midseason fruit accounted for, on the average, 50.7 million

boxes compared with 38.9 million boxes of Late or Valencia oranges.

During this period, increased production was in evidence in all

the major product differentiations associated with Florida oranges.

In the 1952-53 season, Interior production amounted to 62.7 million

boxes, or 86.8 per cent of the state's total production, while in the

1961-62 season, Interior production accounted for 102.2 million boxes,

or 90 per cent of the total Florida production. Thus, the Interior

district increased production in both absolute and relative terms.

The Indian River district, on the other hand, declined in relative

terms but registered an increase in absolute terms, increasing from

5.8 million boxes in 1952-53 to 6.0 million boxes in 1961-62. Over

this same period Valencia," or Late oranges, also gained in absolute








Table l.--Florida orange production, by type and area of production,
1952-53 through 1961-62.


Indian River Districta Interior District
Crop Total
Season Early and Late Early and Late All
Midseason (Valencia) Midseason (Valencia) Oranges

----------------------------------(000 Boxes)b--- ---------------------

1952-53 5,790 3,665 36,510 26,235 72,200

1953-54 5,718 4,084 44,482 37,016 91,300

1954-55 5,853 3,622 46,147 32,778 88,400

1955-56 6,026 3,789 45,474 35,711 91,000

1956-57 6,771 4,086 47,529 34,614 93,000

1957-58 5,277 3,313 47,423 26,487 82,500

1958-59 4,786 3,716 42,314 35,184 86,000

1959-60 5,083 3,968 43,917 38,532 91,500

1960-61 5,852 4,051 45,148 31,649 86,700

1961-62 6,014 5,227 50,886 51,273 113,400

10-Year
Average 5,717 3,952 44,983 34,948 89,600

aThe figures for the Indian River district were derived by using
county estimated production. The counties included in the Indian
River district are Volusia, St. Lucie, Indian River, and Brevard.

bBoxes containing a net weight of 90 pounds each.

Source: These data were adapted from Florida Citrus Fruits, Annual
Summary, 1952-53 through 1961-62, Florida Crop and Livestock Reporting
Service, Orlando, Florida.


and relative terms. In the 1952-53 season, Valencia production amounted

to 29.9 million boxes, or 41 per cent, of Florida production. In the

1961-62 season, Valencia production accounted for 56.5 million boxes,

or 50 per cent of total orange production in the state. Early and









Midseason fruit increased from 42.3 million boxes in 1952-53 to 56.9

million boxes in 1961-62.

From this analysis, these major product differentiations evince

an imposing magnitude as they establish irrefutable lines of differences

within Florida orange production. Other differentiations in addition

to these cited above occur also within these delineated segments, such

as size of fruit, grade of fruit and, to a lesser degree, packinghouse

or grove brand names.


California orange production

California has three major orange-producing areas, but, unlike

Florida, they form no real differentiation based upon area of production.

The production areas are categorized as Central, Southern, and Desert

Valley districts. Orange production In California averaged 33.4 mil-

lion boxes during the ten-year period 1952-53 through 1961-62 (Table 2).

Only two major orange types are produced In the state, Valencia and the

Washington Navel. Valencia production dominates and during this period

averaged an annual production of 20.1 million boxes compared with 13.3

million boxes of Navels.

During this period total California production declined from 46

million boxes in 1952-53 to 22.5 million boxes In 1961-62. Valencia

and Navel shares have varied within these dates from a percentage ratio

of 55-45 In favor of Valenclas In the 1953-54 season to a 67-33 per-

centage ratio In favor of Valenclas In 1961-62.


Production potential

The Florida orange production base has expanded markedly during

the past decade. This expansion has been stimulated by the natural







Table 2.--California orange production, by type, 1952-53 through 1961-62.



Crop Navels and Valencia Total All
Season Miscellaneousa Oranges
-------------------------(000 boxes)---------------------

1952-53b 16,630 29,400 46,030

1953-54b 14,460 17,940 32,400

1954-55c 15,330 24,090 39,420

1955-56c 15,170 23,200 38,370

1956-57c 15,400 20,500 35,900

1957-58c 9,100 14,100 23,200

1958-59c 16,900 23,300 40,200

1959-60c 13,500 17,700 31,200

1960-61c 9,000 16,000 25,000

1961-62c 7,500 15,000 22,500

10-Year
Average 13,299 20,123 33,422

includes small quantities of tangerines.

bBoxes containing a net weight of 77 pounds each.

cBoxes containing a net weight of 75 pounds each.

Source: Citrus Fruits by States Production Use Value
.Statistical Bulletins 296, October 1961, and 201, January 1957, United
States Department of Agriculture, Statistical Reporting Service, Crop
Reporting Board, Washington, D. C.


growth of a dynamic industry, on the one hand, as well as a production

reaction to the advent and successful marketing of frozen orange con-

centrate and chilled juice, on the other. In the 1951-52 season, the

total acreage in Florida was 324.8 thousand acres. By the 1961-62

season, the total acreage had increased to 429.8 thousand acres, an








increase of 32.3 per cent.l

A citrus tree survey which was conducted in 1961 revealed that

Florida orange groves contained a total of 37.8 million trees (Table

3). Of this total, 17.9 million were Early-Midseason and 19.9 million

were Valencias. Also the 1961 survey revealed that a high proportion

of Florida orange trees were of nonbearing age. These trees, less than

four years of age, were more heavily distributed to the Valencia oranges

than to the Early-Midseason oranges, 6.9 and 5.1 million, respectively.

An additional 5.4 million trees were in the five-to-nine-year age group.

Thus, 17.4 million of 37.8 million trees were nine years of age or less.

The oldest trees in the state, categorized as 25 or more years, were

of an average age of 34 years. Of the 11.1 million trees in this

category, 5.3 million were Early-Midseason and 5.8 million were

Valencias.

Based upon the assumption that the percentage change in tree numbers

occurring during the 1951-52 through 1960-61 period is typical of the

changes to come in the next ten-year period, the estimated tree numbers

in 1970-71 will be 46.4 million. This represents a 19 per cent increase

in tree numbers. Under this assumption, however, there will be fewer

nonbearing trees than was true in 1961. Nonbearing or two-year average

age trees in 1971 are estimated to be 4.3 million, 7.7 million trees

fewer than in the nonbearing category in 1961. This results from the

assumed normality of the per-annum increase in tree setting estimates

based upon the period 1951-52 through 1960-61. During these years,

frozen orange concentrate and chilled juice emerged as major trends in


IFlorida Crop and Livestock Reporting Service, Florida Citrus
Fruit, Annual Summary, 1961, Orlando, Florida.







Table 3.--Florida Early-Midseason, Valencia and all oranges estimated tree distribution, by age,
1961,a 1966, and 1971.




Early-Midseason Valencia All Oranges
Average Age Production Year Production Year Production Year
of Treeb
(Years) 1961 1966 1971 1961 1966 1971 1961 1966 1971


----------------------------------Thousands of trees-----------------------------------

2.0 5,045.8 2,010.5c 2,010.5c 6,946.2 2,246.6c 2,246.6c 11,992.0 4,257.1 4,257.1

7.0 3,149.5 5,045.8 2,010.5c 2,290.8 6,946.2 2,246.6c 5,440.3 11,992.0 4,257.1

12.5 1,176.1 3,149.5 5,045.8 2,043.0 2,290.8 6,946.2 3,219.1 5,440.3 11,992.0

19.5 3,139.3 1,176.1 3,149.5 2,922.7 2,043.0 2,290.8 6,062.0 3,219.1 5,440.3

34.0 5,360.2 3,139.3 1,176.1 5,767.9 2,922.7 2,043.0 11,128.1 6,062.0 3,219.1

39.0 -- 5,360.2 3,139.3 -- 5,767.9 2,922.7 -- 11,128.1 6,062.0

42.0 -- -- 5,360.2 -- -- 5,767.9 -- -- 11,128.1

Total 17,870.9 19,881.4 21,891.9 19,970.6 22,217.2 24,463.8 37,841.5 42,098.6 46,355.7

aSource of the 1961 distribution, Florida Crop and Livestock Reporting Service, Orlando, Florida.

bThe age categories for the 1961 citrus tree survey were: 0-4, 5-9, 10-14, 15-24, 25+. These
were transformed to average ages for purposes of estimating tree numbers for 1966 and 1971.

CTwo-year-old trees for 1966 and 1971 estimated by applying the per-annum average increase in
total orange acreage for the years 1951-52 through 1960-61 to the total 1961 tree population.










the utilization of the Florida orange crop. Therefore, the early

portion of the period was characterized by a production reaction

based upon the recognized potential of the expanded processing market.

Logically then, this may be quite representative of the tree-setting

pattern of the 1960's, in that tree-setting may well continue at a

fairly rapid rate for a portion of the period before increased supplies

of oranges force a cessation of expansion.

During the period 1961-1971, Florida orange production is likely

to increase from three sources. One of these increases arises as

present nonbearing trees attain productive maturity. A second increase

springs from expanded bearing surface. As the trees age and become

larger, the per-tree bearing surface expands. Thus, an increase exists

due to the relationship between the age of the tree and the tree's pro-

ductive capacity. The third source of increased production will result

from new tree-settings. As new tree-settings occur in the 1960's and

reach bearing age, total productive capacity will increase.

To develop definitive estimates of orange production in future

years, a relationship must be established between age of tree and

production in addition to the Informational requirements concerning

tree numbers by age groups. Kelly developed such a relationship in

1953 from sample data from 15 thousand groves in Florida.2 Orange

varieties were grouped into Early, Midseason, and Late categories.

Utilizing regression analysis, a quadratic function was fitted to

describe the age-production relationship. From these regression


2Bruce W. Kelly, "A Method for Forecasting Citrus Production in
Florida", Ph.D. dissertation, University of Florida, August 1953.










equations, estimated yields were developed (Table 4). The estimated

yields derived from this study appear to overestimate production.

This discrepancy could easily be a result of the climatic conditions

prevailing during the period in which the primary data were secured.

To narrow this margin of error in estimating potential Florida pro-

duction, the percentage change between the estimated yields for given

tree ages as shown in Table 4 were developed and applied to a historical

series of production. The following assumptions were developed for

estimating production in 1966 and 1971:

(1) Estimated 1961 production is equal to the average
production for the years 1951-52 through 1960-61
multiplied by the estimated number of bearing trees
according to the 1961 tree survey.

(2) The percentage change in production of the 1961 bearing
surface in 1966 and 1971 can be estimated by calculating
the percentage change from the weighted average age of
bearing trees in 1961 to this age plus five and plus
ten based upon Kelly's relationship.

(3) Production addition due to 1961 nonbearing trees can be
estimated by deflating the 1961 per-tree production by the
percentage change in yield of Kelly's relationship from
the 1961 weighted average tree age to the average age of
new production trees in 1966 and 1971.

Another assumption more basic than those related to the mechanics

of estimation is the assumed normality of the basic per-tree production

estimate derived from the period 1951-52 through 1960-61. During these

years, Florida orange trees were exposed to adverse weather conditions

in at least three seasons. Two years the citrus belt was subjected to

freeze damage and in one other year to hurricane damage. Therefore,

recognizing the freeze damage incurred in January 1963, the per-

tree yield for this period may be quite realistic.









Table 4.--Estimated yields of orange trees, by orange type, and age of
tree.



Age of Orange Type
Tree
Early Midseason Late

----------------Boxes per tree---------------------


.479
.822
1.156
1.482
1.798
2.105
2.404
2.693
2.973
3.245
3.508
3.761
4.006
4.242
4.469
4.687
4.896
5.096
5.287
5.469
5.642
5.806
5.962
6.108
6.245
6.374
6.494
6.604
6.706
6.799
6.882
6.957
7.023
7.080
7.128
7.167
7.198
7.219
7.231
7.234
7.229


.317
.725
1.130
1.504
1.848
2.166
2.460
2.731
2.901
3.212 1
3.425
3.621
3.803
3.970
4.125
4.268
4.400
4.521
4.633
4.737
4.832
4.920
5.002
5.077
5.146
5.210
5.269
5.324
5.374
5.421
5.464
5.503
5.540
5.573
5.604
5.633
5.660
5.684
5.707


.141
.514
.876
1.226
1.564
1.891
2.206
2.509
2.801
3.081
3.349
3.606
3.851
4.084
4.306
4.516
4.714
4.901
5.076
5.239
5.391
5.531
5.659
5.776
5.881
5.986
6.068
6.126
6.185
6.232
6.267
6.290
6.302
6.302
6.290
6.267
6.232
6.186
6.128









Table 4.--Continued


Age of Orange Type
Tree
Early Midseason Late

-----------------Boxes per tree--------------------

42 7.214 5.727 6.058
43 7.191 5.747 5.965
44 7.158 5.764 5.872
45 7.117 5.781 5.778


Source: Bruce W. Kelly, "A Method for Forecasting Citrus Production
in Florida", Ph.D. dissertation, University of Florida, August 1953.


Based upon the foregoing assumptions, projected estimates were

made for 1966 and 1971 by a breakdown of Early-Midseason and Late,

or Valencia oranges. The bearing surface of Early-Midseason oranges

in 1961 was estimated to be 12,825,100 trees (Table 5). The non-

bearing surface in that same year was estimated to be 5,045,800 trees.

By applying the average per-tree yield of 3.83 boxes for Early-Mid-

season oranges from 1951-52 through 1960-61 to the 1961 bearing sur-

face, total production was estimated to be 49,120,100 boxes in 1961.

This bearing surface was estimated to be a weighted average age of

22 years. The percentage change due to age between 1961 and 1966,

based upon Kelly's age-production relationship, was found to be 14

per cent. Therefore, the 1961 bearing surface of 12.8 million trees

was estimated to yield 55,996,900 boxes in 1966. The 1961 nonbearing

trees in 1966 will be of an average age of seven years. Deflating

the base production per tree established at 3.83 boxes for 22-year-

old trees to seven-year-old trees based upon Kelly's relationship,

in 1966 an additional production of 8,880,600 boxes was estimated








Table 5.--Estimated production, Florida Early-Midseason oranges, 1961, 1966, and 1971.



Production
Weighted PAddtion Production
Average 1961 1961a Per Cent 1961 Addition Addition
Production Age 1961 Bearing BaseDue to Addition Total
Year Age 961 Bearing Base Due to Surface 1961 Non- Due to Production
Bearing Trees Production Production bearing New Tree
Age Production bearing
Surface Trees Setting

(Years) (000 Trees)(000 Boxes) (Per Cent) (000 Boxes) (000 Boxes) (000 Boxes) (000 Boxes)

1961 22 12,825.1 49,120.1 0 49,120.1 0 0 49,120.1

1966 29 12,825.1 49,120.1 +14b 55,996.9 8,880.6c 0 64,877.5

1971 35 12,825.1 49,120.1 +20d 58,944.1 14,885.1e 3,538.5 77,367.7

aDerived by using average per-tree production 1951-52 through 1960-61 multiplied by estimated
1961 bearing trees (3.83) (12,825.1).
bDerived from age-production relationship developed by Kelly by determining per cent change
between weighted average age 22 years and 29 years.

CDeflated average per-tree production, 1951-52 through 1960-61 from weighted average age 22 years
to 7 years by per cent change in Kelly's relationship (3.83) (.46) (5,045.8) = 8,880.6.
dDerived from age-production relationship developed by Kelly by determining per cent change
between weighted average age 22 years and 35 years.
eDeflated average per-tree production, 1951-52 through 1960-61 from weighted average age 22 to
12.5 years by per cent change in Kelly's relationship (3.83) (.77) (5,045.8) = 14,885.1.

fDeflated average per-tree production 1951-52 through 1960-61 from weighted average age 22
years to 7.0 years by per cent change in Kelly's relationship (3.83) (.46) (2,010.5) = 3,538.5.









from the 5,045,800 nonbearing trees of 1961. Thus, the total yield of

Early-Midseason oranges in 1966 is estimated to be 64,877,500 boxes.

In 1971 the bearing surface of 1961 is estimated to yield 20 per

cent more than in 1961 owing to differences in age of tree. Therefore,

the 1961 production base of 12,851,100 trees is estimated to yield

58,944,100 boxes in 1971. The 1961 nonbearing trees are estimated

to yield 14,885,100 boxes in 1971, while the 1966 nonbearing trees'

yield will be 3,538,500 boxes. This gives an estimated yield of

77,367,700 boxes of Early and Midseason oranges in 1971.
Ns
Turning now to the projection of Florida Valencia orange pro-

duction, the same basic assumptions were employed. In 1961, there

was an estimated 13,024,400 bearing Valencia orange trees in Florida.

Using the 1951-52 through 1960-61 period to establish the per-tree

production of 3.48 boxes, total production of Valencias in 1961 was

estimated at 45,324,900 boxes.

Differences due to age, derived from Kelly's age-production re-

lationship, were found to be a 14 per cent increase by 1966 and a

17 per cent increase by 1971. Therefore, the 1961 bearing surface is

estimated to yield 51,670,400 boxes in 1966 and 53,030,100 boxes in

1971.

The weighted average age of Valencia trees in 1961 was found to

be 23 years (Table 6). By deflating the established per-tree pro-

duction from 23 years to seven years, the 1966 production resulting

from 1961 nonbearing trees was estimated to be 7,015,700 boxes. The

total Valencia production for 1966 was estimated at 58,686,100 boxes.

Using the same deflation procedure, the 1961 nonbearing trees

were estimated to yield 14,725,900 boxes in 1971 and the 1966 non-







Table 6.--Estimated production, Florida Valencia oranges, 1961, 1966, and 1971.


.. Production
Weighted Production Production
Average 1961 1961a Per Cent 1961 Addition Addition
ProductionAge 1961 Bearing Base Change Bearing Due to Due Total
Age 1961 Bearing Base Due to
Year r r rDue to Surface 1961 Non- Production
Bearing Trees Production baig New Tree
Surface Age Production bearing Setting
Surface STrees tting

(Years) (000 Trees)(000 Boxes) (Per Cent)(000 Boxes)(000 Boxes) (000 Boxes)(000 Boxes)

1961 23 13,024.4 45,324.9 0 45,324.9 0 0 45,324.9

1966 30 13,024.4 45,324.9 +14b 51,670.4 7,015.7c 0 58,686.1

1971 36 13,024.4 45,324.9 -17d 53,030.1 14,725.9e 2,269.1f 70,025.1

Derived by using average per-tree production 1951-52 through 1960-61 multiplied by estimated
1961 bearing trees (3.48) (13,024.4) = 45,324.9.
bDerived from age-production relationship developed by Kelly by determining per cent change
between weighted average age 23 years and 30 years.

Deflated average per-tree production, 1951-52 through 1960-61 from weighted average age 23
years to 7 years by per cent change in Kelly's relationship (3.48) (.29) (6,946.2) = 7,015.7.
dDerived from age-production relationship developed by Kelly by determining per cent change
between weighted average age 23 years and 36 years.
e
Deflated average per-tree production, 1951-52 through 1960-61 from weighted average age 23
years to 12.5 years by per cent change in Kelly's relationship (3.48) (.61) (6,946.2) = 14,725.9.

fDeflated average per-tree production, 1951-52 through 1960-61 from weighted average age 23
years to 7 years by per cent change in Kelly's relationship (3.48) (.29) (2,246.6) = 2,269.1.










bearing trees, 2,269,100 boxes. Total Valencia production was esti-

mated to be 70,025,100 boxes in 1971.

To summarize these estimated yields, total Florida orange pro-

duction was estimated to be 94.4 million boxes in 1961, 123.6 million

boxes in 1966, and 147.4 million boxes in 1971 (Table 7).

No similar work has been done in the area of age-production re-

lationships for California oranges. However, research has progressed

in the projection of orange acreage to 1970 and 1980.3 Between 1960

and 1970, acreage of Valencia oranges is estimated to decline from

86,438 acres to 74,650 acres, while Navel orange acreage is estimated

to increase from 72,595 acres to 78,300 acres. The projections to 1980

indicate little change in Valencia acreage, but Navel acreage is esti-

mated to increase to 85,700 acres, approximately a seven thousand acre

increase between 1970 and 1980 compared with about a six thousand acre

increase from 1960 to 1970.

From these projections, undoubtedly Florida orange producers and

marketers must concern themselves further with the utilization of their

fruit during the 1960's. Valencia production in Florida, based upon

these projections, will increase by 17.0 million boxes or 32 per cent

by 1971. Early and Midseason production will increase 18.4 million

boxes or 31 per cent during the same period. In total, this represents

an increase in Florida production of 35.4 million boxes, an amount

equivalent to or exceeding the state's entire production in the 1942-

43 or any prior season.


R. C. Rock and R. G. Platt, Economic Trends in the California
Orange Industry. 1961, Agricultural Extension Service, University of
California, November, 1961.








Table 7.--Estimated production, all Florida oranges, 1961, 1966, and 1971.



Production Production
Pro- 1961 1961 1961 Addition Addition Total
duction Bearing Base Bearing Due To Due to Pro-
Year Trees Production Surface 1961 Non- New Tree duction
Production bearing Setting
Trees

(000 Trees)(000 Boxes)(000 Boxes)(000 Boxes) (000 Boxes)(000 Boxes)

1961 25,849.5 94,445.0 94,445.0 0 0 94,445.0

1966 25,849.5 94,445.0 107,667.3 15,896.3 0 123,563.6

1971 25,849.5 94,445.0 111,974.2 29,611.0 5,807.6 147,392.8

Source: Tables 5 and 6.


This enlarged production in Florida will be offset to some degree

by a reduction of orange acreage in California. Valencia acreage has

been projected to decline 13.6 per cent by 1970, but Washington Navel

acreage has been projected to increase by 7.9 per cent. The net change

in acreage for all California oranges, using these projections, will be

7,983 acres or 5.0 per cent.


Utilization trends and population trends

The amount of Florida oranges utilized in fresh market sales has

declined substantially in the past decade, while the number of oranges

used for processing has risen rapidly. The decline in fresh sales has

occurred notwithstanding increases in production. Florida Early-Mid-

season movement to fresh market has declined from 17.0 million boxes

in the 1951-52 season to 11.5 million boxes in 1961-62 (Table 8).

Valencia fresh sales declined from 13.6 million boxes in the 1951-52

season to the six million box level in 1957-59, gaining to the 9 mil-

lion box level in the 1959-60 season. The 1960-61 season again










registered a decline to 6.3 million boxes. Yet the 113 million box

crop of Florida oranges In the 1961-62 season led to higher fresh

sales In both Early-Midseason and Valencia categories, 11.5 and 9.4

million boxes, respectively.

Over the period 1951-52 through 1961-62, utilization ratios be-

tween fresh and processed Florida oranges were altered substantially.

In the 1951-52 season, 30.6 million boxes or 39 per cent of the crop

were utilized in fresh sales compared with a remaining 61 per cent or

47.5 million boxes used for processing. This emphasis on processing

has grown continuously since the early fifties. In the 1961-62 season,

which had a total sales utilization of 112.6 million boxes, 20.9 million

boxes or 19 per cent moved through fresh market outlets, while 91.7 mil-

lion boxes or 81 per cent were used for processing.

California fresh orange sales and processed orange sales have de-

clined during the past decade at a rather constant rate with respect

to shares. Fresh sales for the period 1951-52 through 1961-62 have

ranged between 72 and 79 per cent of total sales, with the exception

of the 1957-58 season when fresh sales accounted for 86 per cent. In

that season Florida incurred freeze damage and registered a total sales

volume of some eight million boxes below the decade average.

Sales of California oranges In the fresh market have declined from

27.2 million boxes In the 1951-52 season to 15.1 million boxes in the

1961-62 season (Table 9). Valencia fresh sales have declined from 19.7

million boxes in the 1952-53 season to 8.4 million boxes In the 1961-

62 season while Navel fresh sales have declined from a high of 14.8

million boxes in 1952-53 to a low of 6.7 million boxes in 1961-62.









Table 8.--Florida Early-Midseason and Valencia orange utilization,
1951-52 through 1961-62.



Orange Type

Season Early-Midseason Valencia All

Fresh Fresh Fresh
Fresh Processed Fresh Processed Fresh Processed
Sales Sales Sales

------------------------Thousands of boxes--------------------

1951-52 16,991 26,559 13,652 20,948 30,643 47,507

1952-53 15,212 26,838 10,637 19,063 25,849 45,901

1953-54 14,563 35,337 13,283 27,567 27,846 62,904

1954-55 16,320 35,380 10,837 25,313 27,157 60,693

1955-56 14,500 36,700 11,066 28,184 25,566 64,884

1956-57 13,984 39,966 10,132 28,268 24,116 68,234

1957-58 11,993 40,407 6,114 23,436 18,107 63,843

1958-59 10,574 36,176 6,263 32,337 16,837 68,513

1959-60 11,747 36,888 9,018 33,182 20,765 70,070

1960-61 10,441 40,199 6,359 29,041 16,770 69,270

1961-62 11,540 44,935 9,375 46,775 20,915 91,710


Source: Florida


Citrus Fruits, Annual Summary,


Crop and Livestock Reporting Service, Orlando, Florida.


(1952-1962), Florida


The decline in the fresh orange market can be traced primarily to

the successful marketing of frozen orange concentrate. In 1950, per

capital consumption of fresh oranges was 26.9 pounds (Table 10). By

1960, it had declined to 19.6 pounds, a decrease of 27 per cent. During

this same decade, per capital consumption of frozen orange concentrate

increased more than threefold, from 1.52 to 5.58 pounds. In the









Table 9.--California Valencia and Navel orange utilization, 1951-52
through 1961-62.



Orange Type

Valencia Navel All
Season
Fresh Processed Fresh Processed Fresh Processed
Sales Sales Sales

-----------------------Thousands of boxes----------------------

1951-52 16,895 8,499 10,338 1,783 27,233 10,282

1952-53 19,670 9,300 14,785 1,600 34,455 10,900

1953-54 13,028 4,557 11,945 2,135 24,973 6,692

1954-55 15,000 8,730 12,816 2,071 27,816 10,801

1955-56 14,330 8,550 13,070 1,623 27,400 10,173

1956-57 13,150 7,060 13,280 1,720 26,430 8,780

1957-58 10,978 2,880 8,485 375 19,463 3,255

1958-59 14,600 8,390 14,530 2,080 29,130 10,470

1959-60 10,980 6,060 11,550 1,650 22,530 7,710

1960-61 10,880 4,960 8,250 510 19,130 5,470

1961-62 8,400 4,210 6,660 700 15,060 4,910


Source: Florida


Citrus Fruit. Annual Summary


Crop and Livestock Reporting Service, Orlando, Florida.


(1952-1962), Florida


mid-fifties, chilled juice sales influenced in the market distribution of

orange products. The 1955 per capital consumption of chilled juice was

.94 pounds and by 1960 had increased to 2.11 pounds. Another market de-

cline registered in the 1950 decade was related to canned orange products.

In 1950, per capital consumption of these products amounted to 3.37 pounds,

but declined to only 2.13 pounds by 1960, a decrease of 37 per cent.


,









Table O0.--Per capital consumption of fresh, canned, chilled, and frozen
orange products, United States, 1950-1960.



Product Classification
Year
Fresh Canned Chilleda Frozenb

(lb.) (lb.) (lb.) Product Single
Weight Strength
(lb.) Bases
(lb.)c

1950 26.9 3.37 .. 1.52 5.12

1951 28.8 3.81 .. 2.19 7.22

1952 27.9 3.58 .. 3.53 11.44

1953 27.6 3.13 .. 4.08 12.85

1954 24.5 3.08 .. 4.40 13.93

1955 25.1 2.96 .94 4.94 15.81

1956 22.9 2.24 1.05 4.86 15.48

1957 21.9 2.45 1.71 5.32 16.99

1958 17.8 2.66 1.60 4.32 13.27

1959 20.1 1.91 1.87 5.42 16.64

1960 19.6 2.13 2.11 5.58 17.62


aChilled fruit juice
Florida; does not include
duced for local sale.


is produced commercially from fresh fruit in
reconstituted frozen juices or juice pro-


Includes single strength and concentrated juices of all citrus
products.
CConcentrated fruit juices converted to single strength on basis
of 3.525 pounds to 1.

Source: Supplement for 1961 to Consumption of Food in the United
States, Agricultural Handbook No. 62, Agricultural Marketing Service,
USDA.









The fluctuations in market shares between the various sectors of

the orange industry are especially vital in Florida, since a major pro-

portion, approximately 80 per cent, of its crop is utilized in the

processing market. The impact of the technological advances in frozen

concentrate and chilled products on the Florida industry is sufficient

to warrant study, notwithstanding the need for evaluation resulting

from increased supplies available for the national market.

California, on the other hand, has had a relatively constant market

share situation with regard to fresh and processing. Further, western

growers are facing a declining acreage in oranges, primarily from

continued urbanization in citrus producing areas.

The United States' population increased 20.9 per cent between 1951

and 1962. In 1951 the estimated population was 153.7 million and by

1962 it had mushroomed to an estimated 185.9 million (Table 11). The

average annual rate of increase from 1955 to 1961 was 2,931,454 per

annum, If this rate of increase is maintained, the estimated 1966

population will be 197.7 million persons, and in 1971 the census will

record 212.3 million.

Although United States' population is making rapid gains, this

increase in consumers will not solve the anticipated excess orange

production problem. Projected yields of Florida orange production

indicate 147.4 million boxes in 1971 and projected United States popu-

lation indicates 212.3 million persons in that same year.

This projection represents an increase over 1961 levels of 29.3

million persons and 52.9 million boxes of oranges, or 1.8 boxes per

additional person. However, consumption rates per capital tend to be

quite stable. The per capital consumption of all citrus fruits for the








Table ll.--United States population, by years, 1951-1962.


Year Persons Increase

1951 153,691

1952 156,421 2,730

1953 159,012 2,591

1954 161,761 2,749

1955 164,607 2,846

1956 167,509 2,902

1957 170,496 2,987

1958 173,367 2,871

1959 176,551 3,184

1960 180,007 3,456

1961 183,025 3,018

1962 185,937 2,912


Source:
Agriculture.


Agricultural


Statistics


1962, U. S. Department of


decade 1950-60 averaged 84.1 pounds. This represents less than one box

of citrus fruit to a consumer. Thus, to utilize the anticipated increase

in orange production, new uses for oranges must be found, or marketing

policies must be altered to effect a shift in consumption rates.


Position of Florida and California in
the fresh orange market

Aggregated over the various product differentiations, Florida and


Per capital consumption derived from Consumption of Food in the
United States, U. S. Department of Agriculture Handbook No. 62, August
1961.









California oranges compete to some degree in most major terminal market

areas east of the Rockies (Table 12). Of the 41 markets included in

this tabulation, Florida dominates 10 in terms of carlot unloads and

California predominates in 31. However, in several of the larger termi-

nal markets, the relative shares between Florida and California are

much closer to equality. In markets such as Cincinnati, Cleveland,

New York, Philadelphia, Pittsburgh, and Providence, the shares ranged

in a 40 60 division between California and Florida. In Cincinnati,

for alternate seasons from 1955 through 1961, Florida unloads accounted

for an average of 57 per cent of the total Florida-California oranges

coming into the market. On the other hand, in Cleveland during this

same period, an average of 56 per cent of the California-Florida oranges

were from California.

Over these same years, market shares have demonstrably changed in

several of the markets. For example, Florida shares have increased in

Albany and Columbia, while California shares have multiplied in Dallas,

Fort Worth, and Denver. The California share increase in these markets

can be attributed partially to increased Texas orange production. In

these six years Texas producers were recouping losses suffered in the

extensive freeze damage of 1949 and 1951.

It must be recognized, however, that these data do'possess limi-

tations relevant to an analysis of emphasis shifts within the fresh

orange market. Since the data are aggregated over several types and

varieties of oranges as well as intrastate production areas, an analysis

of shifts can be stated only in the most general fashion. Further,

such broad analyses make no allowance for transshipments. Although an

analysis of unloads may yield no appreciable changes within a given






Table 12.--Orange unloads in selected U. S. cities, two-year intervals, 1955-1961.


Calendar Year
Cities 1955 1957 1959 1961

Florida California Florida California Florida California Florida California

Albany, N. Y. 44 198 181 313 122 279 138 194
Atlanta, Ga. 955 45 956 38 745 72 725 41
Baltimore, Md. 1,085 356 961 312 744 433 801 254
Birmingham, Ala. 48 40 623 27 527 39 389 26
Boston, Mass. 1,530 1,616 1,146 1,761 802 2,081 755 1,264
Buffalo, N. Y. 103 522 347 502 210 568 186 235
Chicago, Ill. 1,835 2,003 1,577 1,776 1,049 2,347 1,033 1,303
Cinn., Ohio. 508 347 509 341 354 401 348 195
Cleveland, 0. 724 886 714 848 546 960 554 503
Columbia, S. C. 71 16 454 32 454 28 414 21
Dallas, Texas 267 277 248 266 0 345 32 188
Denver, Colo. 150 387 88 494 31 578 23 440
Detroit, Mich. 820 1,505 667 1,509 419 1,542 531 885
Ft. Worth, Tex. 98 83 45 93 19 108 5 62
Houston, Tex. 0 111 208 255 55 385 25 154
Indianapolis, Ind. 7 235 306 252 243 372 270 180
Kansas C., Mo. 175 397 188 442 100 569 107 281
L.A., Calif. 38 3,731 5 4,320 0 4,626 22 2,913
Louisville, Ky. 62 68 392 66 451 97 289 45
Memphis, Tenn. 91 37 337 94 229 111 134 66
Miami, Fla. O 0 596 15 769 63 498 65
Milwaukee, Wis. 65 493 170 518 99 541 145 273
Minneapolis, Minn. 6 743 132 801 45 878 52 365
Nashville, Tenn. 73 33 200 16 131 24 101 2
New Orleans, La. 566 93 524 101 298 112 246 64
New York, N. Y.b 4,994 4,036 5,033 3,978 3,262 5,042 3,250 3,294
Philadelphia, Pa. 2,321 1,505 2,230 1,521 1.537 1,805 1,844 1,151
Pittsburg, Pa. 844 1,111 709 1,321 456 1,301 505 768








Table 12.--Continued


Calendar Year

1955 1957 1959 1961
Cities

Florida California Florida California Florida California Florida California

Portland, Ore. 53 154 39 548 0 623 32 390
Providence, R. I. 142 195 205 166 129 195 121 81
St. Louis, Mo. 444 658 362 667 196 722 171 412
Salt Lake City, U. 1 21 13 423 0 447 13 275
San Antonio, Tex. 2 85 86 162 27 183 13 84
San Francisco, Cal.c 0 1,550 1 1,648 2 1,752 6 1,141
Seattle, Wash.d 98 707 51 321 3 459 71 520
Washington, D. C. 523 128 523 167 482 222 398 132
Wichita, Kans. O 15 18 122 5 138 12 119

aMinneapolis includes St. Paul, Minnesota.
New York includes Newark, N. J.

cSan Francisco includes Oakland, California.

Seattle includes Tacoma, Washington.

Source: Fresh Fruit and Vegetable Unloads, by Commodities, States and Months, USDA, AMS-428,
February 1962, and similar publications.









market, substantial changes within orange utilization patterns may

have been present from either Florida or California. For example,

a marked shift could have developed from California Valencias to

California Navels, or there may have been substantial changes among

Early, Midseason, and Late Florida oranges. In the same manner, major

production shifts may have emerged regarding fruit produced in the

Indian River and Interior sections of Florida.

As orange production rises, these variables will assume more im-

portance and an assessment of consumer preferences with regard to the

various orange products will become more crucial to the allocation of

supplies among market sectors.


Marketing periods

The Florida orange production year begins around the first of

October with Early oranges. Early orange production is most intense

in November and December and generally continues through February.

Midseason fruit harvest and shipment begins early in November and

continues through March. Heaviest production of Midseason fruit runs

from December through February. Temple oranges, often classified as

a Midseason fruit, are harvested from late November through mid-April,

with heaviest production in January and February. Late or Valencia

orange harvest begins about the first of February and continues to some

degree throughout the summer months. Heaviest production occurs in the

months of March through May.

California orange production is more of a year-around proposition

than is Florida's. California Washington Navel harvest and shipment

begins from early-to-mid-November and continues generally through










April. Valencia harvest in California usually overlaps Navel harvest

in early April and continues through October.

Consequently, California and Florida fruit meet in the marketplace

throughout most of the year. During the period 1954-62, May was the

heaviest shipment month for California oranges, averaging 4,822 carlots

or 11.1 per cent of annual shipments (Table 13). At this season, pri-

marily Valencias are available from either state, along with a negligible

amount of Florida Temples. In contrast, December is the heaviest orange

shipment month for Florida. An average of 5,114 carlots were shipped

from Florida in December during the period 1954-1962. In that month

Florida Early, Midseason and Temples are available for shipment. August

and September are lightest months for Florida orange shipment, averaging

in the period 1954-1962 only 211 carlots or 0.6 per cent of annual ship-

ments.

California, during the 1954-1962 period, shipped an average of more

than 2,000 carlots of oranges each month of the year, ranging from a

high of 4,822 carlots in May to a low of 2,385 carlots in November.

Florida, contrastingly, shipped an average of as low as 76 carlots

in September and as high as 5,114 in December during these identical

years. Throughout the five months, November through March, Florida

shipped more than 57 per cent of its total annual fresh shipments

compared to California shipments of 40 per cent during the same

five months.

The anticipated production increases in Florida will place larger

amounts of fruit on the national market in two critical periods. The

Early-Midseason and Temple increases will face keen competition frcm

California's Washington Navel fruit. The Navel season, starting in










Table 13.--Carlot shipments, California and Florida oranges, by months,
1954 through 1962.



Month
Year and
State
Jan. Feb. Mar. Apr. May June

--------------------------------------------Carlots---


1954
California
Florida
1955
California
Florida
1956
California
Florida
1957
California
Florida
1958
California
Florida
1959
California
Florida
1960
California
Florida
1961
California
Florida
1962
California
Florida


California
Total
Average

Florida
Total
Average


4,215
5,406

4,198
5,195

3,483
4,672

3,451
4,584

3,341
3,551

4,521
3,619

4,175
4,552

2,946
3,118

2,512
4,717


4,550
5,780

4,113
5,383

4,381
4,668

3,429
4,021

3,082
3,306

4,712
3,203

4,164
4,010

2,678
3,180

1,971
4,320


4,238 5,486
6,659 5,444


4,757
5,249

5,448
4,994

4,408
4,601

2,875
3,062

6,103
2,441

3,563
3,680

2,624
2,755


4,746
4,539

6,566
4,279

4,797
3,703

3,206
2,091

6,451
2,120

3,519
3,116

2,411
2,294


2,558 2,039
4,221 3,257


32,842 33,080 36,574
3,649 3,676 4,064


39,414
4,379


37,871
4,208


37,662
4,185


39,221
4,358


30,843
3,427


5,630 4,662
4,276 2,136


4,926
3,803


5,893
2,252


7,337 5,553
3,759 2,142


5,633
3,329


5,141
1,888


4,201 3,163
1,552 332


6,060
1,541

3,620
2,876

3,304
2,038

2,684
3,271


43,395
4,822


26,445
2,938


4,246
548

3,054
859

2,912
965

2,298
1,863


36,922
4,102


12,985
1,443










Table 13.--Extension


July Aug. Sept. Oct. Nov. Dec. Total


4,050
6,455


51,374
45,106


3,055 50,950
6,709 41,075


3,629
5,928

3,423
4,536

4,040
4,404

4,069
5,286


56,080
37,741

47,290
36,639

35,914
22,152

53,814
23,823


3,412 37,246
4,388 26,891


3,983
692

5,354
814

4,359
511

4,222
822

2,875
47

4,117
182

2,829
168

2,917
152

2,084
687


3,616
144

4,630
210

4,597
185

3,865
244

2,609
2

3,640
43

2,514
103

2,527
5

2,191
283


32,740 30.189 30,752 22,738 21,469 32,349 392,271
3,638 3,354 3,417 2,526 2,385 3,594 43,585


4,075 1,219 683 15,398 36,719 46,025 289,339
453 135 76 1,711 4,080 5,114 32,149


4,074
87

4,415
80

4,323
96

3,584
248

2,510


3,922
25

2,939
15

2,806
36

2,179
96


3,216
2,896

3,134
2,292

3,463
1,478

2,749
3,134

1,879
765

2,789
1,510

1,919
478

1,987
1,287

1,602
1,558


3,654
5,131

1,729
4,549

2,941
5,029

2,588
5,529

2,133
'3,040

3,184
3,305

1,538
2,646

1,609
3,205

2,093
4,285


31,205
23,528

28,398
32,384


2,484
4,493

4,187
3,826









November, will climax in December and January. During these same two

months, based upon current production and marketing schedules, Early

Florida fruit still will be strong, the Midseason fruit will be at

peak production, and Temple oranges will peak during January. Increased

supplies of Florida Valencia oranges will be met in the marketplace

during February, March, and April by some Florida Midseason and Temple

oranges, as well as by California Valencias harvested beginning around

the first of April.

As orange supplies increase, a comparable need will demand more

thorough knowledge of the market for oranges and orange products. The

allocation among market sectors and geographic markets based upon sounder

perception of the total orange market can refine the efficiency with

which the crops are marketed and consequently enhance the position of

the orange industry.


Alternative Adjustments Available to the
Florida Orange Industry


During the coming decade, per capital orange production is apparently

going to expand at a fairly rapid rate. The increase in production,

based upon projected yields, will definitely occur in Florida. Cali-

fornia production, meanwhile, is expected to be maintained at a rather

constant level. Therefore, the prime responsibility of merchandising

larger orange crops must rest with Florida producers and marketers.

To move effectively prodigious crops of oranges, shrewder attention

must be focused upon marketing policies and alternative adjustments

available to the industry. The effective utilization of alternative

adjustments to solve the dilemma of increased production depends,









beyond question, upon the accuracy with which the industry estimates

the demand relationships for its products.

Recognizing this adjustment to be the problem, it is necessary to

postulate the demand relationships existing in the orange market and

to examine possible alternative adjustments available to the orange

industry, in order to attain maximum effectiveness in marketing as

supply levels increase.


The demand situation

Florida oranges are marketed basically in four forms: (1) fresh

oranges, (2) chilled juice and products, (3) canned juice and products,

and (4) frozen concentrates. Each of these market sectors possesses

a separate aggregate demand relationship encompassing a family of

subsector demand curves relevant to the given sector. Within this

system of demand relationships, variations exist in levels and slopes

of the several demand functions, thus creating differences in price

and cross-price elasticities of demand at the sector and subsector

levels.

Graphically, these postulated sector demand relationships can be

depicted as in Figure 1. DI, D2, D3, and D4 represent, respectively,

chilled juice and products, canned juice and products, fresh oranges,

and frozen concentrates. Given the availability of these component

aggregate relationships, a composite function may be obtained by a

summation of the components, such as shown by DT. This composite is

an aggregated demand relationship over the various sectors and sub-

sectors making up the total orange market. Not only are these sector

relationships affected by the availability and prices of other orange










Price


D D D
Quantity

Figure 1.-Hypothetical demand relationships for Florida fresh oranges and processed orange products.









products, but also by the availability and prices of other substitute

citrus and noncitrus products.

To exploit fully the competitive situation, a detailed delineation

of demand relationships must be formulated to include the various sectors

of the industry. Since there are within each sector discernible product

differentiations, these characteristics must be accounted for. Recog-

nition of the existing product differentiations within a given sector

will allow any adjustment procedure to be applied with maximum ef-

ficiency.

The demand function for fresh oranges.--Within the Florida fresh

orange sector, differentiating characteristics which must be considered

include areas of consumption, areas of production, varietal-type dif-

ferences, sizes, and grades. It appears valid to assume that different

consuming areas possess distinct preferences regarding fresh oranges;

therefore, levels of demand and the respective functional relationships

are likely to differ between these areas. The Indian River and Interior

districts of production provide a second differentiation to be considered,

since fruits from the two areas are viewed as differentiated products,

at least at the grove and wholesale levels.

The varietal-type complex presupposes even further delineation.

