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 KuhnTucker 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 196061 through 196667. . . 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 ProductRegion 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 ProductRegion 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 ProductRegion Due to Optimum
Generic Advertising for Various Sized
Budgets. . . . . . . . . ... 72
11. Fresh Fruit. Monthly Total Net Revenue
Received by ProductRegion Due to Optimal
Generic Advertising for Various Sized
Budgets. . . . . . . . . .. 74
12. Monthly Allocation of the Florida Citrus Com
mission's Annual Advertising Budget by
ProductRegion 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
ProductRegion 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 ProductRegion for
Selected Budgets. . . . . . . . 84
15. Fresh Products. Historical and Theoretical
Monthly Allocations of the Florida Citrus
Commission's Annual Advertising Budget by
ProductRegion 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 ProductRegion 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 Productsby 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 NovemberMay, 1960
through 1967. . . . . . .. 186
50. Pacific Region. Estimated Retail Demand
Coefficients for Fresh Citrus Products
Using Equations [D.5] and [D.6] for
NovemberMay, 1960 through 1967. . .. 188
51. Mountain Region. Estimated Retail Demand
Coefficients for Fresh Citrus Products
Using Equations [D.5] and [D.6] for
NovemberMay, 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 NovemberMay, 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 NovemberMay, 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 NovemberMay, 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 NovemberMay, 1960 through 1967. . 198
56. Middle Atlantic Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for NovemberMay, 1960 through 1967. . 200
57. South Atlantic Region. Estimated Retail
Demand Coefficients for Fresh Citrus
Products Using Equations [D.5] and [D.6]
for DecemberMay, 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, 195759=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 anoptimum 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 productregion 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 selfhelp 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 193536 season to 188.1 million boxes in the 196667
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 13/5 bushels.
Table 1. Total Florida Orange and Grapefruit Produc
tion and Total Florida Citrus Commission Advertising Expendi
tures for all Citrus Products, Crop Years 196061 through
196667
Crop Orange Grapefruit Advertising
Year Production Production Expenditures
(million boxes)a (million dollars)
196061 86.7 31.6 3.06
196162 113.4 35.0 3.52
196263 74.5 30.0 3.09
196364 58.3 26.3 4.01
196465 86.2 31.9 2.96
196566 100.4 34.9 2.57
196667 144.5 43.6 8.79
One box equals 13/5 bushels.
Source: Annual Statistical Report, Florida Citrus
Mutual, Statistics and Economics Division, Lakeland, Florida,
196667 Season and Advertising Expenditure Files of the
Florida Citrus Commission, Lakeland, Unpublished, 196061
through 196667 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. 22541.
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. 21019.
13Sidney Hollander, Jr., "A Rationale for Advertising
Expenditures," Harvard Business Review, Vol. XXVII, No. 1,
January, 1949, pp. 7987.
14Joel Dean, "Cyclical Policy on the Advertising
Appropriation," Journal of Marketing, Vol. XV, January,
1951, No. 3, pp. 26573.
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 shortrun 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. 82636.
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 longrange advertising programs are: (1) the
price elasticity of demand, (2) the longrun 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. 81337.
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 firstorder conditions and the suffi
cient secondorder 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 JudgeWallace 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:
McGrawHill Book Company, 1958.
18T. Takayama and G. G. Judge, NonLinear 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. 80120.
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 KuhnTucker 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 TheilVan 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, "NonLinear 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. 48192.
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. 120.
2411. S. Houthakker, "The Capacity Method of Quadratic
Prograpui.ing,, EconometrJca,Vol.XXVIII,1960,pp. 6287.
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.23.
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, midseason,
and Valencia varieties. Ninetyfive 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 fiftyfour market combinations to which a
share of the annual budget can be committed. Therefore, there
are fiftyfour potential productmarkets 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 productregions.
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
productregions.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 semidefinite. 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 productregions
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 productregions 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 crosssectional observations.
The only time element used in the study was the attempt to
measure the lagged response to advertising expenditures in
estimating the productregion 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 productregion, and the second phase involved the
advertising allocation problem.
The technique used to estimate the productregion
total revenue equations was the method of leastsquares
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 productregion 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 productregions."
