Title: Optimal allocation of the Florida citrus industry's generic advertising budget /
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Title: Optimal allocation of the Florida citrus industry's generic advertising budget /
Physical Description: 319 leaves : ill. ; 28 cm.
Language: English
Creator: McClelland, Edward L
Publication Date: 1969
Copyright Date: 1969
 Subjects
Subject: Citrus -- Marketing   ( lcsh )
Citrus fruit industry   ( lcsh )
Agricultural Economics thesis Ph. D
Dissertations, Academic -- Agricultural Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1969.
Bibliography: Includes bibliographical references (leaves 215-217).
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Edward Lowe McClelland.
 Record Information
Bibliographic ID: UF00097766
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000415072
oclc - 37701822
notis - ACG2295

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OPTIMAL ALLOCATION OF THE FLORIDA CITRUS

INDUSTRY'S GENERIC ADVERTISING BUDGET














By
EDWARD LOWE McCLELLAND













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
1969











ACKNOWLEDGMENTS


The author wishes to express sincere gratitude to

Dr. Leo Polopolus, Chairman of the Supervisory Committee,

for his untiring guidance and inspiration throughout the

preparation of this dissertation.

Special appreciation is extended to the other

members of the Supervisory Committee. Dr. Lester H. Myers

contributed substantially to the technical development

of the study. Dr. W. W. McPherson, Dr. Clyde E. Murphree,

*and Dr. R. H. Blodgett made significant contributions by

their constructive criticisms in reviewing the dissertation.

This study was financed and supported by the Florida

Citrus Commission. The author is indebted to Mr. Edward A.

Taylor for the authorization of the purchase of the special

data required for the study. Mrs. Patricia Dorrio and

Mrs. Josie Hilton are acknowledged for their assistance in

obtaining the necessary advertising data.

The author is also indebted to Miss Anne Smitht and

Mrs. Carla Morgan for their assistance in typing the pre-

liminary drafts of the paper and to Mrs. Carol Leonard for

typing the final manuscript. Appreciation is also extended

to Mr. T. L. Brooks, Jr. for drawing the illustrations

presented in the paper.

Finally, I would like to thank my parents for their

patience and moral support during the period of my q:.jraduate

studies.













TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS. . . . . . . . . .ii

LIST OF TABLES. . . . . . . . .. . v

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

CHAPTER

I. INTRODUCTION. . . . . . . . . 1

Statement of the Problem . . . . . 1
Objective of the Study . . . ... . 2
Data Requirements. . . . . . . 4
The Florida Citrus Commission. . . . 6
Review of the Literature. ..... .... 7

Advertising Theory. . . . . . 7
Nonlinear Programming Models. . . ... 14

II. DEVELOPMENT OF THE ALLOCATION MODEL. . . .. 18

Assumptions. .. . . . . . . 25
Methodology Considered . . . . . 26
Data Restrictions. . . . . . .. .29
Least Squares Regression . . . ... .30
Quadratic Programming ... . . . .. 32
An Hypothetical Allocation Model . . .. .35

III. ESTIMATION OF THE TOTAL REVENUE FUNCTIONS . 38

Florida Citrus Commission Advertising and
Promotional Programs. . . . . .. 38
Pegression Model for Processed Products .. 39
Regression Model for Fresh Products. ... .44
Statistical Considerations of the Regression
Equations. . . . . . . .. .46

IV. THE RESULTS OF THE ALLOCATION MODEL. . . .. 53

The Allocation Model. . . . . . .. 53
The Allocation of the Advertising Budgets. 57
Alternative Advertising Budget Allocations
for Processed Products. . . . .. 58


iii







TABLE OF CONTENTS.--Continued.


CHAPTER


Pag


Alternative Advertising Budget Allo-
cations for Fresh Fruit. .. ... 66
Estimated Total Net Revenues Derived
from Alternative Budget Allocations. 71
Composite Advertising Budget Alloca-
tion. . . . . . ... . 77
A Comparison of Historical and Theo-
retical Advertising Budget Alloca-
tions . . . . . . . 80

The Kuhn-Tucker Conditions .. . .... 88
Limitations of the Allocation Model ..... 92

V. SUMMARY . . . .. . . . . . 96

Objective. ... . . . . . .. 97
The Allocation Model . . . . . . 98
The Results. . . . . . . .... 99
Future Research Recommendations .. .. .103

NDICES . . . . . . . . . . .106

PPENDIX A . . . . . . . . . .. 07

JPPENDIX B . . . . . . . . . ...117

PPENDIX C . . . . . . . . . . 130


APPENDIX D . .

APPENDIX E . .

APPENDIX F . .

BIBLIOGRAPHY . .

BIOGRAPHICAL SKETCH


. . . . . . . 133

. . . . . . . ..158

. . . . . . . 204

. . . . . . . 215

. . . . . . . 218


APPLE

A

A

A


e













LIST OF TABLES


Table Page

1. Total Florida Orange and Grapefruit Production
and Total Florida Citrus Commission Adver-
tising Expenditures for all Citrus Products,
Crop Years 1960-61 through 1966-67. . . 8

2. Processed Products. Results of the Analysis of
Variance Tests to Determine the Statistical
Significance of the Total Revenue Equations 48

3. Fresh Products. Results of the Analysis of
Variance Tests to Determine the Statistical
Significance of the Total Revenue Equations 49

4. Processed Products. Monthly Allocation of the
Florida Citrus Commission's Annual Adver-
tising Budget by Product-Region for Various
Sized Budgets. . . . . . . . .. 60

5. Processed Products. Percentage of the Florida
Citrus Commission's Annual Advertising
Budget Allocated by Geographical Regions
for Various Sized Budgets. . . . . .. 65

6. Processed Products. Percentage of the Florida
Citrus Commission's Annual Advertising Budget
Allocated by Product Form for Various Sized
Budgets. . . . . . . . . .. 66

7. Fresh Products. Monthly Allocation of the
Florida Citrus Commission's Annual Adver-
tising Budget by Product-Region for Various
Sized Budgets. . . . . . . . .. 68

8. Fresh Products. Percentage of the Florida
Citrus Commission's Annual Advertising
Budget Allocated by Geographical Regions
for Various Sized Budgets. . . . . .. 70

9. Fresh Products. Percentage of the Florida
Citrus Commission's Annual Advertising
Budget Allocated by Product Form for Various
Sized Budgets. . . . . . . . .. 71







LIST OF TABLES.--Continued.


Table Page

10. Processed Products. Monthly Total Net Revenue
Received by Product-Region Due to Optimum
Generic Advertising for Various Sized
Budgets. . . . . . . . . ... 72

11. Fresh Fruit. Monthly Total Net Revenue
Received by Product-Region Due to Optimal
Generic Advertising for Various Sized
Budgets. . . . . . . . . .. 74

12. Monthly Allocation of the Florida Citrus Com-
mission's Annual Advertising Budget by
Product-Region for Various Sized Budgets
for Both Processed and Fresh Products. ... 78

13. Processed Products. Historical and Theoretical
Monthly Allocation of the Florida Citrus
Commission's Annual Advertising Budget by
Product-Region for Selected Budgets. . . 81

14. Processed Products. Total Net Revenue Received
for the Historical and Theoretical Monthly
Allocations of the Florida Citrus Commission's
Advertising Budget by Product-Region for
Selected Budgets. . . . . . . . 84

15. Fresh Products. Historical and Theoretical
Monthly Allocations of the Florida Citrus
Commission's Annual Advertising Budget by
Product-Region for Selected Budgets. . .. 86

16. Fresh Products. Total Net Revenue Received
for the Historical and Theoretical Monthly
Allocations of the Florida Citrus Commi-
sion's Advertising Budget by Product-
Region for Selected Budgets. . . . .. 87

17. Calculation of the Marginal Revenue Products
and Marginal Cost by Product-Region Asso-
ciated with the Allocation of 2.8 and 1.0
Million Dollar Budgets for Fresh Fruit
Products in Table 5. . . . . . .. 90

18. New England Region. Estimated Coefficients of
Total Revenue Received Regressed on Monthly
Advertising Expenditures for Processed
Products Using Equations [3.1] through [3.4]
for the Period July, 1960 through June, 1967.118






LIST OF TABLES.--Continued.


Table Page

19. Pacific Region. Estimated Coefficients of
Total Revenue Received Regressed on Monthly
Advertising Expenditures for Processed
Products Using Equations [3.1] through [3.4]
for the Period July, 1960 through June, 1967..119

20. Mountain Region. Estimated Coefficients of
Total Revenue Received Regressed on Monthly
Advertising Expenditures for Processed
Products in the Mountain Region Using Equa-
tions [3.1] through [3.4] for the Period
July, 1960 through June, 1967. . . .. .120

21. West North Central Region. Estimated Coeffi-
cients of Total Revenue Received Regressed
on Monthly Advertising Expenditures for
Products Using Equations [3.1] through
[3.4] for the Period July, 1960 through
June, 1967. . . . . . . ... ..121

22. West South Central Region. Estimated Coeffi-
cients of Total Revenue Received Regressed
on Monthly Advertising Expenditures for
Processed Products Using Equations [3.1]
through [3.4] for the Period July, 1960
through June, 1967. . . . . ... ..122

23. East North Central Region. Estimated Coeffi-
cients of Total Revenue Received Regressed
on Monthly Advertising Expenditures for
Processed Products Using Equations [3.1]
through [3.4] for the Period July, 1960
through June, 1967. . . . . ... ..123

24. East South Central Region. Estimated Coeffi-
cients of Total Revenue Received Regressed
on Monthly Advertising Expenditures for
Processed Products Using Equations [3.1]
through [3.4] for the Period July, 1960
through June, 1967. . . . . ... ..124

25. Middle Atlantic Region. Estimated Coefficients
of Total Revenue Received Regressed on
Monthly Advertising Expenditures for
Processed Products Using Equations [3.1]
through [3.4] for the Period July, 1960
through June, 1967. . . . . . .. 125


vii







LIST OF TABLES.--Continued.


Page


Table


26.






27.






28.







29.







30.





31.





32.


East South Central, Middle Atlantic, and
South Atlantic Regions. Estimated Coeffi-
cients of Total Revenue Received Regressed
on Monthly Advertising Expenditures for
Fresh Products Using Equations [3.5] and
[3.6], November through May for the Years
1960 through 1967. . . . . . ..

Regional Price and Cross Elasticity Estimates
for Canned Single Strength Grapefruit
Juice and Selected Products Calculated
from Equation [D.1] for the Period January,
1961 through June, 1967. . . . . ..


Regional Price and Cross Elasticity Estimates
for Canned Single Strength Orange Juice
and Selected Products Calculated from
Equation [D.2] for the Period January,
1961 through June, 1967. . . . .


Regional Price and Cross Elasticity Estimates
for Frozen Concentrated Orange Juice and
Selected Products Calculated from Equation
[D.3] for the Period January, 1961 through
June, 1967 . . . . . . . .


129





144





145


14 6


viii


South Atlantic Region. Estimated Coefficients
of Total Revenue Received Regressed on
Monthly Advertising Expenditures for
Processed Products Using Equations [3.1]
through [3.4] for the Period July, 1960
through June, 1967. . . . . . ... 126

New England, Pacific, and Mountain Regions.
Estimated Coefficients of Total Revenue
Received Regressed on Monthly Advertising
Expenditures for Fresh Products Using Equa-
tions [3.5] and [3.6], November through
May for the Years 1960 through 1967. .. 127

West North Central, West South Central, and
East North Central Regions. Estimated
Coefficients of Total Revenue Received
Regressed on Monthly Advertising Expendi-
tures for Fresh Products Using Equations
[3.5] and [3.6], November through May
for the Years 1960 through 1967. . . .. 128







LIST OF TABLES.--Continued.


Table Page

33. Regional Price and Cross Elasticity Estimates
for Chilled Orange Juice and Selected
Products Calculated from Equation [D.4]
for the Period January, 1961 through June,
1967. . . . . . . . . . 147

34. Regional Price and Cross Elasticity Estimates
for Fresh Florida Oranges and Selected
Products Calculated from Equation [D.5]
for the Period November through May, 1960
through 1967. ............... 148

35. Regional Price and Cross Elasticity Estimates
for Fresh Florida Grapefruit and Selected
Products Calculated from Equation [D.6]
for the Period November through May,
1960 through 1967. . . . . . .. 149

36. Period of Lag in Consumer Purchases of Canned
Single Strength Grapefruit Juice in
Response to Retail Advertising Expenditures
on Various Citrus Products by Regions, in
Months, January, 1961 through June, 1967 .154

37. Period of Lag in Consumer Purchases of Canned
Single Strength Orange Juice in Response
to Retail Advertising Expenditures on
Various Citrus Products-by Region, in
Months, January, 1961 through June, 1967. 154

38. Period of Lag in Consumer Purchases of Frozen
Concentrated Orange Juice in Response to
Retail Advertising Expenditures on Various
Citrus Products by Region, in Months,
January, 1961 through June, 1967. . . 155

39. Period of Lag in Consumer Purchases of Chilled
Orange Juice in Response to Retail Adver-
tising Expenditures on Various Citrus
Products by Region, in Months, January,
1961 through June, 1967 ........ .. 155

40. New England Region. Estimated Retail Demand
Coefficients for Processed Citrus Products
Using Equations [D.1] through [D.4] for
the Period July, 1960 through June, 1967 .. 159






LIST OF TABLES.--Continued.