Under this category, thought must be given to differences in consumer

preference with respect to Early, Midseason, and Late oranges, as well

as within these several varietal differences. Beyond these differen-

tiations are those resulting from grade and size of the common orange

types and varieties.

Certainly, then, the aggregate demand relationship for fresh oranges

is composed of countless differentiations. These differences must be










evaluated in the adjustment to increased supply levels of oranges

available for the national market.

The demand functions for processed oranges.--In the processed

sectors there are three basic forms of orange products--chilled, canned,

and frozen concentrates. Differentiations contained within these proc-

essed products must also be taken into account, and these are generally

the same without regard to form. To some degree, Florida processed

orange products maintain an identification as to area of production

within the state. Therefore, processed Indian River and Interior fruit

must be recognized as possibly differentiated products to the degree

that the area of production is identified with the product.

Evident differences also exist in the demand relationship based

upon consuming areas. For example, frozen orange concentrate accrues

differences arising from consumer preferences in unlike areas of the

market.

In all of the processed products another differentiation results

from brand names, normally classified into three categories: (1)

nationally advertised brands, (2) chain grocery store brands, and

(3) packer brands. Within brands further differences also result

from container sizes.

Thus, in developing the aggregate functional demand relationships

for each of the fresh and processed orange products, such a relation-

ship is an average over the various product differentiations. The

more complex the delineation within a particular market sector, the

sounder the knowledge for basing any adjustment to changing supply

conditions.










The importance of the sector analysis

The question arises, "What is the importance of the sector demand

relationships?" Knowledge of the component relationships provides the

basis for effective adjustment by the firms within the industry and the

industry itself. Additional Information from delineating the demand

relationships within the component or sector further refines facts

available for adjustments to changing levels of total orange output.

Consequently the reliability of any estimated demand relationships will

determine the success of the ensuing adjustment process.

The industry can avail itself of several adjustment alternatives

in coping with the problem of increasing supplies. These may be

categorized as adjustments in promotional activity, pricing policy,

product policy, and optimum allocation. Adjustments in each of these

categories require a knowledge of the demand structure and the func-

tional relationships therein.


Promotional policy

The prime concern of the Florida orange industry regarding pro-

motional activity is effectiveness in attaining the goals of any

promotional program. Basically, promotional activity of any specific

form is employed to effect a change in the demand relationship for

oranges. This change, if successful, is anticipated to initiate

shifts in the level and slope of the demand function whereby a more

favorable demand situation is created. Hence, effective promotional

activity results in some combination of increasing the level and

changing the elasticity of demand for oranges and orange products.

At the industry level, where much of the promotional activity










presently originates, two major considerations must be reckoned with. They

are (1) the allocation of promotional funds among market sectors, and (2)

the allocation of promotional funds among geographic market areas. As sup-

ply levels increase, the allocation becomes more important to the adjust-

ment process toward higher levels of output.

Recognizing the multi-use characteristics of the orange crop, the

firm, sector, or industry must decide wisely the allocation of promotional

funds. To allocate effectively these funds, management must forecast esti-

mates of the demand relationships for the products involved.

The allocation among sector markets depends upon the promotional

goals. Astute promotion initiating a shift in combination of level and

slope of the demand relation will result in higher prices or movement of

larger quantities at the same price, If the demand relation is relatively

elastic, effective promotional activity yields a more significant quantity

effect than price effect. Thus, in the matter of increasing supplies,

promotional activity could better assist movement of larger supplies if

applied in sectors of the greatest price elasticity for the demand relation.

However, another consideration in undertaking the allocation of pro-

motional funds is the substitution among products. Given equal degrees

of elasticity, a greater benefit would be derived if promotional funds

were allocated in the sector with the least degree of economic substi-

tution with respect to other orange products. In other words, to assist

adjustment to larger supplies, the greatest benefit would be derived from

promotional funds if allocated in the sector with the most elastic demand

relation and the least amount of substitution or smallest cross-price

elasticity of demand for other Florida orange products.









Pricinq policy

Another alternative available to the orange industry is adjustment

in pricing policy. Currently, on-tree prices are determined within the

framework of the purely competitive model notwithstanding an industry

market structure that departs noticeably from the competitive model.

If the industry were to engage further in vertical and horizontal in-

tegration to such an extent that a preponderance of the oranges produced

were marketed under a central authority, price policy would assume ut-

most significance in adjustment to increasing supply levels.

In a situation of rising supplies and decline in price, such de-

clines could be adjusted in a fashion to move toward a revenue maximizing

or revenue loss minimizing condition, whichever the case may be. If

the industry were operating in the elastic segment of the demand function,

then adjustments in price consistent with the demand situation within

given sectors would tend toward a maxima with regard to increasing revenue.

On the other hand, if the industry were operating in the inelastic segment

of the demand function, as supplies increased, the adjustment of prices

in the various sectors consistent with the sector demand relationships

would gravitate toward a minimization of revenue losses. Thus, a price

reduction in the sectors possessing the most elastic demand relationships

would increase revenue if the industry were operating in the elastic seg-

ment of the demand function. Contrarily, if the industry were operating

in the inelastic segment of the demand function, a price reduction in the

sectors with greatest elasticity would move toward a minimized revenue

loss.

Another consideration in pricing policy lies in the utilization of

demand relationships within a given sector. If, for example, there existed










within the fresh orange sector a functional price-quantity relationship

for Indian River fruit which was at a higher level and possessed a greater

elasticity than that for Interior fruit of like size and grade, a price

reduction for only Indian River fruit would increase revenue over an

equal price reduction for both fruits. A gain would ensue from the

elasticity character, since a price reduction for the Indian River fruit

under this hypothetical situation would yield a greater than proportionate

increase in the quantity marketed.

Further, notwithstanding increased supplies, the industry under

conditions of extreme inequality among the various sector demand func-

tions may raise prices in some sectors while lowering prices in other

sectors. If, for illustrative purposes, within the four sectors of

the orange market, two of the demand functions were highly inelastic

and two others were to a high degree elastic, price adjustments in

both directions may increase revenue. Upward movement of price in the

sectors with inelastic demands will lead to some quantity marketed

losses, but by an amount less than proportionate to the loss in price.

A decline in price in the elastic sectors will lead to an increase in

the quantity marketed by an amount more than proportionate to the price

decline. On balance, it is conceivable that such price adjustments may

increase revenue along with the increased supply levels.

The structure of the Florida industry is such that these adjust-

ments could be effected easily. The Citrus Exchange, along with similar

sales organizations representing growers' cooperatives, could organize

into a sales agency either through the organizational structure allowed

under the Capper Volstead Act or under the Marketing Orders and Agree-

ment Act.










Product policy

Another alternative similar to the pricing adjustment alternative is

product adjustment. Product adjustments among sectors of the industry could

be on a similar basis to those described under price adjustments. Any in-

creased supplies could be absorbed by adjustment of products to the various

sectors within the marketing system in the most favorable fashion, that

is, in the sector where increased quantities would have the least price

effects. Industry controlled allocation could seek to maximize revenue

along with increasing supplies.

If the industry were producing in the inelastic segment of the de-

mand relationship by allocating among the four product markets based

upon the relative elasticities, it could seek to minimize revenue losses.

For example, if the industry were producing in the inelastic portion,

but only one or two of the sector demand functions were inelastic in

nature, revenue losses would tend to be minimized by allocation of

greater quantities to the sectors possessing the elastic demands. This

follows since such an allocation would result in a less than proportionate

decline in price. Therefore, the loss incurred wculd be less than if

equal increments of the increased supplies were applied to the various

market sectors.

If, on the other hand, the industry were producing in the elastic

portion of the demand relationship, greater revenue gains would be found

by allocation of increased supplies to the sectors possessing elastic

demand functions. In this case, revenue losses resulting from quantity

increases would be less than a proportionate amount of the actual quan-

tity increase, and, thus, greater revenue.









Optimum allocation

Either of the two alternatives, price adjustment or product adjust-

ment, may be looked upon as intermediary steps to complete and optimum

allocation from the revenue standpoint. To maximize net revenue at the

industry level, complete knowledge of two economic forces, costs and

revenue, must be sought. The equation of the marginal quantities of

these two functional relationships will result in a maximization of net

revenue. The unique point of complete maximization occurs where industry

marginal costs are minimized and equated with industry marginal revenues

for the several orange products involved.

From the cost side of the equation, knowledge of the industry marginal

cost function is obligatory for each of the four orange product markets.

To minimize marginal costs for the industry, firm costs are required at

each possible level of production, since cost minimization requires that

the individual member firms' marginal costs be equated. This process could

be accomplished by allocating quotas to the individual member firms in

such a manner as to equate the marginal cost for each firm to the marginal

cost of every other firm for their respective quotas. If this allocative

procedure is followed, industry costs for any given level of output will

be minimized.

The foregoing analysis indicates the ideal situation from the stand-

point of minimizing industry costs. It requires that the firms within

the industry must yield to some central authority the ultimate decisions

relative to rates of output by individual firms. Although this procedure

attains an optimum condition in the industry cost structure, it is not a

necessary requirement for the utilization of the maximization principle.

As the industry chooses to deviate from the minimization of costs, total










net revenue declines. However, within the confines of any given system

of output allocation among firms and any industry cost level, net revenue

maximization can be attained by equation of the marginal cost and revenue

functions.

From the revenue side of this equality, full maximization requires

complete knowledge of the demand for oranges within sectors of the industry.

For a program of supply management, there must be information to guide

allocation of supplies among the various market sectors. A method must

be devised to show the marginal revenue for the industry's entire volume.

The availability of the sector demand functions would allow a summation

yielding a composite demand function for all oranges. From the sector

and composite demand relationships, marginal revenue functions can be

derived.

To determine optimum allocation among sectors, the industry output

must be allocated to equate the sector marginal revenue functions with the

marginal cost functions. In this allocative procedure, it may well be

determined that total industry output may be beyond the amount required

for maximization of revenue. Thus, to attain maximization of net revenue,

in addition to the allocation among market sectors, the need could exist

for limiting the total output to less than available supplies. In such

an event, economic abandonment of a portion of present supplies would be

a logical procedure to follow.

In contrast, if available supplies were less than the optimum out-

put, further expansion of the productive capacity of the industry would

increase revenue. Present supplies under this situation should be al-

located in such a manner as to minimize industry marginal cost.











It is recognized that total knowledge of the cost and revenue aspects

of an industry are rarely secured on a simultaneous basis. The utilization

of complete information concerning the demand relationships for the products

of the industry can be a practical intermediate step toward net revenue

maximization. Gross revenue maximization can be attained without cost

information. From the various sector demand relationships, the industry

demand function for all oranges can be obtained and, subsequently, a

total revenue function can be derived.

These functional relationships can be used to maximize gross revenue

by equating the marginal revenue functions for the four sectors. The

point of marginal revenue equation would be the quantity dictated by the

high point on the total revenue function, which also would be, of course,

the point of unit elasticity on the industry demand curve. Maximum

revenue would be received if supplies in each of the sector categories

were so allocated that the quantities of each would yield a marginal

revenue of zero. This is true only if the total supply offerings are

equal to or in excess of the high point on the total revenue function.

On the other hand, if total supplies are less than the quantity

dictated by the peak of the total revenue function, then maximizing

gross revenue would be a process of equating the sector revenues at

a point which would absorb all available supplies. This would, in

turn, allocate quantities and dictate prices among the various market

sectors.













CHAPTER II

PREVIOUS RESEARCH RELATING TO CITRUS DEMAND


Examination of Data Sources


The study of demand relationships has become an increasingly im-

portant field of research over the past several decades. A major dif-

ficulty the demand analyst has encountered in the past, and presently

faces to a lesser degree, is the source of data for estimating demand

relationships. Data from many sectors of the economy have been col-

lected in such a manner that the researcher has reason to question their

reliability as basic input data for demand estimation. Basically, this

situation stems from the fact that these data were not collected for

the purpose of demand estimation and consequently are not generally in

the form desired for such utilization. Further complications arise

from the analytical tools available to cope with and parcel out the

sources of variability existing in the basic data. Much of the data

available for demand estimation possess aggregation problems which

limit their usefulness. For commodities differentiated on the basis

of grade and size, much of the available data are presented in ranges

or averages. When these types of data are used for the estimation of

demand parameters, the results must be accompanied with many restrictive

qualifications.

Initially, estimates of demand relationships were derived from

yearly series of national aggregates. The input data used for this

44










early demand work were plagued, quite naturally, with many inadequacies.

Over the course of time these inadequacies have been remedied to some

extent. The severe problems associated with actual reporting of sta-

tistics two or three decades ago are presently of no major consequence,

with the technological advances which have occurred. The agencies whose

responsibility it is to gather statistics on production and utilization

have constantly sought to improve sampling and estimation procedures. In

addition, they have substantially broadened their base of reporting to

include further breakdown concerning grade, size, and other differenti-

ations.

However, from the standpoint of demand estimation, there still exists

many problems with time series data. During the past two decades, tech-

nological advances have taken place with extreme rapidity along with

changes in the consumption habits of the population. In many cases these

changes have caused difficulties in utilizing time series data. The in-

creased introduction of convenience into food and fiber processes has

operated to change the demand relationships over time, and compensation

for these factors appears to be quite difficult. Not only has the process

included innovations such as reduction of food preparation time but also

the introduction of old products in new forms. For example, orange con-

centrate came into existence in the middle 1940's. Compensation for the

effects of orange concentrate on other orange and citrus sales would be

extremely difficult.

Another question with regard to time series data lies in the identi-

fication of variables. While demand theory dictates the dependent variable

to be quantities taken and the independent or explanatory variables to be









prices, there is some debate as to the validity of time series data con-

forming to these theoretical requisites.

The use of consumption statistics and quoted prices from a series

to estimate elasticity coefficients appears to overstate price effects.

This is a result of exogenous variables upon which no quantitative measure

can be placed or at least, given the present state of the arts, has not

been quantitatively measured. For example, with regard to most commodities,

society is subjected to considerable merchandising and promotional activi-

ties. The extent to which these activities are effectual is included in

consumption disappearance. Demand work has generally taken on the charac-

teristic of estimating coefficients of elasticity rather than the creation

of demand surfaces recognizing price and other variables as explanatory

changes in consumption. Thus, when time series data are used for the esti-

mation of demand parameters and further defined in terms of price elasti-

city coefficients, the effects of price are overstated.

Disregarding the accuracy of estimating coefficients of elasticity

from time series data, a severe limitation does exist from the standpoint

of the range of variability in the proposed independent variables. The

range of prices existing over time resulting from the normal situation

is very limited. It therefore, follows that measurement of demand

relationships is acutely limited with regard to the scope of the function.

Another source of data for demand estimation that has gained much

favor in recent years is that generated from consumer panels. These data

are held by some to be superior to national and regional data collected

by the various data procurement agencies of state and national govern-

ment. However, these cross-sectional data are not without inherent

faults. They are to some extent subject to some of the difficulties

encountered in a general time series. Notable is the limitation in the








range of price or explanatory variables. Also, there exists the same dif-

ficulty as in time series with regard to the over estimation of price ef-

fects when these data are used for elasticity coefficient estimation. The

method of data collection, recall through personal interview or mailed

questionnaire, makes the data questionable from the standpoint of ac-

curacy, while yet another difficulty lies in the possibility of a non-

representative sample.

As a result of the difficulties found in these data sources and with

the evolution and advancement of research methodology, much consideration

has been given to the possible generation of basic input data from contr6l-

led pricing experiments. This technique has gained, in some quarters,

great impetus in forming the basis for estimating functional demand re-

lationships. The assets and liabilities of this method of procedure will

be discussed fully in a later section, since it was selected as the method

of procurement of the data for the empirical demand work upon which this

dissertation is based.


Citrus Demand Work


Over the years, more demand work has been directed to aggregation

of commodity groups than to individual commodities. Relatively little

research attention has been devoted toward an assessment of demand re-

lationships for individual commodities. This void is especially true

with regard to citrus products. Further, there has not been as much

work utilizing time series analyses as might be suspected.

Time series demand estimation has been more nearly confined to

basic agronomic commodities and meat products. However, some work has

advanced in specific fruit and vegetable areas and over fruit and vege-









table commodity groups. Brandow estimated demand relationships for

apples, recognizing orange production as an independent variable asso-

ciated with apple purchases.

More directly in the citrus field, Hoos and Boles reported a func-

tional relationship between California f.o.b. orange prices and four

independent variables.2 The variables included were (1) California fresh

shipments; (2) fresh shipments from other areas; (3) index of U. S. non-

agricultural income (1935 39 = 100); and (4) time. They found that

for the period 1925 through 1950, omitting the war years, 1942-45, that

some 89 per cent of the variation in California f.o.b. prices for summer

oranges was explained by these variables.

Powell and Godwin, using short term observed price-quantity data,

estimated demand relationships for fresh oranges. The purpose of this

study was to analyze demand relationships for certain citrus and non-

citrus products using data obtained under normal retail store performance

in Jacksonville, Florida and Memphis, Tennessee. To obtain information

with respect to income levels, each city was divided into low, medium,

and high income areas.

The data collection process included weekly visits to each of the

stores, an inventory being taken and recorded for each product included

in the study. All additions to stock received subsequent to the previous


G. E. Brandow, A Statistical Analysis of Apple Supply and Demand
(University Park, Pennsylvania, Agricultural Experiment Station, Penn-
sylvania State University, AE and RS No. 2, January 1956).
S. Hoos and J. N. Boles, Oranges and Oranqe Products Chanqing
Economic Relationships (Berkeley, California: California Agricultural
Experiment Station Bulletin 731, 1952).

3L. A. Powell and M. R. Godwin, Economic Relationships Involved in
Retailing Citrus Products (Gainesville, Florida: Florida Agricultural
Experiment Stations Bulletin 567, August 1955).










visit were also listed. From this information sales volume was determined

by subtracting the ending inventory for the current period from the sum

of stock receipts and the ending inventory of the preceding period. To

maintain exacting price-quantity data, inventories were taken each time

prices for the concerned commodities were changed.

Principal fruits included in the study were oranges, apples, grape-

fruit, and tangerines. In addition, five processed citrus juices and four

noncitrus juices were included.

Of the four fresh fruits, oranges ranked first in terms of quantity

sold accounting for in excess of 40 per cent of the volume. From the

standpoint of value, apples were the leading fruit of the four in

Jacksonville. In Memphis, however, in the low income strata, the value

of apples and oranges were of about equal magnitude, while the total value

of oranges exceeded that of apples in the other two income strata.

Estimated price elasticity coefficients in low, medium, and high

income areas of Jacksonville were 1.206, 1,329, and 0.860, respectively.

In a similar analysis utilizing the data gathered in Memphis, price

elasticity coefficients estimated for low, medium, and high income areas

were 1.782, 1.665, and 1.143, respectively. It was further noted that

orange concentrate was increasingly regarded as a fair substitute for

fresh oranges. This consumer preference may partially account for the

slightly higher coefficients derived from the Memphis study, conducted

approximately nine months later than the Jacksonville study.

In 1952, Godwin, using controlled pricing techniques, developed a

functional quantity-price relationship utilizing controlled prices per








4
dozen of oranges. Seven levels of price were included in the study,

three 5 cent deviations on either side of the mean price. The methodo-

logical procedure followed was the artificial inducement of price vari-

ation above and below the established market price over a relatively

short period of time. This study was done at the retail level of distri-

bution utilizing seven supermarkets in central Kentucky. As higher prices

were induced the total volume sold in the stores tended to decline.

A functional relationship was derived by fitting an orthogonal

polynomial. The coefficient of price elasticity for the curve as a

whole was 1.160. The degree of elasticity varied considerably over the

range of prices tested, with greatest elasticity near the established

market level. An elasticity approximating unity was found at a discount

of 15 cents per dozen. At prices representing an increase of 10 and

15 cents above the normal market, the demand function becomes inelastic.

Using similar methodology, Godwin and Powell studied the effects

of price on frozen orange concentrate. This study was conducted in 10

supermarkets in the Lower Delaware Valley area of Pennsylvania, and

New Jersey. The test prices differentials included in the study were

as follows: the price in effect at the time the study was initiated;

prices 3, 6, and 8 cents per 6-ounce can below the market price; and

one, 4 cents higher. By this method, consumers were subjected to re-

tail prices varying over a range of 12 cents per can. Although the

retail units carried three types of orange concentrate--namely, a

nationally advertised brand, a private label, and a packer label--no


M. R. Godwin, Customer Response to Varying Prices for Florida
Oranges (Gainesville, Florida: Florida Agricultural Experiment Stations
Bulletin 508, December 1952).










distinction was made with regard to the appropriate deviation dictated by

the pricing differential. For example, when the six cent deviation was

applied, each type of concentrate was reduced by six cents.

The prices employed in the study were 8.5, 10.5, 13.5, 16.5 and

20.5 cents per 6-ounce can. Analysis of the results of the pricing

experiment indicated marked variation in concentrate purchases over the

range of prices tested. Variations in purchase rates in response to

the induced prices indicated that customer sensitivity to price change

declined continuously as price was varied from the lowest to the highest

test price. The theoretical price of 12.5 cents per can was found to

be the price at which unit elasticity was found. At test prices below

this level, the demand function grew more elastic, and, conversely, at

higher levels the demand function became more inelastic.

An interesting aspect of this study was the provision in the ex-

perimental design to compensate for possible price carryover effects

attributable to storability of orange concentrate. This possibility

was treated by the continuance of the same price treatment in each

store for a period of several weeks.

In summary, a relatively small amount of work has been done in the

area of demand estimation for citrus fruits. This gap is especially

true prior to 1950, and since that time most consistent attention has

been devoted to this economic area by the Florida Agricultural Experiment

Station, specifically by Professors Godwin and Powell. A further area

long neglected in all commodity demand work is that of economic substi-

tution among products. As methodological advances progress, it appears

that the substitution effects of price changes will move to the fore-

front as a significant area of economic research.













CHAPTER III

PURPOSE OF PRESENT RESEARCH AND SPECIFIC PROBLEM ORIENTATION



The present study was designed to investigate the competitive re-

lationships among Florida Indian River, Florida Interior and California

Valencia oranges for fresh market. This project constitutes one phase

of a broad research program, the objective of which is to determine the

nature of economic competition among citrus producing areas of the United

States by obtaining estimates of demand and substitution relationships for

principal citrus products.

The production of citrus fruits provides much of the farm income

in Arizona, California, Florida, and Texas. These citrus crops are

marketed in many forms. At present little is known about the economic

interrelationships among these products in the marketplace. The multi-

plicity of the products produced in the citrus industry makes the question

of the interrelationships among them highly complex. However, the dynamics

of the citrus industry are such that there is a need to identify and assess

the importance of these relationships.


The Specific Problem


Interregional competition within the orange industry is primarily

in the fresh fruit sector. In the United States the majority of oranges

for fresh market is produced in Florida and California. On the basis

of the ratio of fresh fruit sales to processing sales the former is more









vital to California than Florida. However, recognizing that Florida oranges

are marketed along with California oranges throughout the orange season,

the economic interrelationships in the fresh market are of utmost importance

to Florida. Another pressing question is the degree of economic competition

between oranges produced in the Indian River and Interior districts of

Florida. Disregarding differences resulting from variety, grade, size,

and other distinguishing characteristics, within Florida and California

in reality three differentiated producing areas produce and market oranges.

Further, there exists three separate demand functions for oranges produced

in these three areas, and to some degree economic substitution rates among

them.

The purpose of this research was to measure the degree to which price

changes could alter the consumption patterns of the three types of oranges.

The measures sought were defined in terms of price and cross-price elas-

ticities of demand. Stated formally the specific objectives were these:

(1) Estimate price elasticity of demand coefficients for Florida
Indian River, Florida Interior, and California oranges and,

(2) Estimate cross-price elasticity of demand coefficients for
Florida Indian River, Florida Interior, and California
oranges with respect to the prices of the other two oranges.

Since there were within each of the three producing areas differences

in oranges as to varieties, grades, and sizes, determinations were neces-

sary to ascertain which of the characteristics within these variables to

use in the measurement of the demand relationships.


Variety

In the determination of the variety over which the demand relation-

ships were to be measured, two major considerations evolved. One of

these was related to the relative volumes produced and the second to the









degree of competition in the marketplace between the Florida and California

varieties.

The major variety produced in Florida is the Valencia. This variety

is also predominant in California production. Valencia oranges from the

Indian River and Interior districts of Florida are marketed along with

California Valencias throughout the season. Few other orange varieties

are available for the national market during the spring and early summer

months when the Valencias are in peak production. During the 10 year

period 1952 through 1961, Valencia oranges accounted for an average of

43.4 per cent and 60.2 per cent of total orange production, respectively,

for Florida and California. Thus, the Valencia fruit from each of the

three areas was selected as the most important fruit for which to esti-

mate demand relationships.


Fruit sizes

Based upon information relative to the distribution of sizes of

fruit produced in the three areas, consideration was given as to what

size or sizes must be included in the study to realize an effective

measure of demand relationships for Florida and California Valencia

oranges. The sizes predominant in Florida Valencia production are from

size 163 to size 252 (Table 14). The average diameter of this fruit

ranges from 3.063 inches for size 163 to 2.625 inches for size 252.

During the season immediately preceding the study, 21.3 per cent

of the Indian River Valencia oranges moving through interstate commerce


Percentages derived from the report of the Growers Administrative
Committee, Lakeland, Florida.









was of the size 163, and 36.22 per cent of the Interior Valencia fell

into this category. In this same season 41.02 per cent of the Indian

River Valencia oranges moving into interstate commerce was of size 200,

and 40.52 per cent of the Interior fruit was of this size.

California Valencia oranges, characteristically smaller than Florida

Valencias, also have two dominant sizes: size 113 and size 138, which

have an average diameter of 2.600 inches and 2.240 inches, respectively

(Table 14).

During the season immediately preceding the study, 33.0 per cent

of the Valencia oranges marketed by a leading California citrus marketing

firm was of size 138. In this same season 31.7 per cent of the Valencia

oranges produced in the central California area, approximately 90 per cent

of the State's production, was of size 113, and 32.9 per cent was of

size 138.3

Historically the sizes of predominance indicated above have been

the norm. This pattern, therefore, evolved consideration of two sizes

from each state over which the demand estimate should be made.

Based upon this information and recognizing the limitations placed

upon the study from the standpoint of capital and management, the Cali-

fornia size 138 was selected as the representative size California Valencia

for the study. An ordering of Florida Valencia oranges was made, with

the first choice being the size 200 and the second choice the size 163.


2 Ibid.

Derived from data of the Valencia Orange Administrative Committee,
Los Angeles 15, California.









Table 14.--Size distribution, Florida Indian River,a Florida Interior, and California Valencia
oranges, 1960-61 season.



Area of Production

Florida California

Indian River District Interior District

Container Average Per cent of Container Average Per cent of Container Average Per cent of
Size Diameter Total Size Diameter Total Size Diameter Total

Number Inches Per cent Number Inches Per cent Number Inches Per cent

96 3.527 .1 96 3.527 .1 72 3.040 2.0
125 3.313 5.5 125 3.313 7.7 88 2.840 11.0
163 3.063 21.3 163 3.063 36.2 113 2.600 31.0
200 2.875 41.0 200 2.875 40.5 138 2.420 33.0
252 2.625 30.2 252 2.625 15.0 163 2.290 15.0
324 2.313 1.9 324 2.313 .5 180 2.220 7.0
-- -- -- -- ---- 245 1.980 1.0

aDerived from Interstate shipments; source: Growers Administrative Committee and Shippers
Advisory Committee Report, Lakeland, Florida.

Derived from data furnished by one of the leading California citrus marketing firms. These
data represent the entire 1960-61 season's volume of this firm.










This decision led, as further explanation will indicate, to form the

basis for two major experiments.


Fruit grades

Dominance of the U. S. No. 1 grade in all three areas of production

established it as the grade over which to measure the demand relationships.


Specifications of the Research Problem


By virtue of the size distribution for Florida Valencia oranges,

the desirable measure of competitive relationships between Florida and

California fruit would include both of the modal sizes of Florida Valencia

oranges. The inclusion of sizes 200 and 163 from the Indian River and

Interior Districts of Florida and size 138 from California evolves into

six basic relationships for study (Table 15). These relationships pro-

vide quantitative measures of the nature of competition among these fruits

in terms of price and cross-price elasticity of demand. Within each re-

lationship the effect of the price of one specific orange type upon the

quantity taken of the same orange type defines the price elasticity of

demand. On the other hand, the effect of the price of one specific orange

type upon the quantity taken of another orange type defines the cross-price

elasticity of demand.

The basic procedure selected to obtain data of the type required to

measure the competitive relationships between Florida and California

Valencia oranges consisted of a series of experimental tests conducted

at the retail level of distribution under controlled conditions.









Table 15.--Basic demand relationships, Florida Indian River sizes 200 and
163, Florida Interior sizes 200 and 163, and size 138 California Valencia
oranges



Quantities taken of As a Function of the
Valencia oranges Prices of

Area of Production
and Size Area of Production

Florida: Florida Indian River Florida Interior California
Indian River: Fruit Size
Size 200 200 200 138
Size 163 163 163 138
Interior:
Size 200 200 200 138
Size 163 163 163 138
California:
Size 138 200 200 138
Size 138 163 163 138


Rationale Underlyina Method Selection


Controlled experimentation offer an opportunity to overcome some of

the inherent difficulties found in secondary data. The researcher can

adequately describe, with precision, the demand side of the market for

a specific commodity. By creating the controlled situation, he can cope

successfully with such variables as advertising, quality levels, display

size, and location, plus commodity characteristics such as size and grade.

During the reasonably short time required for generating adequate data,

he can comfortably assume constancy of consumer income, prices of other

goods, general level of prices, and consumer tastes and preferences.

One advantage of controlled experimentation to estimate demand re-

lationship lies in the fact that the researcher can obtain parametric









estimates of demand for a dynamic industry. The relative rapidity with

which data can be collected by experimentation makes the approach quite

suitable for studying the demand for products under the stress of final

product changes and innovations.

The major advantage of the controlled experiment is the ability to

manipulate price and thereby describe a wide range of price-quantity re-

lationships beyond the experience of the market. When an industry is

undergoing rapid production changes, demand relationships estimated from

data generated in controlled pricing experiments can yield results which

have application to the changing supply situation. For example, Florida

orange production increased 30 per cent from the 1960-61 to the 1961-62

season, a heretofore unheard of increase. It is not reasonable to assume

that demand estimates from a historical production base and the uncontrolled

experience of the market could yield demand information which would cover

this great a change. By utilizing a controlled pricing scheme and deviating

price above and below the normal market situation, estimates of price elas-

ticity can provide a basis for determining direct price effects of larger

changes in supply conditions.

In addition to obtaining direct price effects in terms of price

elasticities, the controlled experiment is conducive to the exploration

of economic substitution rates. By inclusion of two or more major com-

modities or ccimodity characteristics and manipulating price over them,

one can obtain estimates of the cross elasticity of demand. Price manip-

ulation, coupled with adequate control, provides for observation of the

decision-making process in an atmosphere of varying price differentials

between a good and assumed substitute goods. For example, in the present

research problem, there is, in addition to the concern over the effects










of Florida Indian River price upon Florida Indian River sales, an especial

interest in the effects of California price upon Florida Indian River

sales. The controlled pricing experiment allows the pursuit of information

to answer such questions.

These characteristics render controlled experimentation one of the

most powerful generative devices the economist has today for providing

input data to estimate demand and substitution relationships.

Notable among the disadvantages of the experimental approach is the

high cost involved in the effective generation of data for the estimation

of demand relationships. There must be a system of adequate mechanics to

facilitate the data collection. This requires a number of personnel as

well as a system to compensate for losses directly relating to the study.

The costs involved in creating the controlled situation can be classified

into three categories: administrative, logistical, and operational losses.

The extent these vary with respect to shares is dependent primarily on

the nature of the study. Administrative costs include all outlays for

physical procurement of the data, such as enumerator, delivery and super-

visory personnel. Logistical costs can be incurred as a result of personal

delivery to the stores, outlays for physical storage of the commodity

or commodities, and other costs involved with the physical handling

of the product. Operational losses arise as a result of payments for

price differentials below the normal market, payments for quality main-

tenance in the case of a perishable commodity, and other preagreed pay-

ments.

The disadvantage most often mentioned is that in such a study the

researcher gains knowledge of great substance but relatively limited

generality. The validity of this alleged disadvantage is really a










question of scale, stemming from the limited population reached by a given

experiment and the difficulty in obtaining a localized representative popu-

lation. Conceptually, if a researcher could divide a commodity market into

regions which would provide a cross section of the market population, and

if representative cities were selected in each region to conduct experi-

ments, he could gain generality and still maintain substance of unquestion-

able validity. Once the cities were selected, a cross section of the city

population based on census tracts and other known information could be ob-

tained. If, for example, the midwestern and eastern United States' market

for fresh Florida oranges were divided into 5 or 6 regions, with appropriate

cities selected to represent these regions, estimates of demand relation-

ships would yield the composite demand for the entire market area.















CHAPTER IV

RESEARCH METHODOLOGY



In an analysis of the demand for fresh oranges, economic logic

must provide the framework within which the statistical computations

are made in obtaining estimates of demand and substitution relation-

ships. The theoretical framework, within which the demand relation-

ships for fresh Valencia oranges were developed, was regarded as

lying within the body of neoclassical demand theory doctrines. This

theory is based upon the premise that each consumer possesses a given

set of preferences. Further, it is assumed that each consumer chooses

from among alternative combinations of goods and services. This selec-

tion is done in such a manner as to maximize satisfaction within the

confines of a given set of market prices and is subject to the level of

income available for expenditure on consumption of these goods and ser-

vices. Thus, the quantity of a given orange type purchased by an ag-

gregation of consuming units, per unit of time, as of a particular time,

was assumed to be a function of (1) the prices of that particular orange

type; (2) the prices of other orange types; (3) the prices of closely

related substitutable products; (4) tastes, preferences, and real income;

and (5) the attitude of the group concerning future prices of oranges

and substitute products.









The Economic Model


A model conceptualizing the demand relationship for fresh Valencia

oranges may be written as follows:

ijk = f(Xli, X2i' X3i; XlXl' Xj' X an,' a2' an+l, (4.1)

where:

Yijk = quantity disappearance in the k-th observation of
the i-th Valencia orange type as the j-th level
of prices of all goods and services, consumer in-
come, and other preference factors.

Xli = price of a particular Valencia orange type.

X2i = price of a second Valencia orange type.

X31 = price of a third Valencia orange type.

X.j = the general level of prices of all goods and services.

X2j = consumer income.

X 3j...X = other preference factors.

al a2...an+l = a set of parameters that connect Yi with all
factors X., and X..
n nj

The economic model attempts to portray the relationships believed

to exist in the real world situation between the preference of consumers

for Valencia oranges and the monetary values placed upon these pref-

erences. The model, therefore, has many explanatory variables, variations

which, either separately or in combination, affect quantity disappear-

ance. In demand analyses, quantitative measurements have been placed

directly on a portion of these variables, while the remainder are passive

elements affecting the quantitatively measurable variables. The effect

of price of a given Y. on purchases of the same Y. is measured in terms
I I
of the price elasticity of demand. Changes in the purchase rates of

a given Y., resulting frcm changes in the price of a second or third










Y., are measured as the cross elasticity of demand. A change in purchases

of a given Y. resultant of a change in consumer income is measured defin-

itively in terms of income elasticity of demand. Other explanatory vari-

ables, the general level of prices of all goods and services, and other

preference factors operate to modify the measurements attainable in the

quantitative measures of the elasticity coefficients.

Specifically, this model specifies the quantity-price relationships

for the three Valencia oranges at a given level of other variables. It

is designed within this framework to explain the behavior patterns of

consumers as well as modifications resulting from a changing orange

price structure.


The Statistical Model


In the generation of data reflecting consumer decisions regarding

the purchase of fresh oranges, two fundamental assumptions are (1) in

the aggregate, consumers possess a basis for discrimination in their

decision-making process relative to purchases, and (2) in the aggre-

gate, consumers possess sufficient information to render their basis

for discrimination operational. With these assumptions and the basic

objectives of estimating coefficients of price and cross-price elasti-

city, the statistical model was developed.

The economic model depicted in equation 4.1 was conceptual and

no attempt was made to estimate all the parameters involved. Rather,

data were generated to estimate the effects of price and changing price

structure upon quantity disappearance of each of the three Valencia

orange types, other variables remaining constant. Consistent with these

requirements, the statistical model formulated to describe the functional









demand relationships for fresh market Valencia oranges produced in the

three areas is as follows:


Y' =
Y-ijk

Y2-ijk

Y3-ijk


1' 0

13~


+ 3X-i + j312X2-j + 13X3-k + l-ijk

* P21XI-i + 322X2-j + 3233-k + 62-ijk

+ 331X-i + -332X2-j + P33X-k + 63-ijk


(4.2)

(4.3)

(4.4)


Yi-ijk


Y2-ijk


Y3-ijk


N 0'

/3,1'


320'

A12


30

P13


A21' P22' A23


331' P32' 133



ijk' X2-ij


l-ijk' 2-iJ.i


= log of the quantity of Florida Indian River Valencia
oranges purchased.

= log of the quantity of Florida Interior Valencia
oranges purchased.

= log of the quantity of California Valencia oranges
purchased.

= log of regression constants (Y intercepts).

= regression coefficients associated with Florida
Indian River Valencia oranges (price elasticity
and two cross elasticity estimates).

= regression coefficients associated with Florida
Interior Valencia oranges (price elasticity and
two cross elasticity estimates).

= regression coefficients associated with California
Valencia oranges (price elasticity and two cross
elasticity estimates).

, X' -. = log of prices of Florida Indian River,
S-ijk Florida Interior, and California Valencia
oranges.

, E. = random disturbance associated with Y,
S Y and Y;.
23


This system of equations allows the simultaneous consideration of

the direct and cross-price effects on quantity disappearance at the

retail level for the three orange types. Verbally, the expressions

stipulate that the quantity taken of any specific orange type is a

function of a constant ("Y" intercept), the price of the orange type


where:










in question, the prices of the other types of oranges available, and a

random disturbance which is assumed to be normally, and independently,

distributed with a mean of zero and constant variance.


Assumptions

There are several assumptions both explicit and implicit to the

model formulation. Explicit assumptions relate to the statistical

formulation, while the implicit assumptions'are those which must be

made in order to couch the model in the theory of demand.

In constructing the model as a linear logarithmic function, two

basic considerations must be made. One of these relates to the neces-

sity for transformation of the variables to logarithms, and the other re-

lates to the logic of the utilization of constant elasticity coefficients

derived from the logarithmic equations.

The use of the logarithmic function provides a corrective measure

to insure against nonadditivity when the treatment effects are of a

multiplicative nature. Common is the assumption of multiplicative ef-

fects in economic data. If the operations producing the data are of

such a nature that the effects are really not additive, then the sums

of squares attributable to such effects do not represent the true effects.

Effects which are multiplicative on the original scale of measurement be-

come additive on the logarithmic scale. By transforming to the log-

arithmic scale, additivity is introduced. This introduction of addi-

tivity rules out interaction effects between prices and the error term

associated with quantity disappearance. In effect, this conclusion means

that regardless of what the level of prices P. may be, a random term of

a given magnitude always has the same effect on quantity disappearance.










In regards to the logic of the assumption of constancy, with respect

to the price elasticity, it appears to be a feasible assumption, especially

as the first approximation. Although the elasticity of demand with respect

to price may change from one price to another, it is desirable to obtain

an average elasticity over some specified range of prices. Such an esti-

mate of price elasticity may be quite sufficient for guidance in some of

the preliminary adjustments outlined in Chapter I. It is recognized that

a more sophisticated estimate relating to given price levels would be re-

quired as the adjustment process moves close to the maximizing position.

However, since such a position is not eminently foreseeable, the constant

elasticity function produced by the logarithmic regression is quantitatively

appropriate at the present stage of adjustment.

Although the parameters in equations 4.2-4.4 are assumed to be multi-

plicative, they are further assumed to be independent. The controlled

manipulation of price according to a predetermined plan forces conformity

to this assumption. In addition, controlled price manipulation coupled

with managed unlimited supplies clearly identifies the dependent variable

as quantities taken and the independent variables as prices.

Assumptions necessary and sufficient for the application of the

statistical model to test the postulated economic model include the

assumptions underlying consumer demand. These assumptions must remain

constant as price is varied in order to determine the direct and cross

effects of price.

Of major importance is the movement incurred in the general level of

prices. In the relatively short period of time required for generating

data in a controlled experiment at the retail level of distribution,

the assumption of constancy of the general level of price appears quite










feasible.

Another variable eliciting much concern in the estimation of demand

relationships is that of consumer income. Here again, during the short

time required to generate the data through retail store experimentation,

It can be safely assumed that no significant variation occurred.

To control a source of variation which limited time periods do not

preclude, much attention was devoted to the control of advertising and

merchandising promotional activities. Since these forces form the basis

for short run changes in consumer tastes, preferences, and expectations,

It becomes Imperative to impose restrictions on these activities. To

accomplish this objective, advertisement and merchandising promotional

programs for fresh oranges were eliminated during the test period. With

regard to longer-run changes In tastes and preferences, the time element

in controlled experimentation is sufficiently short to preclude any basic

changes in these factors.


The Experimental Model


The experimental model selected for generating the data required

to estimate the parameters of equations 4.2-4.4 was the Triple Cube

design. This design, an outgrowth of the central composite designs

developed by G.E.P. Box and Associates, was developed by T. E. Tramel



For a description of the Box design see: Box, G.E.P. and Hunter,
J.S., "Experimental Designs for Exploration and Exploitation of Response
Surfaces," Proceedings of Symposium on Design of Industrial Experiments
(Nov. 5-9, 1956) pp. 138-192, Institute of Statistics of the Consolidated
University of North Carolina, and Box, G.E.P., Haden, R.J., and Hunter,
J.S., Experimental Designs for Multifactor Experiments, Institute of
Statistics Mimeo No. 71, Raleigh, North Carolina, 1953.









and suggested for use in Agronomic-Economic fertilizer experiments.2

The original Box design is considered quite efficient in estimating

parameters of a quadratic function. In the development of the basic design,

Box and his associates were interested primarily in industrial experiments,

and consequently the requirements for such work were well adapted to a very

limited number of observations dictated by the single cube.

Generally, more variables can be controlled in industrial work than

in economic work. Therefore, for an equal level of precision, a greater

number of observations is needed in the latter than in the former. Repli-

cation is one solution to this problem. An alternate solution is to modify

the basic design to accommodate a wider range of measurement. Such a pro-

cedure gave rise to the Triple Cube.

A total of 15 treatment combinations are derived from the original

Box design. With respect to the cube, the treatment combinations may

be divided into three categories: (a) those forming the corners of the

cube, (b) those on the three major axes, and (c) the one at the center

of the cube. Thus, the cube plotted in three dimensional space reflects

eight treatment combinations from the corners of the cube, six treatment

combinations on the major axes equidistant off each face, and one combi-

nation located in center of the cube (Figure 2C).3



Tramel, T.E., "A Suggested Procedure for Agronomic-Economic
Fertilizer Experiments,".' Chapter 15, Economic and Technical Analysis
of Fertilizer Innovations and Resource Use, edited by: Baum, E.L.,
Heady, E.O., Pesek, J.T., and Hildreth, C.G., The Iowa State College
Press, Ames, Iowa, 1957.

The original Box design also had the observation in the center
of the cube such as is shown in Figure 2A.

















X (.1, 1, .1)
(-1, -1, 1)-
(-1, -1, -1),

X/
X3
(-2, 2,


I /


Figure 2.--Component cubes of the Triple Cube Design.


X3


S(1, -1)
- (o, 0, 0)


-Xl


X3

(3, 3, 3)










- -X,



(3, -3, 3)


(-3, 3,


Xi-










(-3, 3, -









The modification developed by Tramel was the addition of two more

cubes, increasing the number of treatment combinations by 16 (Figure 2B,

Figure 2C). Hence, total treatment combinations were increased to 31,

24 of which are formed by the corners of the three cubes, while the

remaining are those on the major axes plus the one in the center of the

system as in the original design (Figure 3).