27
In singleequation 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 productregion. 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 196667 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 productregion. 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 pricequantity 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 productregions
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 semidefinite (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 KuhnTucker
conditions for optimality are satisfied.6 As in the calculus,
satisfying the KuhnTucker conditions assures at least a
local optimum.
The necessary condition of the KuhnTucker 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,
NorthHolland 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. 481492.
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 KuhnTucker 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 productregions 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, McGrawHill
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 productregions. 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 productregion
MNRP2 = marginal net revenue product derived in the
second productregion
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 productregions 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 semidefinite
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 giveaway 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 productregion 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 productregion, and the three remaining
linear advertising variables are used to estimate the secon
dary sources of revenue for each productregion 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 seventyeight 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 productregion.
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 productregion were of prime
concern. 'To meet the KuhnTucker 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 productregion, 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 productregions out of a possible thirtysix
productregions were found to have the necessary sign
properties of own product advertising to be used in the
allocation model. The productregions 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 productregions 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 productregions 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 productregion. 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 productregion are
presented in Appendix B.
Of the eighteen possible fresh fruit productregions,
fourteen were estimated having the necessary sign properties
of own product advertising to be used in the allocation
model. The four fresh productregions 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
productregions is more important than the omission of the
fresh orange productregion 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 productregion 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 thirtytwo 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
CSSGJNE .18 2.84 2.24 6 77
CSSOJNE .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
CSSGJP .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
CSSGJM .19 2.84 2.31 6 71
CSSOJM .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
CSSGJWNC .14 1.97c 2.31 6 71
CSSOJWNC .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
CSSOJWSC .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
CSSOJENC .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
CSSGJESC .49 12.32 2.24 6 77
CSSOJESC .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
CSSGJMA .33 6.24 2.24 6 77
CSSOJMA .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
CSSGJSA .30 5.19 2.31 6 71
CSSOJSA .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
Producta R2 F Fb Freedom
Region (calculated) tabularr) Regression Residual
FRFLONE .58 14.91 2.58 4 44
FRFLOP .10 1.21c 2.58 4 44
FRFLGP .21 2.97 2.58 4 44
FRFLGM .16 2.07c 2.58 4 44
FRFLOWNC .11 1.36c 2.58 4 44
FRFLGWNC .25 3.63 2.58 4 44
FRFLOWSC .07 0.84c 2.58 4 44
FRFLGWSC .21 2.99 2.58 4 44
FRFLOENC .47 9.57 2.58 4 44
FRFLGENC .29 4.39 2.58 4 44
FRFLOESC .14 1.85c 2.58 4 44
FRFLOMA .29 6.12 2.83 3 43
FRFLOSA .22 3.10 2.58 4 44
FRFLGSA .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 productregions 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 196162 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 timeseries data
is autocorrelation. The extent of autocorrelation was
tested by calculating a DurbinWatson d statistic for each
estimated total revenue equation. The DurbinWatson 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, McGrawHill
Book Company, Inc., 1963, pp. 177179.
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 productregion.
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 KuhnTucker 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 productregion 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
productregion 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 righthand side vector of the alloca
tion model.
'After the total net revenue equations for each
productregion 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 productregions. (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 productregion. 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 KuhnTucker 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
productregion, the most economically feasible budget was
determined. Budgets larger than this figure result in nega
tive net marginal revenue products for every productregion,
and budgets smaller than this figure result in positive net
marginal revenue products for every productregion 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 productregions 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 productregion 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
productregions.