Table Page


41. Pacific Region. Estimated Retail Demand
Coefficients for Processed Citrus Pro-
ducts Using Equations [D.1] through [D.4]
for the Period July, 1960 through June,
1967. . . . . . . . . .. 162

42. Mountain Region. Estimated Retail Demand
Coefficients for Processed Citrus Products
Using Equations [D.1] through [D.4] for
the Period July, 1960 through June, 1967 .. 165

43. West North Central Region. Estimated Retail
Demand Coefficients for Processed Citrus
Products Using Equations [D.1] through
[D.4] for the Period July, 1960 through
June, 1967. . . . . . . . .. 168

44. West South Central Region. Estimated Retail
Demand Coefficients for Processed Citrus
Products Using Equations [D.1] through
[D.4] for the Period July, 1960 through
June, 1967. . . . . . . ... 171

45. East North Central Region. Estimated Retail
Demand Coefficients for Processed Citrus
Products Using Equations [D.1] through
[D.4] for the Period July, 1960 through
June, 1967. . . . . . . . ... 174

46. East South Central Region. Estimated Retail
Demand Coefficients for Processed Citrus
Products in the East South Central Region
Using Equations [D.1] through [D.4] for
the Period July, 1960 through June, 1967. 177

47. Middle Atlantic Region. Estimated Retail De-
mand Coefficients for Processed Citrus
Products Using Equations [D.1] through
[D.4] for the Period July, 1960 through
June, 1967. . . . . . . . ... 180

48. South Atlantic Region. Estimated Retail
Demand Coefficients for Processed Citrus
Products Using Equations [D.1] through
[D.4] for the Period July, 1960 through
June, 1967. . . . . . . . ... 183






LIST OF TABLES.--Continued.


Table Page


49. New England Region. Estimated Retail Demand
Coefficients for Fresh Citrus Products
in the New England Region Using Equations
[D.5] and [D.6] for November-May, 1960
through 1967. . . . . . .. 186

50. Pacific Region. Estimated Retail Demand
Coefficients for Fresh Citrus Products
Using Equations [D.5] and [D.6] for
November-May, 1960 through 1967. . .. 188

51. Mountain Region. Estimated Retail Demand
Coefficients for Fresh Citrus Products
Using Equations [D.5] and [D.6] for
November-May, 1960 through 1967. . .. 190

52. West North Central Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for November-May, 1960 through 1967. . 192

53. West South Central Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for November-May, 1960 through 1967. . 194

54. East North Central Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for the November-May, 1960 through 1967. 196

55. East South Central Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for November-May, 1960 through 1967. . 198

56. Middle Atlantic Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for November-May, 1960 through 1967. . 200

57. South Atlantic Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for December-May, 1960 through 1967. . 202







LIST OF TABLES.--Continued.


Table Page


58. New England Region Population in Millions,
Monthly, July, 1960 through June, 1967. 205

59. Pacific Region Population in Millions, Monthly
July, 1960 through June, 1967. . . .. .206

60. Mountain Region Population in Millions,
Monthly, July, 1960 through June, 1967. .. 207

61. West North Central Region Population in
Millions, Monthly, July, 1960 through
June, 1967. . . . . . . . .. 208

62. West South Central Region Population in
Millions, Monthly, July, 1960 through
June, 1967. . . . . . . . .. 209

63. East North Central Region Population in
Millions, Monthly, July, 1960 through
June, 1967. . . . . . . . .. 210

64. East South Central Region Population in
Millions, Monthly, July, 1960 through
June, 1967. . . . . . ... 211

65. Middle Atlantic Region Population in Millions,
Monthly, July, 1960 through June, 1967 . 212

66. South Atlantic Region Population in Millions,
Monthly, July, 1960 through June, 1967 .213

67. Consumer Price Index for Food Purchased for
Home Consumption, 1957-59=100, Monthly,
July, 1960 through June, 1967. . . .. .214


xii













LIST OF ILLUSTRATIONS


Figure Page

1. Geographical Marketing Regions of the United
States. . . . . . . . . 3

2. The Three Possible Solutions To A Simple
Advertising Discrimination Model. ... .24

3. Marginal Net Revenue Products for Given
Processed Product Advertising Budgets .59

4. Marginal Net Revenue Products for Given
Fresh Product Advertising Budgets. ... 67


xiii













CHAPTER I


INTRODUCTION


Statement of the Problem


As with any economic enterprise, the Florida citrus

industry wishes to increase sales revenues and at the same

time reduce marketing costs. Although the Florida Citrus

Commission has carried on extensive advertising programs,

no economic decision model has been devised to allocate a

given annual advertising budget to maximize sales revenue

net of advertising costs for the citrus industry. The

allocation of expenditures by historical and intuitive

processes may yield returns that are not the maximum attain-

able for the industry. Advertising expenditures for given

product types in given market areas may need to be either

increased or decreased to increase total revenue net of

advertising costs. A crucial aspect of the problem is the

measurement of the relative competitive strength among

products by geographical region for a given advertising

dollar. With the aid of a quantitative economic decision

model, the reallocation of advertising funds may be more

appropriately committed.

The definition of this problem does not necessarily

require the allocation of an-optimum number of dollars to

1







spend but rather the optimum allocation of a given sum of

dollars by product and region.


Objective of the Study


The objective of this study is to develop an economic

model that will become a decision tool in the allocation of

the Florida Citrus Commission's annual advertising budget

in terms of geographical regions and citrus products.

Ideally, the allocation of the advertising budget would include

products and regions, as well as advertising media, adver-

tisement content, and the timing of expenditures. For rea-

sons of simplification and lack of sufficient data, only the

allocation among products and regions is considered.

The products used in this study are canned single

strength orange juice, canned single strength grapefruit juice,

frozen concentrated orange juice, chilled orange juice,

fresh oranges, and fresh grapefruit. The geographical

regions selected for this study conform to the census regions

defined by the United States Census Bureau. The New England,

Pacific, Mountain, West North Central, West South Central,

East North Central, East South Central, Middle Atlantic, and

South Atlantic census regions are presented in Figure 1.

There are inherent problems associated with these large

regions due to the lack of homogeneity of consumer buying

characteristics within the designated geographic areas.

Unfortunately, less aggregative regional data are unavailable.
















































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Data Requirements


The data used in this study are generic or commodity

advertising expenditures, sales records for each product-

region, a price index for food purchases for home consumption,

and regional population figures. These data series were

implemented on a monthly basis for the period July, 1960

through June, 1967.

The advertising expenditures were extracted from the

Florida Citrus Commission's accounting files. Each account-

ing invoice was dated and recorded by product type and adver-

tising medium utilized. These data were aggregated by

months and divided regionally according to media purchased.

Since the media were not circulated strictly within the

geographical boundaries of the defined regions, the resultant

advertising expenditures are only estimates of the actual

advertising efforts within each region. It was assumed that

consumer response to advertising across regional boundaries

mutually cancel each other, so the estimated expenditures in

each area measure the true advertising efforts within any

given geographical region.

The sales data used to make the retail demand estimates

were purchased directly from the Market Research Corporation

of America. These data included the quantity of product sold

and the total revenue received for each product purchased




1The term product-region is used to denote any given
sale of the ith product in the jth geographical region.







within each region for the period July, 1960 through June,

1967. The source of the data was a nationwide consumer

panel of representative household units located throughout

the United States. From the itemized sample of the consumer

panel purchases, regional estimates of total consumer

purchases were obtained by the use of regional inflators.

The reported quantity of citrus products sold and total

revenue received are therefore regional estimates of the true

regional sales figures.

To complete the data necessary for the study, popula-

tion data, and a price index were also obtained. Regional

population figures were reported throughout the period of
2
the study by Sales Management publications. The population

data were used to reduce total quantities of product sold to

a per capital basis. The price index selected was the index

of food purchases for home consumption which was published

by the United States Department of Labor on a monthly basis

for the required period. The price index was used to

inflate all monetary units to the common price level of

June, 1967.




2The Dartnell Corporation, "Survey of Buying Power,"
Sales Management, the Magazine of Marketing, Chicago,
Illinois, the June 10 Issues, 1961 through 1967.

3U. S. Department of Labor, Bureau of Statistics,
Consumer Price Index, U. S. Government Printing Office,
July, 1960 through June, 1967 Issues.




6

The Florida Citrus Commission


In 1935 the Florida Citrus Commission was established

by an act of the Florida State legislature. This enactment

was in response to the leading Florida citrus growers and

shippers who saw the need for the regulation of product stand-

ards and to initiate an industry program to promote Florida's

cit-.rus fruit. The need for such legislation was to combat

the promotional efforts of the California citrus industry

'.ihich had been organized in 1907 and to secure a national

mia:rklt for the increased production of Florida citrus products.

The advertisement and promotion of Florida citrus

products are carried out through a self-help tax program.

Tax revenues are derived from a fixed fee assessed on every

box of citrus fruit harvested for commercial markets. All

ta>:es levied, as directed by the Florida Citrus Code,4 are

due and payable by the processor or fresh fruit packer when

the citrus fruit is first handled in the primary channels of

tralde. The tax rate is fixed for a given crop year but may

be changed between succeeding years. When special advertising

campaigns are authorized, additional taxes can be levied

under a special state "Campaigns" Act. Since the tax is

fixed on each box of fruit produced, the revenues made

available each year will vary directly with the size of the

crop harvested. Historically, the production of Florida




4Florida Citrus Commission, State of Plori(n Citr: u
Frul.t La:., Chapter 601.15, Lakeland, Florida, D.ce; ,- o -.93 5.

51bid., Chapter 601.152







oranges and grapefruit grew from 27.4 million boxes in

the 1935-36 season to 188.1 million boxes in the 1966-67

crop season.6 During the same period consumer advertising

expenditures rose from $364,000 to nearly $9.0 million. The

totals for the annual production of citrus fruit and

advertising budgets for the period of this study are shown

in Table 1.

The actual commitment of funds to an advertising

program is approved by the Florida Citrus Commission and is

managed jointly by the Citrus Commission and a contracted

advertising agency. It is the advertising agency's responsi-

bility to design and to implement the advertising program.

Designing a campaign includes defining sales markets, select-

ing advertising media, and creating the advertisement copy.

The final selection among advertising proposals has been

made by intuitive and historical decision criteria.


Review of the Literature


Advertising Theory

During the decade of the 1950's interest in agricultural

generic advertising was stimulated as the result of large

farm surpluses. It was generally assumed that by expanding

markets these accumulated surpluses could be reduced. The

prime objective of advertising strategies is to manipulate

or move the demand curve for a given product to the right,




60ne Florida box is equivalent to 1-3/5 bushels.






Table 1. Total Florida Orange and Grapefruit Produc-
tion and Total Florida Citrus Commission Advertising Expendi-
tures for all Citrus Products, Crop Years 1960-61 through
1966-67



Crop Orange Grapefruit Advertising
Year Production Production Expenditures

(million boxes)a (million dollars)

1960-61 86.7 31.6 3.06

1961-62 113.4 35.0 3.52

1962-63 74.5 30.0 3.09

1963-64 58.3 26.3 4.01

1964-65 86.2 31.9 2.96

1965-66 100.4 34.9 2.57

1966-67 144.5 43.6 8.79



One box equals 1-3/5 bushels.

Source: Annual Statistical Report, Florida Citrus
Mutual, Statistics and Economics Division, Lakeland, Florida,
1966-67 Season and Advertising Expenditure Files of the
Florida Citrus Commission, Lakeland, Unpublished, 1960-61
through 1966-67 seasons.







thus increasing the quantity of product sold and the total

revenue received. If a goal of an industry is increased

total revenue, then the economic merits of advertising can

be judged as to the resulting effects on total revenue.

Advertising theory in the body of economic literature

had a late start. Neoclassical economic theory provided

little room for advertising within the framework of pure

competition. This theory implied that firms engaged in

advertising would go out of business in the short run

because their selling costs would lead to increasing average

unit costs above the market price. It was not until the

development of the theories of monopolistic competition that

advertising began to be seriously considered in economic

theory.