Tramel in his work measured the relative efficiency of the Triple

Cube as compared with the original Box design and found a considerable

increase in efficiency. The greatest increase in precision was found

in the estimation of the intercept and in the interaction terms. How-

ever, a worthwhile increase in precision was brought about in the esti-

mation of the quadratic terms.

The utilization of this design for the allocation of price treat-

ments to generate input data for demand estimation is particularly ap-

propriate. Aside from the efficiency gains resulting from the use of

the Triple Cube, it allows a wide range of price levels. Application

of the design permits the use of nine price levels in combinations dic-

tated by the Triple Cube. Using the major axes as a focal point and

mean level, four deviations on either side of the mean are available.

The availability of nine price levels was considered quite adequate

for the measurement of demand relationships for the three Valencia

orange types.

Another question of significance related to the likelihood of dif-

ferent base prices for the three Valencia oranges used in the study.



Tramel, op. cit.


























X20---_
S -4
X2 -


Figure 3.--The Triple Cube Design.










The Triple Cube accommodated this requirement in that the base prices

could be different for all three orange types if this were the case

at the time of market entry.

A last important influence on the selection of the Triple Cube was

that it adapts quite well to the experimental approach to demand esti-

mation. The fact that this approach has high capital requirements has

placed many researchers in this area in a position of estimating functional

relationships on a much smaller scale, either in terms of number of com-

modities considered or in terms of price levels over which to estimate.

On the one hand, a more orthodox design which accommodates three or more

commodities may also require a large number of retail stores, an impos-

sibility from the standpoint of management and resources. On the other

hand, increases in the number of price levels utilizing some of the more

conventional experimental models lengthens the time required to generate

the data to an unbearable financial extent. More frequently than not,

the more conventional experimental models impose some combination of the

aforementioned problems, so the researcher is forced to choose among

fewer price levels or fewer commodities or both.

The Triple Cube alleviates these problems to a degree. It provides

a fractional replication with respect to treatment combinations which

have semiorthogonal properties. Therefore, it requires fewer observational

periods to generate adequate data to estimate the demand parameters, for

a given number of price levels, and allows estimation of these parameters

for three commodities or commodity characteristics. These properties make

it a highly desirable experimental model for demand estimation.











Limitations of the Model Formulation


Unlike some of the more orthodox experimental approaches, the

model formulation had no inherent facility to account for or parcel

out extraneous variation. Retail stores in a metropolitan area will

vary considerably. This variation can be classified basically into

two categories: (1) differences in store volumes and (2) differences

in clientele. These variations are generally a result of socio-economic

differences as well as differences in the population base the store serves.

Since volume of the individual store is affected by the population

base the store serves, a correction for difference in traffic flows

would tend to eliminate this source of variation. Thus, to compensate

for these differences, a transformation, in the form of a reduction of

sales to a per 100 customer basis, was planned.

Clientele differences are basically in the realm of socio-economic

considerations, in that these could be due to ancestral differences,

economic differences, and social differences. This category presupposes

an adequate cross section of these population characteristics over which

to measure demand relationships. Careful selection of stores can insure

coverage of the heterogeneity of the market population. Although it is

desirable to have a measure across this heterogeneous population, it

is also desirable to reduce the heterogeneity to more homogeneous popu-

lation by removing differences in purchase habits among the various store

populations. Since the product with which the research was concerned

was in the produce line, fresh orange purchases were assumed to be a

function of produce purchases. Therefore, to remove differences in pur-

chase habits of the clientele of the various stores, a measurable variable,









value of produce sales, was planned for inclusion.


The Statistical Model Redefined


Consistent with the transformation of sales to a per 100 customer

base and the addition of the variable, value of produce sales, the

statistical model redefined is as follows:

Yj .. =30 + plXl i + + X' I+3X3 + I X + (4.5)
-ijkm = 10 P -i- + 122-j 13X-k 14Xm -ijkm

2-ijkm = 20 + 21X-i + 22X2-j + P23X3-k + 24m + 2-ijkm (4.6)

Y3-ijkm = P30 + -31XI-i + I32X2-j + P33-Xk + '34Xm + 3-ijkm (47)

where:

Y-ijkm = log of the quantity of Florida Indian River Valencia oranges
purchased per 100 customers.

Y'-ijkm log of the quantity of Florida Interior Valencia oranges
purchased per 100 customers.

Y-.km = log of the quantity of California Valencia oranges pur-
chased per 100 customers.

P;1, 20', 30 = log of regression constants ("Y" intercepts).
P11, P12' 13 = regression coefficients associated with Florida
Indian River Valencia oranges (price elasticity
and 2 cross elasticity coefficients).

P21' P22' P23 = regression coefficients associated with Florida
Interior Valencia oranges (price elasticity and
2 cross elasticity coefficients).

P31' 32' 133 = regression coefficients associated with California
Valencia oranges (price elasticity and 2 cross
elasticity coefficients).

P14' P24' 134 = regression coefficients associated with value of
produce sales per 100 customers with respect to
YV, Y2, and Y3.

X' ., Xj' '-k= log of prices of Florida Indian River, Florida
Interior, and California Valencia oranges.










E6' ..m' E ..ijk' ,ii = random disturbances associated with
1i-ijkm' 2-ijkm 3-ijkm Yi, Y' and Y'.
1' 2 and


Specifications of Experimental Test


Upon completion of the delineation of variables, construction of

the economic model, and formulation of a statistical model to test the

economic model, evaluations were made concerning the specifications of

the tests to be conducted.


Size limitations

The size of the tests was limited by three major factors: (1)

dictates of the experimental design, (2) management, and (3) resources.

Attention was given to each of these in formulating the specifications

of the tests.

The Triple Cube design used for the data generating model dictated

a requirement of 31 pricing periods or observations per replicate. A

further consideration was the fact that there was no accounting for the

differences in time periods inherent in the model. To compensate for

time, a system of balance must be built into the design layout.

The first element was the length of the observational period.

The alternatives considered were one-half week periods, two-day periods,

and one-day periods. The process of logical determination of an adequate

time period was not only a function of consumer habits in relation to

frequency of grocery purchase but also a function of the habits sur-

rounding the commodity of interest, fresh oranges.

The decision, recognizing the needed control of variation due to

differences in days as well as in weeks, was to use a one-day observational

period. It was recognized that normally the distribution of shoppers is










more heavily concentrated in the latter part of the week. However, consumers

shopping in the early portion of the week may be quite unlike those in the

latter part of the week. In fact, it appears reasonable that when looking

at the aggregation of consumers shopping in a given week, one might well

have a different population on each day. The time for grocery shopping

in a given household tends toward an institutional arrangement by habit.

Further, credence is added to the daily observational period upon exami-

nation of consumer habits with regard to the purchase of fresh oranges.

Basically the grocery shopper enters a grocery store for one of two pur-

poses, the purchase of a full grocery order or the selection of a few

items such as milk, bread, or occasionally meats to fill in between

grocery orders. In general, most items in the grocery budget are pur-

chased at one time during the week. It was considered that, in the

main, fresh oranges would be an unlikely item to be purchased between

grocery orders. Therefore, daily observational periods would not create

undesirable distortion in consumer purchase rates.

The removal of time period variation as indicated above had to be

built into the design layout. Since the generating model dictated 31

price combinations to appear in each store used in the study, 31 ob-

servational periods were also required. Identification of an obser-

vational period as one day further required 31 operational days. Pro-

jecting a six-day operational week, two alternatives were considered

to compensate for time period variation by a system of balancing treat-

ments over days:

1. Using three stores and randomly assigning the 31 pricing treat-
ments to ore store and then balancing the treatments over two-
day periods in the two remaining stores. This would result in
every pricing treatment appearing once on a Monday-Tuesday,
a Wednesday-Thursday, and a Friday-Saturday at some time during
the study.









2. A second alternative, and the optimum, was to use six stores
in which the 31 pricing treatments were randomly assigned in
one store and balanced over days for the remaining five stores.
This plan would result in a complete balancing of pricing
treatments over days, since each treatment would appear once
on each day in some store included in the study.

Upon examination of capital resources available for this work and

the human resources considered essential for the conduct of the study,

it was evident that the inclusion of the two experiments of six stores

was prohibitive. However, the resource outlay could support the utili-

zation of nine stores. In conformance with the restrictions from the

standpoint of resources, two simultaneous experiments were conducted,

utilizing both alternatives of balancing pricing treatments over time.

From one of these experiments data were generated for the estimation of

demand relationships for California size 138, Florida Indian River size

200, and Florida Interior size 200 Valencia oranges. This particular

experiment was conducted in six stores and thus contained complete

balance in the compensation for time period variation. The second

experiment was for the generation of data to measure the demand re-

lationships for Florida Indian River size 163, Florida Interior size

163, and California size 138 Valencia oranges. This experiment was

conducted in three stores and contained a pricing treatment balance

over two-day periods, a partial compensation for variation due to

differences in time periods. The selection of Monday-Tuesday, Wednesday-

Thursday, and Friday-Saturday for the three sets of two periods was

based upon the assumption that these pairs of days would be the most

comparable from the standpoint of the consumers patronizing the stores.


Price differentials

The generating model utilized in the study allowed for nine levels









of price. To insure a range of prices which would be relevant under

foreseeable changes in the quantities available for the fresh orange

market, much thought was given to the size of the differential to be

used. On the basis of prices per dozen for fresh oranges, a four cent

differential was selected. Among the factors relating to the differen-

tials was the need for conformity to conventional pricing procedures.

Accordingly, the differentials had to be even integers greater than one

to produce odd cents per dozen pricing, starting from a base stated

in odd cents. Further, from the desire to cover the relevant range

of prices foreseeable and to force substitution within the range, the

four cent differential was selected. Thus, from a given base price

there would be deviations of -16, -12, -8, -4, +4, +8, +12 and +16

cents. The 31 treatment price combinations in terms of four cent

differentials are shown in Table 16.


Experimental design layout

The allocation of pricing treatments to stores was of crucial

concern, since the system of balance over time periods had to be

built into the design layout. In the experiment involving Florida

Indian River size 200, Florida Interior size 200, and California

size 138 Valencia oranges, the 31 pricing treatments were randomly

assigned to one store and balanced over the other five stores.5 This

assigning was done so that each treatment appeared in a store on each

day of the week at some time during the test (Table 17). For example,



Hereafter, the experiment involving Florida Indian River and
Interior size 200 and California size 138 will be referred to as
Component I.










Table 16.--Treatment price combinations, in terms of four cent devia-
tions, used in estimating demand relationships for Florida
and California Valencia oranges for fresh market.



Florida Florida California
Indian River Interior Oranges
Oranges Oranges


-16
0
0
-12
-12
-12
-12
-8
-8
-8
-8
4
-4
-4
-4
0
+4
+4
+4
+4
+8
+8
+8
+8
+12
+12
+12
+12
0
0
+16


0
-16
0
-12
-12
+12
+12
-8
-8
+8
+8
-4
-4
+4
+4
0
+4
+4
-4
-4
+8
+8
-8
-8
+12
+12
-12
-12
0
+16
0


0
0
-16
-12
+-12
-12
+12
-8
- 8
-8
+8
-4
+4
-4
+4
0
+4
-4
+4
-4
+8
-8
+8
-8
+12
-12
+12
-12
+16
0
0







Table 17.--Component I experimental price design for the study of the competitive relationships among
size 200 Florida Indian River, size 200 Florida Interior, and size 138 California Valencia
oranges, Grand Rapids, Michigan, April-May, 1962.



Store Number
Day of
Week 1 2 3 4 5 6
Week
IR Int. Cal. IR Int. Cal. IR Int. Cal. IR Int. Cal. IR Int. Cal:. IR Int. Cal.

- - - - - - - - - -Price differential- - - - - - - - - -

Monday -12 +12 -12 0 0 +16 + 4 4 4 + 8 + 8 8 4 4 -4 + 4 + 4
Tuesday -12 -12 +12 + 4+ 4 + 4 + 8+ 8 8 0 0 +16 + 4 4 4 +4 4 + 4
Wednesday -4 + 4 +4 + 4 4 + 4 0 Q +16 + 4+ 4 +4 + 8 + 8 8 + 4+ 4 4
Thursday 8 8 8 + 4 + 4 -4 + 4 + 4 +4 + 4 4 +4 0 0 +16 +12 -12 -12
Friday + 8 8 8 +12 -12 -12 + 4 4 + 4 + 4 + 4 4 + 4 + 4 + 4 0 +16 0
Saturday 0 -16 ;0 0 0 0 + 4 + 4 4 +12 -12 -12 + 4 4 + 4 -12 -12 -12

Monday -12 +12 +12 -12 -12 -12 +12 -12 -12 0 +16 0 + 4 + 4 4 -16 0 0
Tuesday 4 4 + 4 -16 0 0 0 +16 0 -12 -12 -12 +12 -12 -12 -12 +12 -12
Wednesday 8 + 8 8 -12 +12 -12 -12 -12 -12 -16 0 0 0 +16 0 -12 -12 +12
Thursday 4 + 4 4 -12 +12 +12 -16 0 0 -12 +12 -12 -12 -12 -12 4 + 4 + 4
Friday +16 0 0 4+ 4 + 4 -12 +12 -12 -12 -12 +12 -16 0 0 8 8 8
Saturday +12 +12 +12 8 8 8 -12 -12 +12 4+ 4 + 4 -12 +12 -12 + 8 8 8

Monday 8 + 8 + 8 + 8 8 8 4 + 4 + 4 8 8 8 -12 -12 +12 0 -16 0
Tuesday 0 0 0 0 -16 0 8 8 8 + 8 8 8 4 + 4 + 4 -12 +12 +12
Wednesday 0 0 -16 -12 +12 +12 + 8 8 8 0 -16 0 8 8 8 4 4 + 4
Thursday +12 -12 +12 4 4 + 4 0 -16 0 -12 +12 +12 + 8 8 8 8 + 8 8
Friday + 8 8 + 8 8 + 8 8 -12 +12 +12 4 4 +4 0 -16 0 4 + 4 4
Saturday 8 8 + 8 4 + 4 4 4 4 + 4 8 + 8 8 -12 +12 +12 +16 0 0









Table 17.--Continued


Store Number
Day of
Week 1 2 3 4 5 6

IR Int. Cal. IR Int. Cal. IR Int. Cal. IR Int. Cal. IR Int. Cal. IR Int. Cal.

- - - - - -- - - - - --Price differential- - - - - - - - - -

Monday + 8 + 8 + 8 +16 0 0 8 + 8 8 4 + 4 4 4 4 + 4 +12 +12 +12
Tuesday 4 4 4 +12 +12 +12 4 + 4 4 +16 0 0 8 + 8 -8 -8 +8 + 8
Wednesday + 4 4 4 8 + 8 + 8 +16 0 0 +12 +1+1212 4 + 4 4 0 0 0
Thursday + 8 + 8 8 0 0 0 +12 +12 +12 -8 + 8 + 8 +16 0 0 0 0 -16
Friday 0 0 +16 0 0 -16 8 + 8 + 8 0 0 0 +12 +12 +12 +12 -12 +12
Saturday + 4 + 4 +4 +12 -12 +12 0 0 0 0 0 -16 -8 +8 +8 + 8 8 +8

Monday + 4 4 + 4 + 8 8 + 8 0 0 -16 +12 -12 +12 0 0 0 8 8 + 8
Tuesday + 4+ 4 4 8 8 + 8 +12 -12 +12 + 8 8 + 8 0 0 -16 + 8 + 8 + 8
Wednesday +12 -12 -12 + 8 + 8 + 8 + 8 8 + 8 8 8 + 8 +12 -12 +12 4 4 4
Thursday 0+16 0 4 4 4 8 8 + 8 + 8 + 8 + 8 + 8 8 + 8 +4 4 4
Friday -12 -12 -12 + 4 4 4 + 8 + 8 + 8 4 -4 4 8 8 + 8 + 8 + 8 8
Saturday -16 0 0 + 8 + 8 8 4 4 4 + 4 4 4 + 8 + 8 + 8 0 0 +16


Monday
Tuesday
Wednesday
Thursday
Friday
Saturday


+12 +12 -12 a a a a a a a a a a a a a a a
a a a a a a a a a +12 +12 -12 a a a a a a
a a a +12 +12 -12 a a a a a a a a a a a a
a a a a a a a a a a a a +12 +12 -12 a a a
a a a a a a +12 +12 -12 a a a a a a a a a
a a a a a a a a a a a a a a a +12 +12 -12











price differentials of -12+12-12 appeared on Monday of week one in store

one, on Tuesday of week two in store six, on Wednesday of week two in

store two, on Thursday of week two in store four, on Friday of week two

in store three, and on Saturday of week two in store five.

Only one treatment combination, +12+12-12, remained for allocation

in the sixth week. This arrangement provided some flexibility in that

a missed observation could be secured by repeating the price treatment

associated with it during the final week. The one restriction upon this

was if a missing observation occurred on the day of the week that the

+12+12-12 treatment was to be applied, then the appropriate day of the

following week must be added to secure the missing observation. The

letters a, a, a, indicate the days in the final week available for such

a procedure (Table 17).

In the experimental test including Florida Indian River size 163,

Florida Interior size 163, and California size 138 Valencia oranges,

the price treatment allocative procedure was essentially the same with

the exception of the balance concept. With only three stores, balance

was reduced to two day periods. Each treatment appeared in a store on

a Monday-Tuesday, Wednesday-Thursday, or Friday-Saturday at some time

during the study. As in the allocation procedure in Component I, the

31 pricing treatments were randomly assigned to days in store 7 and



Hereafter, the experiment involving Florida Indian River and
Interior size 163 and California size 138 will be referred to as
Component II.










balanced over the two day-periods in the remaining two stores (Table

18).


Requirements and Specifications of Experimental Units


The selection of a test site and test stores within the test city

required careful consideration. With the realization that the validity

of the estimated relationships depended upon the limited population

reached by a given experiment, much effort was devoted to a delineation

of the factors affecting selection and to determination of the most

effective selection.


Selection of test site

In the marketing of fresh oranges, Florida and California fruit

meet in competition from the Rocky Mountains to the Eastern seaboard.

The competition between the fruit of the two areas is especially heavy

in the midwest. Therefore, the area west of Pittsburg, Pennsylvania,

and east of Chicago, Illinois, was designated as the area in which the

study would be conducted.

Within the specified area other factors affected the selection of

the test city. It was recognized that the population base over which

the measurement of demand relationships were to be made could be ex-

panded greatly by the selection of a high population density trading

area. This led to the selection of a relatively large and heavily

populated metropolitan area. To insure further a representative sample

population, the area was to be characterized by moderate industrialization

and an adequate cross section of social, ancestral, and income strata.

To meet these prerequisites, metropolitan areas in excess of





85


Table 18.--Component II experimental price design for the study of the
competitive relationships among size 163 Florida Indian River,
size 163 Florida Interior, and size 138 California Valencia
oranges, Grand Rapids, Michigan, April-May, 1962.



Store Number
Day of
Week 7 8 9

IR Int. Cal. IR Int. Cal. IR Int. Cal.

--------------------Price differential-------------------

Monday -12 +12 -12 0 0 +16 + 4 4 4
Tuesday -12 -12 +12 + 4 + 4 + 4 + 8 + 8 8
Wednesday 4 +4 +4 +4 4 +4 0 0 +16
Thursday 8 8 8 + 4 + 4 4 + 4 + 4 + 4
Friday + 8 8 8 +12 -12 -12 + 4 4 + 4
Saturday 0 -16 0 0 +16 0 + 4 + 4 4

Monday -12 +12 +12 -12 -12 -12 +12 -12 -12
Tuesday 4 4 + 4 -16 0 0 0 +16 0
Wednesday 8 + 8 8 -12 +12 -12 -12 -12 -12
Thursday 4 + 4 4 -12 -12 +12 -16 0 0
Friday +16 0 0 4 + 4 + 4 -12 +12 -12
Saturday +12 +12 +12 8 8 8 -12 -12 +12

Monday 8 + 8 + 8 + 8 8 8 4 + 4 + 4
Tuesday 0 0 0 0 -16 0 8 8 8
Wednesday 0 0 -16 -12 +12 +12 + 8 8 8
Thursday +12 -12 +12 4 4 + 4 0 -16 0
Friday + 8 8 + 8 8 + 8 8 -12 +12 +12
Saturday 8 8 + 8 4 + 4 4 4 4 + 4

Monday + 8 + 8 + 8 +16 0 0 8 + 8 8
Tuesday 4 4 4 +12 +12 +12 4 + 4 4
Wednesday +4 4 4 8 + 8 + 8 +16 0 0
Thursday + 8 + 8 8 0 0 0 +12 +12 +12
Friday 0 0 +16 0 0 -16 8 + 8 + 8
Saturday + 4 + 4 + 4 +12 -12 +12 0 0 0

Monday + 4 4 + 4 + 8 8 + 8 0 0 -16
Tuesday + 4 + 4 4 8 8 + 8 +12 -12 +12
Wednesday +12 -12 -12 + 8 + 8 + 8 + 8 8 + 8
Thursday 0 +16 0 4 4 4 8 8 + 8
Friday -12 -12 -12 + 4 4 4 + 8 + 8 + 8
Saturday -16 0 0 + 8 + 8 8 4 4 4




Full Text

PAGE 1

DEMAND AND SUBSTITUTION RELATIONSHIPS FOR FLORIDA AND CALIFORNIA VALENCIA ORANGES PRODUCED FOR FRESH MARKET By WILLIAM FRED CHAPMAN, JR. A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA December, 1963

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AGRICULTURAL LIBRARY

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ACKNOWLEDGMENTS The writer wishes to express sincere appreciation to his supervisory committee chairman, M. R. Godwin, for his advice, council, and encouragement throughout all phases of the graduate study program. Professor Godwin spent many hours discussing, guiding, and developing the research philosophy of the author, the culmination of which is expressed in this thesis. For his honest and sincere concern in the development of the student to a degree seldom found, an unrepayable debt of gratitude is due. Appreciation is extended to the members of the author's supervisory committee, composed of R. H. Blodgett, H. G. Hamilton, W. T. Manley, and W. B. Riggan, whose contributions to the graduate program have been of material benefit. An especial note of thanks is also expressed to L. C. Martin and W. T. Manley of Economic Research Service, United States Department of Agriculture for providing the essential freedom and favorable environment for conducting the research from fchich this thesis evolved. Much valuable assistance in typing and in making necessary statistical computations was provided by Mrs. Christine Ward, Mrs. Irene Jolly, Mrs. Judy Cannington, Mrs. Earline Thompson, and Mr. T. L. Brooks. The final manuscript was typed by Mrs. Carole Puller. For the untiring efforts of L . W. Hicks in reproducing the final manuscript, and to K. E. Ford for preparing the illustrations, the author is grateful. Finally, the sacrifice, encouragement, and devotion of the author's wife, Nancy, and children, Tony and Nancy Jean, is gratefully acknowledged and sincerely appreciated. ii

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS jj LIST OF TABLES viii LIST OF ILLUSTRATIONS xii LIST OF APPENDIX TABLES xiv Chapter I. INTRODUCTION 1 Statement of the General Problem 2 Florida orange production 2 California orange production 5 Production potential 5 Utilization trends and population trends 17 Position of Florida and California in the fresh orange market 23 Marketing period 27 Alternative Adjustment Available to the Florida Orange Industry 31 The demand situation 32 The importance of the sector analysis 36 Promotional policy 36 Pricing policy 38 Product policy kO Optimum allocation ... 41 II. PREVIOUS RESEARCH RELATING TO CITRUS DEMAND kk Examination of Data Sources kk Citrus Demand Work 47 III. PURPOSE OF PRESENT RESEARCH AND SPECIFIC PROBLEM ORIENTATION 52 The Specific Problem 52 Variety 53 Fruit sizes 54 Fruit grades 57 Hi

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TABLE OF CONTENTS-Continued Page Specifications of the Research Problem 57 Rationale Underlying Method Selection 58 IV RESEARCH METHODOLOGY 62 The Economic Model 63 The Statistical Model 64 Assumptions 66 The Experimental Model 68 Limitations of the Model Formulation 7k The Statistical Model Redefined 75 Specifications of Experimental Test 76 Size limitations 76 Price differentials 78 Experimental design layout 79 Requirements and Specifications of Experimental Units 8k Selection of test site 8k Selection of test stores 87 Orange pricing 88 Display control 88 Supply quality and storage 95 Merchandising restrictions 96 Informational Requirements 97 Cooperative Arrangements 98 V CHARACTERISTICS OF THE TEST STORES 100 General Description of Test Stores 100 Stores departmentalized 100 Degree of self service 101 Trading Stamp plan 101 Sales and Store Traffic 102 Customer count and sales 102 Daily distribution of store traffic 1 0k Iv

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TABLE OF CONTENTS-Continued Page Daily distribution of store sales 105 Daily distribution of produce sales ', i, 108 Daily distribution of total sales per customer . . 110 Daily distribution of produce sales per customer . 110 VI AN EXAMINATION OF THE BASIC INPUT DATA— FRESH ORANGE SALES 114 Aggregate Sales by Fruit Type 114 Sales by store 116 Sales by week 117 Sales by day 117 Sales per 100 Customers by Fruit Types 120 Sales by store 120 Sales by week 122 Sales by day 122 VII CHARACTERISTICS OF THE DEMAND FOR FLORIDA AND CALIFORNIA VALENCIA ORANGES 126 Generalized Presentation of the Systems of Demand Equations 126 Requirements Necessary and Sufficient for Economic Consistency 129 Method of Analysis 130 Coefficient estimation utilizing the method of least squares 131 Coefficient testing by students "t" test 132 Price and Substitution Effects 133 Tests Involving Florida Size 200 and California Size 138 133 Direct price effects 138 Differences among price elasticity estimates . . . 142 Cross-price effects 145 Differences between cross elasticity estimates . . 146 Summary of price effects 148 Tests Involving Florida size 163 and California Size 138 149 v

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TABLE OF CONTENTS-Continued Page Direct price effects 15*+ Differences between price elasticity estimates. . . . 159 Cross-price effects 160 Summary of price effects 161 Differences in Demand Estimates Due to Size 161 VIII THE ECONOMIC INTERACTION AMONG THE THREE VALENCIA ORANGES 167 Derivation of Price Estimating Equations from Demand Equations 167 Generalized Presentation of Systems of Price Estimating Equations 169 Economic Consistency Requirements 171 The Effects of Supply Interactions 172 Tests Involving Florida Size 200 and California Size 138 173 Prime product effect on price 1 76 Competing product effects on price 177 Summary of product effects 1 78 Tests Involving Florida Size I63 and California Size 138 178 Prime product effect on price 182 Competing product effects on price 182 Summary of product effects 1 83 IX EVALUATION OF FINDINGS 185 Effects of Major Changes in Price and Supply Conditions for Florida Valencia Oranges 1 87 Effect of various price conditions on customers purchases ]88 Effect of various supply conditions on retail prices 193 General Implications to the Florida Orange Industry — An Overview 198 vi

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TABLE OF CONTENTS— Continued Page X SUMMARY 202 Characteristics of the Test Stores 203 Sales and Store Traffic 203 Fresh Orange Sales 203 Total sales of fresh oranges 204 Sales per 100 customers 204 Demand Relationships for Florida and California Valencia Oranges 204 Component I --Florida size 200 and California size 138 204 Component ll--Florlda size 163 and California size 138 205 Differences In elasticities due to size 206 The Economic Interaction Among the Three Valencia Oranges 206 Component I --F lor i da size 200 and California size 138 206 Component I l--Flor Ida size 163 and California size 138 207 Price and Supply Interactions 207 Effect of price Interaction on purchase rates . . . 208 Effect of supply Interaction on prices 209 APPENDIXES 210 BIBLIOGRAPHY 255 VI

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LIST OF TABLES Table p age 1. Florida orange production, by type and area of production, 1952-53 through 1961-62 *» 2. California orange production, by type, 1952-53 through 1961-62 6 3. Florida Early-Midseason, Valencia and all oranges estimated tree distribution, by age, 1961 , 1966, and 1971 8 k. Estimated yields of orange trees, by orange type, and age of tree 11 5. Estimated production, Florida Early-Midseason oranges, 1961, 1966 and 1971 13 6. Estimated production, Florida Valencia oranges, 1961 , 1966, and 1971 15 7. Estimated production, all Florida oranges, 1961 , 1966, and 1971 17 8. Florida Early-Midseason and Valencia orange utilization, 1951-52 through 1961-62 19 9. California Valencia and Navel orange utilization, 1951-52 through 1961-62 20 10. Per capita consumption of fresh, canned, chilled, and frozen orange products, United States, 1950-60 21 11. United States population, by years, 1951-62 23 12. Orange unloads in selected U. S. cities, two-year intervals, 1955-61 25 13. Carlot shipments, California and Florida oranges, by months, 195** through 1962 29 \k. Size distribution, Florida Indian River, Florida Interior, and California Valencia oranges, 1960-61 season 56 15. Basic demand relationships, Florida Indian River sizes 200 and I63, Florida Interior sizes 200 and I63, and size I38 California Valencia oranges 58 viii

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LIST OF TABLES— Continued Table Page 16. Treatment price combinations, in terms of four cent deviations, used in estimating demand relationships for Florida and California Valencia oranges for fresh market. . 80 17. Component I experimental price design for the study of the competitive relationships among size 200 Florida Indian River, size 200 Florida Interior and size 1 38 California Valencia oranges, Grand Rapids, Michigan, April-May, 1962 81 18. Component II experimental price design for the study of the competitive relationships among size I63 Florida Indian River, size I63 Florida Interior, and size I38 California Valencia oranges, Grand Rapids, Michigan, April-May, 1962. . 85 19. Component I price design for the study of the competitive relationships among size 200 Florida Indian River, size 200 Florida Interior, and size I38 California Valencia oranges, Grand Rapids, Michigan, April-May, 1962 89 20. Component II price design for the study of the competitive relationships among size I63 Florida Indian River, size 163 Florida Interior, and size I38 California Valencia oranges, Grand Rapids, Michigan, Apr i 1-May, • 1962 * . . . . 9' 21. Arrangement of displays of Florida Indian River, Florida Interior, and California Valencia oranges, Component I, in a study of the competitive relationships between Florida and California oranges 95 22. Arrangement of displays of Florida Indian River, Florida Interior, and California Valencia oranges, Component II, in a study of the competitive relationships between Florida and California oranges 96 23. Number of customers, produce sales, total sales, and proportions of total sales in produce, by component and store, experimental tests, Grand Rapids, Michigan, April-May, 1962 103 2k. Customer traffic, by component, store, and day of week, and daily percentage distribution by component, experimental tests, Grand Rapids, Michigan, April-May, 1962 106 25. Total sales, by component, store and day of week, and daily percentage distribution by component, experimental tests, Grand Rapids, Michigan, April-May, 1962 107 ix

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LIST OF TABLES --ContjjTued Table Page 26. Produce sales, by component, store and day of week, and daily percentage distribution by component, experimental tests, Grand Rapids, Michigan, April-May, 1962 109 27. Total sales per customer, by component, store and day, experimental tests, Grand Rapids, Michigan, April-May, 1962 Ill 28. Produce sales per customer, by component, store and day, experimental tests, Grand Rapids, Michigan, April-May, 1962 113 29. Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by store, experimental test, nine stores, 31 operational days, Grand Rapids, Michigan, April-May, 1962 115 30. Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by week, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962 118 31. Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by day, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962 119 32. Florida Indian River, Florida Interior, California, and total Valencia orange sales per 100 customers, by component, by store, experimental test, nine stores, 31 operational days, Grand Rapids, Michigan, April-May, 1962 121 33. Florida Indian River, Florida Interior, California, and total Valencia orange sales per 100 customers, by component, by week, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962 123 3^. Florida Indian River, Florida Interior, California, and total Valencia orange sales, per 100 customers, by component, by day, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962 124 35. Measures of dispersion and tests of significance for relevant coefficients in the demand equations for Florida Indian River size 200, Florida Interior size 200, and California size 1 38 Valencia oranges 136 x

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LIST OF TABLES— Continued Table Page 36. Effects of price changes upon purchases of Florida Indian River size 200, Florida Interior size 200, and California size 1 38 Valencia oranges, Component I, experimental tests, Grand Rapids, Michigan, April-May, 1962 149 37. Measures of dispersion and tests of significance for relevant coefficients in the demand equations for Florida Indian River size I63, Florida Interior size I63, and California size 1 38 Valencia oranges 152 38. Effects of price changes upon purchases of Florida Indian River size I63, Florida Interior size I63, and California size I38 Valencia oranges, Component II, experimental tests, Grand Rapids, Michigan, April-May, 1962 1 63 39« Effects of quantity changes upon prices of Florida Indian River size 200, Florida Interior size 200 and California size I38 Valencia oranges 179 kO. Effects of quantity changes upon price of Florida Indian River size 163, Florida Interior size I63, and California size 138 Valencia oranges ]8k k] . Effects of various conditions of increased and decreased retail prices of Florida Indian River and Florida Interior Valencia oranges upon consumer purchases of Florida Indian River Valencia oranges I89 k2. Effects of various conditions of increased and decreased retail prices of Florida Interior and Florida Indian River Valencia oranges upon consumer purchases of Florida Interior Valencia oranges 192 43. Effects of various conditions of increased and decreased supplies of Florida Indian River and Florida Interior Valencia oranges upon prices of Florida Indian River Valencia oranges 19^ kk. Effects of various conditions of increased and decreased supplies of Florida Indian River and Florida Interior Valencia oranges upon prices of Florida Interior Valencia oranges 197 xi

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LIST OF ILLUSTRATIONS Figure Page 1. Hypothetical demand relationships for Florida fresh oranges and processed orange products 33 2. Component cubes of the Triple Cube Design 70 3. The Triple Cube Design 72 k. Display and pricing placards used in the study of the competitive relationships among Florida and California Valencia oranges, Grand Rapids, Michigan, April-May, 1962 93 5. Valencia orange display location on produce counter, in the study of competitive relationships among Florida and California Valencia oranges, Grand Rapids, Michigan, April-May, 1962 9*+ 6. The effect of price changes for Florida Indian River size 200 Valencia oranges upon retail sales of Florida Indian River size 200 Valencia oranges, Florida 200-Cal ifornia 138 test \k0 7. The effect of price changes for Florida Interior size 200 Valencia oranges upon retail sales of Florida Interior size 200 Valencia oranges, Florida 200-Cal i fornia 1 38 test 141 8. The effect of price changes for California size 1 38 Valencia oranges upon retail sales of California size 138 Valencia oranges, Florida 200-Cal ifornia 1 38 test. . . 1^3 9. The effect of price changes for Florida Indian River size 200 Valencia oranges upon retail sales of Florida Interior size 200 Valencia oranges, and the effect of price changes for Florida Interior size 200 Valencia oranges upon retail sales of Florida Indian River size 200 Valencia oranges, Florida 200-Cal ifornia 1 38 test.. . 1^7 10. The effect of price changes for Florida Indian River size I63 Valencia oranges upon retail sales of Florida Indian River size 1 63 Valencia oranges, Florida I63Cal ifornia 1 38 test I56 • • XI 1

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LIST OF ILLUSTRATIONS— Continued Figure Page 11. The effect of price changes for Florida Interior size I63 Valencia oranges upon retail sales of Florida Interior size I63 Valencia oranges, Florida I63California 1 38 test 157 12. The effect of price changes for California size 1 38 Valencia oranges upon retail sales of California size 138 Valencia oranges, Florida 163-Cal i fornia 1 38 test. . . 1 58 13. The effect of price changes for Florida Indian River size I63 Valencia oranges upon retail sales of Florida Interior size I63 Valencia oranges, Florida 163Cal ifornia 1 38 test 162 XIII

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LIST OF APPENDIX TABLES Table Page 1. Quantity of Florida Indian River size 200, Florida Interior size 200, and California size 1 38 Valencia oranges sold per 100 customers, and value of produce sales per 100 customers, by observation number, date, and price combination, Component I, experimental tests, six stores, Grand Rapids, Michigan, April-May, 1962 219 2. Quantity of Florida Indian River size I63, Florida Interior size I63, and California size 1 38 Valencia oranges sold per 100 customers, and value of produce sales per 100 customers, by observation number, date, and price combination, Component II, experimental tests, three stores, Grand Rapids, Michigan, April-May, 1962 226 3. Coding and transformation instructions for demand analyses, Florida Indian River, Florida Interior and California Valencia oranges 231 XIV

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CHAPTER I INTRODUCTION The fresh orange market Is an Important segment of the Florida orange Industry. Cash receipts to Florida growers from the sale of oranges are in excess of $200 million annually. Although the fresh orange segment amounts to only approximately 20 per cent of the total market for oranges, It is of sufficient importance to warrant attention as to maintenance or expansion of its position. To maintain or improve the position of this market, the industry has need of definitive information that describes the demand relationships faced in the fresh orange market. The major source of competition fresh Florida oranges face in the marketplace is California's orange production. At present little is known about the relative values consumers attach to oranges produced in either state nor the magnitude of price change necessary to Induce them to vary or alter purchase habits. Historically, the price competition between the two areas has been quite favorable to California. Consumer preference Is the only basis upon which the California product can enter the market with a price differential over the Florida product. If oranges from the two states were, in fact, perfect substitutes, retail prices should be the same. Yet by virtue of an advertiser-created preference, the California product can command a higher price. Thus, consumer preference allows California producers to compete effectively with Florida producers and, 1

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thereby, defray cost differences resulting frcm the productive process as well as differences in transportation charges. This retail price differential has existed for such a long period of time that it is difficult to determine how much of it arises from consumer preference and how much stems from an institutional situation developed over the years at the terminal market level. During the past two decades, technological changes and innovations have revolutionized the orange industry, especially in Florida. The introduction of frozen orange concentrate and chilled orange juice has altered substantially the relative market outlet volumes for Florida oranges. The amount of Florida fruit moving to fresh market has declined with a corresponding increase in the amount moving through processing channels./ This pattern occurred during a period of rapid expansion in Florida production and a slight decline in California production. With this succession of technological advances, it is reasonable to assume a change in the competitive citrus marketing situation between the two states. Yet comparatively little research has been directed toward an assessment of the values consumers place upon these fruits. Statement of the General Problem Florida orange production Florida orange production is characterized by six major product differentiations. The first major differentiation encompasses two distinct areas of production: the Indian River district, comprised of four counties along the east coast, and the interior district, made up of the remaining citrus-producing counties in the state. It is an

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accepted fact at the production and wholesale levels that fruits produced in the two areas are differentiated products, and some price differential does exist between the two areas. Within each of these producing areas three other major different!' ations result from a type-varietal complex. The fruits produced in each area are generally classified as Early, Midseason, and Late. The principal varieties of Early fruit are Hamlin and Parson Brown; Midseason fruit varieties are Pineapple, Homosassa, and Temple; and the Late oranges are exclusively Valencias. In the crop seasons 1952-53 through 1961-62, total Florida production averaged 89.6 million boxes of oranges annually (Table 1). Production of oranges in the Interior district averaged 79.9 million boxes, or slightly over 89 per cent of the state total, while the Indian River district produced an annual average of 9.7 million boxes. Early and midseason fruit accounted for, on the average, 50.7 million boxes compared with 38.9 million boxes of Late or Valencia oranges. During this period, increased production was in evidence in all the major product differentiations associated with Florida oranges. In the 1952-53 season, Interior production amounted to 62.7 million boxes, or 86.8 per cent of the state's total production, while in the 1961-62 season, Interior production accounted for 102.2 million boxes, or 90 per cent of the total Florida production. Thus, the Interior district increased production in both absolute and relative terms. The Indian River district, on the other hand, declined in relative terms but registered an increase in absolute terms, increasing from 5.8 million boxes in 1952-53 to 6.0 million boxes in 1961 -62 . Over this same period Valencia, or Late oranges, also gained in absolute

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Table 1. — Florida orange production, by type and area of production, 1952-53 through 1961-62.

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Midseason fruit increased from 1+2.3 million boxes in 1952-53 to 56.9 million boxes in 1961-62. From this analysis, these major product differentiations evince an imposing magnitude as they establish irrefutable lines of differences within Florida orange production. Other differentiations in addition to these cited above occur also within these delineated segments, such as size of fruit, grade of fruit and, to a lesser degree, packinghouse or grove brand names. California orange production California has three major orange-producing areas, but, unlike Florida, they form no real differentiation based upon area of production. The production areas are categorized as Central, Southern, and Desert Valley districts. Orange production In California averaged 33.** million boxes during the ten-year period 1952-53 through 1961-62 (Table 2). Only two major orange types are produced in the state, Valencia and the Washington Navel. Valencia production dominates and during this period averaged an annual production of 20.1 million boxes compared with 13.3 million boxes of Navels. During this period total California production declined from k6 million boxes in 1952-53 to 22.5 million boxes In 1961-62. Valencia and Navel shares have varied within these dates from a percentage ratio of 55-^5 In favor of Valenclas In the 1953-5** season to a 67-33 percentage ratio in favor of Valenclas in 1961-62. Production potential The Florida orange production base has expanded markedly during the past decade. This expansion has been stimulated by the natural

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Table 2.--Cal Ifornia orange production, by type, 1952-53 through 1961-62. Crop Season Navels and Miscel laneous 3 Valencia Total All Oranges

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Increase of 32.3 per cent. A citrus tree survey which was conducted in 1961 revealed that Florida orange groves contained a total of 37.8 million trees (Table 3). Of this total, 17.9 million were Early-Midseason and 19.9 million were Valencias. Also the 1961 survey revealed that a high proportion of Florida orange trees were of nonbearing age. These trees, less than four years of age, were more heavily distributed to the Valencia oranges than to the Early-Midseason oranges, 6.9 and 5.1 million, respectively. An additional 5.4 million trees were in the five-to-nine-year age group. Thus, 17.*+ million of 37.8 million trees were nine years of age or less. The oldest trees in the state, categorized as 25 or more years, were of an average age of 34 years. Of the 11.1 million trees in this category, 5.3 million were Early-Midseason and 5.8 million were Valencias. Based upon the assumption that the percentage change in tree numbers occurring during the 1951-52 through 1 960-61 period is typical of the changes to come in the next ten-year period, the estimated tree numbers in 1970-71 will be 46.4 million. This represents a 19 per cent increase in tree numbers. Under this assumption, however, there will be fewer nonbearing trees than was true in 1961. Nonbearing or two-year average age trees in 1 97 1 are estimated to be 4.3 million, 7.7 million trees fewer than in the nonbearing category in 1961. This results from the assumed normality of the per-annum increase in tree setting estimates based upon the period 1951-52 through 1960-61. During these years, frozen orange concentrate and chilled juice emerged as major trends in 'Florida Crop and Livestock Reporting Service, Florida Citrus Fruit, Annual Summary, 1961, Orlando, Florida.

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8 CD >• C O 4-> 3 -O QJ qj u 4J a) 4J CD E in r*. QJ CTi i/t a) tj en c C CO 10 u • O vO SO — cn a> o « c — fa vO CTi CO — o c — > o (A (0 QJ ca o i fO m -o "u o -O CO C o u 3 -a £ QU c QJ co > CD a> > c o u 3 TJ O u Q. CTi vO vO CTi vO C o ro QJ T3 CD LU I. (0 a> >c o 4J u 3 •a o u Q_ cn vO vO CA vO cn cn vO vO cn vO cn — — O — O — r*»

PAGE 24

9 the utilization of the Florida orange crop. Therefore, the early portion of the period was characterized by a production reaction based upon the recognized potential of the expanded processing market. Logically then, this may be quite representative of the tree-setting pattern of the 1960's, in that tree-setting may well continue at a fairly rapid rate for a portion of the period before increased supplies of oranges force a cessation of expansion. During the period 1961-1971, Florida orange production is likely to increase from three sources. One of these increases arises as present nonbearing trees attain productive maturity. A second increase springs from expanded bearing surface. As the trees age and become larger, the per-tree bearing surface expands. Thus, an increase exists due to the relationship between the age of the tree and the tree's productive capacity. The third source of increased production will result from new tree-settings. As new tree-settings occur in the I960 ' s and reach bearing age, total productive capacity will increase. To develop definitive estimates of orange production in future years, a relationship must be established between age of tree and production in addition to the informational requirements concerning tree numbers by age groups. Kelly developed such a relationship in 1953 from sample data from 15 thousand groves in Florida. Orange varieties were grouped into Early, Midseason, and Late categories. Utilizing regression analysis, a quadratic function was fitted to describe the age-production relationship. From these regression Bruce W. Kelly, "A Method for Forecasting Citrus Production in Florida", Ph.D. dissertation, University of Florida, August 1953.