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 ProductRegion for Various Sized Budgets
Projecta Annual Advertising Budget
Region (million dollars)
5.3 4.7 3.3 1.9 0.5
  (dollars)       
CSSGJNE 6,039 5,971 5,898 5,298 4,303
CSSOJNE 0 0 0 0 0
FCOJ NE 36,700 34,650 32,500 14,450 0
COJ NE 0 0 0 0 0
CSSGJP 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
CSSGJM 0 0 0 0 0
CSSOJM 0 0 0 0 0
FCOJ M 59,614 57,229 50,119 31,619 0
COJ M 845 808 637 288 0
CSSGJWNC 0 0 0 0 0
CSSOJWNC 0 0 0 0 0
FCOJ WNC 16,983 13,604 0 0 0
COJ WNC 0 0 0 0 0
CSSOJWSC 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
CSSOJENC 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
CSSGJESC 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
CSSGJMA 39,830 38,908 34,631 25,887 16,142
CSSOJMA 180 0 0 0 0
FCOJ MA 30,068 11,639 0 0 0
COJ MA 15,515 10,447 0 0 0
CSSGJSA 15,196 14,713 12,473 7,892 2,788
CSSOJSA 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
productregion 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 productregion 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 productregion, 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 productregions. 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
productregions with total net revenue functions that have
relatively steep slopes change more rapidly than the amount
of funds allocated to productregions having total net rev
enue functions that are less steep when the size of the
advertising budget is varied.
Since all productregions 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 productregion 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 productregions 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 productregions 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 productregions
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 productregions were omitted since
the total net revenue functions for these productregions
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 ProductRegion for Various Sized Budgets
Producta
Region Annual Advertising Budget
(million dollars)
2.8 2.5 2.0 1.5 1.0
FRFLONE
FRFLOP
FRFLGP
FRFLGM
FRFLOWNC
FRFLGWNC
FRFLOWSC
FRFLGWSC
FRFLOENC
FRFLGENC
FRFLOESC
FRFLOMA
FRFLOSA
FRFLGSA
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 productregions. 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 productregion 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 productregion 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 ProductRegion
for Various Sized Budgets for Both Processed and Fresh
Products
P ta Annual Advertising Budget
Product (million dollars)
Region
8.1 7.2 5.3
CSSGJNE 6,039 5,933 5,838
CSSOJNE 0 0 0
FCOJ NE 36,700 33,500 30,650
COJ NE 0 0 0
FRFLONE 8,870 8,650 7,743
CSSGJP 4,785 4,105 1,189
FCOJ P 23,296 14,171 0
COJ P 15,315 15,167 14,529
FRFLOP 22,986 18,073 0
FRFLGP 7,853 7,620 6,624
CSSGJM 0 0 0
CSSOJM 0 0 0
FCOJ M 59,614 55,856 39,730'
COJ M 845 787 538
FRFLGM 2,988 2,956 2,815
CSSGJWNC 0 0 0
CSSOJWNC 0 0 0
FCOJ WNC 16,983 11,660 0
COJ WNC 0 0 0
FRFLOWNC 497 0 0
FRFLGWNC 7,469 7,409 7,153
CSSOJWSC 61,345 57,588 41,462
FCOJ WSC 19,969 17,414 6,448
COJ WSC 0 0 0
FRFLOWSC 13,100 12,508 9,970
FRFLGWSC 5,893 5,762 5,198
CSSOJENC 3,676 3,192 1,115
FCOJ ENC 40,859 35,052 10,130
COJ ENC 0 0 0
FRFLOENC 43,296 42,421 38,666
FRFLGENC 77,861 76,922 72,890
Table 12.Continued.
Producta Annual Advertising Budget
Region (million dollars)
8.1 7.2 5.3
   (dollars)    
CSSGJESC 5,948 5,387 4,887
FCOJ ESC 1,953 810 0
COJ ESC 0 0 0
FRFLOESC 8,604 8,543 8,279
CSSGJMA 39,830 38,378 32,148
CSSOJMA 180 0 0
FCOJ MA 30,068 1,035 0
COJ MA 15,515 7,531 0
FRFLOMA 39,019 37,836 32,760
CSSGJSA 15,196 14,435 11,172
CSSOJSA 34,320 32,324 23,757
COJ SA 7,074 6,331 3,143
FRFLOSA 29,687 29,397 28,151
FRFLOSA 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 196667 budget was chosen,
to represent a small crop year the 196566 budget was chosen,
and to represent a mediumsized 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 196667, mean 196067,
and 196566 budgets were calculated to be $0.11, $1.76, and
$3.00, respectively, for each productregion 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 196667 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
196667 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 196667, mean 196067,
and 196566 budgets, respectively. The 196566 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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