One of the first economists to explain the effects

of advertising in economics was Chamberlin. Chamberlin

developed the monopolistically competitive model by defining

three variables -- market price, product differentiation,

and selling costs. By varying each of these variables in

turn, equilibrium points in the market structure were identi-

fied. In the treatment of selling costs it was shown that

the demand curve is affected through imperfect knowledge

of the market and through the potential of altering consumer's

wants by sales appeal. While the cost of production is the

cost of satisfying demand by increased supply, selling costs




7Edward H. Chamberlin, The Theory of Monopolistic
Competition, 8th Edition. Cambridge, Massachusetts: Harvard
University Press, 1965.







are the costs of increasing quantities sold by shifting the

demand curves to the right. In order to remain in business

the entrepreneur must cover all production and selling costs

in the long run.

Another early contributor to advertising theory was

Borden.8 A study conducted by Borden in 1938 involved the

effect of advertising upon the demand for California oranges.

The advertising programs of Sunkist Growers were analyzed for

the period 1907 through 1935. The results of the study

showed that the demand for California oranges had been

substantially increased by advertising programs which intro-

duced new consumers, increased use among limited consumers,

and encouraged continued use among present consumers. Borden

hypothesized that advertising is most effective when industry

demand is expanding, where the product can be differentiated,

where hidden qualities exist in the product that cannot be

judged at the time of purchase, and when strong emotional

buying motives exist.

In 1939 Wellman was among the first to use the method

of least squares regression analysis to determine the relation-

ship between sales and selling costs on a geographical basis.9




8Neil H. Borden, The Economic Effects of Advertising,
Chicago, Illinois, Richard D. Irwin, Inc., 1942.

Neil H. Borden, Advertising In Our Economy, Chicago,
Illinois, Richard D. Irwin, Inc., 1945.

9H. R. Wellman, "The Distribution of Selling Effort
Among Geographic Areas," Journal of Marketing, Vol. III,
January, 1939, pp. 225-41.







The assumptions made in Wellman's paper were: (1) areas

are independent with respect to sales such that one area is

not affected by the amount of selling effort employed in

other areas; and (2) units of selling effort (dollars) are

homogeneous. The latter assumption was made because selling

effort, defined in dollar units, is the best measurement of

promotional penetration into consumer audiences. The distri-

bution of selling effort was made by equating marginal sales

to marginal selling costs among regions.

One of the first writers to consider generic adver-

tising in an oligopolistic market was Boulding.10 In pure

competition advertising is not feasible by individual firms,

but advertising programs can be conducted by an association

to expand the total demand for a product, e.g., "Drink More

Florida Orange Juice." According to Boulding, such industry

advertising is also characteristic of perfect oligopoly.

Selling costs incurred for the benefit of the individual

firm, however, grow in importance as the products become

more heterogeneous.11 If a product is homogeneous, the

benefits of generic advertising will be shared among all firms

through an expanded market. As the product becomes more

heterogeneous, brand advertising by individual firms becomes

more important as firms seek to capture a larger share of the

market. Boulding's economic analysis develops the firm's




10Kenneth Boulding, Economic Analysis, New York,
Harper & Bros., 1941.

11Ibid., p. 617.







equilibrium positions for varying degrees of oligopoly

and selling cost outlays.

A spatial advertising model was developed by Nordin

which assumed that the relationship between sales and

regional advertising expenditures was an exponential

function.12 Given an advertising budget, regional expendi-

tures were equated to the ratios of selling costs divided

by sales revenues.

A defense for the economics of advertising was offered

by Hollander.13 However, he points out that many advertising

managers fail to realize that advertising appropriations are

the cause of sales but are customarily treated as the results

of sales. There is also seldom any serious attempt to show

the extent of capitalizing goodwill resulting from continuing

advertising programs other than in accounting records.

An incremental method of allocating advertising costs

was introduced by Dean.14 The optimal allocation of adver-

tising funds can be accomplished by substantially increasing

advertising expenditures from one market period to the next




12J. A. Nordin, "Spatial Allocation of Selling Expense,"
Journal of Marketing, Vol. VII, January, 1943, pp. 210-19.

13Sidney Hollander, Jr., "A Rationale for Advertising
Expenditures," Harvard Business Review, Vol. XXVII, No. 1,
January, 1949, pp. 79-87.

14Joel Dean, "Cyclical Policy on the Advertising
Appropriation," Journal of Marketing, Vol. XV, January,
1951, No. 3, pp. 265-73.








until marginal revenues are equated with marginal production

costs, plus marginal selling costs. Measuring current

demand by current advertising is complicated by: (1) "average"

differences of copy, (2) lags in consumer response to adver-

tising, (3) the short-run nature of an advertising program,

and (4) the multiplicity of advertisements among brands.

Several static equilibrium models were developed by

Dorfman and Steiner15 in order to demonstrate the firm's

optimal decisions in pricing, advertising expenditures, and

product quality. Of special interest were the models of

joint optimization of the advertising budget with both fixed

and variable product prices. Conceptually, the optimization

of advertising expenditures and variable prices is the more

realistic model, but the problem of inseparable variables

makes the computational aspects of large models difficult

indeed. If fixed prices can be assumed, the Dorfman and

Steiner model of optimal advertising with fixed prices makes

the computational aspects of most applications feasible. The

theorem tested in the article was that the firm's maximum

profits are obtained by equating marginal advertising expendi-

tures to the ordinary elasticity of demand for the firm's

product.




15R. Dorfman and P. O. Steiner, "Optimal Advertising
and Optimal Quality," American Economic Review, Vol. XLIV,
No. 5, December, 1954, pp. 826-36.







Nerlove and Waugh published a paper on the cooperative

advertising of Florida and California fresh oranges.16

Organized groups which have no control over the supply of

their product are most likely to engage in cooperative

advertising. Without supply controls the most significant

factors in long-range advertising programs are: (1) the

price elasticity of demand, (2) the long-run effects of

advertising on demand, (3) the price elasticity of industrial

supply, (4) the nature of industrial economies and disecono-

mies of scale, and (5) the rates of return to alternative

forms of investment. The authors conclude that explicit
\
advertising expenditures cannot be made unless some estima-

tion is made of the elasticities of advertising and the

industry supply curve.


Nonlinear Programming Models

Several alternatives are available in choosing a

nonlinear programming model to allocate advertising expendi-

tures. In general, nonlinear models are composed of a

functional equation and a number of constraint equations.

The functional equation is a mathematical expression of the

economic objective to be maximized or minimized. The con-

straint equations limit the allocation of resources to the

quantities of resources on hand. A basic premise for




16Marc Nerlove and Frederick V. Waugh, "Advertising
Without Supply Control: Some Implications of a Study of the
Advertising of Oranges," Journal of Farm Economics, Vol. XLIII,
November, 1961, No. 4, Part I, pp. 813-37.







economists to follow is to select a model that is consistent

with economic theory.

The first method available for use in solving nonlinear

problems is calculus. Henderson and Quandt give a mathemati-

cal review of maxima and minima.17 General solutions to

problems of both unconstrained extrema and constrained

extrema using Lagrange multipliers are presented. In both

instances the necessary first-order conditions and the suffi-

cient second-order conditions for extrema are discussed for

maxima and minima problems.

The structural nature of nonlinear spatial equilibrium

problems was reviewed by Takayama and Judge.18 Solutions to

problems were compared using gradient methods, reactive

programming, the Judge-Wallace algorithm19 for spatial

problems, and quadratic programming. Of the methods discussed



17James M. Henderson and Richard E. Quandt, Micro-
economic Theory -- A Mathematical Approach, New York:
McGraw-Hill Book Company, 1958.

18T. Takayama and G. G. Judge, Non-Linear Formulations
of Spatial Equilibrium Models and Methods for Obtaining Solu-
tions, Department of Agricultural Economics, Agricultural
Experiment Station, University of Illinois College of
Agriculture in cooperation with Farm Production Economics
Division, Economic Research Service, U. S. Department of
Agriculture, November, 1963.

19G. G. Judge and T. D. Wallace, "Estimation of Spatial
Price Equilibrium Models," Journal of Farm Economics,
Vol. XL, 1958, pp. 801-20.







the modified simplex method of quandratic programming yielded

the most efficient results. The model featured a quadratic

functional equation with linear constraints. A solution

was assured in a finite number of iterations.

A survey of nonlinear programming was conducted by

Dorn.20 The paper traced the history of computational

techniques of nonlinear programming since the development of

modern digital computers. Quadratic programs were empha-

sized using alternative algorithms to obtain solutions to

problems in both the physical and behavioral sciences. The

necessary, and sufficient Kuhn-Tucker conditions for opti-

malit.vy21 were discussed in each solution.

An extensive work on quadratic programming and appli-

cations was published by Boot.22 The major algorithms

discussed were the Theil-Van de Panne combinatorial method,23

the Houthakker capacity procedure,24 and quadratic programs

solved .within the framework of a Simplex Tableau. The



20i-. S. Dorn, "Non-Linear Programming -- A Survey,"
IManagement Science, Vol. IX, No. 2, January, 1963.

211i. W. Kuhn and A. W. Tucker, "Nonlinear Programming,"
Proceedings of the Second Berkeley Symposium on Mathematical
Statistics and Probability, (ed.) G. Neyman, Berkeley;
University of California Press, 1951, pp. 481-92.

22John C. G. Boot, Quadratic Programming, North-
Holland Publishing Company, Amsterdam, and Rand McNally
and Company, Chicago, Illinois, 1964.

2311. Theil and C. Van de Panne, "Quadratic Programming
as an 1.:x,:ension of Conventional Quadratic Maximization,"
Ijana g c! nt Sc.cncc Vol.VII,1960, pp. 1-20.

2411. S. Houthakker, "The Capacity Method of Quadratic
Prograpui.ing,, EconometrJca,Vol.XXVIII,1960,pp. 62-87.







special anomalies of trivial constraints, dependency, and

degeneracy were considered. Dependency occurs in quadratic

programming when the number of nonzero variables is less

than the number of equations in the system. A problem is

degenerate when the solution is not altered when a specific

equality constraint is satisfied or is not satisfied. The

theory developed by Boot was used in allocating the surplus

milk production in the Netherlands to the manufacture of

various dairy products and to develop the pricing policies

for each dairy product.













CHAPTER II


DEVELOPMENT OF THE ALLOCATION MODEL


The prerequisites to model building are a knowledge

of the systems or forces which generate the observed data

and an explicit objective which is to be achieved through

the manipulation of the data. A model is an abstraction

or symbolic representation of the problem to be solved, and

the structural form of the model is derived from theorems

and axioms of the disciplines in which the observed data are

embedded. The determination as to whether or not the objec-

tive is being achieved is made by evaluating a return func-

tion or measure of effectiveness.1 The return function or

measure of effectiveness is a statement of the level of

attainment of the objective function. Once the return func-

tion or measurement of effectiveness has reached an ultimate

state, a solution to the problem has been generated.

In economics, data are passively generated by systems

that are stochastic, dynamic, and simultaneous in nature.

After a system of observed data has been defined, a model is

designed to test economic theorems that were involved in the




1George L. Nemhauser, Introduction to Dynamic
Programming, New York, John Wiley and Sons, Inc., 1966, pp.2-3.

18







data generation process. The theories for the analysis of

these systems have been developed within a variety of frame-

works such as consumer behavior, the firm, and institutions.

Within each of these areas of study specific economic

principles have been outlined to develop the structure of

a given economic model.

The principle used in allocating economic resources

involves the concept of marginality. Economic resources

are committed to a productive activity to the extent that the

marginal costs of the contributions of these resources are

equal to the marginal benefits gained from the activity. If

more than one activity is considered, resources are allocated

to the system until the marginal net benefits are equated

over all activities. The unit of measurement used in economic

analysis is the dollar because the monetary unit is the common

denominator of economic costs and returns.

The data used in this study were generated by the

production and marketing systems of the Florida citrus

industry. The harvest of Florida orange crops normally begins

in October of each year and ends the following July. The

total annual orange production consists of early, mid-season,

and Valencia varieties. Ninety-five percent of the grape-

fruit crop is harvested during the months of October through

May.

The citrus harvest is marketed in both processed and

fresh product forms. Approximately 20 percent of the orange

production is sold fresh, 60 percent is sold as frozen concen-







treated orange juice, and the remaining 20 percent is sold as

canned single strength and chilled orange juice. The grape-

fruit crop is divided about equally between processed and

fresh forms. The processed citrus products are sold on a

twelve month basis, and the bulk of the fresh products are

sold during November through May of each season.