PAGE 25

10 equations, estimated yields were developed (Table k) . The estimated yields derived from this study appear to overestimate production. This discrepancy could easily be a result of the climatic conditions prevailing during the period in which the primary data were secured. To narrow this margin of error in estimating potential Florida production, the percentage change between the estimated yields for given tree ages as shown in Table k were developed and applied to a historical series of production. The following assumptions were developed for estimating production in 1966 and 1971: (1) Estimated 1961 production is equal to the average production for the years 1951-52 through 1960-61 multiplied by the estimated number of bearing trees according to the 1 961 tree survey. (2) The percentage change in production of the I96I bearing surface in I966 and 1971 can be estimated by calculating the percentage change from the weighted average age of bearing trees in 1961 to this age plus five and plus ten based upon Kelly's relationship. (3) Production addition due to 1961 nonbearing trees can be estimated by deflating the I96I per-tree production by the percentage change in yield of Kelly's relationship from the I96I weighted average tree age to the average age of new production trees in I966 and 1971. Another assumption more basic than those related to the mechanics of estimation is the assumed normality of the basic per-tree production estimate derived from the period 1951-52 through 1 960-61 . During these years, Florida orange trees were exposed to adverse weather conditions in at least three seasons. Two years the citrus belt was subjected to freeze damage and in one other year to hurricane damage. Therefore, recognizing the freeze damage incurred in January I963, the pertree yield for this period may be quite realistic.

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11 Table 4. --Estimated yields of orange trees, by orange type, and age of tree. Age of Orange Type T ree Early Midseason Late Boxes per tree1 .479 2 .822 3 1.156 .317 .141 4 l.i+82 .725 .514 5 1.798 1.130 .876 6 2.105 1.504 1.226 7 2.404 1.848 1.564 8 2.693 2.166 1.891 9 2.973 2.460 2.206 10 3.245 2.731 2.509 11 3.508 2.901 2.801 12 3.761 3.2H 3.081 13 4.006 3.425 3.3^9 14 4.242 3.621 3.606 15 4.469 3.803 3.851 16 4.687 3.970 4.084 17 4.896 4.125 4.306 18 5.096 4.268 4.516 19 5.287 4.400 4.714 20 5.469 4.521 4.901 21 5.642 4.633 5.076 22 5.806 4.737 5.239 23 5.962 4.832 5.391 24 6.108 4.920 5.531 25 6.245 5.002 5.659 26 6.374 5.077 5.776 27 6.494 5.146 5.881 28 6.604 5.210 5.986 29 6.706 5.269 6.068 30 6.799 5.324 6.126 31 6.882 5.374 6.185 32 6.957 5.421 6.232 33 7.023 5.464 6.267 34 7.080 5.503 6.290 35 7.128 5.5^0 6.302 36 7.167 5.573 6.302 37 7.198 5.604 6.290 38 7.219 5.633 6.267 39 7.231 5.660 6.232 40 7.234 5.684 6.186 41 7.229 5.707 6.128

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12 Table 4. — Continued Age of Orange Type Tree Early Midseason Late Boxes per tree42 7.214 5.727 6.058 43 7.191 5.747 5.965 44 7.158 5.764 5.872 ^5 7.H7 5.781 5.778 Source: Bruce W. Kelly, "A Method for Forecasting Citrus Production in Florida", Ph.D. dissertation, University of Florida, August 1953. Based upon the foregoing assumptions, projected estimates were made for 1966 and 1 971 by a breakdown of Early-Midseason and Late, or Valencia oranges. The bearing surface of Early-Midseason oranges in 1961 was estimated to be 12,825,100 trees (Table 5). The nonbearing surface in that same year was estimated to be 5,045,800 trees. By applying the average per-tree yield of 3.83 boxes for Early-Midseason oranges from 1951-52 through 1 960-61 to the 1961 bearing surface, total production was estimated to be 49,120,100 boxes in I96I. This bearing surface was estimated to be a weighted average age of 22 years. The percentage change due to age between I96I and 1966, based upon Kelly's age-production relationship, was found to be 14 per cent. Therefore, the 1 961 bearing surface of 12.8 million trees was estimated to yield 55,996,900 boxes in 1966. The I96I nonbearing trees in 1 966 will be of an average age of seven years. Deflating the base production per tree established at 3.83 boxes for 22-yearold trees to seven-year-old trees based upon Kelly's relationship, in 1966 an additional production of 8,880,600 boxes was estimated

PAGE 28

13

PAGE 29

14 from the 5,045,800 nonbearing trees of 1961. Thus, the total yield of Early-Midseason oranges in 1 966 is estimated to be 64,877,500 boxes. In 1971 the bearing surface of 1961 is estimated to yield 20 per cent more than in I96I owing to differences in age of tree. Therefore, the 1961 production base of 12,851,100 trees is estimated to yield 58,944,100 boxes in 1971. The I96I nonbearing trees are estimated to yield 14,885,100 boxes in 1971, while the 1966 nonbearing trees' yield will be 3,538,500 boxes. This gives an estimated yield of 77,367,700 boxes of Early and Midseason oranges in 1971. Turning now to the projection of Florida Valencia orange production, the same basic assumptions were employed. In 1961, there was an estimated 13,024,400 bearing Valencia orange trees in Florida. Using the 1951-52 through 1960-61 period to establish the per-tree production of 3.48 boxes, total production of Valencias in 1961 was estimated at 45,324,900 boxes. Differences due to age, derived from Kelly's age-production relationship, were found to be a 14 per cent increase by I966 and a 17 per cent increase by 1971. Therefore, the I96I bearing surface is estimated to yield 51,670,400 boxes in I966 and 53,030,100 boxes in 1971. The weighted average age of Valencia trees in I96I was found to be 23 years (Table 6). By deflating the established per-tree production from 23 years to seven years, the I966 production resulting from I96I nonbearing trees was estimated to be 7,015,700 boxes. The total Valencia production for 1966 was estimated at 58,686,100 boxes. Using the same deflation procedure, the 1961 nonbearing trees were estimated to yield 14,725,900 boxes in 1971 and the 1 966 non-

PAGE 30

c o (U u 3 o -a o Q. C o c — o O 0) O) w — 4-> l_ C O +J H— 3 — O CD (D I< Zlfl a. ca "3 C CO VD ca vO ca m CD CO c fO s_ o o c CD CO CO "3 O c o o 3 a o a. o o 4-> fO E en LLl I vO (D -Q CO C I o c c — o o o (J) C W 0) U CD O 4-> d — a) — id i_ "O "3 3 v£> 0) HO "D Q CA XI l< — a. \o c U) oo to o c a) o a> en 4-» (D L 0) I00 13 — ii iuv£ ait) 4-> cncA c o .C (D — — fD cn lln— oi u m u CD > Cn (D D 2 < < CD U) c o 4-> 1_ O CO d a) "3 >o V. Q. in 0) X o 00 o o o in CD X o 00 o o o in a) X CO o o o in a) X o oo o o o c CD t_> i x o oo o o o in o o o in fO CA — — • • • •3" vD LA CM CO CM CA <•£> O LA -4CO LA O l^» VO — CA vO CM * CM u CA en -dCM CA LA LA — CM o r^ •J" — o vO LA — -3" LA .a -ao CA O CA LA CA CM CA -5CM O CA CM CA ft LA J" CA CM CA LA -d-d-dCM CM O O CA CM O CA vO CA CA vO — vO l^» CA CA "3 CD 4-> co E w CD -Q "D CD 3 E SO O CA x: U> 3 O i_ CM LA LA CA C • O CA O CM 3 CA "O •> LA V. J0. II --aCD CM Q.O Ik (D CA CD — ro ^ U Ci)^-» > CO CO J" • CD CA C w in 3 in d) >. -Q U 4J 3 CD CD > c >> -Q u >» Xi TJ in CO 0) 1_ c O 4-> O 3 T3 O u o. i 0) en ro CA E O U -3 4-> xi i_ X) CA CM • 0) « en la co — o cu » eni^ co LII > CO^-s CM a • 0) so 4J.3x: CA en » .vO 3 eIa O CM CM CO LA — I — o a> — S>£ 4-> O c 3 — a 1 c L. 0) CD O a. i_ CD XJ > co in i_ D CO cu a) ^ >« co — t^ <*. u in L. CO (!) — — » XI vO CO I J>s o • — SO CA — CA^ en— xj 3 x: O in -d l. c a) x: o a 4J .o a) • > in a> L. o co 0) a. > x: vo in ca c o -o — c CO in u co CD CA CM m CD en co o 3 o o L. Q. CD i en a) co en i_ CO CD > E co o u -a M0) 4-1 o x: — a> 3 c a> (D 3 4-1 CD X) CD o •3 CA • CA LA CM CM 1^ CD •> enjco — CD II en co • CO SO -a"3 O^ 0) « 4-> VO x:^_^ en 3 vO E w o L. ^4CO _ -3" vO CA O vO CA Q. x: x: in en c 3 o O — U. 4J x: co 4-> .— Q) CM L. LA i in LA > CA — -XL c o c O cnx> co i CO CD 3 en cm co tII CD > CO^— » vO •3 • CD vO x: cm en •» — CM 3 Eln O CM L. • SO CO I -3" o • \D CA CAw x: o. en — 3 x: O m v. c x: o CM CO LA — I (D — u LA CA W c — O CD — ii 4-> O c 3 — -3 4-> 1 c L. CD CD O a CD CD en o. co «> CD X) > co in i_ 3 ro CD CD u >. co — r-». 14cd o Q 4-> Iin 1_ ro CD

PAGE 31

16 bearing trees, 2,269,100 boxes. Total Valencia production was estimated to be 70,025,100 boxes in 1971. To summarize these estimated yields, total Florida orange production was estimated to be 94. 4 million boxes in 1961, 123.6 million boxes in 1966, and 147.4 million boxes in 1971 (Table 7). No similar work has been done in the area of age-production relationships for California oranges. However, research has progressed in the projection of orange acreage to 1970 and 1 980 . -^ Between i960 and 1970, acreage of Valencia oranges is estimated to decline from 86,438 acres to 74,650 acres, while Navel orange acreage is estimated to increase from 72,595 acres to 78,300 acres. The projections to 1980 indicate little change in Valencia acreage, but Navel acreage is estimated to increase to 85,700 acres, approximately a seven thousand acre increase between 1970 and I98O compared with about a six thousand acre increase from i960 to 1970. From these projections, undoubtedly Florida orange producers and marketers must concern themselves further with the utilization of their fruit during the 1960's. Valencia production in Florida, based upon these projections, will increase by 17.0 million boxes or 32 per cent by 1971. Early and Midseason production will increase 18.4 million boxes or 31 per cent during the same period. In total, this represents an increase in Florida production of 35.4 million boxes, an amount equivalent to or exceeding the state's entire production in the 194243 or any prior season. 3 R. C. Rock and R. G. Piatt, Economic Trends in the California Orange Industry, 1961 , Agricultural Extension Service, University of California, November, 1961.

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17 Table 7. — Estimated production, all Florida oranges, 1961, 1966, and 1971. Production Productfon Pro1961 1961 1961 Addition Addltion Tota , duction Bearing Base Bearing Due To Due to Pro _ Year Trees Production Surface 1961 NonNew j ree duction Production bearing Settinq Trees (000 Trees) (000 Boxes) (000 Boxes) (000 Boxes) (000 Boxes) (000 Boxes) 1961 25,81+9.5 94.M+5.0 94, •+5.0 94,445.0 1966 25,849.5 94,445.0 107,667.3 15,896.3 123,563.6 1971 25,849.5 94,445.0 111,974.2 29,611.0 5,807.6 147,392.8 Source: Tables 5 and 6. This enlarged production in Florida will be offset to some degree by a reduction of orange acreage in California. Valencia acreage has been projected to decline 13.6 per cent by 1970, but Washington Navel acreage has been projected to increase by 7.9 per cent. The net change in acreage for all California oranges, using these projections, will be 7.983 acres or 5.0 per cent. Utilization trends and population trends The amount of Florida oranges utilized in fresh market sales has declined substantially in the past decade, while the number of oranges used for processing has risen rapidly. The decline in fresh sales has occurred notwithstanding increases in production. Florida Early-Midseason movement to fresh market has declined from 17.0 million boxes in the 1951-52 season to 11.5 million boxes in 1961-62 (Table 8). Valencia fresh sales declined from 13.6 million boxes in the 1951-52 season to the six million box level in 1957-59, gaining to the 9 million box level in the 1959-60 season. The 1960-61 season again

PAGE 33

18 registered a decline to 6.3 million boxes. Yet the 113 million box crop of Florida oranges in the 1961-62 season led to higher fresh sales in both Early-Midseason and Valencia categories, 11.5 and 9.*+ million boxes, respectively. Over the period 1951-52 through 1961-62, utilization ratios between fresh and processed Florida oranges were altered substantially. In the 1951-52 season, 30.6 million boxes or 39 per cent of the crop were utilized in fresh sales compared with a remaining 61 per cent or ^7.5 million boxes used for processing. This emphasis on processing has grown continuously since the early fifties. In the 1961-62 season, which had a total sales utilization of 112.6 million boxes, 20.9 million boxes or 19 per cent moved through fresh market outlets, while 91.7 million boxes or 81 per cent were used for processing. California fresh orange sales and processed orange sales have decl ined during the past decade at a rather constant rate with respect to shares. Fresh sales for the period 1951-52 through 1961-62 have ranged between 72 and 79 per cent of total sales, with the exception of the 1957-58 season when fresh sales accounted for 86 per cent. In that season Florida incurred freeze damage and registered a total sales volume of some eight million boxes below the decade average. Sales of California oranges In the fresh market have declined from 27.2 million boxes in the 1951-52 season to 15.1 million boxes in the 1961-62 season (Table 9). Valencia fresh sales have declined from 19.7 million boxes in the 1952-53 season to 8.*+ million boxes In the I96I62 season while Navel fresh sales have declined from a high of \k.8 million boxes in 1952-53 to a low of 6.7 million boxes in 1961-62.

PAGE 34

19 Table 8. — Florida Early-Midseason and Valencia orange utilization, 1951-52 through 1961 -62. Orange Type Season Early-Midseason Valencia All Fresh D , Fresh D . Fresh D , _ . Processed c , Processed c . Processed Sales Sales Sales

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20 Table 9. — California Valencia and Navel orange utilization, 1951-52 through 1961-62. Orange Type

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21 Table 10. --Per capita consumption of fresh, canned, chilled, and frozen orange products, United States, 1950-1960. Year

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22 The fluctuations in market shares between the various sectors of the orange industry are especially vital in Florida, since a major proportion, approximately 80 per cent, of its crop is utilized in the processing market. The impact of the technological advances in frozen concentrate and chilled products on the Florida industry is sufficient to warrant study, notwithstanding the need for evaluation resulting from increased supplies available for the national market. California, on the other hand, has had a relatively constant market share situation with regard to fresh and processing. Further, western growers are facing a declining acreage in oranges, primarily from continued urbanization in citrus producing areas. The United States' population increased 20.9 per cent between 1951 and 1962. In 1951 the estimated population was 153.7 million and by 1962 it had mushroomed to an estimated 185.9 million (Table 11). The average annual rate of increase from 1955 to 1961 was 2,931 ,45^ per annum, |f this rate of increase is maintained, the estimated I966 population will be 197.7 million persons, and in 1971 the census will record 212.3 mil 1 ion. Although United States* population is making rapid gains, thisN increase in consumers will not solve the anticipated excess orange production problem. Projected yields of Florida orange production indicate \ky .k million boxes in 1971 and projected United States population indicates 212.3 million persons in that same year. This projection represents an increase over 1961 levels of 29.3 million persons and 52.9 million boxes of oranges, or 1.8 boxes per additional person. However, consumption rates per capita tend to be quite stable. The per capita consumption of all citrus fruits for the

PAGE 38

23 Table 11. — United States population, by years, 1 S5 1-1 962 . Year Persons Increase 1951 153,691 1952 156,421 2,730 1953 159,012 2,591 1S54 161,761 2,749 1955 164,607 2,846 1956 167,509 2,902 1957 170,496 2,987 1958 173,367 2,871 1959 176,551 3,184 1960 180,007 3,456 1961 183,025 3,018 1962 185,937 2,912 Source: Agricultural Statistics 1962 . U. S. Department of Agriculture. decade 1950-60 averaged 84.1 pounds. This represents less than one box of citrus fruit to a consumer. Thus, to utilize the anticipated increase in orange production, new uses for oranges must be found, or marketing policies must be altered to effect a shift in consumption rates. / Position of Florida and California in the fresh orange market Aggregated over the various product differentiations, Florida and Per capita consumption derived from Consumption of Food in the United States . U. S. Department of Agriculture Handbook No. 62, August 1961 .

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2k California oranges compete to seme degree in most major terminal market areas east of the Rockies (Table 12). Of the ^1 markets included in this tabulation, Florida dominates 10 in terms of carlot unloads and California predominates in 31. However, in several of the larger terminal markets, the relative shares between Florida and California are much closer to equality. In markets such as Cincinnati, Cleveland, New York, Philadelphia, Pittsburgh, and Providence, the shares ranged in a kO 60 division between California and Florida. In Cincinnati, for alternate seasons from 1955 through 1961, Florida unloads accounted for an average of 57 per cent of the total Florida-California oranges coming into the market. On the other hand, in Cleveland during this same period, an average of 56 per cent of the California-Florida oranges were from California. Over these same years, market shares have demonstrably changed in several of the markets. For example, Florida shares have increased in Albany and Columbia, while California shares have multiplied in Dallas, Fort Worth, and Denver. The California share increase in these markets can be attributed partially to increased Texas orange production. In these six years Texas producers were recouping losses suffered in the extensive freeze damage of 19^+9 and 1951. It must be recognized, however, that these data do possess limitations relevant to an analysis of emphasis shifts within the fresh orange market. Since the data are aggregated over several types and varieties of oranges as well as intrastate production areas, an analysis of shifts can be stated only in the most general fashion. Further, such broad analyses make no allowance for transshipments. Although an analysis of unloads may yield no appreciable changes within a given

PAGE 40

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PAGE 41

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PAGE 42

27 market, substantial changes within orange utilization patterns may have been present from either Florida or California. For example, a marked shift could have developed from California Valencias to California Navels, or there may have been substantial changes among Early, Midseason, and Late Florida oranges. In the same manner, major production shifts may have emerged regarding fruit produced in the Indian River and Interior sections of Florida. As orange production rises, these variables will assume more importance and an assessment of consumer preferences with regard to the various orange products will become more crucial to the allocation of supplies among market sectors. Marketing periods The Florida orange production year begins around the first of October with Early oranges. Early orange production is most intense in November and December and generally continues through February. Midseason fruit harvest and shipment begins early in November and continues through March. Heaviest production of Midseason fruit runs from December through February. Temple oranges, often classified as a Midseason fruit, are harvested from late November through mid-April, with heaviest production in January and February. Late or Valencia orange harvest begins about the first of February and continues to some degree throughout the summer months. Heaviest production occurs in the months of March through May. California orange production is more of a year-around proposition than is Florida's. California Washington Navel harvest and shipment begins from ear lyto-mid-November and continues generally through

PAGE 43

28 April. Valencia harvest in California usually overlaps Navel harvest in early April and continues through October. Consequently, California and Florida fruit meet in the marketplace throughout most of the year. During the period 1954-62, May was the heaviest shipment month for California oranges, averaging 4,822 carlots or 11.1 per cent of annual shipments (Table 13). At this season, primarily Valencias are available from either state, along with a negligible amount of Florida Temples. In contrast, December is the heaviest orange shipment month for Florida. An average of 5,11*+ carlots were shipped from Florida in December during the period 1954-1962. In that month Florida Early, Midseason and Temples are available for shipment. August and September are lightest months for Florida orange shipment, averaging in the period 1954-1962 only 211 carlots or 0.6 per cent of annual shipments. California, during the 1954-1962 period, shipped an average of more than 2,000 carlots of oranges each month of the year, ranging from a high of 4,822 carlots in May to a low of 2,385 carlots in November. Florida, contrastingly, shipped an average of as low as 76 carlots in September and as high as 5,114 in December during these identical years. Throughout the five months, November through March, Florida shipped more than 57 per cent of its total annual fresh shipments compared to California shipments of 40 per cent during the same five months. The anticipated production increases in Florida will place larger amounts of fruit on the national market in two critical periods. The Early-Midseason and Temple increases will face keen competition frcm California's Washington Navel fruit. The Navel season, starting in

PAGE 44

29 Table 13. — Carlot shipments, California and Florida oranges, by months, 195*+ through 1962. Year and

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Table 13. — Extension 30 July Aug. Sept. Oct. Nov. Dec. Total 3,983 692

PAGE 46

31 November, will climax in December and January. During these same two months, based upon current production and marketing schedules, Early Florida fruit still will be strong, the Midseason fruit will be at peak production, and Temple oranges will peak during January. Increased supplies of Florida Valencia oranges will be met in the marketplace during February, March, and April by some Florida Midseason and Temple oranges, as well as by California Valencias harvested beginning around the first of April . As orange supplies increase, a comparable need will demand more thorough knowledge of the market for oranges and orange products. The allocation among market sectors and geographic markets based upon sounder perception of the total orange market can refine the efficiency with which the crops are marketed and consequently enhance the position of the orange industry. Alternative Adjustments Available to the Florida Orange Industry During the coming decade, per capita orange production is apparently going to expand at a fairly rapid rate. The increase in production, based upon projected yields, will definitely occur in Florida. California production, meanwhile, is expected to be maintained at a rather constant level. Therefore, the prime responsibility of merchandising larger orange crops must rest with Florida producers and marketers. To move effectively prodigious crops of oranges, shrewder attention must be focused upon marketing policies and alternative adjustments available to the industry. The effective utilization of alternative adjustments to solve the dilemma of increased production depends,

PAGE 47

32 beyond question, upon the accuracy with which the industry estimates the demand relationships for its products. Recognizing this adjustment to be the problem, it is necessary to postulate the demand relationships existing in the orange market and to examine possible alternative adjustments available to the orange industry, in order to attain maximum effectiveness in marketing as supply levels increase. The demand situation Florida oranges are marketed basically in four forms: (1) fresh oranges, (2) chilled juice and products, (3) canned juice and products, and (k) frozen concentrates. Each of these market sectors possesses a separate aggregate demand relationship encompassing a family of subsector demand curves relevant to the given sector. Within this system of demand relationships, variations exist in levels and slopes of the several demand functions, thus creating differences in price and cross-price elasticities of demand at the sector and subsector levels. Graphically, these postulated sector demand relationships can be depicted as in Figure 1. D, , D 2 , 03. and D^ represent, respectively, chilled juice and products, canned juice and products, fresh oranges, and frozen concentrates. Given the availability of these component aggregate relationships, a composite function may be obtained by a summation of the components, such as shown by Dj. This composite is an aggregated demand relationship over the various sectors and subsectors making up the total orange market. Not only are these sector relationships affected by the availability and prices of other orange

PAGE 48

33 u "8 « o> e D "TJ v> 1 O VI 0> C O D O u 3 .0)

PAGE 49

3*+ products, but also by the availability and prices of other substitute citrus and noncitrus products. To exploit fully the competitive situation, a detailed delineation of demand relationships must be formulated to include the various sectors of the industry. Since there are within each sector discernible product differentiations, these characteristics must be accounted for. Recognition of the existing product differentiations within a given sector will allow any adjustment procedure to be applied with maximum efficiency. The demand function for fresh oranges . — Within the Florida fresh orange sector, differentiating characteristics which must be considered include areas of consumption, areas of production, varietal-type differences, sizes, and grades. It appears valid to assume that different consuming areas possess distinct preferences regarding fresh oranges; therefore, levels of demand and the respective functional relationships are likely to differ between these areas. The Indian River and Interior districts of production provide a second differentiation to be considered, since fruits from the two areas are viewed as differentiated products, at least at the grove and wholesale levels. The varietal-type complex presupposes even further delineation. Under this category, thought must be given to differences in consumer preference with respect to Early, Midseason, and Late oranges, as well as within these several varietal differences. Beyond these differentiations are those resulting from grade and size of the common orange types and varieties. Certainly, then, the aggregate demand relationship for fresh oranges is composed of countless differentiations. These differences must be

PAGE 50

35 evaluated in the adjustment to increased supply levels of oranges available for the national market. The demand functions for processed oranges . — In the processed sectors there are three basic forms of orange products--chi 1 led, canned, and frozen concentrates. Differentiations contained within these processed products must also be taken into account, and these are generally the same without regard to form. To some degree, Florida processed orange products maintain an identification as to area of production within the state. Therefore, processed Indian River and Interior fruit must be recognized as possibly differentiated products to the degree that the area of production is identified with the product. Evident differences also exist in the demand relationship based upon consuming areas. For example, frozen orange concentrate accrues differences arising from consumer preferences in unlike areas of the market. In all of the processed products another differentiation results from brand names, normally classified into three categories: (1) nationally advertised brands, (2) chain grocery store brands, and (3) packer brands. Within brands further differences also result from container sizes. Thus, in developing the aggregate functional demand relationships for each of the fresh and processed orange products, such a relationship is an average over the various product differentiations. The more complex the delineation within a particular market sector, the sounder the knowledge for basing any adjustment to changing supply conditions.

PAGE 51

36 The importance of the sector analysis The question arises, "What is the importance of the sector demand relationships?" Knowledge of the component relationships provides the basis for effective adjustment by the firms within the industry and the industry itself. Additional information from delineating the demand relationships within the component or sector further refines facts available for adjustments to changing levels of total orange output. Consequently the reliability of any estimated demand relationships will determine the success of the ensuing adjustment process. The industry can avail itself of several adjustment alternatives in coping with the problem of increasing supplies. These may be categorized as adjustments in promotional activity, pricing policy, product policy, and optimum allocation. Adjustments in each of these categories require a knowledge of the demand structure and the functional relationships therein. Promotional policy The prime concern of the Florida orange industry regarding promotional activity is effectiveness In attaining the goals of any promotional program. Basically, promotional activity of any specific form is employed to effect a change in the demand relationship for oranges. This change, If successful, is anticipated to initiate shifts in the level and slope of the demand function whereby a more favorable demand situation is created. Hence, effective promotional activity results In some combination of increasing the level and changing the elasticity of demand for oranges and orange products. At the industry level, where much of the promotional activity

PAGE 52

37 presently originates, two major considerations must be reckoned with. They are (1) the allocation of promotional funds among market sectors, and (2) the allocation of promotional funds among geographic market areas. As supply levels increase, the allocation becomes more important to the adjustment process toward higher levels of output. Recognizing the multi-use characteristics of the orange crop, the firm, sector, or industry must decide wisely the allocation of promotional funds. To allocate effectively these funds, management must forecast estimates of the demand relationships for the products involved. The allocation among sector markets depends upon the promotional goals. Astute promotion initiating a shift in combination of level and slope of the demand relation will result in higher prices or movement of larger quantities at the same price, If the demand relation is relatively elastic, effective promotional activity yields a more significant quantity effect than price effect. Thus, in the matter of increasing supplies, promotional activity could better assist movement of larger supplies if applied in sectors of the greatest price elasticity for the demand relation. However, another consideration in undertaking the allocation of promotional funds is the substitution among products. Given equal degrees of elasticity, a greater benefit would be derived if promotional funds were allocated in the sector with the least degree of economic substitution with respect to other orange products. In other words, to assist adjustment to larger supplies, the greatest benefit would be derived from promotional funds if allocated in the sector with the most elastic demand relation and the least amount of substitution or smallest cross-price elasticity of demand for other Florida orange products.

PAGE 53

38 Pricing pol icy Another alternative available to the orange industry is adjustment in pricing policy. Currently, on-tree prices are determined within the framework of the purely competitive model notwithstanding an industry market structure that departs noticeably from the competitive model. If the industry were to engage further in vertical and horizontal integration to such an extent that a preponderance of the oranges produced were marketed under a central authority, price policy would assume utmost significance in adjustment to increasing supply levels. In a situation of rising supplies and decline in price, such declines could be adjusted in a fashion to move toward a revenue maximizing or revenue loss minimizing condition, whichever the case may be. If the industry were operating in the elastic segment of the demand function, then adjustments in price consistent with the demand situation within given sectors would tend toward a maxima with regard to increasing revenue. On the other hand, if the industry were operating in the inelastic segment of the demand function, as supplies increased, the adjustment of prices in the various sectors consistent with the sector demand relationships would gravitate toward a minimization of revenue losses. Thus, a price reduction in the sectors possessing the most elastic demand relationships would increase revenue if the industry were operating in the elastic segment of the demand function. Contrarily, if the industry were operating in the inelastic segment of the demand function, a price reduction in the sectors with greatest elasticity would move toward a minimized revenue loss. Another consideration in pricing policy lies in the utilization of demand relationships within a given sector. If, for example, there existed

PAGE 54

39 within the fresh orange sector a functional price-quantity relationship for Indian River fruit which was at a higher level and possessed a greater elasticity than that for Interior fruit of like size and grade, a price reduction for only Indian River fruit would increase revenue over an equal price reduction for both fruits. A gain would ensue from the elasticity character, since a price reduction for the Indian River fruit under this hypothetical situation would yield a greater than proportionate increase in the quantity marketed. Further, notwithstanding increased supplies, the industry under conditions of extreme inequality among the various sector demand functions may raise prices in some sectors while lowering prices in other sectors. If, for illustrative purposes, within the four sectors of the orange market, two of the demand functions were highly inelastic and two others were to a high degree elastic, price adjustments in both directions may increase revenue. Upward movement of price in the sectors with inelastic demands will lead to some quantity marketed losses, but by an amount less than proportionate to the loss in price. A decline in price in the elastic sectors will lead to an increase in the quantity marketed by an amount more than proportionate to the price decline. On balance, it is conceivable that such price adjustments may increase revenue along with the increased supply levels. The structure of the Florida industry is such that these adjustments could be effected easily. The Citrus Exchange, along with similar sales organizations representing growers' cooperatives, could organize into a sales agency either through the organizational structure allowed under the Capper Volstead Act or under the Marketing Orders and Agreement Act.

PAGE 55

kO Product pol icy Another alternative similar to the pricing adjustment alternative is product adjustment. Product adjustments among sectors of the industry could be on a similar basis to those described under price adjustments. Any increased supplies could be absorbed by adjustment of products to the various sectors within the marketing system in the most favorable fashion, that is, in the sector where increased quantities would have the least price effects. Industry controlled allocation could seek to maximize revenue along with increasing supplies. If the industry were producing in the inelastic segment of the demand relationship by allocating among the four product markets based upon the relative elasticities, it could seek to minimize revenue losses. For example, if the industry were producing in the inelastic portion, but only one or two of the sector demand functions were inelastic in nature, revenue losses would tend to be minimized by allocation of greater quantities to the sectors possessing the elastic demands. This follows since such an allocation would result in a less than proportionate decline in price. Therefore, the loss incurred wculd be less than if equal increments of the increased supplies were applied to the various market sectors. If, on the other hand, the industry were producing in the elastic portion of the demand relationship, greater revenue gains would be found by allocation of increased supplies to the sectors possessing elastic demand functions. In this case, revenue losses resulting from quantity increases would be less than a proportionate amount of the actual quantity increase, and, thus, greater revenue.

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41 Optimum al location Either of the two alternatives, price adjustment or product adjustment, may be looked upon as intermediary steps to complete and optimum allocation from the revenue standpoint. To maximize net revenue at the industry level, complete knowledge of two economic forces, costs and revenue, must be sought. The equation of the marginal quantities of these two functional relationships will result in a maximization of net revenue. The unique point of complete maximization occurs where industry marginal costs are minimized and equated with industry marginal revenues for the several orange products involved. From the cost side of the equation, knowledge of the industry marginal cost function is obligatory for each of the four orange product markets. To minimize marginal costs for the industry, firm costs are required at each possible level of production, since cost minimization requires that the individual member firms' marginal costs be equated. This process could be accomplished by allocating quotas to the individual member firms in such a manner as to equate the marginal cost for each firm to the marginal cost of every other firm for their respective quotas. If this al locative procedure is followed, industry costs for any given level of output will be minimized. The foregoing analysis indicates the ideal situation from the standpoint of minimizing industry costs. It requires that the firms within the industry must yield to some central authority the ultimate decisions relative to rates of output by individual firms. Although this procedure attains an optimum condition in the industry cost structure, it is not a necessary requirement for the utilization of the maximization principle. As the industry chooses to deviate from the minimization of costs, total

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k2 net revenue declines. However, within the confines of any given system of output allocation among firms and any industry cost level, net revenue maximization can be attained by equation of the marginal cost and revenue functions. From the revenue side of this equality, full maximization requires complete knowledge of the demand for oranges within sectors of the industry, For a program of supply management, there must be information to guide allocation of supplies among the various market sectors. A method must be devised to show the marginal revenue for the industry's entire volume. The availability of the sector demand functions would allow a summation yielding a composite demand function for all oranges. From the sector and composite demand relationships, marginal revenue functions can be derived. To determine optimum allocation among sectors, the industry output must be allocated to equate the sector marginal revenue functions with the marginal cost functions. In this al locative procedure, it may well be determined that total industry output may be beyond the amount required for maximization of revenue. Thus, to attain maximization of net revenue, in addition to the allocation among market sectors, the need could exist for limiting the total output to less than available supplies. In such an event, economic abandonment of a portion of present supplies would be a logical procedure to follow. In contrast, if available supplies were less than the optimum output, further expansion of the productive capacity of the industry would increase revenue. Present supplies under this situation should be allocated in such a manner as to minimize industry marginal cost.

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h}, It Is recognized that total knowledge of the cost and revenue aspects of an industry are rarely secured on a simultaneous basis. The utilization of complete information concerning the demand relationships for the products of the industry can be a practical intermediate step toward net revenue maximization. Gross revenue maximization can be attained without cost information. From the various sector demand relationships, the industry demand function for all oranges can be obtained and, subsequently, a total revenue function can be derived. These functional relationships can be used to maximize gross revenue by equating the marginal revenue functions for the four sectors. The point of marginal revenue equation would be the quantity dictated by the high point on the total revenue function, which also would be, of course, the point of unit elasticity on the industry demand curve. Maximum revenue would be received if supplies in each of the sector categories were so allocated that the quantities of each would yield a marginal revenue of zero. This is true only if the total supply offerings are equal to or in excess of the high point on the total revenue function. On the other hand, if total supplies are less than the quantity dictated by the peak of the total revenue function, then maximizing gross revenue would be a process of equating the sector revenues at a point which would absorb all available supplies. This would, in turn, allocate quantities and dictate prices among the various market sectors.

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CHAPTER I I PREVIOUS RESEARCH RELATING TO CITRUS DEMAND Examination of Data Sources The study of demand relationships has become an increasingly important field of research over the past several decades. A major difficulty the demand analyst has encountered in the past, and presently faces to a lesser degree, is the source of data for estimating demand relationships. Data from many sectors of the economy have been collected in such a manner that the researcher has reason to question their reliability as basic input data for demand estimation. Basically, this situation stems from the fact that these data were not collected for the purpose of demand estimation and consequently are not generally in the form desired for such utilization. Further complications arise from the analytical tools available to cope with and parcel out the sources of variability existing in the basic data. Much of the data available for demand estimation possess aggregation problems which limit their usefulness. For commodities differentiated on the basis of grade and size, much of the available data are presented in ranges or averages. When these types of data are used for the estimation of demand parameters, the results must be accompanied with many restrictive qual if ications. Initially, estimates of demand relationships were derived from yearly series of national aggregates. The input data used for this

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h5 early demand work were plagued, quite naturally, with many inadequacies. Over the course of time these inadequacies have been remedied to some extent. The severe problems associated with actual reporting of statistics two or three decades ago are presently of no major consequence, with the technological advances which have occurred. The agencies whose responsibility it is to gather statistics on production and utilization have constantly sought to improve sampling and estimation procedures. In addition, they have substantially broadened their base of reporting to include further breakdown concerning grade, size, and other differentiations. However, from the standpoint of demand estimation, there still exists many problems with time series data. During the past two decades, technological advances have taken place with extreme rapidity along with changes in the consumption habits of the population. In many cases these changes have caused difficulties in utilizing time series data. The increased introduction of convenience into food and fiber processes has operated to change the demand relationships over time, and compensation for these factors appears to be quite difficult. Not only has the process included innovations such as reduction of food preparation time but also the introduction of old products in new forms. For example, orange concentrate came into existence in the middle 1 940 ' s. Compensation for the effects of orange concentrate on other orange and citrus sales would be extremely difficult. Another question with regard to time series data lies in the identification of variables. While demand theory dictates the dependent variable to be quantities taken and the independent or explanatory variables to be

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46 prices, there is some debate as to the validity of time series data conforming to these theoretical requisites. The use of consumption statistics and quoted prices from a series to estimate elasticity coefficients appears to overstate price effects. This is a result of exogenous variables upon which no quantitative measure can be placed or at least, given the present state of the arts, has not been quantitatively measured. For example, with regard to most commodities, society is subjected to considerable merchandising and promotional activities. The extent to which these activities are effectual is included in consumption disappearance. Demand work has generally taken on the characteristic of estimating coefficients of elasticity rather than the creation of demand surfaces recognizing price and other variables as explanatory changes in consumption. Thus, when time series data are used for the estimation of demand parameters and further defined in terms of price elasticity coefficients, the effects of price are overstated. Disregarding the accuracy of estimating coefficients of elasticity from time series data, a severe limitation does exist from the standpoint of the range of variability in the proposed independent variables. The range of prices existing over time resulting from the normal situation is very limited. It therefore, follows that measurement of demand relationships is acutely limited with regard to the scope of the function. Another source of data for demand estimation that has gained much favor in recent years is that generated from consumer panels. These data are held by some to be superior to national and regional data collected by the various data procurement agencies of state and national government. However, these cross-sectional data are not without inherent faults. They are to some extent subject to some of the difficulties encountered in a general time series. Notable is the limitation in the

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47 range of price or explanatory variables. Also, there exists the same difficulty as in time series with regard to the over estimation of price effects when these data are used for elasticity coefficient estimation. The method of data collection, recall through personal interview or mailed questionnaire, makes the data questionable from the standpoint of accuracy, while yet another difficulty lies in the possibility of a nonrepresentative sample. As a result of the difficulties found in these data sources and with the evolution and advancement of research methodology, much consideration has been given to the possible generation of basic input data from contrdlled pricing experiments. This technique has gained, in some quarters, great impetus in forming the basis for estimating functional demand relationships. The assets and liabilities of this method of procedure will be discussed fully in a later section, since it was selected as the method of procurement of the data for the empirical demand work upon which this dissertation is based. Citrus Demand Work Over the years, more demand work has been directed to aggregation of commodity groups than to individual commodities. Relatively little research attention has been devoted toward an assessment of demand relationships for individual commodities. This void is especially true with regard to citrus products. Further, there has not been as much work utilizing time series analyses as might be suspected. Time series demand estimation has been more nearly confined to basic agronomic commodities and meat products. However, some work has advanced in specific fruit and vegetable areas and over fruit and vege-

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48 table commodity groups. Brandow estimated demand relationships for apples, recognizing orange production as an independent variable associated with apple purchases. More directly in the citrus field, Hoos and Boles reported a functional relationahip between California f.o.b. orange prices and four independent variables. The variables included were (l) California fresh shipments; (2) fresh shipments from other areas; (3) index of L). S. nonagricultural income (1935 -39= 1 00) ; and (k) time. They found that for the period 1925 through 1950, omitting the war years, 19^2-45, that some 89 per cent of the variation in California f.o.b. prices for summer oranges was explained by these variables. Powell and Godwin, using short term observed price-quantity data, 3 estimated demand relationships for fresh oranges. The purpose of this study was to analyze demand relationships for certain citrus and noncitrus products using data obtained under normal retail store performance in Jacksonville, Florida and Memphis, Tennessee. To obtain information with respect to income levels, each city was divided into low, medium, and high income areas. The data collection process included weekly visits to each of the stores, an inventory being taken and recorded for each product included in the study. All additions to stock received subsequent to the previous G. E. Brandow, A Statistical Analysis of Apple Supply and Demand (University Park, Pennsylvania, Agricultural Experiment Station, Pennsylvania State University, AE and RS No. 2, January 1956). 2 S. Hoos and J. N. Boles, Oranges and Orange Products Changing Economic Relationships (Berkeley, California: California Agricultural Experiment Station Bulletin 731, 1952). 3 L. A. Powell and M. R. Godwin, Economic Relationships Involved in Retailing Citrus Products (Gainesville, Florida: Florida Agricultural Experiment Stations Bulletin 567, August 1955).

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k9 visit were also listed. From this information sales volume was determined by subtracting fche ending inventory for the current period from the sum of stock receipts and the ending inventory of the preceding period. To maintain exacting price-quantity data, inventories were taken each time prices for the concerned commodities were changed. Principal fruits included in the study were oranges, apples, grapefruit, and tangerines. In addition, five processed citrus juices and four noncitrus juices were included. Of the four fresh fruits, oranges ranked first in terms of quantity sold accounting for in excess of kO per cent of the volume. From the standpoint of value, apples were the leading fruit of the four in Jacksonville. In Memphis, however, in the low income strata, the value of apples and oranges were of about equal magnitude, while the total value of oranges exceeded that of apples in the other two income strata. Estimated price elasticity coefficients in low, medium, and high income areas of Jacksonville were 1.206, 1 ,329» and 0.860, respectively. In a similar analysis utilizing the data gathered in Memphis, price elasticity coefficients estimated for low, medium, and high income areas were 1.782, 1.665, and 1.1^3, respectively. It was further noted that orange concentrate was increasingly regarded as a fair substitute for fresh oranges. This consumer preference may partially account for the slightly higher coefficients derived from the Memphis study, conducted approximately nine months later than the Jacksonville study. In 1952, Godwin, using controlled pricing techniques, developed a functional quantity-price relationship utilizing controlled prices per

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50 dozen of oranges. Seven levels of price were included in the study, three 5 cent deviations on either side of the mean price. The methodological procedure followed was the artificial inducement of price variation above and below the established market price over a relatively short period of time. This study was done at the retail level of distribution utilizing seven supermarkets in central Kentucky. As higher prices were induced the total volume sold in the stores tended to decline. A functional relationship was derived by fitting an orthogonal polynomial. The coefficient of price elasticity for the curve as a whole was 1.160. The degree of elasticity varied considerably over the range of prices tested, with greatest elasticity near the established market level. An elasticity approximating unity was found at a discount of 15 cents per dozen. At prices representing an increase of 10 and 15 cents above the normal market, the demand function becomes inelastic. Using similar methodology, Godwin and Powell studied the effects of price on frozen orange concentrate. This study was conducted in 10 supermarkets in the Lower Delaware Valley area of Pennsylvania, and New Jersey. The test prices differentials included in the study were as follows: the price in effect at the time the study was initiated; prices 3, 6, and 8 cents per 6-ounce can below the market price; and one, k cents higher. By this method, consumers were subjected to retail prices varying over a range of 12 cents per can. Although the retail units carried three types of orange concentrate—namely, a nationally advertised brand, a private label, and a packer label--no k M. R. Godwin, Customer Response to Varying Prices for Florida Oranges (Gainesville, Florida: Florida Agricultural Experiment Stations Bulletin 508, December 1952).