The advertising and promotional strategies of the

Florida Citrus Commission are implemented for convenience

on a crop year basis. Specific advertising campaigns can

be conducted throughout the year for processed products, but

advertising is limited to the harvest periods of oranges and

grapefruit for fresh products.

Development of the budget allocation model is based

upon the objective to be accomplished. The objective in this

case is to distribute a given amount of advertising funds

across Florida's national retail market for citrus products

in such a manner that net returns to the industry will be

increased through increased revenues, decreased advertising

costs, or a combination of the two. Since there are six

product forms and nine geographical regions defined, there

are a maximum of fifty-four market combinations to which a

share of the annual budget can be committed. Therefore, there

are fifty-four potential product-markets where revenues can

be increased and/or advertising costs decreased.

In formulating the model the essential parameters

must be defined in order to identify salient forces operating

within the system which generated the observed data. Given







the objective, it is necessary to define the measure of'

effectiveness which will precisely indicate whether or not

the objective is being achieved. When the measure of effec-

tiveness is clearly defined, most of the significant aspects

of the problem are readily identifiable. The measure of

effectiveness chosen was total revenue net of advertising

expenditures, and the predetermined variables were generic

advertising expenditures.

A number of algorithms might have been chosen to solve

the allocation problem. The most common method would be to

employ the techniques of calculus and Lagrange multipliers

for constrained maxima. However, due to the nonnegativity

constraints imposed in this study and for sake of speed and

accuracy, a computerized quadratic program was chosen to

solve for the optimal solutions.

The dimensional considerations which arose at this

point were to make the advertising allocations on a monthly

basis in total dollar units. The functional equation defined

as total net revenue was expressed as a quadratic function

of total dollar expenditures.

If the problem was solved for maximum total net revenue,

the final allocation could exceed the advertising budget for

any given crop year. The budget constraint equation was

defined in total dollar units to limit the amount of expendi-

tures allocated to the quantity of available funds in the

advertising budget. The constraint equation limited the

advertising expenditures over all product-regions.




22

A more subtle restriction imposed on the allocation

model was the requirement that all budgetary expenditures be

nonnegative. This imposition prevents a fictitious maximiza-

tion of the functional equation. Intuitively, a negative

cost is a revenue which is inconsistent with the reality

of allocating advertising funds.

The final solution to the problem is obtained by

equating the marginal net revenue products across all

product-regions.2 The economic justification for this

process is enumerated in the simple advertising discrimina-

tion model in Figure 2.3 Three different theoretical solu-

tions are possible in allocating the budget. These solu-

tions may over exhaust, just exhaust, or under exhaust the

advertising budget.

For simplification only two markets are considered in

the example and the total revenue curves are assumed to be

parabolic and positive semi-definite. Market One has a

marginal net revenue product defined as MNRP1, and Market

Two has a marginal net revenue product defined as MNRP2. In

Figure 2a the budget is over exhausted since MNRPI and

MNRP2 intersect in the region where the marginal net revenue




2Advertising as defined in this study is a resource
or factor, and the marginal revenue product is the first
derivative of total revenue with respect to advertising.

3The term advertising discrimination model is used
instead of the term economic discrimination model because
the quadratic program discriminates among product-regions
in order to optimally allocate the advertising budget.







products equated are positive. Advertising expenditure OA

is allocated to Market One, and O'A is allocated to Market

Two. OA plus O'A equals the total fixed advertising budget

00'. In Figure 2b the budget is just exhausted since MNRPI

and MNRP2 intersect where the marginal net revenue product

curves are equated to zero. Advertising expenditure OA is

allocated to Market One, and O'A2 is allocated to Market

Two. OA plus O'A equals the fixed budget 00'. In Figure

2c the fixed budget is under exhausted MNRPI and MNRP2

intersect in the region where the marginal net revenue

products are negative. Advertising expenditure OA is allo-

cated to Market One, and O'A2 is allocated to Market Two.

The Advertising funds AIA2 are not allocated to either Market

One or Market Two but are withheld from the advertising cam-

paign. OAt plus O'A2 plus AIA2 equals the total fixed

budget 00'.

Two conditions are necessary before the discrimina-

tion model can operate profitably. The markets must be

segregated, and the slopes and/or the intercept points of the

marginal net revenue product functions have to be signifi-

cantly different from each other.

For the immediate problem there are two practical

solutions to the allocation model. The first is the possi-

bility that the budget constraint is not exhausted. This

implies that the citrus industry could save money and increase

net returns by reducing the amount of money required for

generic advertising programs. The second possible solution









MNRPI


MNRP2


0 A
Fig. 2a


MNRPI
MNRP2


Fig. 2b


MNRF~


MNRP2


0 AI
Fig. 20


Figure 2. The Three Possible Solutions To A Simple Advertising
Discrimination Model


Market
One


Market
Two


Market
One


Market
Two


Market
One


Market
Two







exhausts the advertising budget. In this situation, as

well as in the first, the final solution indicates the optimal

allocation of funds among product-regions which maximizes

net returns to the industry.


Assumptions


The model assumes that a dollar spent for a given

advertising copy and advertising medium is as efficient in

generating sales as any other choice of advertising copy and

media. Advertising media and advertisement selection were

not considered in this study although it is recognized that

these parameters play an integral part in penetrating consumer

audiences' buying habits. Response rates for given media

and advertising copy are largely a psychological phenomenon,

and their measurement is outside the economic framework of

this allocation model.

Regions are assumed to be independent with respect to

sales of Florida citrus products. For example, Florida

citrus sales in the New England Region are assumed to be

unaffected by citrus sales in the Middle Atlantic Region,

and vice versa. The relationships measured were the inter-

actions of citrus product prices, quantities of products sold,

and advertising expenditures within regions.

The timing of advertising expenditures on a seasonal

basis was not considered because data limitations did not

provide an adequate number of cross-sectional observations.

The only time element used in the study was the attempt to







measure the lagged response to advertising expenditures in

estimating the product-region total revenue and demand

equations.


Methodology Considered


The study was divided into two separate sections. The

first phase was the estimation of the total revenue functions

for each product-region, and the second phase involved the

advertising allocation problem.

The technique used to estimate the product-region

total revenue equations was the method of least-squares

regression. Since the total revenue functions were assumed

to be parabolic, the regression model was formulated as a

quadratic function. The nature of the total revenue func-

tions made the selection of the nonlinear algorithm a logical

choice in solving the allocation problem.

Because the advertising budget constraint is linear,

the functional equation expressed as total revenue net of

advertising expenditures will be quadratic because a linear

cost function subtracted from the quadratic total revenue

function yields the quadratic total net revenue function.

ToLal net revenue in each product-region expressed as the

square of the advertising expenditures results in a linear

marginal net revenue product function when the total net

revenue function is differentiated with respect to advertis-

ing expenditures. 'Equating all marginal net revenue product

functions subject to the budget constraint optimally allo-

cactes the advertising expenditures over all product-regions."





27

In single-equation models one variable is defined as

dependent while the remaining variables are classified as

independent. The choice of the dependent variable is made

by postulating the variable that is influenced the greatest

degree by the other variables. In this study it is readily

apparent that the purpose of advertising expenditures is to

increase revenues.

The units used in the regression model were total

dollars. The total revenue figures used were the actual

dollar figures reported by the Market Research Corporation

of America by product-region. The advertising expenditures

used were the compiled figures obtained from the accounting

records of the Florida Citrus Commission. Estimates of the

quantities of product sold due to optimal generic advertising

were measured in fluid gallons of single strength equivalent

juice. Conversion factors used in this study appear in

Appendix A.

The number of years included in the time series was

limited by the amount of money available to purchase the

total revenue and quantity data from the Market Research

Corporation of America. It was decided to purchase data

for the most recent crop year and continue back through time

on an annual basis until this budget was exhausted. The

resultant period of data purchased was July, 1960 through

June, 1967. This period of time witnessed two significant

shifts in citrus crop production which were due to the freeze

in December, 1962 and to the 1966-67 recovery from the 1962







freeze in new plantings and restorationof old groves. It

is felt that these two shifts in production during the

period of the study aid in estimating and identifying the

total revenue functions in each product-region. The dramatic

shifts in supply allowed proportional shifts in the size

of the advertising budget providing a wide range of observa-

tions of revenues and expenditures which aided in estimating

the quadratic functions.

IThe choice of using a month as the time unit in the

study was made because the purchased price-quantity series

were reported on a monthly basis.\ Aggregating these data

on an annual basis would provide only seven annual observa-

tions. Given the number of parameters in the regression

model, the statistical calculations on an annual basis would

result in estimates with zero degrees of freedom. The

monthly observations do provide sufficient degrees of free-

dom to make reasonable statistical tests. It is felt that

the period of a month allows adequate time for the marketing

forces to dampen out spurious factors and short enough to

capture the relevant economic factors in the system.

To minimize the effect of spurious price variations

in the regression model, a price index was selected to

inflate the total revenues and advertising expenditures to

a common base. The price index used was the index of food

purchases for home consumption, and the base period of the

study was June, 1967. The argument for using the last period

as the base period was that these inflated prices approximate

current prices better than choosing an earlier base period.







Data Restrictions


The sources of data used in this study were given

in Chapter I. The products and regions chosen were restricted

by the consumer panel data sampled by the Marketing Research

Corporation of America. As a result, the Florida Citrus

Commission's advertising invoice data had to be tailored

to conform to the purchased sales data by product and by

geographical region.

Brand advertising expenditure data were omitted

from this study. It is recognized that brand advertising

plays an important role in the promotion of Florida's citrus

products for individual firms. With a knowledge of the allo-

cations of total brand advertising expenditures by product-

regions, the Florida Citrus Commission's budget could be

more efficiently allocated to complement brand advertising

expenditures in order to increase the total national consump-

tion of Florida citrus products. Since the brand advertising

expenditures of the larger processing and packing firms were

not available for this study, only generic advertising

expenditures could be considered.

Sales data for imitation and synthetic citrus flavored

products were similarly not used in this study because the

necessary regional sales data were not available. Some of

the new synthetic products are substitute products for

Florida citrus products, but the lack of necessary sales

data prohibits measuring the degree of substitutability of

these given products.







Although brand advertising data and the price data

of competing synthetics were unobtainable for this study,

it is believed that the solutions to the present allocation

problem are not too seriously biased. Solace might be

realized by the fact that regional consumer purchasing

characteristics are generally known by the major firms in the

citrus industry. With this information available it may not

be too unreasonable to assume that the regional distribution

of brand advertising expenditures of the firms within the

industry are similar to the regional distribution of the

Florida Citrus Commission's advertising expenditures. There-

fore, the generic advertising campaigns would complement the

collective brand advertising efforts of the firms within the

Florida citrus industry.


Least Squares Regression


The form of the regression model for k observations

in matrix notation is


[2.1] Y = Xb + u


where


Y = (kXl) column vector of the dependent variable

X = (kXm) matrix of independent variables

b = (kXl) column vector of regression coefficients

u = (mXl) column vector of stochastic distrubance terms

k = number of observations

m = number of independent variables







The econometric implications and assumptions of the single-

equation model for parameter estimation were examined by

Johnston.4 The crucial assumptions are:


1. E[u] = 0

2. E[uu'] = o2I

3. X is a set of fixed numbers

4. X has rank m

If the assumptions stated above are strictly adhered to, the

resulting parameter estimations will be best linear unbiased

estimations. When one or more of the assumptions of the

model are violated, Johnston offers remedies to the model.such

that given these violations the "best" alternative estimates

can be made.

In estimating the regression equations several

considerations have to be taken into account. The first

goodness of fit or how well the observed data describe the

total revenue functions. A second consideration is the lagged

response to given advertising expenditures.

Goodness of fit describes the consistency with which

the estimated revenue curves describe the true population

parameters. The estimated regression coefficients should

be consistent in theory with respect to sign, to the magni-

tudes of the advertising coefficients, to the standard errors




4j. Johnston, Econometric Methods, New York, McGraw-
Hill Book Company, Inc., 1963.






of the estimates, and to the coefficients of determination.

Taking each of these factors into account, a judgment can be

made in determining just how well the estimates represent

the true parameters.

Since lags are an important consideration in adver-

tising strategy, they had to be treated in some manner in

this study. An advertising lag is the time interval elapsed

between consumer exposure to retail advertising until the

culmination of a sale in response to the advertising stimulae.

Advertising expenditures were incorporated into the total

revenue estimates in monthly intervals from zero to six

months of sales lag. The significant period of lag response

to advertising was tested by the Student's t distribution in

the treatment of lags in Appendix D.