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51 distinction was made with regard to the appropriate deviation dictated by the pricing differential. For example, when the six cent deviation was applied, each type of concentrate was reduced by six cents. The prices employed in the study were 8.5, 10.5, 13.5, 16.5 and 20.5 cents per 6-ounce can. Analysis of the results of the pricing experiment indicated marked variation in concentrate purchases over the range of prices tested. Variations in purchase rates in response to the induced prices indicated that customer sensitivity to price change declined continuously as price was varied from the lowest to the highest test price. The theoretical price of 12.5 cents per can was found to be the price at which unit elasticity was found. At test prices below this level, the demand function grew more elastic, and, conversely, at higher levels the demand function became more inelastic. An interesting aspect of this study was the provision in the experimental design to compensate for possible price carryover effects attributable to storability of orange concentrate. This possibility was treated by the continuance of the same price treatment in each store for a period of several weeks. In summary, a relatively small amount of work has been done in the area of demand estimation for citrus fruits. This gap is especially true prior to 1950, and since that time most consistent attention has been devoted to this economic area by the Florida Agricultural Experiment Station, specifically by Professors Godwin and Powell. A further area long neglected in all commodity demand work is that of economic substitution among products. As methodological advances progress, it appears that the substitution effects of price changes will move to the forefront as a significant area of economic research.

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CHAPTER I I I PURPOSE OF PRESENT RESEARCH AND SPECIFIC PROBLEM ORIENTATION The present study was designed to investigate the competitive relationships among Florida Indian River, Florida Interior and California Valencia oranges for fresh market. This project constitutes one phase of a broad research program, the objective of which is to determine the nature of economic competition among citrus producing areas of the United States by obtaining estimates of demand and substitution relationships for principal citrus products. The production of citrus fruits provides much of the farm income in Arizona, California, Florida, and Texas. These citrus crops are marketed in many forms. At present little is known about the economic interrelationships among these products in the marketplace. The multiplicity of the products produced in the citrus industry makes the question of the interrelationships among them highly complex. However, the dynamics of the citrus industry are such that there is a need to identify and assess the importance of these relationships. The Specific Problem Interregional competition within the orange industry is primarily in the fresh fruit sector. In the United States the majority of oranges for fresh market is produced in Florida and California. On the basis of the ratio of fresh fruit sales to processing sales the former is more 52

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53 vital to California than Florida. However, recognizing that Florida oranges are marketed along with California oranges throughout the orange season, the economic interrelationships in the fresh market are of utmost importance to Florida. Another pressing question is the degree of economic competition between oranges produced in the Indian River and Interior districts of Florida. Disregarding differences resulting from variety, grade, size, and other distinguishing characteristics, within Florida and California in reality three differentiated producing areas produce and market oranges. Further, there exists three separate demand functions for oranges produced in these three areas, and to some degree economic substitution rates among them. The purpose of this research was to measure the degree to which price changes could alter the consumption patterns of the three types of oranges. The measures sought were defined in terms of price and cross-price elasticities of demand. Stated formally the specific objectives were these: (1) Estimate price elasticity of demand coefficients for Florida Indian River, Florida Interior, and California oranges and, (2) Estimate cross-price elasticity of demand coefficients for Florida Indian River, Florida Interior, and California oranges with respect to the prices of the other two oranges. Since there were within each of the three producing areas differences in oranges as to varieties, grades, and sizes, determinations were necessary to ascertain which of the characteristics within these variables to use in the measurement of the demand relationships. Variety In the determination of the variety over which the demand relationships were to be measured, two major considerations evolved. One of these was related to the relative volumes produced and the second to the

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5k degree of competition in the marketplace between the Florida and California varieties. The major variety produced in Florida is the Valencia. This variety is also predominant in California production. Valencia oranges from the Indian River and Interior districts of Florida are marketed along with California Valencias throughout the season. Few other orange varieties are available for the national market during the spring and early summer months when the Valencias are in peak production. During the 10 year period 1952 through 1961, Valencia oranges accounted for an average of Wi.k per cent and 60.2 per cent of total orange production, respectively, for Florida and California. Thus, the Valencia fruit from each of the three areas was selected as the most important fruit for which to estimate demand relationships. Fruit sizes Based upon information relative to the distribution of sizes of fruit produced in the three areas, consideration was given as to what size or sizes must be included in the study to realize an effective measure of demand relationships for Florida and California Valencia oranges. The sizes predominant in Florida Valencia production are from size 163 to size 252 (Table )k) . The average diameter of this fruit ranges from 3.063 inches for size 163 to 2.625 inches for size 252. During the season immediately preceding the study, 21.3 per cent of the Indian River Valencia oranges moving through interstate commerce Percentages derived from the report of the Growers Administrative Committee, Lakeland, Florida.

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55 2 was of the size 163 , and 36.2 per cent of the Interior Valencia fell • 2 into this category. In this same season 41.0 per cent of the Indian River Valencia oranges moving into interstate commerce was of size 200, 2 and 40.5 per cent of the Interior fruit was of this size. California Valencia oranges, characteristically smaller than Florida Valencias, also have two dominant sizes: size 113 and size 138, which have an average diameter of 2.600 inches and 2.240 inches, respectively (Table 14). During the season immediately preceding the study, 33.0 per cent of the Valencia oranges marketed by a leading California citrus marketing firm was of size 138. In this same season 31.7 per cent of the Valencia oranges produced in the central California area, approximately 90 per cent of the State's production, was of size 113, and 32.9 per cent was of size 138. 3 Historically the sizes of predominance indicated above have been the norm. This pattern, therefore, evolved consideration of two sizes from each state over which the demand estimate should be made. Based upon this information and recognizing the limitations placed upon the study from the standpoint of capital and management, the California size 138 was selected as the representative size California Valencia for the study. An ordering of Florida Valencia oranges was made, with the first choice being the size 200 and the second choice the size 163. 2 lbid . 3 Derived from data of the Valencia Orange Administrative Committee, Los Angeles 15, California.

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56 TO • < o c to to > TO 'E I. o >4TO O •o c to to to to c TO T> u O 03 L. I 0) o > vO — CT* CC — c TO tA . N to i i • Ji2 u 3 D O u a. TO TO L. < TO c u o TO o TO Tl L. o c

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57 This decision led, as further explanation will indicate, to form the basis for two major experiments. Fruit grades Dominance of the U. S. No. 1 grade in all three areas of production established it as the grade over which to measure the demand relationships. Specifications of the Research Probl em By virtue of the size distribution for Florida Valencia oranges, the desirable measure of competitive relationships between Florida and California fruit would include both of the modal sizes of Florida Valencia oranges. The inclusion of sizes 200 and 163 from the Indian River and Interior Districts of Florida and size 138 from California evolves into six basic relationships for study (Table 15). These relationships provide quantitative measures of the nature of competition among these fruits in terms of price and cross-price elasticity of demand. Within each relationship the effect of the price of one specific orange type upon the quantity taken of the same orange type defines the price elasticity of demand. On the other hand, the effect of the price of one specific orange type upon the quantity taken of another orange type defines the cross-price elasticity of demand. The basic procedure selected to obtain data of the type required to measure the competitive relationships between Florida and California Valencia oranges consisted of a series of experimental tests conducted at the retail level of distribution under controlled conditions.

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58 Table 15. --Basic demand relationships, Florida Indian River sizes 200 and 163, Florida Interior sizes 200 and 163, and size I38 California Valencia oranges Quantities taken of As a Function of the Valencia oranges Prices of Area of Production and Size Area of Production Florida: Florida Indian River Florida Interior California Indian River: Fruit Size 200 138 163 138 200 138 163 138 200 138 163 138 Rationale Underlying Method Selection Controlled experimentations offer an opportunity to overcome some of the inherent difficulties found in secondary data. The researcher can adequately describe, with precision, the demand side of the market for a specific commodity. By creating the controlled situation, he can cope successfully with such variables as advertising, quality levels, display size, and location, plus commodity characteristics such as size and grade. During the reasonably short time required for generating adequate data, he can comfortably assume constancy of consumer income, prices of other goods, general level of prices, and consumer tastes and preferences. One advantage of controlled experimentation to estimate demand relationship lies in the fact that the researcher can obtain parametric Size 200

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59 estimates of demand for a dynamic industry. The relative rapidity with which data can be collected by experimentation makes the approach quite suitable for studying the demand for products under the stress of final product changes and innovations. The major advantage of the controlled experiment is the ability to manipulate price and thereby describe a wide range of price-quantity relationships beyond the experience of the market. When an industry is undergoing rapid production changes, demand relationships estimated from data generated in controlled pricing experiments can yield results which have application to the changing supply situation. For example, Florida orange production increased 30 per cent from the 1S60-61 to the 1961 -62 season, a heretofore unheard of increase. It is not reasonable to assume that demand estimates from a historical production base and the uncontrolled experience of the market could yield demand information which would cover this great a change. By utilizing a controlled pricing scheme and deviating price above and below the normal market situation, estimates of price elasticity can provide a basis for determining direct price effects of larger changes in supply conditions. In addition to obtaining direct price effects in terms of price elasticities, the controlled experiment is conducive to the exploration of economic substitution rates. By inclusion of two or more major commodities or commodity characteristics and manipulating price over them, one can obtain estimates of the cross elasticity of demand. Price manipulation, coupled with adequate control, provides for observation of the decision-making process in an atmosphere of varying price differentials between a good and assumed substitute goods. For example, in the present research problem, there is, in addition to the concern over the effects

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60 of Florida Indian River price upon Florida Indian River sales, an especial interest in the effects of California price upon Florida Indian River sales. The controlled pricing experiment allows the pursuit of information to answer such questions. These characteristics render controlled experimentation one of the most powerful generative devices the economist has today for providing input data to estimate demand and substitution relationships. Notable among the disadvantages of the experimental approach is the high cost involved in the effective generation of data for the estimation of demand relationships. There must be a system of adequate mechanics to facilitate the data collection. This requires a number of personnel as well as a system to compensate for losses directly relating to the study. The costs involved in creating the controlled situation can be classified into three categories: administrative, logistical, and operational losses. The extent these vary with respect to shares is dependent primarily on the nature of the study. Administrative costs include all outlays for physical procurement of the data, such as enumerator, delivery and supervisory personnel. Logistical costs can be incurred as a result of personal delivery to the stores, outlays for physical storage of the commodity or commodities, and other costs involved with the physical handling of the product. Operational losses arise as a result of payments for price differentials below the normal market, payments for quality maintenance in the case of a perishable commodity, and other preagreed payments. The disadvantage most often mentioned is that in such a study the researcher gains knowledge of great substance but relatively limited generality. The validity of this alleged disadvantage is really a

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61 question of scale, stemming from the limited population reached by a given experiment and the difficulty in obtaining a localized representative population. Conceptually, if a researcher could divide a commodity market into regions which would provide a cross section of the market population, and if representative cities were selected in each region to conduct experiments, he could gain generality and still maintain substance of unquestionable validity. Once the cities were selected, a cross section of the city population based on census tracts and other known information could be obtained. If, for example, the midwestern and eastern United States' market for fresh Florida oranges were divided into 5 or 6 regions, with appropriate cities selected to represent these regions, estimates of demand relationships would yield the composite demand for the entire market area.

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CHAPTER IV RESEARCH METHODOLOGY In an analysis of the demand for fresh oranges, economic logic must provide the framework within which the statistical computations are made in obtaining estimates of demand and substitution relationships. The theoretical framework, within which the demand relationships for fresh Valencia oranges were developed, was regarded as lying within the body of neoclassical demand theory doctrines. This theory is based upon the premise that each consumer possesses a given set of preferences. Further, it is assumed that each consumer chooses from among alternative combinations of goods and services. This selection is done in such a manner as to maximize satisfaction within the confines of a given set of market prices and is subject to the level of income available for expenditure on consumption of these goods and services. Thus, the quantity of a given orange type purchased by an aggregation of consuming units, per unit of time, as of a particular time, was assumed to be a function of (l) the prices of that particular orange type; (2) the prices of other orange types; (3) the prices of closely related subst i tutable products; (k) tastes, preferences, and real income; and (5) the attitude of the group concerning future prices of oranges and substitute products. 62

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63 The Economic Mode 1 A model conceptualizing the demand relationship for fresh Valencia oranges may be written as follows: Y ijk f(X li' X 2i' V' X lj' X 2j' X nj ; °V V "n+l* (Zfj) where: Yj. k = quantity disappearance in the k-th observation of the i-th Valencia orange type as the j-th level of prices of all goods and services, consumer income, and other preference factors. X.. = price of a particular Valencia orange type. X_. = price of a second Valencia orange type. X,. = price of a third Valencia orange type. X.. = the general level of prices of all goods and services, X_. = consumer income. X-....X . = other preference factors. 3j nj a,, a ...a ., = a set of parameters that connect Y,,. with all i i n+ 1 i j k factors X . , and X . . ni nj The economic model attempts to portray the relationships believed to exist in the real world situation between the preference of consumers for Valencia oranges and the monetary values placed upon these preferences. The model, therefore, has many explanatory variables, variations which, either separately or in combination, affect quantity disappearance. In demand analyses, quantitative measurements have been placed directly on a portion of these variables, while the remainder are passive elements affecting the quantitatively measurable variables. The effect of price of a given Y. on purchases of the same Y. is measured in terms of the price elasticity of demand. Changes in the purchase rates of a given Y., resulting frcm changes In the price of a second or third

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64 Y., are measured as the cross elasticity of demand. A change in purchases i of a given Y. resultant of a change in consumer income is measured definitively in terms of income elasticity of demand. Other explanatory variables, the general level of prices of all goods and services, and other preference factors operate to modify the measurements attainable in the quantitative measures of the elasticity coefficients. Specifically, this model specifies the quantity-price relationships for the three Valencia oranges at a given level of other variables. It is designed within this framework to explain the behavior patterns of consumers as well as modifications resulting frcm a changing orange price structure. The Statistical Model In the generation of data reflecting consumer decisions regarding the purchase of fresh oranges, two fundamental assumptions are (1) in the aggregate, consumers possess a basis for discrimination in their decision-making process relative to purchases, and (2) in the aggregate, consumers possess sufficient information to render their basis for discrimination operational. With these assumptions and the basic objectives of estimating coefficients of price and cross-price elasticity, the statistical model was developed. The economic model depicted in equation 4.1 was conceptual and no attempt was made to estimate all the parameters involved. Rather, data were generated to estimate the effects of price and changing price structure upon quantity disappearance of each of the three Valencia orange types, other variables remaining constant. Consistent with these requirements, the statistical model formulated to describe the functional

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65 demand relationships for fresh market Valencia oranges produced in the three areas is as follows: Y i-ijk = 0io + *11 X i-l + 0l2 X 2-j + ^13 X 3-k + e i-ijk ^ 2 > Y 2-ijk " ^20 " ! *21 X i-| + ^22 X 2-j + ^23 X 3-k + £ 2-ijk ( ^ 3) Y 3-uk " ^30 + ^31 X 1-I + %2 X 2-j + ^33 X 3-k + e 3-ijk <*•*> where: Y'_ ... = log of the quantity of Florida Indian River Valencia J oranges purchased. Y' ... = log of the quantity of Florida Interior Valencia 2-ijk oranges purchased. Y' ... = log of the quantity of California Valencia oranges •* purchased. j3j_, j8' , j3' = log of regression constants (Y intercepts). £.., |3|o» £io regression coefficients associated with Florida Indian River Valencia oranges (price elasticity and two cross elasticity estimates). £ . , 0--, /3__ = regression coefficients associated with Florida Interior Valencia oranges (price elasticity and two cross elasticity estimates). j3 . , jB__, /3__ regression coefficients associated with California * * ** Valencia oranges (price elasticity and two cross elasticity estimates). XJ ... , X' ... , X' . .. = log of prices of Florida Indian River, i-ijK z-ijk i-tjK Flor|da interior, and California Valencia oranges. e i '-u> e o •ii / > €i "t, = random disturbance associated with YJ, l-ijk Z-iJ.k 3-ijK v ^ and Y , i This system of equations allows the simultaneous consideration of the direct and cross-price effects on quantity disappearance at the retail level for the three orange types. Verbally, the expressions stipulate that the quantity taken of any specific orange type is a function of a constant ("Y" intercept), the price of the orange type

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66 in question, the prices of the other types of oranges available, and a random disturbance which is assumed to be normally, and independently, distributed with a mean of zero and constant variance. Assumptions There are several assumptions both explicit and implicit to the model formulation. Explicit assumptions relate to the statistical formulation, while the implicit assumptions' are those which must be made in order to couch the model in the theory of demand. In constructing the model as a linear logarithmic function, two basic considerations must be made. One of these relates to the necessity for transformation of the variables to logarithms, and the other relates to the logic of the utilization of constant elasticity coefficients derived from the logarithmic equations. The use of the logarithmic function provides a corrective measure to insure against nonaddi tivi ty when the treatment effects are of a multiplicative nature. Common is the assumption of multiplicative effects in economic data. If the operations producing the data are of such a nature that the effects are really not additive, then the sums of squares attributable to such effects do not represent the true effects, Effects which are multiplicative on the original scale of measurement become additive on the logarithmic scale. By transforming to the logarithmic scale, additivity is introduced. This introduction of additivity rules out interaction effects between prices and the error term associated with quantity disappearance. In effect, this conclusion means that regardless of what the level of prices P. may be, a random term of a given magnitude always has the same effect on quantity disappearance.

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67 In regards to the logic of the assumption of constancy, with respect to the price elasticity, it appears to be a feasible assumption, especially as the first approximation. Although the elasticity of demand with respect to price may change from one price to another, it is desirable to obtain an average elasticity over some specified range of prices. Such an estimate of price elasticity may be quite sufficient for guidance in some of the preliminary adjustments outlined in Chapter I. It is recognized that a more sophisticated estimate relating to given price levels would be required as the adjustment process moves close to the maximizing position. However, since such a position is not eminently foreseeable, the constant elasticity function produced by the logarithmic regression is quantitatively appropriate at the present stage of adjustment. Although the parameters in equations k.2-k.k are assumed to be multiplicative, they are further assumed to be independent. The controlled manipulation of price according to a predetermined plan forces conformity to this assumption. In addition, controlled price manipulation coupled with managed unlimited supplies clearly identifies the dependent variable as quantities taken and the independent variables as prices. Assumptions necessary and sufficient for the application of the statistical model to test the postulated economic model include the assumptions underlying consumer demand. These assumptions must remain constant as price is varied in order to determine the direct and cross effects of price. Of major importance is the movement incurred in the general level of prices. In the relatively short period of time required for generating data in a controlled experiment at the retail level of distribution, the assumption of constancy of the general level of price appears quite

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68 feasible. Another variable eliciting much concern in the estimation of demand relationships is that of consumer income. Here again, during the short time required to generate the data through retail store experimentation, It can be safely assumed that no significant variation occurred. To control a source of variation which limited time periods do not preclude, much attention was devoted to the control of advertising and merchandising promotional activities. Since these forces form the basis for short run changes in consumer tastes, preferences, and expectations, It becomes Imperative to impose restrictions on these activities. To accomplish this objective, advertisement and merchandising promotional programs for fresh oranges were eliminated during the test period. With regard to longer-run changes in tastes and preferences, the time element in controlled experimentation is sufficiently short to preclude any basis changes in these factors. The Experimental Model The experimental model selected for generating the data required to estimate the parameters of equations k.Z-k.k was the Triple Cube design. This design, an outgrowth of the central composite designs developed by G.E.P. Box and Associates, was developed by T. E. Tramel For a description of the Box design see: Box, G.E.P. and Hunter, J.S., "Experimental Designs for Exploration and Exploitation of Response Surfaces," Proceedings of Symposium on Design of Industrial Experiments (Nov. 5-9, 1956) pp. 138-192, Institute of Statistics of the Consolidated University of North Carolina, and Box, G.E.P., Haden, R.J., and Hunter, J.S., Experimental Designs for Multlfactor Experiments . Institute of Statistics Mimeo No. 71, Raleigh, North Carolina, 1953.

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6S and suggested for use in AgronomicEconomic fertilizer experiments. The original Box design is considered quite efficient in estimating parameters of a quadratic function. In the development of the basic design, Box and his associates were interested primarily in industrial experiments, and consequently the requirements for such work were well adapted to a very limited number of observations dictated by the single cube. Generally, more variables can be controlled in industrial work than in economic work. Therefore, for an equal level of precision, a greater number of observations is needed in the latter than in the former. Replication is one solution to this problem. An alternate solution is to modify the basic design to accomodate a wider range of measurement. Such a procedure gave rise to the Triple Cube. A total of 15 treatment combinations are derived from the original Box design. With respect to the cube, the treatment combinations may be divided into three categories: (a) those forming the corners of the cube, (b) those on the three major axes, and (c) the one at the center of the cube. Thus, the cube plotted in three dimensional space reflects eight treatment combinations from the corners of the cube, six treatment combinations on the major axes equidistant off each face, and one combination located in center of the cube (Figure 2c). 2 Tramel, T.E., "A Suggested Procedure for AgronomicEconomic Fertilizer Experiments, 1 .' Chapter 15, Economic and Technical Analysis of Fertilizer Innovations and Resource Use , edited by: Baum, E.L., Heady, E.O., Pesek, J.T., and Hildreth, C.G., The Iowa State College Press, Ames, Iowa, 1957. 3 The original Box design also had the observation in the center of the cube such as is shown in Figure 2A.

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70 |0,_0, 0) _ x (-3, 3, -3) (3, -3, 3) (-3, -3, -3)k (3, -3, -3) ^3 2 Figure 2.--Componenf cubes of ihe Triple Cube Design.

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71 The modification developed by Tramel was the addition of two more cubes, increasing the number of treatment combinations by 16 (Figure 2B, Figure 2C) . Hence, total treatment combinations were increased to 31, 2k of which are formed by the corners of the three cubes, while the remaining are those on the major axes plus the one in the center of the system as in the original design (Figure 3). Tramel in his work measured the relative efficiency of the Triple Cube as compared with the original Box design and found a considerable increase in efficiency. The greatest increase in precision was found in the estimation of the intercept and in the interaction terms. However, a worthwhile increase in precision was brought about in the estimation of the quadratic terms. The utilization of this design for the allocation of price treatments to generate input data for demand estimation is particularly appropriate. Aside from the efficiency gains resulting from the use of the Triple Cube, it allows a wide range of price levels. Application of the design permits the use of nine price levels in combinations dictated by the Triple Cube. Using the major axes as a focal point and mean level, four deviations on either side of the mean are available. The availability of nine price levels was considered quite adequate for the measurement of demand relationships for the three Valencia orange types. Another question of significance related to the likelihood of different base prices for the three Valencia oranges used in the study. Tramel , op. c?t.

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72 i CO « 3 .P)

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73 The Triple Cube accommodated this requirement in that the base prices could be different for all three orange types if this were the case at the time of market entry. A last important influence on the selection of the Triple Cube was that it adapts quite well to the experimental approach to demand estimation. The fact that this approach has high capital requirements has placed many researchers in this area in a position of estimating functional relationships on a much smaller scale, either in terms of number of commodities considered or in terms of price levels over which to estimate. On the one hand, a more orthodox design which accommodates three or more commodities may also require a large number of retail stores, an impossibility from the standpoint of management and resources. On the other hand, increases in the number of price levels utilizing some of the more conventional experimental models lengthens the time required to generate the data to an unbearable financial extent. More frequently than not, the more conventional experimental models impose some combination of the aforementioned problems, so the researcher is forced to choose among fewer price levels or fewer commodities or both. The Triple Cube alleviates these problems to a degree. It provides a fractional replication with respect to treatment combinations which have semiorthogonal properties. Therefore, it requires fewer observational periods to generate adequate data to estimate the demand parameters, for a given number of price levels, and allows estimation of these parameters for three commodities or commodity characteristics. These properties make it a highly desirable experimental model for demand estimation.

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74 Limitations of the Model Formulation Unlike some of the more orthodox experimental approaches, the model formulation had no inherent facility to account for or parcel out extraneous variation. Retail stores in a metropolitan area will vary considerably. This variation can be classified basically into two categories: (1) differences in store volumes and (2) differences in clientele. These variations are generally a result of socio-economic differences as well as differences in the population base the store serves. Since volume of the individual store is affected by the population base the store serves, a correction for difference in traffic flows would tend to eliminate this source of variation. Thus, to compensate for these differences, a transformation, in the form of a reduction of sales to a per 100 customer basis, was planned. Clientele differences are basically in the realm of socio-economic considerations, In that these could be due to ancestral differences, economic differences, and social differences. This category presupposes an adequate cross section of these population characteristics over which to measure demand relationships. Careful selection of stores can insure coverage of the heterogeneity of the market population. Although it is desirable to have a measure across this heterogeneous population, it is also desirable to reduce the heterogeneity to more homogeneous population by removing differences in purchase habits among the various store populations. Since the product with which the research was concerned was in the produce line, fresh orange purchases were assumed to be a function of produce purchases. Therefore, to remove differences in purchase habits of the clientele of the various stores, a measurable variable,

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75 value of produce sales, was planned for inclusion. The Statistical Model Redefined Consistent with the transformation of sales to a per 100 customer base and the addition of the variable, value of produce sales, the statistical model redefined is as follows: Y i-ijkm = Pio + Vi-i + *12 X 2-J + V3-k + Vm + e l'-ijkm <*'5> Y 2-ijkm " ^20 + *ZI X |-| + Vi-j + ^-k + Y 3-ijkm = ^30 + Vl-1 + ^32 X 2-j + ^33 X 3-k + W + e 3 '-ijkm <*•?> where: Yj_... = log of the quantity of Florida Indian River Valencia oranges purchased per 100 customers. Y'_ ... = log of the quantity of Florida Interior Valencia oranges J purchased per 100 customers. Y* ... = log of the quantity of California Valencia oranges purJ chased per 100 customers. /3| , /3' , £' = log of regression constants ("Y" intercepts). ]3. . , fi,yt )3| o = regression coefficients associated with Florida Indian River Valencia oranges (price elasticity and 2 cross elasticity coefficients). ]3 . , j3„_, /3„ = regression coefficients associated with Florida Interior Valencia oranges (price elasticity and 2 cross elasticity coefficients). jB _. , A,~» |3,, = regression coefficients associated with California Valencia oranges (price elasticity and 2 cross elasticity coefficients). jB., , /3 ? ^i /3,r = regression coefficients associated with value of produce sales per 100 customers with respect to Y], Yj, and Y£. Xj . , X ' . , X ' . = log of prices of Florida Indian River, Florida Interior, and California Valencia oranges.

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76 el . .. , ei . ., , el . ., = random disturbances associated with ^l-ijkm' 2-ijkm' 3-ijkm yl> Y , and yl> Specifications of Experimental Test Upon completion of the delineation of variables, construction of the economic model, and formulation of a statistical model to test the economic model, evaluations were made concerning the specifications of the tests to be conducted. Size limitations The size of the tests was limited by three major factors: (1) dictates of the experimental design, (2) management, and (3) resources. Attention was given to each of these in formulating the specifications of the tests. The Triple Cube design used for the data generating model dictated a requirement of 31 pricing periods or observations per replicate. A further consideration was the fact that there was no accounting for the differences in time periods inherent in the model. To compensate for time, a system of balance must be built into the design layout. The first element was the length of the observational period. The alternatives considered were one-half week periods, two-day periods, and one-day periods. The process of logical determination of an adequate time period was not only a function of consumer habits in relation to frequency of grocery purchase but also a function of the habits surrounding the commodity of interest, fresh oranges. The decision, recognizing the needed control of variation due to differences in days as well as in weeks, was to use a one-day observational period. It was recognized that normally the distribution of shoppers is

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77 more heavily concentrated in the latter part of the week. However, consumers shopping in the early portion of the week may be quite unlike those in the latter part of the week. In fact, it appears reasonable that when looking at the aggregation of consumers shopping in a given week, one might well have a different population on each day. The time for grocery shopping In a given household tends toward an institutional arrangement by habit. Further, credence is added to the daily observational period upon examination of consumer habits with regard to the purchase of fresh oranges. Basically the grocery shopper enters a grocery store for one of two purposes, the purchase of a full grocery order or the selection of a few items such as milk, bread, or occasionally meats to fill in between grocery orders. In general, most items in the grocery budget are purchased at one time during the week. It was considered that, in the main, fresh oranges would be an unlikely Item to be purchased between grocery orders. Therefore, daily observational periods would not create undesirable distortion in consumer purchase rates. The removal of time period variation as indicated above had to be built into the design layout. Since the generating model dictated 31 price combinations to appear in each store used in the study, 31 observational periods were also required. Identification of an observational period as one day further required 31 operational days. Projecting a six-day operational week, two alternatives were considered to compensate for time period variation by a system of balancing treatments over days: 1. Using three stores and randomly assigning the 31 pricing treatments to orte store and then balancing the treatments over twoday periods in the two remaining stores. This would result in every pricing treatment appearing once on a Monday -Tuesday, a Wednesday-Thursday, and a Friday-Saturday at some time during the study.

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78 2. A second alternative, and the optimum, was to use six stores in which the 31 pricing treatments were randomly assigned in one store and balanced over days for the remaining five stores. This plan would result in a complete balancing of pricing treatments over days, since each treatment would appear once on each day in some store included in the study. Upon examination of capital resources available for this work and the human resources considered essential for the conduct of the study, it was evident that the inclusion of the two experiments of six stores was prohibitive. However, the resource outlay could support the utilization of nine stores. In conformance with the restrictions from the standpoint of resources, two simultaneous experiments were conducted, utilizing both alternatives of balancing pricing treatments over time. From one of these experiments data were generated for the estimation of demand relationships for California size 138, Florida Indian River size 200, and Florida Interior size 200 Valencia oranges. This particular experiment was conducted in six stores and thus contained complete balance in the compensation for time period variation. The second experiment was for the generation of data to measure the demand relationships for Florida Indian River size I63, Florida Interior size 163, and California size 138 Valencia oranges. This experiment was conducted in three stores and contained a pricing treatment balance over two-day periods, a partial compensation for variation due to differences in time periods. The selection of Monday-Tuesday, WednesdayThursday, and Friday-Saturday for the three sets of two periods was based upon the assumption that these pairs of days would be the most comparable from the standpoint of the consumers patronizing the stores. Price differentials The generating model utilized in the study allowed for nine levels

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79 of price. To insure a range of prices which would be relevant under foreseeable changes in the quantities available for the fresh orange market, much thought was given to the size of the differential to be used. On the basis of prices per dozen for fresh oranges, a four cent differential was selected. Among the factors relating to the differentials was the need for conformity to conventional pricing procedures. Accordingly, the differentials had to be even integers greater than one to produce odd cents per dozen pricing, starting from a base stated in odd cents. Further, from the desire to cover the relevant range of prices foreseeable and to force substitution within the range, the four cent differential was selected. Thus, from a given base price there would be deviations of -16, -12, -8, -k, +h, +8, +12 and +16 cents. The 31 treatment price combinations in terms of four cent differentials are shown in Table 16. Experimental design layout The allocation of pricing treatments to stores was of crucial concern, since the system of balance over time periods had to be built into the design layout. In the experiment involving Florida Indian River size 200, Florida Interior size 200, and California size 138 Valencia oranges, the 31 pricing treatments were randomly assigned to one store and balanced over the other five stores. This assigning was done so that each treatment appeared in a store on each day of the week at some time during the test (Table 17). For example, Hereafter, the experiment involving Florida Indian River and Interior size 200 and California size I38 will be referred to as Component I .

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80 Table 16. --Treatment price combinations, in terms of four cent deviations, used in estimating demand relationships for Florida and California Valencia oranges for fresh market. Florida Florida Indian River Interior Oranges Oranges Cal ifornia Oranges -16 -16 -16 -12 -12 -12 -12 -12 +12 -12 +12 -12 -12 +12 +12 -8 8 8 8 8 + 8 -8 +8 8 8 +8 +8 k k k k k + k k + k k h +4 + h + k + h + k + h + h k + k k + k + k k k + 8 +8 +8 + 8 +8 8 + 8 8 +8 + 8 8 8 +12 +12 +12 +12 +12 -12 +12 -12 +12 +12 -12 -12 +16 +16 + 16

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O)
PAGE 97

82 vO IA 3 C C s I I I u a) -a e 3 0) u o CO CO CM ro 5 • m o

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83 price differentials of -12+12-12 appeared on Monday of week one in store one, on Tuesday of week two in store six, on Wednesday of week two in store two, on Thursday of week two in store four, on Friday of week two in store three, and on Saturday of week two in store five. Only one treatment combination, +12+12-12, remained for allocation in the sixth week. This arrangement provided some flexibility in that a missed observation could be secured by repeating the price treatment associated with it during the final week. The one restriction upon this was if a missing observation occurred on the day of the week that the +12+12-12 treatment was to be applied, then the appropriate day of the following week must be added to secure the missing observation. The letters a, a, a, indicate the days in the final week available for such a procedure (Table 17). In the experimental test including Florida Indian River size 163, Florida Interior size 163, and California size 138 Valencia oranges, the price treatment al locative procedure was essentially the same with the exception of the balance concept. With only three stores, balance was reduced to two day periods. Each treatment appeared in a store on a Monday-Tuesday, Wednesday-Thursday, or Friday-Saturday at some time during the study. As in the allocation procedure in Component I, the 31 pricing treatments were randomly assigned to days in store 7 and c Hereafter, the experiment involving Florida Indian River and Interior size 163 and California size 138 will be referred to as Component 1 1 .

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Ok balanced over the two day-periods in the remaining two stores (Table 18). Requirements and Specifications of Experimental Units The selection of a test site and test stores within the test city required careful consideration. With the realization that the validity of the estimated relationships depended upon the limited population reached by a given experiment, much effort was devoted to a delineation of the factors affecting selection and to determination of the most effective selection. Selection of test site In the marketing of fresh oranges, Florida and California fruit meet in competition from the Rocky Mountains to the Eastern seaboacd. The competition between the fruit of the two areas is especially heavy in the midwest. Therefore, the area west of Pittsburg, Pennsylvania, and east of Chicago, Illinois, was designated as the area in which the study would be conducted. Within the specified area other factors affected the selection of the test city. It was recognized that the population base over which the measurement of demand relationships were to be made could be expanded greatly by the selection of a high population density trading area. This led to the selection of a relatively large and heavily populated metropolitan area. To insure further a representative sample population, the area was to be characterized by moderate industrialization and an adequate cross section of social, ancestral, and income strata. To meet these prerequisites, metropolitan areas in excess of

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85 Table 18. --Component II experimental price design for the study of the competitive relationships among size 1 63 Florida Indian River, size 163 Florida Interior, and size I38 California Valencia oranges, Grand Rapids, Michigan, April-May, 1S62.

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86 Table 18. --Continued. Store Number Day of Week IR Int. Cal. IR Int. Cal . IR Int. Cal

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87 was at the highest level of the firm's management. Receiving the sanction and support of the firm's top management was ranked essential. This persuasion was no easy task. When approached by a research team with the idea of initiating price movement representing significant departures from the norm in both directions on an item, top management is inclined to envision mass movement of business away from its stores when prices are above the norm and a logistical problem resulting from selling unlimited quantities at prices below the norm. A chain grocery organization located in Grand Rapids, Michigan, indicated a willingness to cooperate in such a research venture. Acknowledging this indicated interest, a conference was arranged with the executive officers of the firm to discuss the ramifications of a controlled pricing experiment superimposed upon a retailing activity. After a thorough explanation of the problem, research methods to be employed, and operational procedures conducive to the generation of data of sufficient caliber, the management of the firm was still willing to cooperate. Selection of test stores To select the best and most appropriate stores for inclusion, all available retail units were inspected. In addition to discussions with corporate headquarters personnel regarding the appropriateness of individual stores with respect to income strata, social strata, and ancestral background of clientele, the individual store managers were interviewed informally to gain a fuller understanding of the nature of clientele and traffic flows in their particular stores. Of the nine stores selected, six were assigned to Component I

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88 and three to Component II. In terms of weekly sales, the stores selected were classified into three groups: small, medium, and large. Each classification contained three stores. The three large stores and the three small stores were assigned to Component I, while the three medium-size stores were assigned to Component II. This division of stores was a result of the homogeneity found in the medium-size stores with respect to previous weekly volumes. It was anticipated that the greatest hetrogeneity with respect to store volume size could be handled better in Component I, with the complete balancing system, than in Component II, with only the partial balancing system. Orange pricing The week prior to market entry, April 9, 1962, the Grand Rapids retail price for Florida Valencia oranges from either district was k$ cents per dozen, and the California Valencia orange price was 59 cents per dozen. These prices became the base prices used in the system. Therefore, Florida Valencia prices ranged by four cent differentials from 33 cents to 65 cents per dozen, and California Valencia prices ranged by four cent differentials from k3 cents to 75 cents per dozen (Tables 19 and 20). A system was established with regard to pricing techniques and pricing changes. Over each of the three displays of oranges a price placard was to be placed designating the area of production and price per dozen (Figure k) . Display control The size of the displays conformed with normal display space for fresh oranges. Further, the displays were maintained near normality

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m •a — — Q. iro O OS iZ 73 C O (0 O u O) c CO f0 c u &i ._ o X — in id c > o .(0 4-t — m c — u • SON — cr» 0) — — > 03 .U •> *• X •— 00 JS fl) — I N u o — 0) P C f0 in < c g Q « • — U £ >. o o Q .— 3 I3Z •M 0) tfl *» • £ •M IB "O u — O u MO m^ I/) o « LO vO la pa .J 5 s 89 PA PA LA Po CTi Po vovo la -3* inJ 1 OM^er» — — LA -3" Po vfi LA LA CTv — PA — LA CTi if\rs\o la la la c V N 8 i. V a. 0) u u a. pa la pa po la ro lTi — po pa — — pa — la ro pa cr\ LA -3" LA PA SO PA -3" vO pa LA -3" -3" pa ^O -3" la LA -d c\crM*\— rj\(^ pa po po la i— po po la — la la LA LA LA S0 -d" PA PA PA PA -3" -d" LA -d PA -d -d" -3" vO la la — la pa pa la ro cr> po a\ po — PA — — vO ir\UM/\N LA LA P^ CT\ PA LA PA Po LA Po (Tv — po pa — — PA — •d -d LA -d LA -d LAPAvOpA-dvO PA LA-d -3" PAVO la pa po pa pa pa — crv po pa po po la — Po crt po •d" LA LA -d LA LA LA VO -d PA PA PA PA -d -d LA -d PA — LA PA PA LA Po C\ Po > Po .— PA — — PA PA PA — <7\ Po pa Po po LA — po rj\ po la — LA -* LA LA LA VD -d PA PA PA PA -d J" LA -d PA J" -d LA — LA PA PA LA Po CA Po (Tl po — PA — — CP» — PA LA LA PovO \D LA -d LA-d LA -d Po vO LA LA LA Po \0 LA P** Q> PA LA PA -d LA -4" LA-d LA PA to CT> PA PA PA LA LA J" LA LA LA LA LA PA LA ro LTl PovO sO LA-d LA C> PA LA PA Po LA -d LA-d LA PAVO 5> PA PA PA — G> 4" LA LA LAVO -3Po — PA — — LTV J" PovO LA LA LA — Po pa — •— PA VO PA IA-3" * PA Po Po LA — Po fj\ PA PA-4 ot LA-J" Po LA Po G\ — po PAVO PAj SO PA "— tTV Po PA Po Po vO-J PA PA PA PA PO rj\ Po •— fr\ r— J" LA -d" Po vO LA Po C\ •— Po PA — PA -3" vO m IflJ Po pa Po Po LA •— PA PA PA PA -S J" •— PA— LA <7\ — PovO LA LA LA Po — LA Po PA r^ — VO -d LA LA -3" VO M,ftiLT\ Lf\PA-3" J" Po LA -d -3" LA-3PACT — tTv — PA — LA LA LA PovO LA LA — PA — LA Po PA •3" PA VO -d LA LA Po C*> po LA — LA LA-d" PA-d" -4-d po lT> pa— po ro \D LA-d" Po vO VO Po tT\ LT>po — — la -d-d* pa -d -d >«

PAGE 105

90 1 c 4J C .so la-* r>»so — r«» q\ q> r* — SO LA-d" * PA-3" — n 9> S>T r "* vo j-dJso la pa — la cn — r*» so ia la la r»»so la P* ro cr> — i*» JIA IA-* SO IA LA— LA LA — — JJJVD sD Jt ia c\ r> r*» o> pa IA LA-* SO IA-3 pa o>, — r«» g> o> LA -CT sO LA -3-d^S33S>^ — LA OA — r> 0> LA IA LA r*. SO IA P*. P». LA LA — IA sO sO LA LA LA I** — r»» la la rx q\ JLA-* -3" LA-tf — P»LA PA P>» Q> J 1 LA J" LA LA-* cr\ pa — r*. r*» p*. la-* r^so so so 9? 9> *** T t: •** J-tf pA-3" J" LA q\ q> — p— r». Jf J VO LA JLA — p* p*. ps. ua la ps.vO SO SO LA LA PX— — P*. LALA PA-tf J" LA Jf «* — f•T P*» LA PA SO LA-* LA 3* LA PA — r>* P*. P*« LA JT r«»vo vO SO LA to to to to u s to to to to to •" • sO to to to to (0 9m sO to to to p*» to to to to to — to to sO to to to — to to sO 10 P"» to to to to 4T) — p> — — p** la io — r*. q\ g> p* JT SO LA-tf * PA LA " " O^ O^ — P»»LA LA — LA PA SO LA LA LA P-SO P* LA LA P"» CT\ PA LA J * LA-* LA r*» la pa rsi LA^t LA LA

PAGE 106

91 Table 20. — Component II price design for the study of the competitive relationships among size 163 Florida Indian River, size 1 63 Florida Interior, and size I38 California Valencia oranges, Grand Rapids, Michigan, April-May, I962.

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92 Table 20. --Continued

PAGE 108

93 o E ig o U •X3 s O c _o u. Oft c o E o a to C .o o "a> c >• 5 Is 8 § D -o a = < V § ^ a> .5 "6 I * J -g a g a> O o *» a §> "2 2 § ° S i Q. _2> •2 D Q > C 3 CD

PAGE 109

s* c D O ~o o> c o V) Q. c .0 Jo 2 .> I E ~O CN *O O (£ "2 >0) -1. -c c £ o 8 J a, 5 1 rf 2 a a o 5 * O ~D g I 1 » J I >>. c a o ^6 .2 o O) _a> c D u. O o '0 c a> ~5 1 1 a? 0) o > o c ^o u

PAGE 110

95 Table 21 .--Arrangement of displays of Florida Indian River, Florida Interior, and California Valencia oranges, Component I, in a study of competitive relationships between Florida and Cal ifornia oranges. Week

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96 Table 22. — Arrangement of displays of Florida Indian River, Florida Interior, and California Valencia oranges, Component II in a study of the competitive relationships between Florida and California oranges. Store Number Week 1 2 3 k 5 6 ABC

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97 fornia Valencia oranges of the specified grade and size were to be handled by the test stores. Such a procedure was necessary since the model utilized in the study could not cope with the additional variation which would be introduced by the inclusion of other type, grade, and size oranges. A second condition was the preclusion of the possibility of using bagged oranges. To engage in such a procedure would create problems of visibility and comparison. Thus, the utilization of loose fruit allowed customers to compare the three fruits and provided a basis for establishing a common unit of sale. A third condition related to pricing. The "per dozen" pricing was to be used for the three test displays, and placards calling attention to price and area of origin must be uniform in all stores and on all displays. Finally, owing to the variation in prices among test stores, the cooperating chain must refrain from advertising or otherwise promoting fresh oranges during the time interval required for the market tests. This ban was necessary to avoid undesired distortions in sales resulting from advertisement or promotion since there was no inherent facility within the model formulation to compensate for the variation induced by promotional activity. Informational Requirements The analytical procedures developed for estimating the demand and substitution relationships for fresh Valencia oranges dictated the necessity for complete information on a daily basis regarding orange sales, departmental sales, and customer counts. The data concerning depart-

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98 mental sales and customer counts were obtained from the cash registers through special arrangements with the cooperator for clearing the machines and furnishing cash register tapes each day. Daily sales of oranges were determined by the research representative in the store, since he had complete responsibility for in-store management of the orange displays. This record involved maintaining a daily beginning and ending inventory and a daily accounting of acquisition of fruit as well as spoilage losses resulting from quality maintenance. Cooperative Arrangements In marketing studies of this type, the possibility inevitably exists that the research activities will result in monetary losses which the cooperating organization is unwilling to assume. Consequently, a satisfactory basis for financial adjustment was worked out to cover fully the losses attributable to the project. There were three sources of financial losses: (1) losses resulting from differentials below the base retail price, (2) losses from quality maintenance, and (3) losses due to changes in the wholesale price. At the initiation of the study a wholesale price was established that would allow the retail cooperator his normal margin. The difference between this established wholesale price and the actual wholesale price, that is delivered price plus margin, was paid to the wholesaler. The arrangement with the retail organization was made up of two components. For the oranges that were eliminated from the displays to maintain the desired quality level, the retail organization was paid at the price the fruit was billed to it from the wholesaler. For all oranges that were sold below the base prices of kS and 59 cents for

PAGE 114

ss Florida and California fruit, respectively, the retail chain was paid the difference between the experimental price and the base price. The success of a controlled experiment of this nature superimposed upon a normal retailing activity is highly dependent upon complete cooperation of the cooperating retail and wholesale organizations. It was deemed necessary that the individual store managers and their staffs and the staff of the wholesale firm be completely informed concerning the project and its procedures. To facilitate this, the executive staff of the retail and wholesale organizations and the individual store managers and their staffs were brought together for a conference prior to the initiation of the study. In this meeting the entire problem was discussed, including merchandising restrictions and the necessity for them, operational methods, and the types of information required.

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CHAPTER V CHARACTERISTICS OF THE TEST STORES The cooperating Grand Rapids chain store organization was one of the two major, agressive chain food store operations in the metropolitan area. Operations of this organization extended over a rather wide range of south central Michigan. Fourteen stores of the chain were located in the Grand Rapids metropolitan area. General Description of Test Stores Of the nine stores selected for the tests, all were in the Grand Rapids metropolitan area. However, two of these stores were located outside the city limits. Still, all nine were considered within the classification of supermarkets. Stores departmentalized The stores were organized well along the lines of departments. Common to all stores were grocery, meat and produce. The grocery departments contained generally a full line of non-perishable canned items, the usual lines of packaged staple goods, frozen foods and juices, a complete line of dairy products, and a limited amount of housewares and novelties. Each meat department offered a complete line of precut prepackaged meats. The produce departments offered a wide assortment of fresh fruits and vegetables and a limited amount of f lor icul tural products. In one store, in addition to departments mentioned above, 100

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01 was a liquor department, while another store had a delicatessen department and a small restaurant. In all stores the return of bottles was not a customer transaction, but rather there was a ticket register for the return of bottle deposits. In the stores having the liquor department, cafeteria, and delicatessen, separate registers were used for these purposes. Consequently, liquor customers and delicatessen customers were not counted as food shoppers, nor were the sales therefrom considered food sales. Degree of self-service As is characteristic of most modern supermarkets, the grocery department was completely self-service. In addition, within the meat and produce departments, self-service prepackaging was used extensively. Usually in the produce departments no more than two people were employed, and generally these were involved primarily in the prepackaging of the various produce items. Thus, all departments were entirely self-service operations. However, customers, at their request, frequently received assistance in the form of special services from any of the departments. In the group of stores used in the study, there was no definite foodlayout arrangement. In some stores the produce displays were the first encountered under normal traffic flow patterns, while in others the produce section was about midway, and in still others produce was last. Trading Stamp plan The chain participated in one of the nationally recognized trading stamp plans. One deviation from what may be considered the norm was that on Wednesdays customers received double stamps for their purchases. This practice substantially altered the weekly traffic distribution.

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102 Ordinary retailing practices of constant stamp issue per unit of sales throughout the week generally tends to produce a customer flow distribution heavily concentrated on Thursday, Friday, and Saturday. However, the Wednesday double stamp plan made it the day of heaviest traffic, while Thursday had a relatively light traffic flow. Of the weekly shoppers patronizing the stores, 27 per cent of them shopped on Wednesdays and purchased 36 per cent of the stores' weekly sales volume. Sales and Store Traffic Sales and store traffic data were acquired daily from each cash register in each of the nine stores. Since the study was concerned primarily with the food operation, sales of auxilliary items, such as in the liquor department contained in one test store and the delicatessen shop and restaurant in another, were not included. Customers shopping In these departments were easily identifiable, since separate cash registers were used for these departments. Customer count and sales During the six-week period in which the experimental tests were conducted, a total of 2^3,040 customers shopped and made purchases in the nine stores (Table 23). Total sales amounted to $1.6 million during the six-week period. Thus, total sales per store averaged approximately $181,600 during the test. On a weekly per-store basis the nine stores averaged sales slightly in excess of $30,000.00. The smallest store, in terms of average sales, had sales of $17,623 compared to the largest with In this work, customers should be Interpreted as being consuming units of one or more persons.

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03 Table 23. — Number of customers, produce sales, total sales, and proportions of total sales in produce, by component and store, experimental tests, Grand Rapids, Michigan, April-May, 1962 . Component

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104 sales of $42,017. Produce sales per store ranged from a low of $8,884 to $20,037 during the test period. Over this period 7.6 per cent of total sales were accounted for by produce items. Variation of produce sales in relation to total sales ranged from a low of 6.21 per cent to a high of 9.01 per cent. Considering the stores of the two components separately, average total sales per store in Component I were $18,488.56 compared with $17,514.87 in Component li stores. Variation between the high and low stores in terms of sales was much greater in Component I than in Component II. The high and low average total sales for Component I and Component II stores were, respectively, $42,017.56 to $17,623.65, and $31,362.44 to $27,731.55. This greater variation in total sales appearing in Component I was consistent with store allocation plans. Since, in this component, a system of complete balance could be introduced, it was easier to compensate for store-to-store differences than in Component II where balance could be maintained only over two-day periods . Daily distribution of store traffic Retail grocery store traffic flow is generally expected to peak on a Thursday, Friday, or Saturday, and these days account for quite a large proportion of weekly store traffic. Owing to the practice of giving a double amount of trading stamps on Wednesdays, considerable deviation from the general case was found in the Grand Rapids test stores. In the nine test stores, 26.8 per cent of the weekly traffic flow

PAGE 120

105 occurred on Wednesday (Table 24). Monday, Tuesday, and Wednesday accounted for a total of 46.8 per cent of weekly store traffic. The range of traffic flow varied from a low of 9.5 per cent on Monday to a high of 26.8 per cent on Wednesday. Thursday traffic flow was only slightly higher than the Monday and Tuesday flows, amounting to 11.4 per cent of the weekly traffic. The distribution of customers by days between components was very close and on Thursday and Friday was the same, 11.4 per cent and 18.9 per cent, respectively. Saturday, averaging 22.9 per cent of the weekly traffic flow, was second only to Wednesday in terms of traffic. The sequential arrangement of the remaining days of the week was Friday, Thursday, Tuesday, and Monday. In terms of patrons, the three low traffic days, Monday, Tuesday and Thursday commanded 9*5 » 10.5, and 11.4 per cent, respectively, of weekly store patronage. Daily distribution of store sales Daily sales were closely aligned but not proportionate to traffic. The average daily patronage on Wednesday was 26.8 per cent of the store traffic, but these patrons purchased 35.6 per cent of the weekly sales of the nine stores (Table 25). Monday, the lightest day in terms of total sales, accounted for only 4.7 per cent of the weekly total. Of near equal magnitude in total sales were Friday and Saturday, with 22.5 and 23.0 per cent, respectively, of weekly sales. The three lightest days, Monday, Tuesday, and Thursday, together accounted for only 18.9 per cent of weekly sales, an amount less than any other single day of the week. Considerable variation between stores was noted. For example,

PAGE 121

C6 c o 3 -Q
PAGE 122

107 -Q C o 3 (/> 0)

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108 store one had sales of $7,500 and store four had sales of slightly less than $6,000 on Mondays. These same stores on Wednesdays were reversed in order and, further, had a much greater difference in sales commanding $35,500 and $90,400, respectively. The differences in daily distributions between components was slight. The greatest difference was noted in Monday operations. In Component II stores, 5.7 per cent of weekly sales were consummated on Monday, while in Component I stores, only 4.3 per cent of the weekly sales volume was found to occur on this day. Daily distribution of produce sales Produce sales were closely related to total sales in the nine test stores. Wednesday was the high volume day, for 33-5 per cent of weekly produce sales were made on that day (Table 26). This figure compares to 35.6 per cent of total sales on Wednesday. The order of produce sales by days, in terms of percentage of weekly produce sales, was the same as was found in total sales. Monday was the lightest day, followed, in ascending order, by Tuesday, Thursday, Friday, Saturday, and Wednesday, The daily distribution of produce sales ranged from 4.1 per cent on Monday to a high of 33.5 per cent on Wednesday. Monday, Tuesday, and Thursday accounted for only 18 per cent of weekly produce sales, a similar percentage to that of total sales occurring on these three days. Of near equal magnitude were Friday and Saturday produce sales, amounting to 23.2 and 25.3 per cent, respectively. Similar variation between stores in terms of daily distribution was found as true for produce sales as for total sales. In all cases but one, the ordering of days with regard to produce sales volume per store

PAGE 124

109 3 O c 0) c o Q. e o o >(0 TJ 1_ 3 4-J A3 LO •a o I/) L. 3 CO D in a) c -a CD 3 CO "O (U 3 O "O C/l CD as CO a) u -D O L. ro a c o 2: a c -3" • CA PA MO CM vO CM • PA LA LA C (D c o Q. E o o pa J• o o ca CA o o CM -3LA PA vO CO — PA vO CA LA CM N IA 4 -3" ^_

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110 was the same. In store three the Friday volume exceeded the Saturday volume. In all other stores the reverse situation existed. Daily distribution of total sales per customer When total purchases were reduced to a per customer basis, considerable variation was eliminated. For example, in Component I, Wednesday gross sales were 8.4 times as large as Monday gross sales, whereas total sales per customer were only 2.9 times greater on Wednesday than on Monday. Total sales per customer ranged from $3«'5 to $9.09 in Component I and from $3.66 to $8.65 in Component II (Table 27). The lowest single store sales per customer occurred in store one, which, for the six Tuesdays included in the test, averaged $2.49. The highest occurred on Wednesdays in store four when total sales per customer were $11.32. Another noticeable difference between total sales and total sales per customer was that the percentage differences between Wednesday and Friday were much larger for total sales than for total sales per customer. Actually, total sales per customer were relatively close in magnitude for the two days. Daily distribution of produce sales per customer Produce sales reduced to a per customer basis yielded an amount which deviates between stores and between days, based upon the peculiarities of the aggregate population served by the individual stores. Produce sales varied from 22 to 64 cents per customer during the average week over all nine stores included in the study (Table 28). Component I variation was greater than Component I I , as was true in total sales. The range in Component I was from 21 cents on Monday to 66 cents on

PAGE 126

Ill in Q. 2. in p in 0) 4J C >.

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112 Wednesday, compared to 25 cents on Monday to 59 cents on Wednesday in Component I I . The per customer average purchase of produce was quite close to the same in both Components for Wednesday and Friday, with a one and two cent differential for Components I and Irrespectively. The variations between stores and the variations between days point out clearly the likelihood of a relationship between the purchase of fresh oranges and the level of produce sales. It is unlikely that given constancy in prices the same quantity of oranges would be purchased on Monday, when produce sales were 21 cents per customer, as on Wednesday, when per customer produce sales were 66 cents.

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113 tj o. TO CC tj c TO i. CJ t/1 ID c I L. Q. 3 >• TO TJ "O CM C MO TO CPi (1) u O >4-> TO C v~JC -Q o Ii o (A O L. C TJ =J TO TJ c O L 0) E O W in o U a a; TO CO 93 U -a C k a. c

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CHAPTER VI AN EXAMINATION OF THE BASIC INPUT DATA-FRESH ORANGE SALES During the 31 operational days, a total of 9,254.6 dozen of oranges were sold In the nine stores included in the study. This volume is slightly in excess of 1,000 packed boxes of fruit. Of this total, 6,279.7 dozen were sold in Component I stores and 2,974.9 dozen in Component II stores. In conformity with the stipulated operational procedures, considerable attention was devoted to the maintenance of display quality at a constant level throughout the testing period. Consequently, as the inventories aged and as the season progressed, removal of the subquality portion of the display became larger. A total of 1,778.3 dozen of oranges, or 16.1 per cent of total orange utilization, was removed from the nine test stores during the 31 days of observation. Of this total, 27.*+ per cent was Florida Indian River fruit, 49.5 per cent was Florida Interior fruit, and 23.1 per cent was California fruit. Aggregate Sales by Fruit Type In the test situations, equal opportunities were allowed for the selection of the three types of Valencia oranges. The California fruit outsold either of the Florida fruits. Total sales of California fruit in the two components amounted to 4,626.4 dozen of oranges or 50 per cent of total sales (Table 29). This figure compared with 2,478.5 dozen of 114

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15 Table 29. --Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by store, experimental test, nine stores, 31 operational days, Grand Rapids, Michigan, April -May, 1962.

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116 Florida Indian River fruit and 2,149.7 dozen of Florida Interior fruit or 26.8 and 23.2 per cent, respectively. Considering the two Components separately, California fruit also outsold either of the Florida oranges. However, on a relative basis, the larger Florida fruit, size 163, commanded a greater share of the market than did the size 200 Florida oranges. Of the 6,279-7 dozen of oranges sold in Component I, 53 per cent was California, 25 per cent Florida Indian River, and 22 per cent Florida Interior fruit. In Component 1 1 , on the other hand, only k$ per cent of the nearly 3,000 dozen oranges sold was the California fruit. This number compared with 29 per cent Florida Indian River and 26 per cent Florida Interior. Sales by store By individual stores, considerable variation was found both in total oranges sold and in oranges sold by type. The greatest quantity of oranges sold during the 31 day operation was in store two of Component I, a total of 1,388 dozen (Table 29). Volume of total orange sales ranged downward to a low of 725.1 dozen. Six of the nine stores involved in the study had total orange sales in excess of 1,000 dozen during the 31 operational days. The greatest volume of sales recorded in a single store for a specific orange type occurred in store seven, with sales of 577.1 dozen of California oranges. In all cases but one, Florida Indian River outsold Florida Interior oranges, and California oranges outsold the Florida Indian River oranges. There was, however, considerable variability in the relative ratios of the three fruits among stores. For example, in store three of Component I, Florida Indian River and Interior sales were, respectively, 230 and

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117 222 dozen, whereas in store two their respective sales were 361 and 271 dozen. Sales by week Weekly sales in Component I ranged from a low of 1,048.9 dozen in the weeks ending May 5 and 12, to a high of 1,442.9 dozen in the week ending April 21 (Table 30). In Component II the range was from a low of 479-7 dozen in the week ending May 12, to a high of 659.5 dozen in the week ending April 21. In the last week of operation, sales of only one day were included, since only one day of that week was utilized as an observational period. In light of this limitation on week six, only weeks one through five are of comparable periods. Within these weeks considerable variation was found within and among orange types. In Component I during these five weeks, Florida Indian River sales ranged from 212 to 4-38 dozen, Florida Interior sales ranged from 216 to 314 dozen, and California sales ranged from 453 to 788 dozen. In terms of percentage change from low to high, Florida Indian River was highest with a change of 107 per cent, followed by California with 74 per cent change, and Florida Interior with 45 per cent change. In Component II, Florida Indian River was followed by Florida Interior and then California in terms of percentage change from low to high, and these were respectively, 155 per cent, 110 per cent, and 82 per cent. Sales by day The daily distribution of orange sales in both components show Wednesday to be the leading day (Table 31). This fact was to a large

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18 Table 30. --Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by week, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April -May, 1962.

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119 Table 31 .--Florida Indian River, Florida Interior, California, and total Valencia orange sales, by component, by day, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April -May, I962. Day

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120 degree, as previously indicated, a function of traffic attracted to the double stamp program on Wednesdays. In Component I, Wednesday was followed, in terms of orange sales, by Friday, Saturday, Thursday, Tuesday, and Monday. This same ordering held for Component li stores, with the exception of a reversal of Monday and Tuesday. Friday and Saturday sales were of near equal magnitude in both Components, varying only from 1,369 to 1,380 dozen in Component I and 603 to 611 dozen in Component II. With only one exception, on Thursdays in Component II, the order of magnitude of orange sales with respect to type was, in descending order, California, Florida Indian River, and Florida Interior. The exception noted was a reversal of Florida Indian River and Florida Interior sales. Sales per 100 Customers by Fruit Types On a per 100 customer base, an average of k.k3 dozen of oranges were sold (Table 32). In Component I stores, an average of 4.52 dozen per 100 customers were sold while in Component II 4.25 dozen per 100 customers were sold. , In Component I stores, the average sale per 100 customers of Florida Indian River Valencias was 1.17 dozen compared with .99 dozen of Florida Interior and 2.36 dozen of the California fruit. This distribution was altered somewhat in Component II stores, where sales per 100 customers were 1.25, 1.10, and 1.90, respectively, for Florida Indian River, Florida Interior, and California Valencia oranges. Sales by store Considerable variation in orange sales per 100 customers was found

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121 Table 32. --Florida Indian River, Florida Interior, California, and total Valencia orange sales per 100 customers, by component, by store, experimental test, nine stores, 31 operational days, Grand Rapids, Michigan, April-May, 1962.

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122 among stores. In Component I, sales per 100 customers ranged from 3.16 to 5.13 dozen (Table 32). Variation among stores was much less in Component II stores, ranging only from 3.88 to 4.52 dozen per 100 customers. Sales per 100 customers by orange type contained wide variations but, with one exception, followed the same pattern of sales. California sales per 100 customers were consistently higher than either of the Florida fruits, and Florida Indian River sales were consistently higher than Florida Interior sales. In one store, Florida Indian River sales were higher than California sales per 100 customers, respectively, 1.71 and 1.59 dozen. Sales by week Weekly sales per 100 customers in Component I varied from a high of 4.94 dozen per 100 customers in the last week to a low of 3.82 dozen per 100 customers in the fifth week (Table 33). However, week six, ending on May 19, had only one-sixth as many observations as the other five weeks, since only one day was used in this week as an observational period. Notwithstanding this fact, sales per 100 customers were fairly stable. In Component II, sales per 100 customers ranged from 3-54 to 4.72 dozen, occurring respectively, in weeks five and three. Weekly variability was greater in Component II than in Component I. The spread between low and high in Component I was 1.12 dozen per 100 customers compared to 1.18 dozen per 100 customers in Component II. Sales by day On a per 100 customer basis, Wednesday was again the leading day with respect to orange sales (Table 34). In Component I, orange purchases per 100 customers were 6.39 dozen compared with 6.11 dozen in

PAGE 138

123 Table 33. --Florida Indian River, Florida Interior, California, and total Valencia orange sales per 100 customers, by component, by week, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962.

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124 Table 34. --Florida Indian River, Florida Interior, California, and total Valencia orange sales, per 100 customers, by component, by day, experimental test, 31 operational days, nine stores, Grand Rapids, Michigan, April-May, 1962.

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125 Component II. Wednesday was followed by Friday and Saturday in both Components as heavy sales days. The lightest day for sales per 100 customers in Component I was Monday and in Component II was Tuesday. In all cases, California fruit outsold either Florida fruit with an overall average of 1.89 dozen per 100 customers per day. This compares with 1.05 dozen of Florida Indian River and .90 dozen of Florida Interior fruit. This pattern was the case on all days in Component I stores. However, in Component II stores on Friday, Interior fruit outsold Indian River, and on Monday the two were of equal magnitude.

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CHAPTER VI I CHARACTERISTICS OF THE DEMAND FOR FLORIDA AND CALIFORNIA VALENCIA ORANGES In conformity with the model postulated to represent the demand relationships believed to exist for fresh Valencia oranges (Equation 4.1), a system of demand equations was developed. Since it is impossible by empirical evaluation to conform completely to the theoretical concepts by measuring the effects of each independent variable, it became necessary to control statistically some portions of this variability and to normalize to a standard consistency, other portions of the variations. The estimating models developed for empirical measurement contained independent variables associated with price and the value of produce sales (Equations k.2-k.k) . Generalized Presentation of the Systems of Demand Equations Consistent with the requisites of the study, two separate investigations were conducted. The general methodological procedures were the same in both components of study. One was concerned with the estimation of demand relationships for Florida Indian River size 200, Florida Interior size 200, and California size 138 Valencia oranges. These sizes represent the modal production size classification from each of the two states. The other reckoned with the demand relationships when the modal size Valencia orange produced in California, size 138, meets in competition with the 126

PAGE 142

127 largest marketable Valencia fruit of consequence from the two areas of Florida, size 163. The generalized form of the systems of demand equations developed for the study and identification by component is as follows: Component I. ^ =b io +b ll P i + b 12 P 2 + b 13 P 3 + b l4 V P s l (7J > Q 2 * b 20 + b 2l P l + b 22 P 2 + b 23 P 3 + b 2k Vp! 4 (7 ' 2 > Q 3 =b 30 +b 31 P i +b 32 P 2 +b 33 P 3 +b 34 V P s 3 (7 * 3) Component I I . % ' bi + Vi + Vs + b 46 P 6 + \ 7 VPS 4 (M) H ' b 50 + b 5 l» p 4 + b 55 P 5 + b 56 P 6 + b 57 Vps 5 (7 ' 5) Q 6 " b 60 + b 64 P i + b 65 P 5 + b 66 P 6 + b 67 Vps 6 (7 * 6) where: Qj and 07 = logs of the quantities of Florida Indian River Valencia oranges purchased per 100 customers of the respective sizes 200 and 163 Q' and Q' = logs of the quantities of Florida Interior Valencia oranges purchased per 100 customers of the respective sizes 200 and 163. Q' and Qi = logs of the quantities of California Valencia oranges purchased per 100 customers of the size I38. b' and b/ n = logs of regression constants associated with Florida Indian River Valencia oranges of the respective sizes 200 and I63. b' and b' = logs of regression constants associated with Florida Interior Valencia oranges of the respective sizes 200 and 1 63 . b' and bi n = logs of regression constants associated with California Valencia oranges of the size 138. b.. and b,, = regression coefficients associated with the price elasticity of demand for Florida Indian River Valencia oranges of the respective sizes 200 and 1 63 -

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128 b and b _ = regression coefficients associated with the price 22 elasticity of demand for Florida Interior Valencia oranges of the respective sizes 200 and 163. b._ and b,., = regression coefficients associated with the price 33 ° elasticity of demand for California Valencia oranges of the size 138. b.„ and b._ = regression coefficients associated with the cross* price elasticity of demand for Florida Indian River Valencia oranges with respect to the price of Florida Interior Valencia oranges of the respective sizes 200 and I63. b._ and b,, = regression coefficients associated with the cross^ 4b price elasticity of demand for Florida Indian River Valencia oranges of the respective sizes 200 and 163 with respect to the price of California Valencia oranges of size 138. b . and b_, = regression coefficients associated with the crossprice elasticity of demand for Florida Interior Valencia oranges with respect to the price of Florida Indian River Valencia oranges of the respective sizes 200 and 163. b._ and bj-x= regression coefficients associated with the cross^ price elasticity of demand for Florida Interior Valencia oranges of the respective sizes 200 and 163 with respect to the price of California Valencia oranges of the size 138. b . and b,, = regression coefficients associated with the crossprice elasticity of demand for California Valencia oranges of size 138 with respect to the price of Florida Indian River Valencia oranges of the respective sizes 200 and 163. b_ and b,,. = regression coefficients associated with the crossprice elasticity of demand for California Valencia oranges of size I38 with respect to the price of Florida Interior oranges of the respective sizes 200 and I63. b., and b,_ = regression coefficients associated with the value of produce sales with respect to QJ • b.i and b,7 = regression coefficients associated with the value of produce sales with respect to Q ' . b_. and b^ 7 = regression coefficients associated with the value of produce sales with respect to 0_ ' .

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129 P 1 and P' = logs of the prices of Florida Indian River Valencia 1 oranges of the respective sizes 200 and 163 . P' and P' = logs of the prices of Florida Interior Valencia oranges of the respective sizes 200 and 163. P' and Pi = logs of prices of California Valencia oranges of i the size I38. Requirements Necessary and Sufficient for Economic Consistency Two general propositions must hold to attain economic consistency throughout the two systems of demand equations for fresh oranges: (1) the quantity of each type of orange sold must vary inversely to changes in the level of prices when a given ratio of prices is maintained and (2) the total quantity of all products must vary inversely with the general level of prices for all products. Thus, both the sign and the relative size of all the parameters can be specified. It follows from both of the general propositions that b' b' , and b' of Component I, and bJ , b' , and bi of Component II, which are the "Y" intercepts, must be positive. One of the necessary conditions for the first proposition to hold is that the coefficient associated with the price of the products in question be negative; that is, the coefficient of price elasticity of demand must be negative. These coefficients are designated as b.., b„„, b,_, in Component I and b,, , b-r, and b,,. in Component II. They represent a measure of the change in Q.! that results from a change of one unit in the respective price when the prices of competing products are held constant. The remainder of the price coefficients measure the change in Q! that results from a change of one unit in the price of a single competing product when other product prices are held constant. By definition, if

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130 the products are competing, a change in P' and P' or P' and Pi would result in a change in the same direction for 0_j and QJ; thus, the coefficients associated with prices of competing products must be positive. The second condition that must be fulfilled in order for the first proposition to hold is that the sum of the coefficients in each equation associated with product prices must be negative, which is to say that the price effect for Q! must be greater than the substitution effect. Therefore, the following conditions must prevail horizontally for each equation. Component I: Component II: Zb ll' b 12* b 13 < ° 2b Vf' b kS' b k6 < ° Ib 2] , b 22 , b 23 < (7.7) Ib 5k , b 55 , b 56 < (7.8) zb 31 , b 32 , b 33 < o » 6V b 65 , b 66 < The second proposition will hold if the sum of the coefficients from the several equations associated with a given P! is negative. That is to say that the effect of a change in the price of a given commodity must have a greater Impact on that particular Q.! than on other OJ's combined. Thus, the following conditions must prevail vertically throughout each of the two systems of equations. Component I: Component II: 2b n , b 21 , b 3) < Zb^, b 5Zf , b 6if < a i2' b 22' b 32 < ° (7,9) a Jf5» b 55' b 65 < ° (7 ' 10) zb 13 , b 23 , b 33 < o ib^, b 56 , b 66 < Method of Analysis In the system of demand equations developed for fresh oranges, the parameters were estimated by least squares techniques. Since the system

PAGE 146

131 of equations was in reduced form, a separate regression equation was fitted for each orange type. Thus, price and cross-price elasticities of demand estimates for each type orange could be secured directly from the logarithmic equations. Coefficient estimation utilizing the method of least squares The form equation developed for estimation of the demand relationships for fresh oranges, in the terms as previously defined, may be written: log Y = log b Q + b ] log P ] + b £ log ? z + b log P •:b^ log Vps (7.11) There are several methods to estimate the parameters b , b., b-, b_ , and b. . The most commonly used method and the one employed in this analysis was that of least squares. This method of estimation of the regression coefficients results in a minimization where 2 (Q-Q) is at a minimum. This is to say that the deviations of the original observations from the regression line, when squared and summed, are at a minimum for any straight line fitted to the sample data. The magnitude of the sum of squares of the deviations may be quite large, but no other straight line than the one estimated by the procedure of least squares results in a greater minimization 2 (Q-Q) 2 . In the equation described previously as the demand relation for fresh oranges, several assumptions concerning the sample population Reduced form equations are those which result when each endogenous variable in a system of equations is written as a linear function of all the predetermined variables in the system. Depending upon the circumstances, they may be (1) algebraically derived from the structural coefficients or (2) fitted by least squares.

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132 were necessary. These were as follows: 1. For each selected price combination there was a normal population of quantities taken of fresh oranges from which a value was observed. 2. Measures of prices were made without error. 3. The errors associated with the measurement of quantities of oranges were assumed to be normally and independently distributed with zero mean and constant variance. Coefficient testing by students "t" test In the calculation of the beta coefficients, estimates were obtained of the dependence of quantities of oranges taken upon the prices for the three orange types. Whether there was an actual dependence in the parent population or whether the indicated dependence arose due to sampling variation was the question to be answered. A null hypothesis was established that in the population the regression coefficient was zero, and acceptance or rejection of the hypothesis was on the basis of the calculated "t" as compared to the tabular value. The test criterion "t" was selected for testing the individual coefficients. The "t" distribution, a symmetrical distribution with mean zero, depends only upon a single parameter, the degrees of freedom. Where the number of observations are greater than 60, the "t" distribution approaches the normal distribution. To use "t" for testing regression coefficients, two quantities are needed, (1) the estimated coefficient, and (2) its standard error. Thus, the null hypothesis for p coefficients stated formally would be as shown: H : b, . = o 1 1 H Q : b ]2 = (7.12) H : b =0 o np

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133 Price and Substitution Effects The study results will be presented by component. Component I consisted of the determination of demand relations among Florida Indian River size 200, Florida Interior size 200, and California size 138 Valencia oranges. In Component II, demand relations were estimated for Florida Indian River size I63, Florida Interior size I63, and California size 1 38 Valencia oranges. Tests Involving Florida Size 200 and California Size 138 The computational results of utilizing the system of demand equations postulated in equations 7.1-7.3 yielded the following estimating equations: a (b io ) (b ]2 ) (b )3 > (b,„) _ Q] = 5.08543 3.07042P] + 1.160C4P£ + 0.18067P4 + 0.967^5Vps (7.13) , ( b 20> (b 21 ) (b 22 ) (b 23 ) (b 2lf ) { Q 2 ' = 3.38002 + 1.56415P] 3.01308P 2 ' + 0.09152P^ + 0.84879Vps (7.1k) a (b' ) (b 31 ) (b 32 ) (b 33 ) (b 34 ) t 0J = 9.98180 + 0.00959P] + 0.13764P 2 ' 2.76462P' + 1.10808V P s (7.15) where: Q.' = log of quantity of Florida Indian River Valencia oranges.
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I3*» From the estimating equations, estimates of price and cross-price elasticity of demand for each of the three products are as follows: Price elasticity of demand for the following: Size 200 Florida Indian River Valencia oranges = b^ = -3.070^2 Size 200 Florida Interior Valencia oranges = t> 22 = -3.013C8 Size 138 California Valencia oranges = b^ = -2. 76^62 Cross-price elasticity of demand for size 200 Florida Indian River Valencia oranges with respect to the price of the following: Size 200 Florida Interior Valencia oranges = bj 2 = 1 . 1600*+ Size 138 California Valencia oranges = b^ = 0.18067 Cross-price elasticity of demand for size 200 Florida Interior Valencia oranges with respect to the price of the following: Size 200 Florida Indian River Valencia oranges = b 21 = 1 .56M5 Size 138 California Valencia oranges = b = 0.09152 Cross-price elasticity of demand for size 1 38 California Valencia oranges with respect to the price of the following: Size 200 Florida Indian River Valencia oranges = b .. = 0.00959 Size 200 Florida Interior Valencia oranges b = 0.1376** Regression coefficient of the value of produce sales associated with the quantity taken of the following: Size 200 Florida Indian River Valencia oranges = b., = 0.967^5 Size 200 Florida Interior Valencia oranges = b^ = 0.8*4879 Size 138 California Valencia oranges = b _. = 1.10808 Testing of the coefficients for significance was made by the application of the "t" test. The hypothesis tested in the case of all coefficients was that of no difference from zero. Stated formally the calculated "t" formula was this: t-f(7.16) s b

PAGE 150

135 where: b = the coefficient of interest and, s, = the standard error associated with that particular coefficient. The coefficients associated with the price elasticity of demand for Florida Indian River size 200 oranges (b,,) and the cross-price elasticity of demand (b.^) for Florida Indian River oranges with respect to the price of Florida Interior oranges were found to be significant at the 99 per cent level (Table 35). Coefficients associated with the price elasticity of demand (b 9 „) for Florida Interior size 200 oranges and the cross-price elasticity of demand (b^,) for Florida Interior oranges with respect to the price of Florida Indian River oranges were also significant at the 99 per cent level. Among the elasticity coefficients for California size 138 oranges, only the price elasticity coefficient (b,..) was found to be s ignif icant. In all equations, the coefficients associated with value of produce sales (b.. , b„, , and b,,) were significant at the 99 per cent level. The coefficient associated with the relationships between produce sales and the purchase of Florida Indian River size 200 Valencia oranges is 0.967^5. The coefficient associated with the relationship between produce sales and the purchase of Florida Interior size 200 Valencia oranges is 0.84879. The relationship between produce sales and the purchase of California size I38 Valencia oranges was described by the coefficient 1.10808. Thus, value or produce sales effected a significant reduction in the regression of each of the demand equations and was effective in removing extraneous variations. The calculated R 2, s were, respectively, 0.68751, 0. 69889, and O.7636O,

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136 Table 35. — Measures of dispersion and tests of significance for relevant coefficients in the demand equations for Florida Indian River size 200, Florida Interior size 200, and California size 1 38 Valencia oranges.

PAGE 152

137 for Florida Indian River, Florida Interior, and California oranges. These coefficients indicate that 69, 70, and 76 per cent, respectively, of the variation in quantities taken of the three orange types was accounted for by the relationship between quantity taken and the independent variables, prices of each orange type and level of produce sales. To test the coefficients of elasticity with respect to economic consistency the tests described on page 129 were applied. For horizontal consistency the test was as follows: (b n ) (b ]2 ) (b 13 ) (a) (-3.07042) + (1.16004) + (0.18067) = -1.72971 (b 2] ) (b 22 ) (b 23 ) (b) (1.56415) + (-3.01308) + (0.09152) -1.35741 (7.17) (b 31 ) (b 32 ) (b 33 ) (c) (0.00959) + (0.13764) + (-2.76462) = -2.61739 Each of the equations yielded coefficients with the appropriate signs to be consistent with the postulated theoretical requirements. The coefficients of price elasticity (b.., b_ ? , and b,,) were all negative, and the remaining coefficients, cross-price elasticities, were positive. For internal consistency within each equation the horizontal sum of the several coefficients of elasticity (price and cross-price) was to be less than zero, and in each of the equations this was the case. A second test dealt with vertical consistency of the several equations. The basis for this test was discussed on page 129. For vertical consistency the test was as follows: (b,,) (b 2] ) (b 31 ) (a) (-3.07042) + (1.56415) + 0.00959) = -1.49668

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138 (b 12 ) (b 22 ) (b 32 ) (b) (1.160(A) + (-3.01308) + (0.13764) = -1.715^0 (7.18) (b, 3 ) (b 23 ) (b 33 ) (c) (0.18067) + (0.09152) + (-2.76462) = -2.49243 In this test the vertical sum of the coefficients from the three equations was to be less than zero. Therefore, the sum of the price elasticity in the first equation (b,,) plus the two cross elasticities in the second and third equation (b . and b .), was to be less than zero. The application of this test resulted in negative sums for each series. Thus, from the standpoint of sign and relative size, the coefficients of elasticity in Component I were consistent with the postulated requirements for economic consistency. Direct price effects To explore effectively the consequences of the resultant estimated demand equations, it is worthwhile to look only at segments of the several equations in the system. The effect of the price of each orange type upon quantities purchased of the same orange type is described by the elasticity of demand with respect to price. In the system of demand equations (7. 137.15). the coefficients of price elasticity are those indicated by the negative values. These further correspond to the beta coefficients b.., b , b in the generalized presentation of the system of demand equations 7.1 through 7-3. Thus, looking at that portion of each demand equation resulting only from the price of each particular orange type, the coefficients associated with the price elasticity of demand are -3.07042, -3.01308, and -2.76462, respectively, for Florida Indian River size 200 Valencia oranges, Florida Interior size 200 Valencia oranges, and Cali-

PAGE 154

139 fornia size I38 Valencia oranges. Consumers responded to price changes for Florida Indian River size 200 Valencia oranges by adjusting their purchases upward and downward by a change in purchase rate of slightly more than 1 to 3 ratio. Specifically, a change of 1 per cent in the price of Indian River fruit perpetrated a reaction on the part of the consumer which resulted in an inverse change in purchase rates of 3.07 per cent. Thus, an increase in the price of 1 per cent resulted in a decrease in the quantity purchased of 3 • 07 per cent. Conversely, a 1 per cent decline in the price of the Indian River fruit brought forth an increase of 3.07 per cent in purchases. The relationship between price and quantities taken is graphically portrayed in Figure 6. Reaction to a price change of Florida Interior size 200 Valencia oranges was only slightly removed from the price reaction for Indian River fruit. A change in the price of Interior fruit of 1 per cent resulted in an inverse change in the quantity purchased by an amount of 3-01 per cent. Thus, a 1 per cent decrease in the price of Interior fruit increased purchase rates by 3.01 per cent while, on the other hand, an increase of 1 per cent brought about a decline in purchase rates of 3.01 per cent. A graphic presentation of the relationship between price and quantity for Florida Interior size 200 oranges is shown in Figure 7. The reaction to price change for California size 1 38 Valencia oranges was somewhat less than the reaction to price changes for either of the Florida products. Thus, it can be said that California Valencias possessed a greater price inelasticity of demand than did the Florida Valencias. A change of 1 per cent in price of the California fruit re-

PAGE 155

140 j o 8 «o o> c P IB O jj o o 0) N E s i _£ O -S § *2 -g Oft o 3 8 o> CM I « a .a o *<1> § c o «n £ 3 O)

PAGE 156

141 >o •8 8 I s s I 4> U a $ Qo .£ o $ B U — c U s o >o CO

PAGE 157

142 suited in 2.76 per cent inverse change in the quantities purchased. Thus, a 1 per cent increase or decrease resulted in, respectively, a 2.8 per cent decrease or increase in the purchases. The price-quantity relationship for the California product is presented in Figure 8. In the case of all three orange types, the degree of price elasticity found indicates a willingness on the part of consumers to spend varying amounts for these products. As prices decline, consumer purchases tend to rise by more than a proportionate amount. However, on the other hand, a price rise will bring about a decline in consumer purchases by more than a proportionate amount. Differences among price elasticity estimates In addition to the degree of elasticity associated with each orange type, considerable interest surrounds the question of significant differences between price elasticity estimates for the three types. The test applied to answer this question was again the "t" test. The formal hypotheses to be tested were as shown: H, : b n -b 22 = H 2 : b n -b 33 = H 3 : b 22 b 33 = o The appropriate "t" formula to test these hypotheses of no difference was this: /s b . . , b . ._ t = ljl lj2 / 2 2 v s k + s k b ijl b ij2 (7.19)

PAGE 158

143 "o vt o £ c s D) c O c o o '0 s 2 £2 I a, oo N PO '•3 *~" •2 1 § J 33 o S ** o «. CN r, CD O C TJ o *c fi -2 u. » o> C 2 o QJ a c

PAGE 159

144 thus; as fol lows: H !

PAGE 160

145 The results of these tests do not allow the rejection of the hypotheses that there are no differences between the coefficients of price elasticity of demand for the three orange types. Stated formally, at the 99 percent level there is insufficient evidence to reject the hypothesis that b . = b = b__. Based upon these tests, direct price effects are not statistically different among the three orange types. Cross-price effects The degree of economic substitution among the several products is expressed in definitive terms by the estimates of the cross elasticity of demand. In order to evaluate the effects of price changes for one product upon sales of another, consider that portion of the system of equations 7.13 7.15 which deals specifically with the cross elasticity estimates. Specifically, the coefficients of substitution are b.., b ,, b 21 ' b 23* b 31 and b 32* For each equation, respectively, Florida Indian River, Florida Interior, and California, the effects of price changes occurring in the second or third types upon purchases in the first type are denoted by these cross elasticity coefficients. In the system of equations for Component I, only two cross elasticity coefficients were found to be significant at the 99 percent level. These were coefficients b2 and b„.. Coefficient b.„ describes the effect of a price change for Florida Interior fruit upon the sales of Florida Indian River fruit, while b ? . describes the effect of a price change for Florida Indian River fruit upon sales of Florida Interior fruit.

PAGE 161

146 A 1 per cent change in the price of Florida Interior fruit initiated a 1.2 per cent change in the purchases of Florida Indian River fruit. On the other hand, a 1 per cent change in the price of Florida Indian River fruit brought about a 1.6 per cent change in the purchase rates of Florida Interior fruit. Increasing Florida Interior fruit prices by 1 per cent resulted in an increase in purchases of Florida Indian River oranges of 1.2 per cent. An increase in Florida Indian River fruit price of 1 per cent effected an increase in the quantity purchased of Florida Interior by 1.6 per cent. Thus, consumers responded stronger to changes in the price of Indian River fruit than the price of Interior fruit. These relationships are shown graphically in Figure 9A 2 per cent increase in the price of Interior fruit yields an increase of 2.4 per cent in purchases of Indian River, while a 2 per cent increase in the price of Indian River fruit brings about an increase in the quantity of Interior fruit purchased of 3.2 per cent. Conversely, a decline of 2 per cent in the price of Interior fruit initiates a decline of 2.4 per cent in the purchases of Indian River, and a diminution in the price of Indian River of 2 per cent brings about a 3.2 per cent decline in the purchase of Interior fruit. Difference*; b etween rross elasticity estimates There is concern about the question regarding the cross elasticity estimates as to whether there are significant differences between them. The appropriate test is the "t" and the formula is shown in equation 7.19. The formal hypothesis to be tested was this: H, : b 12 b 21 = o thus:

PAGE 162

147 S 0) o u c 2 00 'c w o -2 O ^ >o CM * r= n c o a D «o 0) Q> I O o .o c J) c <5 I o o -o -£ -& c o R 4 c a a © CD 1 "S 8 CM c o I. o s "5 > o o • .1 c a> co c D >O u c © o O 8 N C O 'C o u. « "5 O 2 c o a 3 v> CO c p "5 o 5

PAGE 163

148 ; „ b i2 : b 2i / 2 2 b 12 b 2l _ 1.16004 1.56415 y(.3355D 2 + (.31458) 2 = .87828 in this test there is insufficient evidence to reject the hypothesis that b. and b . differ significantly at the 99 per cent level. Summary of price effects In summarizing the effects of price changes upon purchases, the effect of price on a specific orange type is quite the same across types (Table 36). In the tests of significance to determine if there were any differences between price elasticity estimates, none was found. However, notwithstanding the results of the tests, for purposes of estimation the exact coefficient associated with each orange type is the best estimate avai lable. Further scrutiny of the effects of price indicates that the two Florida fruits substitute quite readily for each other under the influence of price changes, while no significant substitution was found between either Florida fruit and the California fruit. Although no significant cross elasticity effects were found between Florida and California Valencia oranges, the regression estimates are the best available for estimation purposes. Allowing credence to this postulation, negligible substitution was found to exist. All estimates of cross elasticity coefficients associated with Florida and California Valencia oranges were in amounts less than two-tenths of 1 per cent.

PAGE 164

149 Table 36. --Effects of price changes upon purchases of Florida Indian River size 200, Florida Interior size 200, and California size I38 Valencia oranges, Component I, experimental tests, Grand Rapids, Michigan, April-May, I962.