Quadratic Programming


The form of the objective function and the inequality

constraints in matrix notation are:


[2.2] To maximize f(X) = a'X 1/2X'CX


[2.3] Subject to G'X

[2.4] X>O


where


f(X) = objective function to be maximized

a = vector of h linear coefficients

C = (hXh) matrix of quadratic coefficients







X = vector of h independent activities to be maximized

G' = (hXl) vector of technical coefficients

b = (hXl) vector of resource constraints

h = number of product-regions


Quadratic programming theory is discussed by Boot.5 The

assumptions associated with the model are: (1) the objective

function is continuous and differentiable, and (2) the C

matrix is positive semi-definite (a concave surface). If

the latter assumption is not satisfied, the algorithm cannot

guarantee a global maximum.

Whether or not a quadratic programming solution is a

maximum or not depends upon whether or not the Kuhn-Tucker

conditions for optimality are satisfied.6 As in the calculus,

satisfying the Kuhn-Tucker conditions assures at least a

local optimum.

The necessary condition of the Kuhn-Tucker theorem is:


[2.5] G'X

[2.6] X>0


[2.7] af(X) gu = 0, for all X in solution.
Mxr s=l r




5John C. G. Boot, Quadratic Programming, Amsterdam,
North-Holland Publishing Company, and Chicago, Illinois,
Rand McNally and Company, 1964.

6H. W. Kuhn and A. W. Tucker, "Nonlinear Programming,"
Proceedings of the Second Berkeley Symposium on Mathematical
Statistics and Probability, edited by J. Neyman, University
of California Press, Berkeley and Los Angeles, 1951,pp. 481-492.






m
[2.8] f(X) g u < 0, for all Xo not in solution.
RX Z gsr s- r
r s=l


where


X = vector of activities in final basis

s = elements of G' matrix
-sr

u = multipliers corresponding to each of the linear

constraints


In economic analysis the first term of the latter two equa-

tions, f(X) is the marginal revenue product of the rth
r
activity, and second term, gsr us, is the marginal cost

associated with the rth activity.

The sufficient condition of the Kuhn-Tucker theorem is:


[2.9] f(Xi, . ., Xt) f(X . ., X ) + (X


where


f(X, . ., Xt) = any point in the neighborhood of

the optimal point

t = number of nonzero activities in

the basis


If the inequality is satisfied, the solution is a maximum

maximorum. If only the equality is satisfied, the solution

is a local maximum. According to Dorfman, et al., it is

possible for a program which satisfies the necessary Kuhn-

Tucker conditions to be the optimal program in the region of







feasibility even though the sufficient conditions are not

satisfied.


An Hypothetical Allocation Model


A simplified example of the optimal allocation of an

advertising budget for two product-regions is illustrated at

this point to show the mechanics of the allocation model.

The total net revenue equations have the following form:

2
[2.10] NR11 = bo + biA11 b2A11 + b3A21


[2.11] NR21 = b' + b'A b'A + b'A
0 1 2 21 3A1


where


NR11 = total net revenue for product one in region one

NR21 = total net revenue for product two in region one

A11 = advertising expenditures for product one in

region one

Azi = advertising expenditures for product two in

region one


Equations [2.10] and [2.11] are the two net revenue functions

for the two defined product regions. The total net revenue

derived from these two functions is a simple summation of the

two equations:




R. Dorfman, P. Samuelson and R. Solow, Linear
Programming and Economic Analysis, New York, McGraw-Hill
Book Company, Inc., 1958, p. 196.






2
[2.12] TNR = bo + biAll b2A11 + b3A21 + bo + biA21

b'A2 + b'A
2 21 3A11


where


TNR = total net revenue derived from the two product-

regions


Differentiating Equation [2.12] with respect to Ai and A2

results in the marginal net revenue products contributed by

advertising in both of the product-regions. These marginal

net revenue products are:


[2.13] MNRPI = (bi + b') 2b2A,A


[2.14] MNRP2 = (b3 + b') 2bj A21


where


MNRPI = marginal net revenue product derived in the

first product-region

MNRP2 = marginal net revenue product derived in the

second product-region


Equating the two marginal net revenue product functions to

zero and solving for AI and A2 gives the optimal advertising

expenditures necessary to maximize total net revenue for

the two product-regions without a budget constraint.

In order to constrain the allocation within an eco-

nomic framework certain other conditions have to be imposed.

Equations [2.10] and [2.11] have to be positive semi-definite







in order to meet the necessary and sufficient optimality

conditions of the model. Two constraints have to be defined

to limit the allocation to a given budget and to restrict

the expenditures allocated to nonnegative quantities. The

constraints are expressed as:


[2.15] B>A11 + A21


[2.16] A11, A21 >0


where


B = advertising budget


Given the functional equation and the linear constraints, the

quadratic program can be solved for the constrained optimal

budget allocation.













CHAPTER III


ESTIMATION OF THE TOTAL REVENUE FUNCTIONS


Florida Citrus Commission
Advertising and Promotional Programs


The Florida Citrus Commission's advertising and

promotional programs are planned to expand the demand for all

varieties of citrus fruit except lemons and limes produced

within the state at the national retail and wholesale levels

of trade. 'Due to the limitations in obtaining data only six

Florida products mentioned previously were considered in this

study. The primary products omitted are tangerines in fresh

and juice forms, chilled grapefruit sections, grapefruit

salads, and specialty fruits. The major'portion of the

national advertising program is directed toward the wholesale

sector in the form of trade publication advertising. Promo-

tional programs, such as trade luncheons, convention displays,

and promotional give-away items, are primarily directed

toward the wholesale and distributive trade sector. However,

the scope of this study is limited to advertising expendi-

tures for national media in the regional retail markets.

The motive is to increase the quantity of the product

sold at the existing or a higher retail price. Modern ad-

vertising theory was developed on the premise that a positive







differential quantity of goods could be sold exclusive of

competitive pricing policies. By estimating total revenue

as a function of advertising expenditures the economic

justification for generic advertising can be made through

the increase of revenues received. "If it is discovered that

the cost of advertising is not recovered in additional

revenues, the justification of an advertising program has

no economic foundation.


Regression Model for Processed Products


The regression models developed to estimate the total

revenue functions for canned single strength grapefruit juice,

canned single strength orange juice, frozen concentrated

orange juice, and chilled orange juice are presented below.

4For each product-region total revenue is expressed as a

function of four linear advertising expenditure variables

representing each processed product, a quadratic variable of

own product advertising expenditures, and a dummy variable

representing time. The linear and quadratic variables of

own product advertising are used to estimate the prime source

of revenue for each product-region, and the three remaining

linear advertising variables are used to estimate the secon-

dary sources of revenue for each product-region due to cross

product effects of advertising. Cross product effects of

advertising may be explained as the effect on sales of one

product due to the efforts of advertising another product.

The time variable is used as a dummy variable representing







those unidentified forces in the system which are highly corre-

lated with time.

The quadratic formulation of the total revenue func-

tions insures a reasonable goodness of fit needed to estimate

the classical parabolic total revenue functions which in turn

are required for the development of the allocation model.

At the same time the regression equations allow for cross

product advertising effects, and the derived marginal revenue

product functions are linear and downward sloping. The

generalized total revenue equations for the four processed

products are expressed as follows:

n n n n
[3.] R.^ = aA + bA +b^ b Anb
[3.1] Rjk alj + b1Ajk + b A2jk + b3jAjk + b jA jk


cyj(Ajk)2 + d T3jk
j ljk 2j jk 3jk 4jk



n b2

n n n n
[3.2] R2jk = a2j + bjkjk + bjA jk + bA jk + b 4jAjk





n 2 jT


c,3j(Anjk) + d32jTjk
n n n n



[3.4] R3jk = a + b4jkA'jk + b jA'jk + b2jkAAjk
n 2 + dtjT 3





cj(Anjk)2 + d4Tjk


i = i, 2, 3, 4 j = 1, 2, . 9

k = 1, 2, . ., 84 n = 0, 1, . ., 6







where


i = number of processed products where

1 = canned single strength grapefruit juice

2 = canned single strength orange juice

3 = frozen concentrated orange juice

4 = chilled orange juice

j = number of geographical regions where

1 = New England

2 = Pacific

3 = Mountain

4 = West North Central

5 = West South Central

6 = East North Central

7 = East South Central

8 = Middle Atlantic

9 = South Atlantic

k = number of monthly observations for the period

July, 1960 through June, 1967

n = number of months which unit advertising expendi-

tures were lagged

R.ijk inflated total revenue received for the ith product

sold at retail in the jth region for the kth

month in dollars.

Ajk = inflated total advertising expenditures lagged by
.th .th
n months for the i product in the j region

for the kth month in dollars






th .c th
T. = time variable for the i product in the j
ijk
region for the kth month where


T. = k
j13k


The equations above were estimated using both unlagged

and lagged advertising expenditure variables. The first

procedure estimated the total revenue functions with coin-

cidental or unlagged advertising variables. The second

procedure used the lagged advertising variables that are

developed in Appendix D. Since the lagged advertising

expenditure scheme was designed for a six months lag, the

number of monthly observations in this estimation procedure

was reduced to seventy-eight observations. In both estima-

tion procedures the time variable was both included and

omitted to determine the effects of time in the total revenue

regression equations. Therefore, four regression equations

were estimated for each product-region.

Two criteria were used to select the best product-

region equation from the four alternatives to be used in the

allocation model. The signs of the own product advertising

expenditure variables within each product-region were of prime

concern. 'To meet the Kuhn-Tucker optimality conditions of a

maximum, the linear own product advertising coefficient had

to be positive, and the quadratic own product advertising

coefficient had to be negative. If the estimated coeffi-

cients met the necessary sign conditions in each equation

for a given product-region, the final choice of the equation







to be used in the allocation model was determined by the

equation which had the highest coefficient of determination.

The selection of the estimated equations to be used in the

advertising expenditure allocation was made by disregarding

the signs or magnitudes of the cross product advertising

coefficients. The equations selected for each product-

region to be used in the allocation model are presented in

Appendix B.

Using the outlined selection criteria above, thirty-

two processed product-regions out of a possible thirty-six

product-regions were found to have the necessary sign

properties of own product advertising to be used in the

allocation model. The product-regions for which total revenue

functions could not be estimated with the desired, specified

properties were canned single strength orange juice in the

Pacific Region, canned single strength grapefruit juice in

the'-East North Central and Middle Atlantic Regions, and

frozen concentrated orange juice in the South Atlantic

Region. The failure to estimate consistent revenue equations

for the latter three product-regions is unfortunate as those

products have historically generated a significant amount

of revenue in their respective regions for the Florida citrus

industry. Rather than fabricate some arbitrary coefficients

for these estimated equations, the four product-regions were

deleted from further analysis in the allocation model.







Regression Model for Fresh Products


Total revenue equations for fresh Florida oranges

and grapefruit are presented below. Since the data for

fresh fruit were only reported for seven months annually,

lagged advertising expenditure variables were not used in

the estimation procedure. The total revenue equations as

a function of coincidental advertising expenditures for

fresh products are expressed as follows:


[3.5] Rsk = a5j + bAjkA + b A csj(A j) + d5Tj
jk j jk 6j 6jk 5jk j 5jk


o o o
[3.6] Rjk = aj + b Asjk + bAsjk c (Ajk)2 + d6Tk


i = 5, 6

k = 1, 2, . ., 49

j = 1, 2, . ., 9.


where


i = number of fresh products where

5 = fresh Florida oranges

6 = fresh Florida grapefruit

j = number of geographical regions

k = number of monthly observations

o = coincidental advertising expenditures
th
R.. = inflated total revenue received for the i product
ljk
sold at retail in the jth region for the k month

in dollars







A.. = inflated total advertising expenditures with no
ljk
advertising lag for the ith product sold at

retail in the jth region for the kth month in

dollars
th .th
T. = time variable for the i product in the j
j13k
region for the kth month where


T.i = k
13k

The fresh fruit total revenue equations were estimated

with the time variable included and excluded from the re-

gression program which resulted in two estimated equations

for each product-region. The criteria for selecting the

better equation of the two regressions were the same as those

in selecting the best processed product equations. The major

consideration was the signs of the own product variables

which are required to meet the optimality conditions. Of

secondary importance was the magnitude of the coefficients

of determination for each equation. The resultant choice

of total revenue functions for each product-region are

presented in Appendix B.

Of the eighteen possible fresh fruit product-regions,

fourteen were estimated having the necessary sign properties

of own product advertising to be used in the allocation

model. The four fresh product-regions that did not meet

the necessary sign conditions were fresh oranges in the

Mountain Region and fresh grapefruit in the New England, East

North Central, and Middle Atlantic Regions. Since approxi-







mately 50 percent of the grapefruit production is marketed

in fresh form, the omission of the three fresh grapefruit

product-regions is more important than the omission of the

fresh orange product-region with respect to product contri-

butions to total revenue for the citrus industry.