PAGE 165

150 Q' = log of quantity of Florida Interior Valencia oranges. /\ Q] log of quantity of California Valencia oranges, o P! log of price of Florida Indian River Valencia oranges. P' «» log of price of Florida Interior Valencia oranges. Pi a log of price of California Valencia oranges. i Vps» log of the value of produce sales. From the estimating equations, estimates of price and cross-price elasticity of demand for each of the three products are as follows: Price elasticity of demand for the following: Size 163 Florida Indian River Valencia oranges = b^ = -3.41702 Size 163 Florida Interior Valencia oranges = b_ 5 = -2.30134 Size 138 California Valencia oranges = b^ = -2.51200 Cross-price elasticity of demand for size 163 Florida Indian River Valencta oranges with respect to the price of the following: Size 163 Florida Interior Valencia oranges b^ 5 0.75021 Size 138 California Valencia oranges = b^ 6 = 0.34375 Cross-price elasticity of demand for size 1 63 Florida Interior Valencia oranges with respect to the price of the following: Size 163 Florida Indian River Valencia oranges » b_. 1 .39183 Size 138 California Valencia oranges = b_^ 0.31440 Cross-price elasticity of demand for size 138 California Valencia oranges wtth respect to the price of the following: Size 163 Florida Indian River Valencia oranges b,. -0.29801 Size 163 Florida Interior Valencia oranges = b^_ = 0.34304 Regression coefficient of the value of produce sales associated with the quantity taken of the following: Size I63 Florida Indian River Valencia oranges b._ = 1 . 0463 1 Size 163 Florida Interior Valencia oranges = b,.1 .20631

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151 Size 138 California Valencia oranges = b, = 0.81061 Again, the testing of the coefficients for significance was made by the application of the "t" test. The hypothesis tested in the case of all regression coefficients was that of no difference from zero. The formula for the calculated "t" was as shown in equation (7. 16). For Florida Indian River size 1 63 Valencia oranges, the coefficient associated with the price elasticity of demand (b..) was found to be significant at the 99 per cent level (Table 37). Neither of the cross elasticity coefficients (b^r and b.,.) were found significant. Coefficients associated with the price elasticity of demand (b-r) for Florida Interior size 1 63 oranges and the cross elasticity of demand (b-.) for Florida Interior with respect to the price of Florida Indian River were significant at the 99 per cent level. Significant substitution of the Interior fruit for California fruit was not found. Among the coefficients relating to California Valencias, the only price coefficient found to be significant was that of the price elasticity of demand. Again, no significant substitution between either Florida fruit and the California fruit was prevalent. In each of the several equations the coefficients associated with the value of produce sales, b,_, b__, and b,._, were significant at the 99 per cent level . The coefficients 1.04631, and 1.2C631 are associated with the relationship between produce sales and the purchase of, respectively, Florida Indian River and Florida Interior size 163 Valencia oranges, and 0.81061 is the coefficient associated with the relationship between produce sales and the purchase of California size I38 Valencia oranges.

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152 Table 37. — Measures of dispersion and tests of significance for relevant coefficients in the demand equations for Florida Indian River size 163, Florida Interior size I63, and California size I38 Valencia oranges. Statistic Relevant Coefficients s b ^ t.Ol t .05 r2 Florida Indian River0.72700 b.. 0.44338 7.70675** 2.6366 1.9884 b^ 5 0.44373 1.69069 2.6366 1.9884 '44 '45 b^ 0.53836 0.63851 2.6366 1.9884 b k7 0.17632 5.93415** 2.6366 1.9884 Florida Inter lorb.. 0.47378 2.93771** 2.6366 1.9884 b c _ 0.47416 4.85350 2.6366 1.9884 0.6695 55 b_ 6 0.57528 0.54651 2.6366 1.9884 b 5? 0.18841 6.40257 2.6366 1.9884 Cal Ifornla0.62074 b 6i+ 0.39052 0.76311 2.6366 1.9884 b 65 0.39083 0.87772 2.6366 1.9884 b 66 0.47419 5.29745** 2.6366 1.9884 b 6? 0.15530 5.21963 2.6366 1.9884 Highly significant Where: s fa refers to the standard error associated with the regression parameters, t refers to the calculated "t" value. l .0\ and t .05 refer » respectively, to the 99 and 95 per cent levels of significance. 2 R refers to the coefficient of determination associated with each orange type.

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153 The value of produce sales was found to effect a significant reduction in the regression in each of the demand equations in Component II. Thus, it was effective in removal of extraneous variation. Seventy-three, 67, and 62 per cent, respectively, of the variation in quantities taken of Florida Indian River size 163, Florida Interior size 163, and California size I38 Valencia oranges was accounted for by the relationship between quantities taken and the independent variables, prices of each orange type, and level of produce sales. The testing of elasticity coefficients for economic consistency was made in the same fashion as in Component I. With regard to consistency of signs, the elasticity coefficients conformed completely to the theoretical requirements. These coefficients (b., , b__, and b,.,) were all negatively signed. Within the cross-price elasticity coefficients, only one did not conform to the theoretical requirements of positive signs. This coefficient, b fi ,, when tested by the application of the "t" test, was found to be not significantly different from zero. To test the consistency with the theoretical requirements regarding the relative size of the coefficients, the two tests (7.9 and 7.10) previously described on page 129 were applied. The test for horizontal consistency was as follows: (»W (b 45 ) (b k6 ) (a) (-3.41702) + (0.75021) + (0.34375) = -2.323C6 (b 5lf ) (b 55 ) (b 56 ) (b) ( 1 .39183) + (-2.30134) + (0.31440) = -0.59511 (7.23) (b 64> (b 65 ) (b 66> (c) (-0.29801) + (0.34304) + (-2.51200)= -2.46697

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154 In each of the equations the horizontal sum of the coefficients was less than zero. Thus, the coefficients were consistent within each equation. The test for vertical consistency described on page 129 was to determine the conformity to the theoretical requirements throughout the entire system of equations. The test for vertical consistency was as fol lows: < b W < b 5l»> (b 64> (a) (-3.^1702) + (1.39183) + (-0.29801) = -2.32320 (b, 5 ) (b 55 ) (b 65 ) (b) (0.75021) + (-2.3013^) + (0.343C4) = -1.2C809 (7-24) < b 46> (b 56> (b 66> (c) (0.34375) + (0.31440) + (-2.51200) = -1.85385 In this test the relative size of the coefficients from the three equations met the specified criteria, the vertical sum of the coefficients were less than zero. Thus, the coefficients in the three equations met the specifications for economic consistency with regard to relative size and with regard to sign. The coefficient with the inconsistent sign was found to be statistically not significant from zero. Direct price effects To investigate the consequences of the effect of the price of each orange type upon sales of that particular orange type, one must examine the coefficients associated with the price elasticity of demand. In equations 7.20 7.22, the price elasticity of demand coefficients are -3.41702, -2.30134, and -2.51200, respectively, for Florida Indian

PAGE 170

155 River size 163, Florida Interior size 163, and California size I38 Valencia oranges. Price changes in Florida Indian River size 163 Valencia oranges brought about a customer response resulting in a change in purchase rates of a ratio of "$.k to 1. Specifically, a change of 1 per cent in the price caused a reaction on the part of the consumer, resulting in an inverse change in quantities purchased of }>.k per cent. Thus, an increase of 1 per cent in the price resulted in a decrease in purchases of "5 .k per cent. On the other hand, a decline of 1 per cent in price led to an increase of 3.^ per cent in purchase rates. A graphic portrayal of this relationship is shown in Figure 10. A less violent reaction resulted from price changes for Florida Interior size I63 Valencias than for the Indian River fruit. A change of 1 per cent in price brought about an inverse change of 2.3 per cent change in customer purchases. A 1 per cent decline in the price of Interior oranges resulted in an increase of 2.3 per cent in consumer purchase rates. Conversely, an increase in the price of 1 per cent brought on a decline of 2.3 per cent in quantities purchased. This relationship is presented graphically in Figure 11. A change in price of 1 per cent for California size 138 Valencia oranges resulted in a change in the opposite direction of purchases in the amount of 2.5 per cent. Thus, purchase rates declined by 2.5 per cent as a result of an increase in price of 1 per cent. Conversely, purchase rates increased by 2.5 per cent when price was decreased by 1 per cent. The price-quantity relationship for California Valencia oranges is shown in Figure 12.

PAGE 171

156 0)
PAGE 172

0) o 157 m § O 0) 1 U 53 .8 C C o U c U V lO 1-1

PAGE 173

00 £2 N 158 . k o E D u >n « o (N c o a 3 0) 0> 8 C o o o> c a _c U 1 a> a. u C

PAGE 174

159 Differences between price elasticity estimates Again, the question arises as to differences in the price elasticity estimates for the three orange types. To ascertain whether there were significant differences among the price elasticity estimates, the "t" test was applied. The formal hypotheses to be tested were as follows: H, : V b 55 = H 2 : b 44 " b 66 ° H 3 : b 55 " b 66 " ° The appropriate "t" formula to test these hypotheses of no differences is shown by equation 7 • 19 • Thus: H l : b 44 " b 55 = ° ; _ b ^ : b ^ /~2 T 2 b 44 b 55 _ (-3.41702) (-2.30134) J .19658 + .22483 = 1.71854 H 2 : b 44 " b 66 " ° \ = (-3.41702) (-2.51200) 7 .19658 + .22486 = 1.39405 Thus, one cannot reject the H : b., b,, = H 3 : b 55 " b 66 " °

PAGE 175

160 " L _ b SS ' b 66 / 2 2 b 55 b 66 = -31M8 Again, one cannot reject the H : b,.^ b,,. = The results of these tests do not allow the rejection of the hypotheses of no difference between the coefficients of price elasticity of demand for the three orange types. Stated formally, at the 99 per cent level there is insufficient evidence to reject the hypothesis that b.. = b^r = b,.,. Thus, based upon these tests, direct price effects are not statistically different among the three orange types. Cross-price effects The estimated coefficient of cross elasticity of demand expresses in definitive terms the degree of economic substitution among the several products. To evaluate the effects of price changes for one product upon sales of another, observe that portion of the system of equations 7.20 7.22 which deals specifically with the cross elasticity estimates. These coefficients are b^ , b^, b^, b^, b^, and b^ . Thus, for each equation, respectively, Florida Indian River, Florida Interior, and California, the effects of price changes occurring in the second or third type upon purchases in the first type are denoted by the cross elasticity coefficients in each equation. In the system of equations for Component II, only one cross elasticity coefficient was found to be significant at the 99 per cent level. This coefficient was b , , which describes the effect of a price change for Florida Indian River fruit upon sales of Florida Interior fruit.

PAGE 176

161 A change of 1 per cent in the price of Florida Indian River fruit brought about a 1.4 per cent change in the quantity of Florida Interior fruit purchased. Thus, an increase in the price of Indian River fruit precipitated an increase in the quantity of Interior fruit purchased of 1.4 per cent. Conversely, a price decline of 1 per cent for Indian River fruit effectuated a decrease in Interior purchases in the amount of 1.4 per cent (Figure 13) . Summary of price effects In summarizing the effects of price changes upon purchases, the effect of price on a specific orange type is similar across types (Table 38). However, a greater degree of variation in direct price effects was found in Component II than was true for Component I. In the tests of significance to determine if there were differences between price elasticity estimates, none was found. However, the exact coefficient associated with each orange type is the best available for estimation of responses. Differences in Demand Estimates Due to Si7e Of considerable interest is the question of differences in the estimated price elasticities of demand with respect to the variation in size of the Florida Indian River and Florida Interior oranges tested. In other words, does a statistically significant difference exist between price elasticities which is due to size? The "t" test was used for testing differences between price elasticity coefficients of similar structural position in the two systems of demand equations. Formally stated, the hypotheses of interest were as follows:

PAGE 177


PAGE 178

163 Table 38. --Effects of price changes upon purchases of Florida Indian River size I63, Florida Interior size I63, and California size I38 Valencia oranges, Component II, experimental tests, Grand Rapids, Michigan, April-May, 1962.

PAGE 179

I6if 2 Massey was used: s 2 / M . .2 / M 2 b.. ( / 1 bfij. N. + s' / N, ...' I b.. n / i. , _LU LLLi _ 2 (7.25) t 2 N ] + 1 N 2 + 1 where: s£ = variance of the particular structural coefficient in i j I Component I . 2 s, = variance of the particular structural coefficient in i j I I Component I I . N. = number of observations in Component I. N. = number of observations in Component II. The calculated "t" formula is: /n b . . , ~ b . . . , t = ''' ''" (7.26) A>„, + s b.. iji ij Where: b... = estimated coefficient in Component I. ijl b.... = estimated coefficient in Component II. ij I I s, = variance of b. . . . b. . . ijl ij I J s, = variance of b b. . . ij I I ij I I J The first hypothesis to test is whether there exist significant differences in the price elasticity of demand for size 200 Florida 2 Discussed in terms of means see W. J. Dixon and J. F. Massey, Jr., Introduction to Statistical Analysis . New York: McGraw Hill Book Company, Second Edition, 1957, pp. 123-124.

PAGE 180

165 Indian River Valencia oranges and size 163 Florida Indian River Valencia oranges. Thus: H. : b.. b,, = 0. Substituting in equation 7-26; * m 3.07042 3.41702 y. 11255 +.19659 = .62338 and the appropriate degrees of freedom for book "t" selection is determined 3 by the use of equation 7.25 • Then: t .01 («) > t; there is insufficient evidence to reject H.. The second hypothesis is a test of differences between the price elasticity estimates for size 200 Florida Interior Valencia oranges and size I63 Florida Interior Valencia oranges. Thus: H 2 : b 22 b 55 = then substituting in equation 7.26 1 _ 3.01308 2.30134 y. 099 14 + .22483 = 1.25046 then: A. t .01 (°°) > t; there is insufficient evidence to reject H . The third hypothesis of interest is that of a determination of differences in the price elasticities of demand for size I38 California 3 Since the degrees of freedom derived for each test using equation 6.19 are in excess of 120 the "t" value of infinity was used as the rejection criteria.

PAGE 181

166 Valencia when faced, on the one hand, with competition of size 200 Florida Valencias and, on the other hand, with competition of size 163 Florida Valencia oranges. In other words, the test is designed to determine whether there is a significant difference between the price elasticity coefficients for California size 138 derived from the two components of the study. Thus: H 3 : b 33 " b 66 " ° then substituting in equation 7.26 1 _ 2.76462 2.51200 7.08929 + .22486 = .45071 then: t .01 (») > t: there is insufficient evidence to reject H_ . a J 3 In testing all three hypotheses regarding differences in the price elasticity estimates due to size, there was not sufficient evidence to reject. Acceptance of these hypotheses is tantamount to subscribing to the thesis that there is, in fact, no difference in the price elasticity estimates for the two sizes of Florida Valencia oranges tested.

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CHAPTER VII I THE ECONOMIC INTERACTION AMONG THE THREE VALENCIA ORANGES In Chapter VII attention was directed to the effects of price upon purchases of the three Valencia oranges. While this is an important aspect of the decision-making problems confronting producers and marketers of fresh oranges, an equally paramount aspect relates to the effects of supply changes upon prices in the marketplace. Leaders of an industry possessing a dynamic character, such as the orange industry, must be cognizant of the interrelationships among products and the effects upon price of changes in output. The present chapter will be devoted to a determination of what effects varying supply levels of the three orange types will have upon price. Derivation of Price Estimating Equations from Demand Equations From the structural demand equations of quantities taken as a function of price, there can be derived a set of equations of prices taken as a function of quantity. These equations yield estimates of price flexibility and cross-price flexibility. The systems of equations 7.1 7.3 and ~] ,k 7.6 in matrix notation 167

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168 may be written: Q = B Q + P where: 0.= the vector of quantities (Component I, Q, , C" » Q, , and Component ii. v V V B_ = the vector of constant terms and BP = the matrix of coefficients for the prices Then: BP = Q B Q and P = B -1 Q. B -1 B Q i .e. , P 2 " -*20 + ?2l Q 1 + ^2 + ^23 Q 3 P 3 = ^30 + ^31 Q 1 + ' Y 32 Q 2 + V>3 where: ^10 = " (b lO C ll + b 20 C 12 + b 30 C 13 } ^20 = " (b 10 C 21 + b 20 C 22 + b 3 C 23 ) ^30 = (b 10 C 31 + b 20 C 3 2 +b 30 C 33 ) ^11 = C ll The X, variable, value of produce sales, was not carried forward into this portion of the analysis since it does not affect the derivation of coefficients of price and cross-price flexibility in the price estimating equations and is not of interpetive value.

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169 "V12 = C 12 ^13 = C 13 ^21 = C 21 7 22 = C 22 7 23 = C 23 7 31 = °31 7 32 = C 32 ^33 = C 33 Generalized Presentation of Systems of Price Estimating Equations The generalized form of the systems of price estimating equations derived from the structural demand equations is as follows: Component I P i-«io + «ll (l 1 + »12 Q 2 + »l3 Q 3 (8J) P 2 = 920 + 921^1 + 922^ + 9 23 Q 3 (8 * 2) p 3 = s 3 V g 31 aj + g 32 Q 2 + g^c(8 ' 3) Component I I Pi " 9^ + 9^04 9 k5 % * S k & (8.4) P 5 9 50 + HM + 9 55 Q 5 + 9 56 Q 6 (8 ' 5) P 6 = 9 60 + %k% + 9 6 5 Q 5 + 9 66 Q 6 (8 ' 6) where: P] and Pt = logs of the prices of Florida Indian River Valencia oranges of the respective sizes 200 and 163 . P' and P' = logs of the prices of Florida Interior Valencia oranges of the respective sizes 200 and 163. P' and Pi = logs of the prices of California Valencia oranges of the 3 b size 138. g' and g/. = logs of regression constants associated with the prices of Florida Indian River Valencia oranges of the respective sizes 200 and 163.

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170 g' and g' = logs of regression constants associated with the prices 20 5 of Florida Interior Valencia oranges of the respective sizes 200 and 1 63 . g' and gi_ = logs of regression constants associated with the prices of California Valencia oranges of size 138. g n and g.. = coefficients associated with the price flexibility of Florida Indian River Valencia oranges of the respective sizes 200 and 163. g . and g__ = coefficients associated with the price flexibility of Florida Interior Valencia oranges of the respective sizes 200 and 163. g and g,, = coefficients associated with the price flexibility ^ of California Valencia oranges of size 138. g and g.,. = coefficients associated with the cross-price flexibility of Florida Indian River Valencia oranges with respect to the quantity of Florida Interior Valencia oranges of the respective sizes 200 and 163. g., and g.^ = coefficients associated with the cross-price flexibility of Florida Indian River Valencia oranges of the respective sizes 200 and 163 with respect to the quantity of California Valencia oranges of size 138. g» . and g^r = coefficients associated with the cross-price flexibility of Florida Interior Valencia oranges with respect to the quantity of Florida Indian River Valencia oranges of the respective sizes 200 and 163. g._ and g,./= coefficients associated with the cross-price flexibility of Florida Interior Valencia oranges of the respective sizes 200 and 163 with respect to the quantity of California Valencia oranges of size 138. g_. and g,., = coefficients associated with the cross-price flexibility of California Valencia oranges of the size 138 with respect to the quantity of Florida Indian River Valencia oranges of the respective sizes 200 and 163. g,_ and g,,. = coefficients associated with the cross-price flexibility of California Valencia oranges of size 1 38 with respect to the quantity of Florida Interior Valencia oranges of the respective sizes 200 and I63. 0_j and 0J = log of the quantity of Florida Indian River Valencia oranges of the respective sizes 200 and I63.

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171 Q' and Q' = log of the quantity of Florida Interior Valencia oranges of the respective sizes 200 and 163. Q' and QJ = log of the quantity of California Valencia oranges 3 b of size 138. Economic Consistency Requirements Two general propositions, somewhat analogous to those for the demand equations, must hold to attain economic consistency throughout the system of price-estimating equations for fresh Valencia oranges. These are (1) the price of each type of orange must vary inversely to changes in the level of supplies available and (2) the general level of prices of all products must vary inversely with the general level of available supplies of all products. Thus, both the sign and relative size of all the parameters can be specified. From both of the general propositions, it follows that g| «, giQ> • •••> 9f. > which are the "y" intercepts, must be positive. One of the conditions necessary for the first proposition to hold is that the coefficients associated with the quantity of the products in question be negative; that is, the coefficient of price flexibility must reflect an inverse relationship. These coefficients are designated as g n , g 22 , g^, g^, g 55> and g fi6 and are a measure in the P. that results from a change of one unit in the respective available supplies, when the supplies of competing products are held constant. The remainder of the coefficients measure the change in the P. as a result of a change of one unit in the quantity of available supplies of a single competing product, when other products are held constant. If the products are competing, a change in C" and Q_ would result in a change in the opposite direction for P,; thus, the coefficients

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172 Associated with quantities of competing products must be negative. The second condition that must be fulfilled in order for the first proposition to hold is that the sum of the coefficients associated with competing products in each equation must be less than the coefficient associated with the prime product, which is to say, that the quantity effect for P. must be greater than the substitution effect. Therefore, the following conditions must prevail within each equation. Component I: Component II: g n 2g 12 , g 13 < o 9zt4 2 9z+5 , g ke < o 9 22 2 g 21 , g 23 < (8.7) 9 55 2 9 jV g 56 < (8.8) 9 33 " 2g 31 , g 32 < g 66 2 g^, g^ < The second proposition will hold if the sum of the coefficients from the several equations associated with a given Q. is such that the effect of a change in the quantity of a given commodity must have a greater impact on that particular P. than on other P. 's combined. Thus, the following conditions must hold vertically throughout each of the two systems of equations. Component I: Component II: g n 2g 21 , g 3 , < g kk Zg 5V %k < 9 22 " 2 9 I2' 9 32 < ° (8,9) 9 55 " 2 %5> 9 65 < ° (8,10) 9 33 ' 29 13' 9 23< ° 9 66 _ 2 9 46' 9 56 < ° The Effects of Supply Interactions The presentation of the results of the derived price estimating equations from the structural demand equations will conform to the procedure used in the presentation of the demand relationships in Chapter

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173 VII. The results will be presented by components.! Component I was concerned with the price-quantity relationships for size 200 Florida Indian River and Florida Interior and size 1 38 California Valencia oranges, while Component II dealt with price-quantity relationships for size 163 Florida fruit from the Indian River and Interior districts and size 138 California f rui t. Tests Involving Florida Size 200 and California Size 138 The computational results of deriving the system of price estimating o equations 8.1 8.3 yielded the following estimating equations: P] = 2.91627 0.406190. P£ = 2.7^982 (g 21 ) 0.21123Q Pi (gjo) (g 31 ) = 3.75158 0.01193Q where: (g 12 ) 0.15784QJ (g 22 ) (g 13 ) 0.03177Q£ (g 23 ) 0Mkh7Q^ 0.02752Q' (g 32 ) (g 33 ) 0.021 18Q^ 0.363190J log of price of Florida Indian River Valencia oranges. (8.11) (8.12) (8.13) Pi = log of price of Florida Interior Valencia oranges. P 3 " 0.1 = 0,= 04 = log of price of California Valencia oranges, log of the quantity of Florida Indian River Valencia oranges, log of the quantity of Florida Interior Valencia oranges, log of the quantity of California Valencia oranges. "For complete method of derivation see Appendix E.

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174 From the estimating equations, estimates of price and cross-price flexibility coefficients for each of the three Valencia orange types are as fol lows: Price flexibility for the following: Size 200 Florida Indian River Valencia oranges = g^ = -0.40619 Size 200 Florida Interior Valencia oranges = g 22 = -0. 41447 Size 138 California Valencia oranges = g„ = -0.36319 Cross-price flexibility for size 200 Florida Indian River Valencia oranges with respect to the quantity of the following: Size 200 Florida Interior Valencia oranges = g, 2 = -0. 15784 Size 138 California Valencia oranges = g } = -0.03177 Cross-price flexibility for size 200 Florida Interior Valencia oranges with respect to the quantity of the following: Size 200 Florida Indian River Valencia oranges = g_, = -0.21123 Size 138 California Valencia oranges = g = -0.02752 Cross-price flexibility for size I38 California Valencia oranges with respect to the quantity of the following: Size 200 Florida Indian River Valencia oranges = g_ , = 0.01 193 Size 200 Florida Interior Valencia oranges = g,« = . 02 1 1 8 Since the coefficients were derived from a set of tested coefficients the significance attached to each was a reflection of the significance attached to the original coefficient in the structural demand equations. The two tests previously described on page 171 were applied to determine economic consistency. The test for consistency within each equation was as shown: (g n ) (g 12 ) (g 13 ) (a) (-0.40619) (-0.15784) (-0.03177) = -0.21658

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75 (g 22 ) (g 2 P ^23^ (b) (-0.41447) (-0.21123) (-0.02752) = -0.17572 (8.14) (g 33 ) (g 31 ) (g 32 ) (c) (-0.36319) (-0.01193) (-0.02118) = -0.33008 Each of the equations yielded coefficients with the appropriate signs to be consistent with the theoretical requirements stipulated. All the coefficients of price flexibility and cross-price flexibility reflected the inverse relationship. The coefficients in the three equations were internally consistent with respect to the relative size, in that the price flexibility coefficient was of a greater negative magnitude than the sum of the cross-price flexibility coefficients. The second test of consistency was concerned with the vertical linkage among the three equations. This test was as follows: (g n ) (g 2l ) (g 31 ) (a) (-0.40619) (-0.21123) (-0.01193) = -0.18303 (g 22 ) (g 12 ) (g 32 ) (b) (-0.41447) (-0.15784) (-0.02118) = -0.23545 (8. 15) (g 33 ) (g 13 ) (g 23 ) (c) (-0.36319) (-0.03177) (-0.02752) = -0.30390 In this test the price flexibility coefficient, with respect to a particular orange type, was to be of a greater negative magnitude than the sum of the cross-price flexibilities associated with the same orange type. Thus, the price flexibility coefficient associated with Florida Indian River size 200 oranges (g»i) was to be of a greater negative value than the sum of the cross-price flexibilities of size 200 Florida Interior (g_j) and size 138 California (g j) oranges with

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176 respect to the quantity of size 200 Florida Indian River oranges. Prime product effect on price In order to examine the effects of a change in quantity upon prices for fresh oranges, attention is first directed to the effect upon price of a specific orange type, with respect to changes in quantity of the same orange type. That portion of the system of equations (8.11 8.13) directed toward an assessment of this question includes the coefficients associated with price flexibility, which are -0.40619, -0.41447, and -0.363 19 » respectively, for Florida Indian River size 200 Valencia oranges, Florida Interior size 200 Valencia oranges, and California size I38 Valencia oranges. With regard to the Indian River fruit, a change of 1 per cent in the quantity offered will result in an inverse change of 0.41 per cent in the price of the fruit. For example, an increase of 1 per cent in the quantity of Indian River fruit would result in a decline in price of 0.41 per cent. Conversely, a decrease of 1 per cent in the quantity of Indian River fruit offered would cause an increase price of 0.41 per cent. The price reaction to a change in quantity of the Florida Interior fruit was only slightly greater than for the Indian River fruit. A 1 per cent change in the quantity of Interior fruit would result in a change of 0.414 per cent in price. Reaction to a change in the quantity of California fruit was somewhat less with regard to price than either of the Florida oranges. A 1 per cent change in the quantity of California oranges would result in only a O.36 per cent inverse change in the price for the fruit.

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177 Competing product effects on price The effect of a change in available supplies of one orange type upon the price of a second orange type is reflected in the coefficient of cross-price flexibility. To evaluate the price consequences on one orange type resultant of changes in the quantities offered of other orange types, consider the cross-price flexibility estimates in equations 8.11 8.13. These are coefficients g 12> g^, g 2l , g 2 ,, g^j, and g, 2 . The reflected statistical significance from the structural demand coefficients yield significant flexibility estimates for g.» and g . only. The coefficient g, ? , 0.15784, reflects the results on the price of Florida Indian River Valencia oranges as quantities of Florida Interior Valencias are varied. The relation of price changes for the Florida Interior Valencias resulting from quantity changes in Florida Indian River is shown by coefficient g_,, 0.21123. Thus, a change in the quantity supplied of Florida Interior size 200 Valencia oranges engenders a change in the opposite direction of a 0.15 to 1 ratio. An increase in the quantity offered of the Interior fruit of 1 per cent results in a 0.166 per cent decline in the price for Indian River fruit. On the other hand, a decline of the quantity offered of Interior fruit by 1 per cent brings about a price increase of 0.16 per cent for the Indian River fruit. Disregarding the lack of statistical significance only negligible effects on price of either Florida orange resultant of quantity changes in California oranges was found. Further, changes in the quantities of Florida oranges had little effect on the price of California oranges, both resulting in less than a 0.02 to 1.0 per cent ratio.

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178 Summary of product effects The effects of quantity changes of a specific orange type is of near equal magnitude (Table 39). A change of 1 per cent in the quantity offered of Florida Indian River, Florida Interior, or California Valencia oranges brought about an inverse change in price of .41, .41, and .36, respectively. The effect of a change in quantity offered of either of the Florida fruits was of a significant magnitude with respect to the price of the other. Florida Interior prices were estimated to change inversely by .21 per cent for each 1 per cent change in the quantity of Florida Indian River fruit. On the other hand, a change of 1 per cent in the quantity of Florida Interior fruit was estimated to result in an inverse change of .16 per cent in the price of Florida Indian River fruit. Only minute changes in price were estimated to result from interaction of supplies of California size 138 Valencia oranges and of the two Florida fruits, Indian River and Interior size 200. Tests Involving Florida Size 163 and California Size 138 The computational results of deriving the system of price estimating •3 equations 8.4 8.6 yielded the following estimating equations: H (9 54 } ( 9 5 5 } (g 56> P^ = 2.75724 0.201290^ 0.51384Q' 0.09186Q£ (8.17) 3 For complete method of derivation see Appendix E.

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179 Table 39. — Effects of quantity changes upon prices of Florida Indian River size 200, Florida Interior size 200, and California size 138 Valencia oranges. A One Per Cent

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180 Price flexibility for the following: Size 163 Florida Indian River Valencia oranges = g^ = -0.33561 Size 163 Florida Interior Valencia oranges = g,-^ = -0.51384 Size 138 California Valencia oranges = g 66 = -0.40327 Cross-price flexibility for size 1 63 Florida Indian River Valencia oranges with respect to the quantity of the following: Size I63 Florida Interior Valencia oranges = gj= -0. 18846 Size 138 California Valencia oranges = g^ 6 = -0.06075 Cross-price flexibility for size 1 63 Florida Interior Valencia oranges with respect to the quantity of the following: Size 163 Florida Indian River Valencia oranges = b ^ = -0.20129 Size 138 California Valencia oranges = g^ ° -0-09186 Cross-price flexibility for size 138 California Valencia oranges with respect to the quantity of the following: Size 163 Florida Indian River Valencia oranges = g^^ = 0.01233 Size 163 Florida Interior Valencia oranges = g,= -0.05612 The coefficients derived from the demand equations reflect the same degree of significance as the original coefficient. Thus, significant coefficients of similar structural position in the demand equations yield significant coefficients in the price flexibility equations. The tests for economic consistency discussed on page 171 were applied to determine the consistency with respect to relative size of the parameters within and among the several equations. The test for internal consistency was as follows: (9^4) (9^5) (9^) (a) (-0.33561) (-0.11846) (-0.06075) = -0.15640

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181 (g 55 ) (9 5k ) (g 56 ) (b) (-0.51384) (-0.20129) (-0.09186) = -0.22069 (8.19) ( 966 ) ( %2f } (9 65 ) (c) (-0.40327) (+0.01233) (-0.05612) = -0.35948Within the three equations, one sign was inconsistent. The coefficient g,. was positive as was tv, in the demand equations. However, the test of significance applied to b/-. indicated no significant difference from zero. Therefore, in the price flexibility equations, coefficient g,. would reflect the same degree of significance. In testing for horizontal consistency, each of the three equations yielded coefficients of such a magnitude that the sum of the cross flexibility coefficients was not as great as the price flexibility coefficient. Thus, the magnitude of the coefficients was found to be consistent with the stipulated requirements. The second test was that of testing consistency of the vertical linkage among the three equations. This test was as below: (9i^) (954) (9 6Z+ ) (a) (-0.33561) (-0.20129) (+0.01233) = -0.14665 (9 55 ) (g k5 ) (g 65 ) (b) (-0.51384) (-0.11846) (-0.05612) = -0.33925 (8.20) ( 9 66 > (9i*> ( 9 5 6> (c) (-0.40327) (-0.06075) (-0.09186) = -0.25066 In this test the coefficients of flexibility proved consistent. In all cases the effect of a change in the quantity on price of a given orange type had a greater impact than the effect of the other two orange types combined.

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182 Prime product effect on price To examine the effects of a change in quantity upon prices for fresh Valencia oranges, attention is first directed to the price flexibility coefficients. Coefficients g^, g,-,-, and g^ in equations 8.16 8.18 are the coefficients of price flexibility. The magnitude of these parameters -0.33561, -0.51384, and -0.40327, respectively, for Florida Indian River size 163, Florida Interior size 163, and California size 138, indicates the level of response in price change accompanying a change in quantity offered. A change of 1 per cent in the quantity offered of the Indian River fruit will result in an inverse change of 0.34 per cent change in price. Comparatively, changes of 1 per cent in the quantities offered of the Florida Interior and California fruit will result in an inverse change in price of 0.51 and 0.40 per cent, respectively. The price reaction was much greater for Interior than Indian River fruit with respect to changes in quantities offered. Further, the reaction was greater for Florida Interior fruit than for California fruit as a result of quantity changes of the two orange types. Competing product effects on price Cross-price flexibility coefficients yield the effect of a change in available supplies of one orange type upon the price of other orange types. In order to evaluate the price consequences on one orange type resulting from changes in the supply situation of other orange types, attention is directed to the cross-price flexibility coefficients in equations 8.16 8.18. These coefficients, g^ , g^, g^, g^, g^, and g^r, algebraically derived from the demand equations, are significant

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183 to the same degree as the elasticity coefficients. Thus, the only coefficient significantly different from zero is the cross-price flexibility coefficient for Florida Interior size 163 Valencia oranges, with respect to changes In the quantity of Florida Indian River size 163 Valencia oranges. Thus, a change in the quantity supplied of Florida Indian River oranges of 1 per cent perpetrates an inverse change in the price of Florida Interior oranges of 0.20 per cent. Summary of product effects The effects of quantity changes of a specific orange type are of greater magnitude differences in Component II than In Component I. A change of 1 per cent In the quantity supplied of Florida Indian River size 163, Florida Interior size 163, or California size I38 brought about an Inverse change In price of .3*+, .51 » and .^0 per cent, respectively (Table kO) . The effect of a 1 per cent change in the quantity offered of Florida Indian River fruit resulted In an estimated .20 per cent inverse change in the price of Florida Interior fruit. The remaining coefficients of cross-price flexibility were negligible. The coefficients of cross-price flexibility for California fruit with respect to the quantity changes of either Florida fruit and the coefficients of crossprice flexibility for either Florida fruit with respect to California quantity changes were all of less magnitude than a ratio .10 to 1 price change per unit change in quantity.

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m Table 40.--Ef f ects of quantity changes upon price of Florida Indian River size 163, Florida Interior size 163, and California size I38 Valencia oranges. A One Per Cent * Inverse Change in Price of Change in the

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CHAPTER IX EVALUATION OF FINDINGS Purchase response to changing price structure for Florida Indian River, Florida Interior, and California Valencia oranges is a major condition which operates to establish the quantity-price relationships among these three orange types. The purchase response found from varying price levels was of nearly .equal magnitude for size 200 Florida Valencia oranges in competition with California size 1 38 Valencias. These demand relationships were further found to be elastic in nature. That is, a greater than proportionate change in purchase rates occurred as a result of a change in price. The changes in purchase rates resulting from a 1 per cent change in price were found to bear an inverse relationship of 3.07, 3.01, and 2.76 per cent, respectively, for size 200 Florida Indian River, size 200 Florida Interior, and size I38 California Valencias. The same general trend was found to exist for size 163 Florida Valencia oranges from the Indian River and Interior districts when faced in competition by size 138 California Valencias. The degree of elasticity was slightly different and possessed a greater variation than was the case for the size 200 Florida fruit. Purchase responses were inverse changes of 3.^, 2.3, and 2.5 per cent per 1 per cent change in price, respectively, for Florida Indian River, Florida Interior, and Cal ifornia f rui t. Of equal or greater importance than that of direct price response 185

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186 is the extent to which consumers will shift purchases from one orange type to another as a result of changing price structure. In both components of study, Florida size 200 and Florida size 163, no significant substitution was found to exist between Florida and California fruit. This lack of substitution indicates that in the marketplace the Valencia oranges from the two states are sufficiently differentiated to preclude substitution as a result of price change over a rather wide range of price levels f 33 to 65 and 43 to 75 cents per dozen, respectively, for Florida and California fruit. It was discovered, however, that consumers in the Grand Rapids, Michigan, market shifted back and forth quite readily between the purchase of Florida Indian River and Florida Interior oranges in response to changing relative price conditions. In the component of study dealing with size 200 Florida oranges, changes of 1 per cent in the price of Interior fruit brought about a purchase response of 1.2 per cent for Indian River fruit. On the other hand, a change of 1 per cent in the price of Indian River fruit yielded a consumer response of a 1.6 per cent change in purchase rates of Interior fruit. In order to consider the effects of changes in supply conditions upon prices, the demand equations were manipulated algebraically to derive a system of price estimating equations. Changes in supply conditions inversely affected prices. For example, a change of 1 per cent in the supply situation for size 200 Florida Indian River Valencias was estimated to affect price inversely by 0.41 per cent. A similar change for Florida Interior size 200 and California size 1 38 was estimated to affect price inversely by 0.41 and O.36 per cent respectively. Changes in the supply situation for Florida fruit had

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187 no appreciable effect on California prices, and conversely changes in California supplies had no appreciable effect on Florida prices. There was, however, a significant effect resulting from supply interaction of the two Florida oranges. A change of 1 per cent in the supply situation for size 200 Interior Valencias was estimated to yield a 0.16 per cent inverse change in the price of Indian River fruit. Changes in supply conditions for Indian River fruit had a greater impact on Interior prices than was true in the reverse situation. A change of 1 per cent in the supply situation for Indian River fruit was estimated to yield a 0.21 inverse change in the price of Interior fruit. Effects of Major Changes in Price and Supply Conditions for Florida Valencia Oranges While the coefficients estimated in Chapters VII and VIM are appropriate for small changes in price and supply conditions, the orange industry is faced with changes of somewhat more imposing magnitudes. Dynamic expansion of supplies on the one hand, and drastic reduction resulting from severe climatic conditions on the other hand, require estimates of the alterations resulting from large changes in supply and price conditions. Godwin and Lloyd, studying demand relationships for celery, developed estimating equations for determining the effects of large supply changes, utilizing coefficients of price flexibility derived from logarithmic equations. The method developed and presented in their Godwin, Marshall R., and Lloyd, Bill f e S., Competition Between Florida and California Celery in the Chicago Market . Florida Agricultural Experiment Stations, Bulletin 636, November I96I, pp. 31-33.

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188 work was used to estimate interaction effects of large price and supply 2 changes for the two sizes of Florida oranges. The economic linkage between Valencia oranges produced in the Indian River, and Interior districts of Florida is of great importance to producers and marketers of Florida oranges. The actions of producers and marketing agencies in either of the two districts not only affect the market conditions for their products but also market conditions for products of the other area. Effect of various price conditions on customer purchases The estimated effects of various price situations on purchases of Florida Indian River oranges is shown in Table 41. The direct price effects of large changes in the price of Indian River fruit are shown along the vertical axis where Interior prices are held constant. The cross-price effects of Interior fruit upon sales of Indian River fruit are shown along the horizontal axis where Indian River fruit prices are held constant. The remaining effects are those resulting from interactions of direct and cross-price effects of the two fruits under various price situations. If the price of Florida Interior fruit remains unchanged, successively lower prices for Indian River fruit will result in consistently larger than proportionate increases in the quantity of Indian River fruit purchased. With no change in the price of Interior fruit, a 10 per cent reduction in the price of Indian River fruit will result in 2 For method of derivation see Appendix F. For purposes of estimating these effects the coefficients derived from Component I were used.

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CO

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190 a 38 per cent increase in consumer purchases of Indian River fruit, while a 10 per cent increase will reduce purchases 25 per cent. These changes in purchase rates of Indian River fruit, resulting only from changes in Indian River prices, are direct price effects. The effects on Indian River purchases resulting from changes in Interior prices are, of course, of less magnitude than the direct price effects. When no changes occur in the price of Indian River fruit, changes in Interior fruit result in a purchase response in Indian River fruit of slightly more than proportionate magnitude. A 10 per cent decrease in the price of Interior fruit will result in a 12 per cent decline in purchases of Indian River fruit. As Interior prices progressively become more attractive, purchase rates of Indian River decline. At a 25 per cent decline in the price of Interior fruit, the cross-price effect reduces purchase rates of Indian River oranges by 28 per cent. Conversely, as Interior orange prices become less attractive, purchase rates for Indian River fruit increase. With an increase of 25 per cent in the price of Interior fruit, Indian River purchase rates increase by 30 per cent. The combination of direct and cross-price effects alter consumption rates markedly. Declines in Interior prices result in declines in Indian River purchases. These may be offset, however, by declines in Indian River prices. Equal declines in the price of both fruits will result in an increase in purchase rates for Indian River fruit. Conversely, increases in the price of both fruits will decrease purchase rates of Indian River oranges. At the extreme of an increase of 25 per cent in both Interior and Indian River prices, a reduction of 35 per cent in purchases of Indian River fruit will occur. However, a 25

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191 per cent increase in Interior prices coupled with a 25 per cent decrease in Indian River prices will result in a 213 per cent increase in Indian River fruit purchases. Considering a maximum change in prices of the two fruits to be + 25 per cent, this is also the situation resulting in maximum increase in purchase rates for Indian River fruit. The greatest reduction in Indian River fruit purchases will result from a price situation of 25 per cent reduction in Interior prices and a 25 per cent increase in Indian River prices, a net decline in Indian River purchase rates of 64 per cent. Similar occurrences in Interior purchase rates result from consumer responses to changing price structure for the Interior and Indian River fruit. Since the direct price effects on the two fruits were of nearly equal magnitude, changes in price of Interior without any change in Indian River prices result in a change in Interior purchase rates of about the same degree as was true for the Indian River fruit. For example, a decrease in the price of Interior fruit of 5 per cent with no change in Indian River prices results in an increase of 17 per cent in Interior purchase rates, the same degree of change as occurred under similar conditions for Indian River fruit (Table kl) . The cross-price effects of Indian River fruit upon Interior purchases were, however, of a greater magnitude than the cross-price effects of Interior fruit upon Indian River purchases. A decline of 10 per cent in Indian River fruit prices will result in a 15 per cent decline in Interior fruit purchases, whereas a decline of 10 per cent in Interior fruit prices will result in only a 12 per cent decrease in Indian River purchases. Combined direct and cross-price effects on purchases of Interior fruit result in an increase of 52 per cent when prices of both

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k.