Statistical Considerations of
the Regression Equations


Several statistical computations can be made to deter-

mine the goodness of fit of the estimated equation in repre-

senting the observed data as a whole. A common measurement

is the coefficient of determination which measures the

percentage of the variation in the dependent variable about

its mean that is explained by the variation in the independent

variables. The coefficient of determination calculated for

each of the estimated equations was used as an aid in the

selection of those equations to be used in the allocation

model. The coefficients of determination ranged in value from

7 percent to 58 percent.

Because some of the coefficients of determination were

initially considered to be quite low it was decided to conduct

another statistical test to measure the goodness of fit of

the total revenue functions. Thus the regression equations

as a whole were tested for statistical significance. The

formal statement of the test or the null hypothesis asserted

was that there was no relationship between the total revenue

variable and the advertising expenditure variables. By

rejecting the null hypothesis a given equation, estimated as







a whole, can be judged to be statistically significant.

The test statistic needed to perform the test was the

F ratio which is calculated by dividing the mean square due

to regression by the mean square due to residual variations

for every product-region equation estimated. If the calculated

F ratio for a given regression is larger than its counterpart

tabular F ratio, the null hypothesis can be rejected. This

implies that the regression equation as a whole is statis-

tically significant.

The statistical test described was conducted for each

equation selected to be used in the allocation model at the

5 percent level of significance. The results of the tests

are presented in Table 2 for the processed products and in

Table 3 for the fresh products. Included in the tables are

the coefficients of determination, the calculated F ratios,

the tabular F ratios, and the statistical degrees of freedom

associated with each equation.

Initially, the coefficients of determination appeared

to be unreasonably low indicating that a large proportion

of the estimated total revenue equations might not be signifi-

cant. The results of the analysis of variance tests indicate

that the estimated equations are generally better than they

had been at first presumed to be. Of the thirty-two estimated

processed product equations, six were found to be nonsignifi-

cant at the 5 percent level of significance. Five of the

fourteen fresh product equations were found to be nonsignifi-

cant.







Table 2. Processed Products. Results of the Analysis
of Variance Tests to Determine the Statistical Significance of
the Total Revenue Equations




a 2 b Degrees of
Product- R F Fb Freedom
Region (calculated) tabularr) Regression Residual



CSSGJ-NE .18 2.84 2.24 6 77
CSSOJ-NE .23 3.48 2.31 6 71
FCOJ -NE .34 7.39 2.35 5 72
COJ -NE .24 4.12 2.24 6 77
CSSGJ-P .55 15.92 2.24 6 77
FCOJ -P .09 1.14c 2.31 6 71
COJ -P .49 11.32 2.31 6 71
CSSGJ-M .19 2.84 2.31 6 71
CSSOJ-M .16 2.32 2.31 6 71
FCOJ -M .16 2.30c 2.31 6 71
COJ -M .29 4.79 2.31 6 71
CSSGJ-WNC .14 1.97c 2.31 6 71
CSSOJ-WNC .27 4.84 2.24 6 77
FCOJ -WNC .45 9.81 2.31 6 71
COJ -WNC .53 14.51 2.24 6 77
CSSOJ-WSC .20 2.88 2.31 6 71
FCOJ -WSC .35 6.43 2.31 6 71
COJ -WSC .35 7.00 2.24 6 77
CSSOJ-ENC .38 7.36 2.31 6 71
FCOJ -ENC .11 1.84C 2.33 5 78
COJ -ENC .47 11.16 2.24 6 77
CSSGJ-ESC .49 12.32 2.24 6 77
CSSOJ-ESC .08 1.21c 2.35 5 72
FCOJ -ESC .36 7.34 2.24 6 77
COJ -ESC .42 9.37 2.24 6 77
CSSGJ-MA .33 6.24 2.24 6 77
CSSOJ-MA .12 2.22C 2.33 5 78
FCOJ -MA .52 14.08 2.24 6 77
COS -MA .54 15.30 2.24 6 77
CSSGJ-SA .30 5.19 2.31 6 71
CSSOJ-SA .27 4.68 2.24 6 77
COJ -SA .22 3.54 2.24 6 77

aA list containing definitions of the symbols used in this
table may be found in Appendix A.

Tabular F values are reported at the .05 level of signifi-
cance.
CF ratio not significant at the .05 level of significance.







Table 3. Fresh Products. Results of the Analysis of
Variance Tests to Determine the Statistical Significance of the
Total Revenue Equations




Degrees of
Product-a R2 F Fb Freedom
Region (calculated) tabularr) Regression Residual


FRFLO-NE .58 14.91 2.58 4 44
FRFLO-P .10 1.21c 2.58 4 44
FRFLG-P .21 2.97 2.58 4 44
FRFLG-M .16 2.07c 2.58 4 44
FRFLO-WNC .11 1.36c 2.58 4 44
FRFLG-WNC .25 3.63 2.58 4 44
FRFLO-WSC .07 0.84c 2.58 4 44
FRFLG-WSC .21 2.99 2.58 4 44
FRFLO-ENC .47 9.57 2.58 4 44
FRFLG-ENC .29 4.39 2.58 4 44
FRFLO-ESC .14 1.85c 2.58 4 44
FRFLO-MA .29 6.12 2.83 3 43
FRFLO-SA .22 3.10 2.58 4 44
FRFLG-SA .32 5.27 2.58 4 44


A list containing definitions of
this table may be found in Appendix A.

Tabular F values are reported at
significance.


the symbols used in


the .05 level of


CF ratio not significant at the .05 level of significance.







The percentage of significant processed product

equations is greater than the percentage of significant

fresh product equations. This was not an unexpected finding.

The problem encountered in fitting the fresh fruit data was

in part due to the structure of the reported fresh fruit

data. If more observations had been available, a better fit

might have been attained. Also, most of the nonsignificant

equations were estimated for product-regions where the contri-

butions to total citrus sales are traditionally weak. Cases

in point would be the sales of fresh Florida oranges in the

Pacific Region or frozen concentrated orange juice in the

Mountain Region.

In the development of the least squares regression

model certain critical assumptions were stated which implied

that the resultant estimators would be best linear unbiased

estimators. It should be pointed out that these assumptions

were not upheld in their entirety.

The advertising and total revenue data used in the

regression model were not free of errors of measurement. The

regional sales data were derived by inflating regional

consumer panel sampled data and therefore subject to errors

in sampling. Fresh fruit sales data were reported on a

seven month annual basis. Fresh fruit sales data were not

purchased for the 1961-62 crop season and had to be synthe-

sized (see Appendix A). The estimates of the sales of fresh

fruit of competing sources of supply had to be adjusted to

comply with reported regional unload data. The advertising







expenditures were extracted from accounting records and

allocated on a regional basis which was, at times an

arbitrary decision. Although there are disadvantages in

using the reported data series, they are the only series

available with which the budget allocation can be made.

One problem that arises in using time-series data

is autocorrelation. The extent of autocorrelation was

tested by calculating a Durbin-Watson d statistic for each

estimated total revenue equation. The Durbin-Watson d sta-

stistics are reported in Tables 18 through 29 in Appendix B.

The problem of autocorrelation can be caused by an

incorrect specification of the model, by the influence of

omitted variables, or by errors of measurement of the depen-

dent variable. The resultant effects of autocorrelation are

unbiased estimates of the regression coefficients which have

unduly large sampling variances, the sampling variances are

seriously underestimated, and the regression equations pro-

vide inefficient predictions.

Because autocorrelation affects the bias of the sam-

pling variance of the regression coefficients, statistical

tests cannot be made because the precise forms of the

t and F tests cannot be obtained. To correct for autocorre-

lation the model must be respecified, more variables must be

included in the model, and/or the measurement error in the




1J. Johnston, Econometric Methods, New York, McGraw-Hill
Book Company, Inc., 1963, pp. 177-179.






dependent variable must be minimized. For the allocation

problem the regression model cannot be respecified and

still meet the necessary conditions for the quadratic

program.

The advertising coefficients, as specified in the

regression model, are of primary interest in this study and

not the testing of statistical hypothesis of the sample

variances of the regression coefficients. Because of

interest in the advertising coefficients, tests of reason-

able, and a priori economic considerations outweigh the auto-

correlation problem. It is recognized, however, that the

use of monthly data tends to aggravate the serial correlation

problem.

The problem of a lagged distribution of advertising

expenditures also produces biased estimators. The problem

of isolating the lag distribution was in part due to the

inability to break the monthly time periods into smaller

time units to determine if the distribution of lag was

readily identifiable. The advertising expenditure data

could have been aggregated by weekly periods, but since

the total revenue data could not have been disaggregated,

the lag distribution was restricted to a monthly basis.













CHAPTER IV


THE RESULTS OF THE ALLOCATION MODEL


The objective of this study was to optimally allocate

the Florida Citrus Commission's advertising budget in order

to maximize the total net revenue received by the citrus

industry over the national retail market. The allocation

of tahe advertising budget included six defined products and

nine geographical marketing areas. The regression model

provided estimated total revenue equations for each product-

region as quadratic functions of advertising expenditures.

Netting out the advertising costs within each region yields

the total net revenue function for each product-region.

Maximizing these total net revenue functions with respect

to advertising costs subject to a budgetary constraint offers

the best allocation of any given advertising budget. The

solution to the optimization problem occurs when the net

marginal revenue products are equated for each product-

region in solution. An optimal allocation is attained by

satisfying the Kuhn-Tucker optimality conditions.


The Allocation Model


The advertising expenditure model for the processed

products as developed below is structured as a quadratic







function. The functional equation is expressed as total

net revenue as a function of total advertising expenditures

for each product within a given geographical region. The

constraints imposed on the model are that the total allo-

cation of advertising expenditures allocated must be nonnega-

tive and not exceed a given budget. 'A solution to the pro-

gram is generated when the marginal net revenue products for

each product-region are equated subject to the specified

constraints.

Since the regression models in the previous section

were expressed as total revenue functions, it is necessary

to net out the advertising expenditures in each product-

region in order to calculate the total net revenue function

for the allocation model. The process of calculating the

total net revenue functions is illustrated by the following

equation where the cross product effects of advertising

have, for notational convenience, been omitted.


[4.1] TNR.. = R.. A..

= a.. + b.A.. c. .(A. ) A..
13 13 13 13 13 13




where


TNR.. = total net revenue for the i product in the
.th
3 region

R.. = total revenue for the i product in the j

region







A. = own product advertising expenditures for the
13
th th
i product in the 3 region


It can easily be seen that total net revenue for a given

product-region is determined by reducing the linear own

product advertising expenditure coefficient by one unit.

The "new" vector of linear advertising expenditure coeffi-

cients comprises the right-hand side vector of the alloca-

tion model.

'After the total net revenue equations for each

product-region have been calculated, the allocation model

for processed products can be illustrated. For simplicity

the functional and constraint equations have been expressed

in matrix notation in Equations [4.2] through [4.4], and

the format of the quadratic programming algorithm can be

found in Appendix C.


[4.2] To maximize TNR(A) = b'A 1/2A'CA


Subject to the constraints


[4.3] B>G'A


[4.4] A>O


where


TNR(A) = total net revenue functional equation to

be maximized expressed as a function of

advertising expenditures







A = vector of advertising activities

b = vector of linear advertising expenditure coeffi-

cients

C = matrix of quadratic advertising expenditure

coefficients

G' = vector of advertising budget coefficients

B = monthly advertising budget


'The purpose of the budget constraint equation is

to limit the allocation of the advertising expenditures

to the size of the advertising budget available." Since it

is assumed that any one dollar is as efficient in generating

total net revenue as any other dollar, the constraint equa-

tion was designed to equate the marginal net revenue products

across all product-regions. (This feature allows the budget

to be divided such that the last dollar awarded any product-

region is equally productive in generating total net revenue
V
as the last dollar awarded to any other product-region. The

resultant budget equation was a simple summation of adver-

tising expenditures. The last constraint, Equation [4.4],

insures that all allocations involve nonnegative expenditures.

After a solution to the quadratic program has been

generated, the values calculated have to be tested by imple-

menting the Kuhn-Tucker optimality conditions. This test

insures that the solution generated is in fact optimal and

meets the imposed constraint criteria.








The Allocation of the Advertising Budgets


Rather than merely calculating one solution, an

array of various sized fixed budgets were assumed, and solu-

tions for these levels of advertising expenditures were

calculated. Given a wide variation in budget sizes and

allocation schemes, it was easy to determine which product-

regions were particularly sensitive to changes in the levels

of advertising expenditures. For all solutions the marginal

net revenue products were calculated to measure the relative

differences among sizes of budgets in order to judge the

economic efficiency of any given budget allocation.