PAGE 208

193 Indian River and Interior fruit are decreased by 25 per cent. At a price increase of 25 per cent for Indian River and a price decrease of 25 per cent for Interior, a 237 per cent increase in purchases of Interior fruit will occur. Little change in purchase rates of Interior fruit results from a two to one ratio increase or decrease in price, respectively, for Indian River and Interior fruit. A 20 per cent increase in the price of Indian River fruit, coupled with a 10 per cent increase in the price for Interior fruit, results in only a 0.8 per cent increase in Interior fruit purchases. Increases in the price of both fruits of 25 per cent result in a 28 per cent decline in Interior fruit purchases. A 25 per cent increase in the price of Indian River fruit only will result in a k2 per cent increase in Interior fruit purchases. However, a decline of 25 per cent in Indian River prices, coupled with a 25 per cent increase in Interior prices, will result in a 67 per cent decline in Interior fruit purchases. This results from the combined effects of direct and cross-price elasticities of demand. Effect of various supply conditions on retail prices Of particular importance to the producers and marketers of fresh oranges is the question of effects of supply conditions upon prices received in the marketplace. Complicating the consequences on a particular orange type of supply increases and decreases is the economic interplay between Indian River and Interior Valencia oranges. The effects of changes in the supply situation of both Interior and Indian River fruit upon prices of Indian River fruit is shown in Table 43. Along the vertical axis is the effect of changes in Indian River

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o

PAGE 210

195 supplies upon Indian River prices, and along the horizontal axis is the effect of changes in Interior supplies upon Indian River prices. A change of 10 per cent in the available supplies of Indian River fruit will result in a k per cent inverse change in the price of Indian River oranges. A 25 per cent decline in the supply situation of Indian River oranges will result in a 12 per cent increase in price, while an increase of 25 per cent in Indian River supplies will force price downward by 9 per cent. These effects, changes in the supply of Indian River fruit without changes in the supply of Interior fruit, are a result of the prime product, Indian River oranges. The effects upon prices for Indian River fruit of changes in the supply situation of Interior fruit, the competing product effect, are indicated along the vertical axis. Without changes in the supply situation of Indian River fruit, a change of 25 per cent in Interior supplies will result in a decline in price of Indian River fruit by 5 per cent. On the other hand, an increase in supplies of Interior fruit will adversely affect Indian River prices by 3 per cent. Acting together, the effects of changes in the supply situation for the two Florida fruits affect prices. A 25 per cent reduction in available supplies of both Indian River and Interior oranges will result in an 18 per cent increase in the price of Indian River fruit, while an increase in the supply situation of both fruits will result in a decline of 12 per cent in the Indian River price. Interaction of a 25 per cent increase in Interior supplies and a 25 per cent decrease in Indian River supplies will produce the net effect of a 9 per cent increase in Indian River fruit prices. The supply conditions of a 25 per cent decline in the supplies of Interior fruit and a 25 per cent increase in Indian

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196 River fruit will result in an adverse effect upon Indian River prices of k per cent. An increase in Interior supplies of 10 per cent along with a decrease in Indian River fruit of 5 per cent is offsetting with respect to price change for Indian River, resulting in no price change for the Indian River fruit. Conversely, a 20 per cent reduction in Interior supplies coupled with a 10 per cent increase in Indian River supplies produces only a 0.7 per cent adverse effect on Indian River orange prices. Similar effects upon Florida Interior prices resulting from supply interactions of Indian River and Interior fruit are noted in Table kk. Prime product effects, Interior supply changes upon Interior prices, are of nearly equal magnitude to prime product effects for Indian River fruit. A 25 per cent reduction in Interior supplies will result in a 13 per cent increase in price, while a 25 per cent increase in Interior supplies will decrease price by 9 per cent. Competing product effects are slightly greater with respect to Interior fruit prices than for Indian River competing product effects. A 25 per cent increase in the supply situation for Indian River fruit will result in a 5 per cent decline in Interior prices. The ratio of change in Interior prices to change in Indian River supplies is approximately one to five. The combined effects of prime and competing product supply changes upon Interior orange prices result in a net increase of 7 per cent, under conditions of a 25 per cent increase in Indian River and a 25 per cent decrease in Interior supplies. Increasing both products supplies by 25 per cent will result in a decline of 13 per cent in the price of Interior oranges. On the other hand, a decrease in supplies

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198 of 25 per cent for both fruits will result in an increase of 20 per cent in Interior prices. A 3 per cent adverse effect on the price of Interior fruit will result from a 25 per cent decline in Indian River supplies coupled with an increase of 25 per cent in Interior supplies. General Implications to the Florida Orange lndustry--An Overview During the coming decade, projected production estimates forecast increasing orange supplies in Florida and a rather constant supply from California. Further, these projections are of a greater magnitude change than the accompanying United States projected population changes. Thus, Florida orange producers and marketers are going to be faced with greater marketing and distribution problems than has been true in the past. The continued introduction of products to compete with oranges and orange products will further complicate the situation. Economic allocation among product markets will become of utmost importance as supplies increase and are faced with more competition in the marketplace. Based upon the results of this study the fresh market may offer a partial solution to the marketing problems associated with increasing supplies. The price elasticity of demand is of such a nature that a more than proportionate effect on purchase rates result from a decline in price. The general concensus of opinion in the industry that the price elasticity of demand for frozen orange concentrate is near unity or slightly inelastic lends further credence to the conclusion that the fresh market may solve, to some degree, the problems of marketing increased supplies. It will be necessary to substantiate, however, the validity of this conclusion with definitive research to determine the exact nature of the demand for frozen concentrate.

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199 If it is found that this inequality exists between the respective price elasticities of demand, supply management and allocation will be of greater importance to the industry. No longer can the study of citrus demand relationships be looked upon as basic research but as operational research necessary to the conduct of marketing activities. If the demand relationships in the processing sectors are found to be less elastic than was true in the fresh market sector, any increased supplies could be absorbed most favorably in the fresh market. This follows since the increased quantities available for market would be allocated in the market sector having the least price effects. Thus, controlled allocation could seek to maximize revenue along with increasing suppl ies. Another consideration evolving from the results of this study is the implications of the lack of economic substitution between fresh oranges produced in Florida and California. The capture of a greater portion of an existing market is often considered to be a feasible approach to solving increased supply problems. Presumably, in considering this as a solution to increasing supplies in Florida, the California share of the fresh orange market is the sector to capture a portion of through some form of competition. The two basic forms of increasing the competitive atmosphere are, price competition resulting from price manipulation and non-price competition evolving from advertisement and promotional activity. Changing price structure for Florida oranges from either district and of either size was found to have no significant effect on California fruit purchases. Thus, price reductions will have no appreciable effect upon the presently established California market. Therefore, Florida producers and marketers must resort to some form of non-price competition.

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200 Analysis of the results of the study indicate that California Valencias, consistently smaller and higher priced than the Florida fruit, commands a differentiated position in the marketplace. Obviously, in the case of a substantial portion of the consumer population purchasing fresh oranges, the California product is considered superior to the Florida product and to such an extent that over a rather wide range of price differences is not sufficient to cause substitution. This leads to the conclusion that if Florida marketers wish to engage in non-price competition they must develop a program which will tend to shift the demand relationship for their product to the right and increase its relative inelasticity. It must be recognized, however, to fully engage in such a program the Florida Industry has need of definitive information concerning the interrelationships of the orange products produced in Florida. Demand information concerning the four sectors of the industry would provide the needed guides to the development of an effective advertising and promotional program. If in the development of definitive demand estimates for the remaining three major sectors of the orange industry, they were found to be less elastic than the fresh sector then greater returns would be realized from effective promotional activity in the fresh market sector. The informational requirements necessary for the effective adjustment to changing conditions within a dynamic industry such as the orange industry clearly dictate a need for a program of definitive operational research dealing with revenue and cost. The severe limitations imposed upon isolated studies of demand and cost relationships are of great magnitude. The all inclusive implications can be utilized only if such study is a part of an integrated program of research. It is anticipated

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201 that many implications from this study will be more clearly formulated as the program of research of which this study is only a part is continued toward the ultimate objectives.

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CHAPTER X SUMMARY The results of this study are based upon two controlled pricing experiments conducted at the retail level of distribution. These experiments were conducted in nine supermarkets of a grocery chain located in Grand Rapids, Michigan, during April and May, 1962. Of major importance in the study was the estimation of price and cross-price elasticities of demand for Florida Indian River and Interior sizes 200 and 163 Valencia oranges and for size 1 38 California Valencia oranges. These fruit varieties and sizes include a major portion of the oranges produced for fresh market in the two states. The experimental design utilized in the study was the Triple Cube design. The utilization of this design was particularly appropriate in that it allowed measurement of demand relationships over nine price levels. The price levels used in the study ranged by four cent differentials from 33 to 65 cents for Florida oranges and from k3 to 75 cents for California oranges. Methodological procedures were the same for the two experimental tests. One of these tests, Component I, was conducted in six stores and was concerned with the generation of input data to estimate price and crossprice elasticities of demand for size 200 Florida Indian River and Florida Interior and size I38 California Valencia oranges. The second test, Component II, was conducted in three stores with the objective of generating 202

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203 input data to estimate price and cross-price elasticities of demand for size 163 Florida Indian River and Florida Interior, and size I38 California Valencia oranges. Characteristics of the Test Stores The stores included in the study were all classified as supermarkets, each containing the normal grocery, meat, and produce departments. As is characteristic of most modern supermarkets, all departments were entirely self-service operations. Upon request, however, customers received assistance in the form of information or special services from any of the departments. Sales and store traffic A total of 243,040 customers shopped and made purchases in the nine test stores during the six-week period of the study. These customers made purchases of $1.6 million during the period of study. Of the $1.6 million, $123.7 thousand was produce sales. With respect to the two components of study, the six stores in Component I served 162.6 thousand customers, and the three stores in Component II served 80.4 thousand during the period of study. Total sales distributed by components were, respectively, $1.1 million and $0.5 million. Fresh Orange Sales A total of 9,254.6 dozen of oranges was sold during the test period. Of this total 6,279.7 dozen were sold in Component I stores and 2,974.9 dozen in Component II stores. Elimination of fruit to maintain a standardized quality control required a removal of 1,778.3 dozen of oranges during the study.

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204 Total sales of fresh oranges California fruit out sold either of the Florida fruits. A total of 4,626.4 dozen of California fruit was sold during the test period compared with 2,478.5 dozen of Florida Indian River and 2,149.5 dozen of Florida Interior fruit. Sales per 100 customers An average of 4.43 dozen per 100 customers was sold during the study. Of this amount, 2.20 dozen per 100 customers were California oranges, and 1.20 and 1 .03 dozen per 100 customers were Florida Indian River and Florida I nterior oranges, respectively. Demand Relationships for Florida and California Valencia Oranges In conformity with the requisites of the study, price and cross-price elasticity coefficients were estimated. The method of least squares was used in the estimation process, and the coefficients were tested for statistical significance by the use of the "t" test. The probability criteria established was at the 99 per cent level. Component I — Florida size 200 and California size I38 Price elasticity estimates for Florida Indian River size 200, Florida Interior size 200, and California size I38 were, respectively, -3.07, -3.01, and -2.76. Each was significant at the 99 per cent level. Estimates of cross-price elasticity were found significant for Florida Indian River oranges with respect to the price of Florida Interior oranges, and for Florida Interior oranges with respect to the price of Florida Indian River oranges. The magnitude of these two coefficients of cross-price elasticity was, respectively, 1.2 and 1.6. The remaining coefficients of

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205 cross-price elasticity, those of California, with respect to the price of the two Florida orange prices and those of the two Florida oranges with respect to California orange prices, were found to be not statistically significant from zero. Tests were made to determine if there were statistically significant differences among the three price elasticity estimates. The results of these tests did not allow the rejection of the null hypothesis. However, the least squares estimated value is the best available estimate of the relationship. In the component of study dealing with size 200 Florida oranges and size I38 California oranges, the effect of a price change on a specific orange type was found to be nearly the same for the three oranges. Scrutiny of cross-price effects indicates that the two Florida oranges substitute quite readily for each other under the influence of price. Component I I --F lor i da size 163 and California size 138 In Component II, price elasticity coefficients were estimated for Florida Indian River size I63, Florida Interior size I63, and California size I38. These estimates were, respectively, -3.42, -2.30, and -2.51. Utilizing the "t" test, each of the price elasticity coefficients were found to be significant at the 99 per cent level. Only one cross-price elasticity coefficient was found to be significant at the 99 per cent level. This coefficient was the cross-price elasticity of demand for size I63 Florida Interior oranges with respect to the price of size 163 Indian River oranges. As in Component I the price elasticities were tested to determine if significant differences existed among them. Here again, there was insufficent evidence to allow rejection of the null hypothesis.

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2C6 Differences in elasticities due to size Considerable interest surrounds the question of differences in price effects due to the size of fruit for the two sizes of Florida oranges included in the study. In this test no significant differences were found to result from price changes with respect to the two sizes of Florida oranges, 163 and 200, included in the study. The Economic Interaction Among the Three Valencia Oranges From the structural demand equations, a set of price estimating equations were algebraically derived. These equations contained coefficients of price and cross-price flexibility. Component I — Florida size 200 and California size 138 Price flexibility estimates were -0.4l, -0.41, and -0.36, respectively, for size 200 Florida Indian River and Interior and size 138 California Valencia oranges. The degree of statistical significance associated with the elasticity coefficient of similar structural position was assumed for the flexibility coefficients. Consequently, the two cross-price flexibility coefficients associated with Florida fruit were considered to be significant. The cross-price flexibility for size 200 Florida Indian River oranges with respect to the quantity of size 200 Florida Interior oranges was -0.16, and the cross-price flexibility coefficient for size 200 Florida Interior oranges with respect to the quantity of size 200 Florida Indian River oranges was -0.21. The effects of quantity changes of specific orange types were of nearly equal magnitudes. Changes of 1 per cent in the quantity supplied will result in a 0.41 , O.k], or 0.36 inverse change in price. The competing product effects result in inverse changes of .16 and .21 per

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207 cent change in the price of Florida Indian River and Florida Interior fruit, with respect to a 1 per cent change in quantities supplied of Florida Interior and Florida Indian River Valencia oranges, respectively. Component II — Florida size 1 63 and California size 138 Estimates of price flexibility for size 163 Florida Indian River and Florida Interior and size 138 California oranges were, respectively, -0.3*+, -0.51, and -O.hO. Thus, changes in the supply situation for the three orange types of 1 per cent will result in inverse changes in price of 0.3^, 0.51, and 0.40 per cent, respectively, for Florida Indian River, Florida Interior, and California oranges. The cross-price flexibility coefficient derived from a significant elasticity coefficient is the cross-price flexibility for size 163 Florida Interior oranges with respect to the quantity of size 163 Florida Indian River oranges. The magnitude of this coefficient was -0.20. Thus, an inverse change in the price of Florida Interior of 0.20 per cent will result from a change of 1 per cent in the quantity supplied of Florida Indian River. Price and Supply Interactions Under conditions of changing price structure or supply situations Florida and California Valencia oranges have little economic linkage. In both components of study no significant cross-price coefficients were found for either Florida fruit with respect to California fruit or California fruit with respect to either Florida fruit. Disregarding the statistical significance attached to the cross-price coefficients, the least squares estimates are of negligible magnitude. Although economic substitution was not found between either Florida fruit and the California fruit, a considerable degree of economic linkage

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208 was found in Component I of the study between the Florida Indian River and Florida Interior fruits. Consumers readily substitute these two products. However, they are not considered equally good substitutes. The Interior fruit was more readily substituted for Indian River fruit than was Indian River fruit substituted for Interior fruit. Because consumers shift between these two fruits in response to changing price situations, their prices are interrelated by the economic forces operating the market. In order to examine the expected behavior of price and supply interaction for these fruits, the price and crossprice elasticities and flexibilities from the analyses were utilized. Effect of price interaction on purchase rates Direct price effects of Florida Indian River fruit and Florida Interior fruit upon sales were found to be of nearly equal magnitude. A 5 per cent reduction in the price of the two fruits results in a 17 per cent increase in purchases. Conversely, a 5 per cent increase in the price of the two fruits results in a 14 per cent decline in purchase rate. At a 20 per cent reduction in price, purchase rates increase 98 and 96 per cent, respectively, for Florida Indian River and Florida Interior. Cross-price effects are not as close as the direct price effects. The change in Indian River prices results in a greater change in Interior purchase rates than changes in purchase rates of Indian River resulting from price changes for Interior fruit. A 25 per cent decrease in the price of Interior fruit reduces Indian River sales by only 28 per cent, while a 25 per cent reduction in the price of Indian River fruit results in a 36 per cent decline in Interior purchases. Interacting together a price increase of 25 per cent for Indian River fruit and a 15 per cent decrease for Interior fruit will result in

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209 a 178 per cent increase in purchase rates of Interior fruit. Under similar price conditions the effect on purchase rates for Indian River is a reduction of 58 per cent. In the former situation, the price increase in Indian River fruit increased purchases of Interior fruit through the cross-price effects and a price decrease for Interior fruit increased purchases through direct price effects. In the latter case a price increase in Indian River fruit reduced Indian River sales through direct price effects, and a reduction in interior prices exerted crossprice pressure to reduce further Indian River sales. Effect of supply interaction on prices Changes in supply conditions for Indian River and Interior fruit interact and affect prices in a similar fashion as price interaction affects purchase rates. For example, a decrease of 25 per cent in the supply conditions for Indian River fruit will result in a 12 per cent increase in price. However, if this were also coupled with a 25 per cent decrease in Interior supplies, then the Indian River price would increase by 18 per cent. Under circumstances of the supply situations' moving in opposite directions, the prime product effect and the competing product effect would be operating against each other. A decrease in Interior supplies of 25 per cent and an increase in Indian River supplies of 10 per cent would result in only a 1 per cent increase in the price of Indian River fruit. Thus, it becomes evident, when economic substitution exists between two or more commodities that the direct effects of price and of supply are important, but gains or losses resulting from direct effects may be offset considerably by substitution effects.

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APPENDIXES

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APPENDIX A FORMS USED FOR DATA MAINTENANCE

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212 Florida Agricultural Experiment Stations Department of Agricultural Economics Project 1096: The Competitive Relationships Between Fla. and Calif. Oranges Form 62-1A Daily Record of Sales Fla. 200's-Calif. 138's Store Number Week _Day Number, Date Enumerator •.»*.** •.'».»* •.»<• A iJU •.*•.'•.'* * t\ *\ /* TYPE OF ORANGES

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213 Florida Agricultural Experiment Station Department of Agricultural Economics Project 1096: The Competitive Relationships Between Fla. and Calif. Oranges Form 62-1 B Dai ly Record of Sales Fla. 163's-Calif. I38's Store Number. Date Week Enumerator Day Number. ************************************* TYPE OF ORANGES, PRICE PER DOZEN ON DISPLAY... Florida I .R. Florida Int. California STORAGE INVENTORY: 1. Number of full containers. 2. Number of oranges in full containers 3. Number of loose oranges... DISPLAY INVENTORY: 4. Number of oranges TOTAL INVENTORY: 5. Summation: Lines 2,3,8.4.. ADDITIONS: 6. Number of full containers. 7. No. of oranges in full containers... TOTAL SUPPLY: 8. Summation: Lines 5 + 7... LOSSES: 9. Number of oranges ENDING INVENTORY: 10. Line 5 Ending Column SALES: 11. Line 8 minus (9 + 10).... Begin End Begi n End Begi n End

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2\k Florida Agricultural Experiment Stations Form 62-2 Department of Agricultural Economics Daily Cash Register Record Project 1 096: The Competitive Relationships Between Fla. and Calif. Oranges Store Number Week Number Enumerator ****************************** * ****** Cash Register Number, Day of Week

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215 Florida Agricultural Experiment Stations Form 62-4 Department of Agricultural Economics Central Storage Record Project 1096: The Competitive Relationships Between Fla. and Calif. Oranges Type of Oranges^ ************************************** Date

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Florida Agricultural Experiment Stations Department of Agricultural Economics Project 1096: The Competitive Relationships Between Fla. and Calif. Oranges 216 Form 62-6 Dai ly Record of Orange Requirements * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Store Number

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217 Florida Agricultural Experiment Stations Department of Agricultural Economics Project 1096: The Competitive Relationships Between Fla. and Calif. Oranges Form 62-7 Weekly summary of store operational losses Week ending_ Store number •k it it * it it * * * * * it * * * it * * * * * * * it it * it it it it it it it it it it PRICE ADJUSTMENT

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APPENDIX B INPUT DATA-COMPONENTS I AND 1 1

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221 L

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APPENDIX C CODING AND TRANSFORMATION INSTRUCTIONS

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231 Appendix Table 3. --Coding and transformation instructions for demand analyses, Florida Indian River, Florida Interior and California Valencia oranges. I tern Coding Column Deflation Transformation Identi f ication: Store Component Price combination Week Day Observation number Variables: (X, (X, (X,
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APPENDIX D COMPUTER INSTRUCTIONS

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233 I. Tabular Analysis — Before Deflation Transformation. 1 Table Number Column Number Dependent Variable Independent Variable Table Description 1 2 18,19,20,21,22,23 24,25,26 27,28,29 Relation between Stores and Produce Sales Relation between Relation between 4

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23k Tabular Analysis — Before Deflation Transformation — Continued. Table -r , .. , Dependent Number .. . , , Variable Column Number Independent Variable Table Description 13 22 23 24 25 26 27 28 24,25,26 27,28,29 \k

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235 Tabular Analysis—Before Deflation Transformation — Continued. _ , , Column Number Table ,. , Dependent Independent Table Description Number .. , , , „ . , , Variable Variable 29 2,3,4 30,31,32 Relation between Price Combination, Component and California 30 2,3,4 33,34,35,36 Relation between Price Combination, Component and Customer Count 31 2,5 18,19,20,21,22,23 Relation between Week, Component and Produce Sales 32 2,5 24,25,26 Relation between Week, Component and Florida Indian River 2,5 27,28,29 Relation between Week, Component and Florida Interior 34 2,5 30,31,32 Relation between Week, Component and Cal ifornia 35 2,5 33,34,35,36 Relation between Week, Component and . Customer Count 2,5

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236 II. Tabular Analys is--Af ter Deflation Transformation. _ . , Column Numbe r Tab le Dependent ndependent Table Description Number .. . , , .. . , , Variable Variable 41 1 18,19,20,21,22,23 Relation between Store and Produce Sales 42 1 24,25,26 Relation between Store and Florida Indian River 43 1 27,28,29 Relation between Store and Florida I nteri or Relation between Store and California Relation between Price Combination and Produce Sales Relation between Price Combination and Florida Indian River Relation between Price Combination and Florida Interior Relation between Price Combination and Cal iforni a Relation between Week and Produce Sales Relation between Week and Florida Indian River 51 5 27,28,29 Relation between Week and Florida I nter ior The deflation transformation will utilize a customer count figure shown in columns 33-36. The deflation is applicable to X. (columns 18, 19, 20, 21, 22, and 23), Y, (columns 24, 25, and 26), Y(columns 27, 28, and 29), and Y, (columns 30, 31, and 32). These deflations are to reduce these variables to a per 100 customer basis, then deflate as follows: *l»* Customer pount , CoK )8> ]g> 2Q> ^ ^ 23 ^ _Col. 33 ,^34, 35. J6. Y l_, Customer Count = Cq) # ^ ^ 26 i Co1 ' 33 »^ 35 ' 36 j, Customer Count _ , fl Y 2 • ioo " Co '« 27. 28, 29 . Customer Count , Y 3 * 100 ~ Co, « 30 ' 31 > 32 tToo" 44

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237 Tabular Analys is--Af ter Deflation Transformation—Continued. Table Number Column Number Dependent Variable I ndependent Variable Table Description 52 5 30,31,32 53 6 18,19,20,21,22,23 54 6 24,25,26 55 6 27,28,29 56 6 30,31,32 57 1,2 18,19,20,21,22,23 58 1,2 24,25,26 59 1,2 27,28,29 60 1,2 30,31,32 61 2,3,4 18,19,20,21,22,23 62 2,3,4 24,25,26 63 2,3,4 27,28,29 64 2,3,4 30,31,32 65 2,5 18,19,20,21,22,23 66 2,5 24,25,26 67 2,5 27,28,29 Relation between Week and California Relation between Day and Produce Sales Relation between Day and Florida Indian River Relation between Day and Florida I nter ior Relation between Day and California Relation between Store, Component and Produce Sales Relation between Store, Component and Florida Indian River Relation between Store, Component and Florida Interior Relation between Store, Component and Cal ifornia Relation between Price Combination, Component and Produce Sales Relation between Price Combination, Component and Florida Indian River Relation between Price Combination, Component and Florida Interior Relation between Price Combination, Component and California Relation between Week, Component and Produce Sales Relation between Week, Component and Florida Indian River Relation between Week, Component and Florida Interior

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238 Tabular Analysis — After Deflation Transformation — Continued. T , . Column Number Table .. . Dependent Independent Table Description Number ., . . , ,, . , , Variable Variable 68 2,5 30,31,32 Relation between Week, Component and Cal ifornia 69 2,6 18,19,20,21,22,23 Relation between Day, Component and Produce Sales 70 2,6 24,25,26 Relation between Day, Component and Florida Indian River 71 2,6 27,28,29 Relation between Day, Component and Florida Interior 72 2,6 30,31,32 Relation between Day, Component and Cal ifornia III. Regressions— X^, Y p Y 2 , Y Deflated 2 Component l--ldentif ication 110111001 through 613166186 Y i-ijk m " Pio + Pn p i-I + 0,2 P 2-j + ^.3 P 3-k + P^ U : + e i-.JI«, • 2-ijk m = P 2 + P 2 l P ). Y 3-ljkm = ^0 + %l P i. Where: Y|_j.^ = log of quantity of Florida Indian River size 200 oranges purchased per 100 customers, Y 2-iikm = '° 9 °^ l^^'tY of Florida Interior size 200 oranges purchased per 100 customers. Y 3 i i km = '° 9 °^ ( 1 uant ' t Y °f California size I38 oranges purchased per 100 customers. 2 Logarithmic Transformations will utilize the natural logarithms.

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239 ^lo' ^20' ^30 = 1og of re 9 ression constants. /3. . , /3.„, j3._ = regression coefficients associated with size 200 Florida Indian River oranges. j3 ?1 , j32 , /3 2 = regression coefficients associated with size 200 Florida Interior oranges. j3 . , j3, , /3 = regression coefficients associated with size 138 California oranges. /3. . , /3_. , ]3,. = regression coefficients associated with value of IH /H * H produce sales (Yj, Y^, Y') . P'_ ., Pi_«» P o_ k log of prices of Florida Indian River, Florida -* Interior and California oranges. ej . ., , ei . ., , el . ., = random disturbances associated with 1-ijkm' 2-ijkm' 3-ijkm v , v , v , 1 ' 2 ' 3 * Component 1 1 — Identification 720111001 through 923165093 Y i-ijkm = ^io + VIY 5-ijkm = ^0 + VlY 6-ijkm = ^60 + W+ V2-j + V 3 '-k + Vm +e i-ijkm + V2-j + VH + Vm + e 5-ijkm + V2-j + ^6 P 3-k + Vm +e 6-ijkm Where: Y/ ... = log of quantity of Florida Indian River size I63 oranges •* purchased per 100 customers. 5-ijkm = log of quantity of Florida Interior size 1 63 oranges purchased per 100 customers. Yi_... = log of quantity of California I38 oranges "'1 m purchased per 100 customers. ^k0' ^50' ^60 = 1og of re 9ression constants. ]3,. , ft.-, £./• = regression coefficients associated with size 1 63 ' Florida Indian River oranges. j3_. , £-,-> Peg = regression coefficients associated with size 1 63 •* " > " > Florida Interior oranges. Pew ^Ac» ^ftA = regression coefficients associated with size I38 W F 65' H 66 California oranges.

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240 /3._, j3 , /3 A regression coefficients associated with value of 47 57 b7 produce sales (Y£, Y' Y£) . Pi ., P' ., Pi . = log of prices of Florida Indian River, Florida l-i 2-j 3-k interior, and Cal ifornia oranges . e, 1 . . . , ei . ., , el . .. = random disturbances associated with kij km 5-ijkm 6-ijkm v , Vl v , V V 6 * IV. Estimating Equations Component I— Identification 110111001 through 613 166186 <» ^i-.jta, " b !o + b n p i-. + b i2 P 2-j + Vi-k + v: (2^ Y 1 = b 1 + b P 1 + b P' + b P 1 + b ,V U; Y 2-ijkm D 20 D 21 l-i D 22*2-j 23 3-k 24 m (O Y' = b 1 + b P' + b P 1 + b P' + b ,V Ki) Y 3-ijkm D 30 D 31 1-1 32 2-j 33 3-k °3Vm a />> «\ Where: Y' ... , Y' .. , Y' ... = logs of quantities of Florida Indian River, i-ijKm /-ijKm ^-ijKm Florida interior, and California sizes 200, 200, and 138 oranges purchased per 100 customers . b' , b' , b' = logs of regression constants. b.., b._, b., = regression coefficients associated with Florida Indian 3 River size 200 oranges (Y } ) . b.., b ? _, b 7 regression coefficients associated with Florida Interior Ci size 200 oranges (Y 2 ) . b_., b,„, b__ = regression coefficients associated with California * i£ ** size 138 oranges (Y ) . b.. , b 2 , b_. regression coefficients associated with the value of produce sales (Component l) . Pi ., Po_:» P's.k = 1°9 S of prices of Florida Indian River, Florida J Interior and California oranges.

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241 Component I I-Identif ication 7201 1 1001 through 923 165 C93 (0 U = b,' + b.,P' 4-ijkm " 40 "44' 1^ Vijk m = b 50 + vi^ Y 6-ijkm = b 60 +b 64 P i. + b, r Pi . + b.,P' . + b.-V 45 2-j 46 3-k 47 m + b 55 P 2-j + b 56 P 3-k + b 57 V m + b 65 P 2-j + b 66 P 3-k + b 67 V m Where: Y/ ... ,•'.-.. , YJ ... = logs of quantities of Florida Indian 4-ijkm 5-ijkm 6-ijkm Rjver> Florida | nte rior, and California sizes 163, 163, and 138 oranges purchased per 100 customers. bj" , b' , bi Q = logs of regression constants. b L2i» b 2it;» b Lfi = regression coefficients associated with Florida HH H5 HO | nd|an River sJze 163 oranges (Y^) . b_, , b cc , b c , = regression coefficients associated with Florida 54 55 5b Interior size 163 oranges (Y $ ) . b^i , b,,-, b, c regression coefficients associated with California 64' 65 66 s . 2e , 38 oranges ^ b. ? , bj.-, bc-j = regression coefficients associated with value of 47 57 o7 p ro duce sales (Component II). P! ., P' , P' . = logs of prices of Florida Indian River, Florida l-i 2-j 3-k interior, and California oranges. V. Deviations Y' Y 1 Component I W Y i-ijkm-Yi-ijkm= d < 2 > Y i-.Jkm Y 2-IJkn, d Component 1 1 (1) Y 4-ijkm " Y 4-ijkm (2) Y* Y' U ' 5-ijkm T 5-ijkm (3) Y' ... YJ. . 61 j km 61 j km d d d Where: Yj, Y£, Y' Y£, Y^ , Y£ = observed values y\ /\ S\ S\ S\ S\ Yj, Y£, Y« Y£, Y^, Y£ = estimated values

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APPENDIX E METHOD OF DERIVATION OF PRICE ESTIMATING EQUATIONS FOR COMPONENTS I AND I I

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243 — —

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zkk i .e. B -1 b 22 b^ b 23 b 32 det B ' b 21 b 33 + b 31 b 23 det B b 2l b 32 I b 22 b 3l det B " b 12 b 33 + b 13 b 32 det B b 11 b 33 ' b 13 b 31 det B ' b 11 b 32 + b 12 b 31 det B b ]2 b 23 b 22 b n det B " b 11 b 23 + b 13 b 21 det B b ll b 22 I b 12 b 2l det B i .e. B C 11 C 12 C 13 C 21 C 22 C 23 Si C 32 C 33 , where the C.'s are the elements of the J inverse matrix immediately above. Price estimating equations P i =g 10 +g ll Q i + 9l2 Q 2 + 9l3 S P 2 " 920 + 921 a i + 9 22 QJ + 9 23 S P 3 = 930 + 9 31 <*{ + 9 32 Q^ + g 33 Q. Where: 9io = -^ b 10 C ll +b 20 C 12 +b 30 C 13 ) 920 " " < b i0 C 2i + b 20 C 22 + b 3 'o C 2 3 ) 9 3 '0 = (b 10 Si + b 20 C 3 2 + b 30 C 33 ) 9 11 = C ll 9 12 = C 12 g 13 = C 13 9 21 = C 21 i 22 '22 9 23 " °23 '31 J 32 = C. '32 g 33 = C 33 Then: C ij " ^ b ijl b ij2 " b ij3 b \\l? ( R )» where b 's are previously defined in the matrix and R is the reciprocal of det B.

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Then: 245 11 '12 13 '21 '22 23 Sl = C 32 = C 33 = (b 22 b 33 ' b 23 b 32 ) ( R } ( b 12 b 33 +b 13 b 32 )( R) (b, 2 b 23 b 22 b 13 ) ( R ) ( " b 21 b 33 + b 23 b 3l )( R } (b„ b 3 3-b 13 b 3l ) (R) (-b n b 23 + b, 3 b 2l )( R) < b 2l b 32 " b 22 b 3 l> ( R ) (" b ll b 3 2 +b 12 b 3l )( R) (b,, b 22 -b 12 b 21 ) ( R)

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246 b 55 b 56 .

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2hl Price estimating equations p i = 9io + %k % + g 45 Q 5 + 9 ^6 Q 6 P 5 = 9 50 + 9 54 % + 9 55 Q 5 + 9 56 Q 6 P 6 " g 60 + Hk % + 9 65 Q 5 + 9 66 Q 6 Where: 94o = " (b 40 C ^ + b 50 C 45 + b 60 9^ = c 4i+ 954 = C 54 9 6*t = C 64 945 = C k5 9 55 = C 55 9 65 = C 65 S46 = C 46 9 56 " C 56 9 66 = C 66 Then: C. = (b. M b.._ b.., b...) ( R ), where b's are as previously ij 1 j 1 ij2 ij3 U 4 'J defined in the matrix and R is the reciprocal of det B. Then: C kk = (b 55 b 66 " b 56 b 65 ) ( R } C ^ = ( b 45 b 66 +b ^6 b 65 )( R) C 46 = (b 45 b 56 " b 55 b ^> ( R ) c 54 = (b 54 b 66 +b 64 b 56 )( R) C 55 = (b ^ b 66 " b k6 b Gi? ( R > C 56 = ( b 44 b 56 +b 46 b 54 )( R) C 64 = (b 5« b 65 " b 55 b 64 } ( R ) c 65 = ( b ^ b 65 + b 45 b 64 )( R) C 66 = (b M* b 55 b k5 V ( R >

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APPENDIX F METHOD OF DETERMINING EFFECTS OF VARIOUS PRICE AND SUPPLY CONDITIONS OF FLORIDA INDIAN RIVER AND FLORIDA INTERIOR VALENCIA ORANGES

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249 Section Method of Determining Effects of Va rious Price Conditions Upon Quantities Taken of Florida Indian River and Florida Interior Oranges Given: *l m Ho+h} P i + ^22 P 2 Where: Q' = log of quantity of Florida Indian River Valencia oranges. 0" = log of quantity of Florida Interior Valencia oranges. P' = log of price of Florida Indian River Valencia oranges. P' = log of price of Florida Interior Valencia oranges. ]3{ |3' = log of regression constants. 6,. = regression coefficients (j = 1,2). ]3 . = regression coefficients (j = 1,2). For small price changes, the estimating equations in terms of percentages can be expressed as follows: • ^1 = /Vl + ^2 ^2 = ^21^1 + ^22*2 Where: dO_ Q. = (100) -T1 = the percentage change in 0^ 1 Q. }

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250 dQ 2 Q, = (100) — = the percentage change in Q . dP, 0. = (lOO) p — = the percentage change in P.. I k ] 1 dP 2 9 = (100) p — = the percentage change in P_. 2 and, from the estimating equations which the model yielded, n = -3.07042 |B 12 = +1.16004 /3 21 +1.56415 i3 22 = -3.01308 However, for large price changes, the following estimating equations expressed in terms of logarithms are required: >i 'WWi Where: ^ = log (1 + q1 ) ^ 2 = log (1 + — ) A 3> *2 AP. e, = log (1 + p1 ) 1 AP, e 2 = log (1 + p-*-) 2 Substituting the estimated values for p> ]]t j3 ]2> /3 j , and j3 V, = -3.07042e ] + 1.160049

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251 i{j 2 = +1.564150, 3.013089 2 Percentage changes in 0. and Q 2 associated with assumed percentage changes in P. and P can be determined by solving for f ] for given 0. and resorting to the following formulae: For f. > Antilog {f. + 4.60517) 100 = percentage increase in Q.y For if/. < 100 antilog (f-. + 4.60517) = percentage decrease in Q, .

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252 Section I Method of Determining Effects of Various Supply Conditions Upon Prices of Florida Indian River and Florida Interior Oranges P l = -YlO + ^l Q i + 'Vl2 Q 2 P 2 = ^20 + ^21 Q i + -V22 Q 2 Where: P] = log of price of Florida Indian River Valencia oranges. P' = log of price of Florida Interior Valencia oranges. Q.J = log of quantity of Florida Indian River Valencia oranges. Q_i = log of quantity of Florida Interior Valencia oranges. 7J , y± = log of regression constants. 7. . = regression coefficients (j = 1,2). 7o • = regression coefficients (j = 1,2). For small supply changes the estimating equations in terms of percentages can be expressed as follows: K \ =, Yll r l + ^12 T 2 K 2 =, Y21 T 1 + ^22 T 2 Where: dP l K, = (100) r — = the percentage change in P. dP 2 K ? = (100) — = the percentage change in P_ 2 L

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253 da, T, = (100) — = the percentage change in Q. dQ 2 T» = (100) r — = the percentage change in Q ? and, from the estimating equations which the model yielded, 7 n = -0.40619 7 12 = -0.15784 7 21 = -0.21123 7 22 = -0.41447 However, for large supply changes, the following estimating equations expressed in terms of logarithms are required: *i 'Vn *\ * *Vi2 ^ s 2 = 7 21 rj, + 7 22 -n 2 Where: AP, e, log (1 + p1 ) 1 1 AP 2 e 2 log (1 + ~) * 2 AG, r), = log (1 + q— ) AQ 2 rj 2 = log (1 + q— ) 2 Substituting the estimated values for 7,,, 7, 2 , 7 2 ,, and 7 22 , £. = -0.406197), 0.15784t) 2 £ 2 = -0.211237), 0.41447t) 2 Percentage changes in P. and P associated with assumed changes in 0_,

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25^ and (L can be determined by solving by ^ for given 17 , and resorting to the following formulae: For 4, > Antilog (£, + 4.60517) 100 = percentage increase in Py For |j < 100 antilog (£, + 4.60517) = percentage decrease in Py

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BIBLIOGRAPHY Brandow, G. E. A Statistical Analysis of Apple Supply and Demand . Pennsylvania Agricultural Experiment Station AE and RS No. 2, 1956. Box, G. E. P., Haden, R. J., and Hunter, J. S. Experimental Designs for Multif actor Experiments . Institute of Statistics Mimeo No. 71, Raleigh, North Carolina, 1953. Box, G. E. P. and Hunter, J. S. "Experimental Designs for Exploration and Exploitation of Response Surfaces," Proceedings of Symposium on Design of Industrial Experiments . (Nov. 5-9, 1956) pp. 138-192, Institute of Statistics of the Consolidated University of North Carolina, 1956. Dixon, W. J., and Massey, J. F., Jr. Introduction to Statistical Analysis . 2nd ed. New York: McGraw Hill Book Company, Inc., 1957. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary . I962. Orlando, Florida, 1963. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1961 . Orlando, Florida, 1962. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. I960. Orlando, Florida, 1961 . Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1959 . Orlando, Florida, I960. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1958 . Orlando, Florida, 1959. Florida Crop and Livestock Reporting Service. Florida C itrus Fruit Annual Summary. 1957 . Orlando, Florida, 1958. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1956 . Orlando, Florida, 1957. Florida Crop and Livestock Reporting Service. Florida C itrus Fruit Annual Summary. 1Q55 . Orlando, Florida, 1956. Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1954 . Orlando, Florida, 1955. 255

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256 B I BL I OGRAPHY— Continued Florida Crop and Livestock Reporting Service. Florida Citrus Fruit Annual Summary. 1953 . Orlando, Florida, 195**. Godwin, Marshall R. Customer Response to Varying Prices for Florida Oranges . Florida Agricultural Experiment Stations Bulletin 508, 1952. Godwin, Marshall R., and Powell, L. A., Sr. Consumer Reaction to Varying Prices for Frozen Orange Concentrate . Florida Agricultural Experiment Stations Bulletin 589, 1957. Hoos, S., and Boles, J. N. Oranges and Orange Products Changing Economic Relationships . California Agricultural Experiment Station Bulletin 751, 1952. Kelly, Bruce W. A Method for Forecasting Citrus Production in Florida . Ph. D. Dissertation, University of Florida, 1953. Powell, L. A., Sr., and Godwin, Marshall R. Economic Relationships Involved in Retailing Citrus Products . Florida Agricultural Experiment Stations Bulletin 567, 1955. Powell, L. A., Sr., O'Regan, William G. and Godwin, Marshall R. Experimental Pricing as an Approach to Demand Analysis . Florida Agricultural Experimental Stations Bulletin 592, 1958. Rock, R. C, and Piatt, R. G. Economic Trends in the California Orange Industry . California Agricultural Extension Service Report, 1961. Tramel, T. E. "A Suggested Procedure for AgronomicEconomic Fertilizer Experiments," Economic and Technical Analysis of Fertilizer Innovations and Resource Use . Edited by: Baum, E. L., Heady, E. 0., Pesek, J. T. and Hildreth, C. G., Ames, Iowa: The Iowa State College Press, 1957. U. S. Department of Agriculture. Agricultural Statistics. 1962 . U. S. Government Printing office, 1962. U. S. Department of Agriculture, Agricultural Marketing Service, Crop Reporting Board. Citrus Fruits by States Production Use Value . Statistical Bulletin 201, U. S. Government Printing Office, 1957. U. S. Department of Agriculture, Statistical Reporting Service, Crop Reporting Board. Citrus Fruits by States Production Use Value . Statistical Bulletin 296, U. S. Government Printing Office, 1961.

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257 B I BL I OGRAPHY— Continued U. S. Department of Agriculture, Consumption of Food in the United States 1909-52. Supplement for 1961 . Agricultural Handbook No. 62, U. S. Government Printing Office, 1962. U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Unloads. Months . U. S. Government Pr U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Unloads. Months . U. S. Government Pr U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Unloads. Months . U. S. Government Pr U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Unloads, U. Months . U. S. Government Pr S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Shipment Months. U. S. Government Pr U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Shipmen ts Months . U. S. Government Pr U. S. Department of Agriculture, Agr Fruit and Vegetable Division Fruit and Vegetable Shipment Months. U. S. Government Pr U. S. cultural Marketing Service, Market News Branch, Fresh By Commodi ties. Stat e s , and nting Office, 1962. cultural Marketing Service, Market News Branch, Fresh By Commodities. States, and nting Office, i960. cultural Marketing Service, Market News Branch, Fresh By Commodities. States, and nting Office, 1958. cultural Marketing Service, Market News Branch, Fresh By Commodities, States, and nting Office, 1956. cultural Marketing Service, Market News Branch. Fresh . By Commodities, States, and nting Office, I963. cultural Marketing Service, Market News Branch, Fresh By Commodities, States, and nting Office, 1962. cultural Marketing Service, Market News Branch. Fresh . By Commodities, States, and nting Office, 1961 . U. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities, States, and Months . U. S. Government Printing Office, i960. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities, States, and Months, U. S. Government Printing Office, 1959.

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258 B I BL I OGRAPHY-Continued U. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities, States, and Months . U. S. Government Printing Office, 1958. U. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities. States, and Months . U. S. Government Printing Office, 1957. U. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments, By Commodities, States, and Months . U. S. Government Printing Office, 1956. U. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities. States, and Months . U. S. Government Printing Office, 1955. U. S. Department of Agriculture, Agricultural Marketing Service, Fruit and Vegetable Division, Market News Branch, Fresh Fruit and Vegetable Shipments. By Commodities. States, and Months . U. S. Government Printing Office, 195^.

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BIOGRAPHICAL SKETCH The author was born on a farm in Anderson County, South Carolina, on April 13, 1 93 1 • He received his elementary and high school education in public schools in Landrum, Greenwood, and Belton, South Carolina, graduating from the Belton High School in 19*6. In January 1957 » a Bachelor of Science degree in Agricultural Economics was received from Clemson College. A Master of Science degree in Agricultural Economics was received from the same institution in August of 1958. In January of 196 1 , he enrolled in the graduate school of the University of Florida. Since that time he has been pursuing work toward the degree of Doctor of Philosophy In Agricultural Economics. He is a member of Alpha Zeta, Gamma Sigma Delta, the American Farm Economics Association, the Southern Economic Association, the Association for the Advancement of Science, the American Statistical Association and the U. S. Army Reserve with the rank of Captain. The author is married to the former Nancy Bryant and they have two children, William Anthony, seven years old, and Nancy Jean, three years old.

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of that committee. It was submitted to the Dean of the College of Agriculture and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Phi losophy. December 21 , I963 ^//^/UV^-v Dean, College of Agriculture Dean, Graduate School Supervisory Committee: US Chairman &L ^U\^ IaJjuiMo^J.M Ct*cKj*/\ U*tMac*.~dj?JZ.~ €. t (:

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"11 li: 7