As an initial solution for both the processed and

fresh products an allocation solution was calculated with

no budgetary constraints. By solving for the budget which

equates marginal net revenue product to zero for each

product-region, the most economically feasible budget was

determined. Budgets larger than this figure result in nega-

tive net marginal revenue products for every product-region,

and budgets smaller than this figure result in positive net

marginal revenue products for every product-region in solu-

tion. Considering only processed products, the optimal

unconstrained budget was found to be $439,510 per month on

a twelve month annual basis. For the fresh fruit products,

the optimal unconstrained budget was found to be $398,303

per month on a seven month annual basis.







Alternative Advertising Budget Allocations
for Processed Products


With the optimum budget per month established for

each group of citrus products, it was decided to calculate

the allocation schemes at various budgetary levels. For

the processed products annual budgets of $5.3, $4.7, $3.3,

$1.9, and $0.5 million were chosen to be allocated. The

resulting allocation schemes are presented in Table 4. The

marginal net revenue products for the processed product-

regions in solution for the various budgets are $0.0, $0.41,

$0.84, $4.45, and $10.42, respectively. These marginal net

revenue products are plotted in Figure 3. A marginal net

revenue product of $2.0, for example, suggests that an addi-

tional dollar of advertising yields two additional dollars

in total net revenue.

In Table 4, ten product-regions in the optimal $5.3

million budget allocation were not given any advertising

expenditures. When the functional equation was differentiated

with respect to own product advertising expenditures, the

constant terms of the first derivative of these product-

regions became negative. Since the total net revenue equa-

tion in each product-region had a positive linear own product

advertising term, the negative constant term of the first

derivatives resulted from the large negative coefficients

of the cross product effects of own product advertising within

a given region. With the imposed nonnegativity constraints

on the model, no expenditures can be allocated to these ten

product-regions.
















10.0-




80-
O\
S8.0-


g \
0 \


. 6.0- \
u \
o \



S4.0-

4(1)


z 2.0-
r4


0.0


0.0 1.0 2.0 3.0 4.0 5.0

Advertising Budget
(Million Dollars)

Figure 3. Marginal Net Revenue Products for Given
Processed Product Advertising Budgets







Table 4. Processed Products. Monthly Allocation of
the Florida Citrus Commission's Annual Advertising Budget'
by Product-Region for Various Sized Budgets



Project-a Annual Advertising Budget
Region (million dollars)

5.3 4.7 3.3 1.9 0.5


- - (dollars) - - - - - - -

CSSGJ-NE 6,039 5,971 5,898 5,298 4,303
CSSOJ-NE 0 0 0 0 0
FCOJ -NE 36,700 34,650 32,500 14,450 0
COJ -NE 0 0 0 0 0
CSSGJ-P 4,785 4,353 2,351 0 0
FCOJ -P 23,296 17,504 0 0 0
COJ -P 15,315 15,221 14,783 13,889 12,891
CSSGJ-M 0 0 0 0 0
CSSOJ-M 0 0 0 0 0
FCOJ -M 59,614 57,229 50,119 31,619 0
COJ -M 845 808 637 288 0
CSSGJ-WNC 0 0 0 0 0
CSSOJ-WNC 0 0 0 0 0
FCOJ -WNC 16,983 13,604 0 0 0
COJ -WNC 0 0 0 0 0
CSSOJ-WSC 61,345 58,960 51,762 33,257 37
FCOJ -WSC 19,969 18,347 10,820 0 0
COJ -WSC 0 0 0 0 0
CSSOJ-ENC 3,676 3,369 1,943 0 0
FCOJ -ENC 40,859 37,173 20,065 0 0
COJ -ENC 0 0 0 0 0
CSSGJ-ESC 5,948 5,588 5,211 2,045 0
FCOJ -ESC 1,953 1,220 524 0 0
COJ -ESC 0 0 0 0 0
CSSGJ-MA 39,830 38,908 34,631 25,887 16,142
CSSOJ-MA 180 0 0 0 0
FCOJ -MA 30,068 11,639 0 0 0
COJ -MA 15,515 10,447 0 0 0
CSSGJ-SA 15,196 14,713 12,473 7,892 2,788
CSSOJ-SA 34,320 33,053 27,172 19,806 1,750
COJ -SA 7,074 6,602 4,414 0 0


aA list containing definitions of the symbols used
in this table may be found in Appendix A.







One other total net revenue equation was deleted

from all of the allocations made in this study. The product-

region dropped from the allocation model was canned single

strength orange juice in the East South Central Region.

This equation was deleted because the funds awarded this

product-region were felt to be unduly high. The net cross

product effects within this region were such that the total

net revenue for canned single strength grapefruit juice and

frozen concentrated orange juice were negative. Another

justification for dropping this equation was that it was the

least significant of all the equations estimated as indicated

in Table 2 in Chapter III.

Two other equations that were altered in order to

prevent a negative total net revenue for canned single

strength grapefruit juice in the New England Region were

the equations for canned single strength grapefruit juice and

frozen concentrated orange juice in that region. The nega-

tivity problem was traced to the interaction terms of canned

single strength grapefruit juice and frozen concentrated

orange juice in both equations. Both terms in their respec-

tive equations were added to the intercept term of each equa-

tion at their mean values. The justification for combing the

terms with the intercepts was that the frozen concentrated

orange juice term in the canned single strength grapefruit

juice equation had a Student's t ratio of -2.65 and the canned

single strength grapefruit term in the frozen concentrated

orange juice equation had a Student's t ratio of 4.07. Since







both terms were so significant, it was believed that the

cross product effects ought to be reflected in the intercept

term rather than deleting them from the equations entirely.

As the size of the budget is decreased, the net mar-

ginal revenue product values increase for those activities

in solution. At the same time the distribution and magni-

tude of the allocations change. The rate of change for any

one product-region is dependent upon the degree of curvature

of the total net revenue functions. Differentiating the

total net revenue equations with respect to advertising

expenditures determines the marginal revenue product for

each product-region, but mathematically the first derivatives

are the slopes of the total net revenue functions. The budget

allocations are solved when the marginal net revenue product

functions are equated across all product-regions. There-

fore, the distribution of the budget among the product-

regions depends upon the relative slopes of the total net

revenue product curves. The amount of funds allocated to

product-regions with total net revenue functions that have

relatively steep slopes change more rapidly than the amount

of funds allocated to product-regions having total net rev-

enue functions that are less steep when the size of the

advertising budget is varied.

Since all product-regions are not included in the

allocation model, the budgetary implications are not fully

obvious. However, enough information is available to draw

some qualitative conclusions. By analyzing the budget







allocation by individual product forms it is seen that

large advertising expenditures are allocated to frozen con-

centrated orange juice in almost all regions. Referring to

the $5.3 million budget allocation in Table 4, the $59,614

allocation to the Mountain Region is most likely an over

estimation since the total revenue function for this product-

region is nonsignificant at the .05 level. Allocations to

canned single strength grapefruit juice are the largest

single sum of money in the whole allocation in the West

South Central Region and also the smallest allocation in

the Middle Atlantic Region. The small allocation in the

Middle Atlantic Region is partially due to the fact that the

total revenue function estimated for that product-region was

found to be nonsignificant at the .05 level. The funds allo-

cated to chilled orange juice were restricted to the fewest

number of regions of any product because of the nonnegativity

restrictions placed upon the model. Nonetheless, allocations

to chilled orange juice are significant in the Pacific and

Middle Atlantic Regions.

From the nature of the national consumption patterns

of Florida citrus products the allocation of the maximum,

economically feasible budget does not depart too far from

reality in total. The results indicate that frozen concen-

trated orange juice requires the largest expenditure in the

more populated regions. Canned single strength orange juice

requires the greatest amount of expenditures in the south-

eastern quadrant of the United States. Chilled orange juice







allocations are the most significant in regions having high

per capital incomes. Canned single strength grapefruit juice

allocations are strongest in the big markets in the eastern

half of the United States.

The allocation model shows the changes in the distri-

bution of advertising expenditures that occur when the adver-

tising budget departs from its optimal value. The results

show that advertising in the Middle Atlantic Region is most

advantageous only when large advertising budgets are available.

Advertising in the East North Central Region is not optimally

feasible at budgetary levels below $3.0 million per year.

The allocation of expenditures for the selected range of

budgets is most evident for canned single strength grapefruit

juice in the New England, Middle Atlantic, and South Atlantic

Regions. Advertising expenditures for canned single strength

orange juice in the South 'Atlantic Region and chilled orange

juice in the Pacific Region are highly stable at all bud-

getary levels. The stability of chilled orange juice in the

Pacific Region may be in part due to the inherent competitive

position of native California chilled orange juice.

The budget allocations in Table 4 were aggregated by

geographical region and by product form to measure the

percentage distribution of the expenditures by regions and

by products as the size of the advertising budgets were in-

creased. Table 5 shows the percentage distributions of the

various processed product budgets allocated by geographical

region. For the most part, the percentages fluctuated in







Table 5. Processed Products. Percentage of the
Florida Citrus Commission's Annual Advertising Budget
Allocated by Geographical Regions for Various Sized Budgets



Region Annual Advertising Budget
(million dollars)

5.3 4.7 3.3 1.9 0.5


- - - (percent)- - - - -

New England 9.7 10.4 13.9 12.8 11.4

Pacific 9.8 9.5 6.3 9.0 34.0

Mountain 13.8 14.9 18.4 20.7 0.0

West North Central 3.9 3.5 0.0 0.0 0.0

West South Central 18.5 19.9 22.7 21.5 0.1

East North Central 10.1 10.4 8.0 0.0 0.0

East South Central 1.8 1.7 2.1 1.3 0.0

Middle Atlantic 19.5 15.7 12.6 16.7 42.5

South Atlantic 12.9 14.0 16.0 18.0 12.0

TOTAL 100.0 100.0 100.0 100.0 100.0




each region as the size of the budget was increased. Table

6 presents the percentage distribution of the various

budgets allocated among the product forms. Frozen concen-

trated orange juice accounts for one half of the budget

expenditures at the high budget levels. Canned single

strength orange juice accounts for the second largest allo-

cation followed by canned single strength grapefruit juice

and chilled orange juice. If more product-regions had met

the nonnegativity and concavity conditions of the allocation




66

Table 6. Processed Products. Percentage of the
Florida Citrus Commission's Annual Advertising Budget Allo-
cated by Product Form for Various Sized Budgets


Product Annual Advertising Budget
(million dollars)

5.3 4.7 3.3 1.9 0.5

- - - - -(percent)- - - - - -
CSSGJ 16.3 17.9 22.0 26.6 61.3
CSSOJ 22.6 24.5 29.4 34.4 4.7
FCOJ 52.3 49.1 41.4 29.8 0.0
COJ 8.8 8.5 7.2 9.2 34.0
TOTAL 100.0 100.0 100.0 100.0 100.0

aA list containing definitions of the symbols used
in this table may be found in Appendix A.

model, the percentage of the budgets allocated to canned

single strength grapefruit juice and chilled orange juice

would be increased. Nine product-regions for these two pro-

ducts do not meet either one or the other of the two conditions.


Alternative Advertising Budget Allocations
for Fresh Fruit

Annual budgets of $2.8, $2.5, $2.0, $1.5, and $1.0

million were used for the fresh fruit allocations, and the

marginal net revenue products for the fresh product-regions

in solution for the various budgets are $0.0, $2.27, $8.77,

$15.97, and $24.51, respectively. These marginal net re-

venue products are plotted in Figure 4. Table 7 presents

the allocations of the various sized advertising budgets

for fresh fruit. Four product-regions were omitted since

the total net revenue functions for these product-regions

did not conform to the sign requirements of the allocation

model.















25.0-

\


20.0- \


O- \

15.0- \
u
r)


o





-,







0.0 1.0 22 3.0 4.0

Advertising Budget
(Million Dollars)

Figure 4. Marginal Net Revenue Products for Given
Fresh Product Advertising Budgets







Table 7. Fresh Products. Monthly Allocation of
the Florida Citrus Commission's Annual Advertising Budget
by Product-Region for Various Sized Budgets



Product-a
Region Annual Advertising Budget
(million dollars)
2.8 2.5 2.0 1.5 1.0


FRFLO-NE

FRFLO-P

FRFLG-P

FRFLG-M

FRFLO-WNC

FRFLG-WNC

FRFLO-WSC

FRFLG-WSC

FRFLO-ENC

FRFLG-ENC

FRFLO-ESC

FRFLO-MA

FRFLO-SA

FRFLG-SA


8,870

22,986

7,853

2,988

497

7,469

13,100

5,893

43,296

77,861

8,604

39,019

29,687

130,180


- -(doll

8,110

5,462

7,024

2,871

0.

7,256

10,990

5,425

40,176

74,511

8,385

34,800

28,652

123,480


ars)- - - -

5,946 3,546

0 0

4,663 2,045

2,538 2,168

0 0

6,649 5,976

4,977 0

4,089 2,607

31,279 21,419

64,960 54,375

7,761 7,069

22,774 9,444

25,700 22,428

104,380 83,209


aA list containing definitions of
this table may be found in Appendix A.


the symbols used in


699

0

0

1,729

0

5,178

0

850

9,716

41,812

6,247

0

18,545

58,082


-------







The format of Table 7 is similar to that of Table 4

for the processed products. Of the regions reporting both

fresh Florida oranges and grapefruit, the allocations of

advertising expenditures are the greatest for grapefruit

except for the Pacific and West South Central Regions. The

inconsistent results may be explained by the fact that the

estimates of the total revenue equations in these two regions

are nonsignificant at the .05 level. The seemingly high

allocation to fresh oranges in the Pacific Region and the

low allocation to fresh oranges in the East South Central

Region may be due to the nonsignificance of the total re-

venue equations in those product-regions. Both regions in

question are suppliers of fresh fruit, so the inconsis-

tencies may reflect the competitive strength of their do-

mestic products. The conclusion that may be drawn from

Table 7 is that grapefruit are allocated more advertising

funds than oranges. This fact can be substantiated by the

fact that the utilization of the Florida grapefruit crop in

fresh form is greater than the utilization of the Florida

orange crop in fresh form.

The budget allocations in Table 7 were aggregated

by geographical region and by product form to measure the

percentage distribution of the advertising expenditures as

the size of the fresh product advertising budgets was in-

creased. The percentage distribution by region of the

budget allocations for fresh fruit are presented in Table 8.

The East North Central and South Atlantic Regions accounted







Table 8. Fresh Products. Percentage of the Florida
Citrus Commission's Annual Advertising Budget Allocated
by Geographical Regions for Various Sized Budgets



Region Annual Advertising Budget
(million dollars)

2.8 2.5 2.0 1.5 1.0


- - - -(percent)- - - --

New England 2.2 2.3 2.1 1.7 0.5
Pacific 7.7 3.5 1.6 1.0 0.0
Mountain 0.8 0.8 0.9 1.0 1.2
West North Central 2.0 2.0 2.3 2.8 3.6
West South Central 4.8 4.6 3.2 1.2 0.6
East North Central 30.4 32.1 33.7 35.4 36.1
East South Central 2.2 2.3 2.7 3.3 4.4
Middle Atlantic 9.8 9.7 8.0 4.4 0.0
South Atlantic 40.1 42.7 45.5 49.2 53.6

TOTAL 100.0 100.0 100.0 100.0 100.0



for the larger percentages of the budgets. The percentages

of the budgets allocated to the New England, Pacific, West

South Central, and Middle Atlantic Regions increased as the

size of the advertising budget increased, and the percentages

of the budgets allocated to the other regions decreased.

Table 9 shows the percentage distribution of the budgets

by product form. As the size of the budgets increased, the

percentage allocated to fresh grapefruit declined, and the

percentage allocated to fresh oranges increased.







Table 9. Fresh Products. Percentage of the Florida
Citrus Commission's Annual Advertising Budget Allocated
by Product Form for Various Sized Budgets




Producta Annual Advertising Budget
(million dollars)

2.8 2.5 2.0 1.5 1.0


- - - - (percent)- - - - - --

FRFLO 41.7 38.2 34.5 29.8 24.6

FRFLG 58.3 61.8 65.5 70.2 75.4

TOTAL 100.0 100.0 100.0 100.0 100.0


aA list containing definitions of the symbols used
in this table may be found in Appendix A.


Estimated Total Net Revenues Derived from Alternative
Budget Allocations

In order to understand the implications of the calcu-

lated allocation schemes above, the estimated total net

revenue figures that would result from these theoretical

budgets are presented in Tables 10 and 11. The optimal

annual budget of $5.3 million for processed products would

result in total net receipts of $33,548,668 per month.

As the size of the budget was reduced to $0.5 million annu-

ally, the total net revenue received would drop to $32,172,654

per month. Without any advertising expenditures the sum of

the intercepts of all the total net revenue equations for

processed products equals $32,917,795 per month. The imple-

mentation of $5.3 million budget yields a $730,873 differen-















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tial of net revenue over cost per month as a result of

generic advertising. Due to the negative interaction of the

linear cross product terms of the total net revenue functions,

the $0.5 million budget yields a negative differential of

$645,141 per month. If the $2.8 million budget were imple-

mented for fresh fruit, the resulting total net revenue

would equal $19,774,221 per month for the seven month fresh

fruit season. Similarly the allocation of a $1.0 million

fresh fruit budget would yield $17,060,623 per month for

the seven month fresh fruit season. Summing the intercepts

of the total net revenue equations yields $11,601,816 per

month with no advertising expenditures. The optimal fresh

fruit budget would yield a differential of net revenue over

cost of $8,172,405 per month for the seven month fresh fruit

season.

A comparison of the differential revenues between the

processed and fresh products with and without advertising

expenditures may indicate fresh fruit expenditures are more

efficient in generating net revenue. There are several

factors to consider, however. First, economic resources

are allocated on a marginal basis, so the allocation of

funds for processed fruit products are equally efficient

as funds allocated for fresh fruit products when the mar-

ginal net revenue product for the processed products are

equal to the marginal net revenue products for the fresh

products. Of the budgets allocated only the 5.3 million

dollar processed product budget can be compared to the







2.8 million dollar fresh fruit budget since the marginal

net revenue products for each product-region in solution

in both allocations are zero.

The selling costs associated with the fresh fruit

allocations in this study were mass media advertising expendi-

tures, but a significant amount of local retail store pro-

motions are associated with the marketing of fresh fruit.

If the costs of these local retail promotions were added

to the mass media expenditures, the resultant allocations

might indicate less money should be used to advertise fresh

fruit. Therefore, the conclusions drawn from the present

allocations would be diluted in light of additional promo-

tional expenditures.

Another aspect of the allocation model is the fact

that the funds for processed products were allocated inde-

pendently of the fresh fruit budgets. Conversely, the fresh

fruit budgets were allocated independently of the processed

product budgets. One of the factors that limits the size

of the processed product allocations and calculated total

net revenue figures is the number of signs of the cross

product advertising variables. 'The processed product model

has two or three cross product variables in each product-

region which in most cases have one or more negative coeffi-

cients that are large in magnitude. The net effect of these

negative cross product effects limits the magnitude and

number of the advertising allocations in solution.







The cross product effects in the fresh fruit model

are limited to at most one variable, and the cross product

terms are for the most part positive and smaller than the

own product coefficients. Therefore, the net results of the

cross product effects in the fresh fruit model are addi-

tive while they are negative in the processed product model.

Some improvement could be made in the processed product

model with a greater knowledge of the lagged effects of

advertising within each product-region and if the true cross

product effects of advertising could be estimated with greater

accuracy. 'One factor that does hinder the measurement of

cross product effects is the reported data series for both

models. The lack of reporting fresh fruit on a twelve month

basis prevents allocating a total budget on a common time

period basis.


Composite Advertising Budget Allocation

Acknowledging the fact that the total revenue func-

tions for the processed products and the fresh products were

estimated independently by product forms, several allocations

were made to determine as a whole, which set of products has

the greater demand for budgetary funds. The results of these

allocations are presented in Table 12. The budgets used

were $8.1, $7.2, and $5.3 million. The size of these budgets

was the summation of the three largest budgets for processed

and fresh products in Tables 4 and 7. The $8.1 million

budget is the composite of the maximum unconstrained alloca-

tions with marginal net revenue products of zero dollars.







Table 12. Monthly Allocation of the Florida Citrus
Commission's Annual Advertising Budget by Product-Region
for Various Sized Budgets for Both Processed and Fresh
Products


P t-a Annual Advertising Budget
Product- (million dollars)
Region
8.1 7.2 5.3


CSSGJ-NE 6,039 5,933 5,838
CSSOJ-NE 0 0 0
FCOJ -NE 36,700 33,500 30,650
COJ -NE 0 0 0
FRFLO-NE 8,870 8,650 7,743
CSSGJ-P 4,785 4,105 1,189
FCOJ -P 23,296 14,171 0
COJ -P 15,315 15,167 14,529
FRFLO-P 22,986 18,073 0
FRFLG-P 7,853 7,620 6,624
CSSGJ-M 0 0 0
CSSOJ-M 0 0 0
FCOJ -M 59,614 55,856 39,730'
COJ -M 845 787 538
FRFLG-M 2,988 2,956 2,815
CSSGJ-WNC 0 0 0
CSSOJ-WNC 0 0 0
FCOJ -WNC 16,983 11,660 0
COJ -WNC 0 0 0
FRFLO-WNC 497 0 0
FRFLG-WNC 7,469 7,409 7,153
CSSOJ-WSC 61,345 57,588 41,462
FCOJ -WSC 19,969 17,414 6,448
COJ -WSC 0 0 0
FRFLO-WSC 13,100 12,508 9,970
FRFLG-WSC 5,893 5,762 5,198
CSSOJ-ENC 3,676 3,192 1,115
FCOJ -ENC 40,859 35,052 10,130
COJ -ENC 0 0 0
FRFLO-ENC 43,296 42,421 38,666
FRFLG-ENC 77,861 76,922 72,890







Table 12.--Continued.


Product-a Annual Advertising Budget
Region (million dollars)

8.1 7.2 5.3


- - - -(dollars)- - - - -

CSSGJ-ESC 5,948 5,387 4,887
FCOJ -ESC 1,953 810 0
COJ -ESC 0 0 0
FRFLO-ESC 8,604 8,543 8,279
CSSGJ-MA 39,830 38,378 32,148
CSSOJ-MA 180 0 0
FCOJ -MA 30,068 1,035 0
COJ -MA 15,515 7,531 0
FRFLO-MA 39,019 37,836 32,760
CSSGJ-SA 15,196 14,435 11,172
CSSOJ-SA 34,320 32,324 23,757
COJ -SA 7,074 6,331 3,143
FRFLO-SA 29,687 29,397 28,151
FRFLO-SA 130,180 128,300 122,150


used


A list containing definitions of the symbols
in this table may be found in Appendix A.





80

The marginal net revenue products for the other two allo-

cations were $0.64 and $1.21, respectively.

The results obtained in the allocations of the $7.2

and $5.3 million budgets were that the fresh fruit products

were awarded more money in the composite allocations than

they were awarded in the independent allocations. The

increased allocations to the fresh products appear incon-

sistent since the actual percentage of utilization of the

Florida citrus crop in fresh form is much less than the

utilization in processed forms. These findings are in part

due to the structure of the reported data where the fresh

fruit data were only reported on a seven month annual basis.

If the data series had been reported on a common time period

basis, the interaction effects could have been estimated

more accurately.


A Comparison of Historical and Theoretical
Advertising Budget Allocations

To gain further insight as to how the advertising

budgets have been allocated in the past, several repre-

sentative budgets were reallocated to determine the dcyree

of optimal allocation for each budget. The results of

these allocations are presented in Tables 13 and 15. To

represent a large crop year the 1966-67 budget was chosen,

to represent a small crop year the 1965-66 budget was chosen,

and to represent a medium-sized budget the mean of the seven

yeirs of budgets was calculated. Table 13 shows both the

historical and theoretical allocations of all three budget:;














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for the processed products. Both the historical and theoreti-

cal budgets are equal for any given year since the actual

funds spent at each budget level were summed, and these

sums were used to represent the theoretical budgets. The

marginal net revenue products for the 1966-67, mean 1960-67,

and 1965-66 budgets were calculated to be $0.11, $1.76, and

$3.00, respectively, for each product-region in solution.

The calculated total net revenues for each processed

product budget allocation is reported in Table 14. In

each case the theoretical total net revenues are greater than

the historical total net revenues. The historical total net

revenue figures show the 1966-67 receipts to be smaller than

the other two allocations. All three cases imply the histori-

cal budgets could have been more prudently expended, and the

1966-67 budget, which was the largest in the study period,

was severely misallocated.

Using the same three budget periods, the historical

and theoretical allocations for the fresh fruit products

were compared in Table 15. The marginal net revenue products

were $28.27, $31.89, and $30.24 for the 1966-67, mean 1960-67,

and 1965-66 budgets, respectively. The 1965-66 budget for

fresh fruit is not the smallest of the budgets as was the

case for the processed products. The three budgets were used

in order to make them compatible with the same processed

product budget periods.

















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