O
6(7/3
Agricultural Economics
Research Report EC 6713
April 1967
THE DEMAND FOR
FROZEN CONCENTRATED ORANGE JUICE
Arlo J. Minden
MAY 8 1967
Y E onomic Research Department
SF Florida Citrus Commission
in cooperation with the
Department of Agricultural Economics
Agricultural Experiment Stations
University of Florida, Gainesville
Agricultural Economics
Research Report EC 6713
April 1967
THE DEMAND FOR FROZEN CONCENTRATED
ORANGE JUICE
Arlo J. Minden
Economic Research Department
Florida Citrus Commission
in cooperation with the
Department of Agricultural Economics
Agricultural Experiment Stations
University of Florida, Gainesville
TABLE OF CONTENTS
Page
SUMMARY ....................... 1 1
THE DEMAND FOR FROZEN CONCENTRATED ORANGE JUICE . 2
PREVIOUS STUDIES . . . . . .... 3
Results of Analysis . . . .... ... 4
Seasonal Changes and Shifts . . .. 9
Projections for Periods of Low Prices . . 13
BIBLIOGRAPHY ................... ....... 16
THE DEMAND FOR FROZEN CONCENTRATED ORANGE JUICE
by
Arlo J. Minden*
SUMMARY
This paper considers the problems of estimating a consumer demand
function for frozen concentrated orange juice, estimating critical
pricing points, estimating changes in the structure and level of demand
resulting from the December 1962 freeze and projecting future price
quantity relationships. Answers to these questions should be helpful
to research workers, policy makers and businessmen concerned with the
demand for frozen concentrated orange juice.
Several studies have been made of the retail demand for frozen
concentrated orange juice. Most of these studies have been concerned
with estimating the elasticity of consumer demand for frozen concentrated
orange juice (FCOJ). However, a plot of monthly retail purchases of FCOJ
against monthly average prices paid suggested that a single linear function
may overstate the pricequantity relationship in certain ranges of the
observations since 1961 and understate it in others.
The results obtained suggest that the demand function for FCOJ is
elastic at prices above 25 cents per 6 oz. can. Price reductions in
the range 28.2 to 25 cents may be associated with increased sales revenue.
A one percent decrease in retail price in this range cbuld generate a 1.93
percent increase in quantity purchased. Price decreases in the range 23 to
*Arlo J. Minden was formerly Research Economist with the Florida
Citrus Commission and Assistant Professor, Florida Agricultural Experiment
Stations, University of Florida, Gainesville, Florida.
2
about 20 cents may actually result in reduced sales revenue. Price reductions
in the range 19 to 16.7 cents may be associated with increased sales
revenue while price reductions below 16.7 cents per 6 oz. can may again
result in reduced sales revenue.
The demand for FCOJ became quite elastic during the few months following
the 1962 freeze. During the 1963 season, because of price and availability
conditions, the level of demand was lower than for any other period studied
and the price elasticity was lower than the months immediately following the
freeze but about the same as for prefreeze period (level refers to the
position of the whole demand curve). The level of demand increased from the
low in 1963 to prefreeze levels or above by January 1966. The retail price
elasticity of demand for FCOJ was1.03 at a retail price of 16.7 cents per
6 oz. can for the 196466 period; slightly more elastic than during the
prefreeze period at the same price.
Projections of pricequantity relationships were made for the 196667
and 196768 seasons. Retail sales of 78 million gallons of FCOJ in 196667
were predicted to earn an average retail price of 15.2 cents per 6 oz. can.
Retail sales of 86.7 million gallons of FCOJ in 196768 were estimated to
result in an average retail price of 13.3 cents per 6 oz. can.
THE DEMAND FOR FROZEN CONCENTRATED ORANGE JUICE
This paper considers the problems of estimating a consumer demand
function for frozen concentrated orange juice, estimating critical pricing
points, estimating changes in the structure and level of demand resulting
from the December 1962 freeze and projecting future price and quantity
relationships.
3
Frozen concentrated orange juice (FCOJ) utilizes about 65 percent
of the annual Florida orange crop and generates retail sales of about
$346.43 million annually, about 41 percent of total retail revenue from
the sale of Florida citrus products. Since sales of FCOJ generate more
revenue than the sale of any other Florida citrus products, it is necessary
and useful to understand the pricequantity relationships demonstrated in
the market for FCOJ in the past when trying to anticipate future demand
conditions.
PREVIOUS STUDIES
Several studies have been made of the retail demand for frozen con
centrated orange juice. Most of these studies have been concerned with
estimating the consumer demand elasticity for FCOJ. Henderson (1) studied
demand and substitution relationships between nationally advertised, private
label and packer brands of FCOJ and estimated the demand elasticity for all
brands to be1.49 for price increases and1.75 for price decreases during
a period in 1964. Riggan (6) using timeseries data found the price
elasticity of demand for FCOJ to be1.00. Stout (7) has estimated the
price elasticity of demand for FCOJ to be in the range2.44 to3.86.
Recent studies by Polopolus (4) and Minden (3) have yielded price elasticity
estimates for FCOJ of1.25 and1.03,respectively. The several elasticity
estimates referred to above were generated over different time periods
and using different types of data. Due to the variation of these estimates,
it is difficult to confidently specify what historical pricequantity
relationships have been; or to make projections for the future. Langham (2)
has considered the problem of structural changes in the demand for FCOJ
as a result of supply restrictions caused by freezes. He found by comparing
4
demand functions for the periods following the freezes of 195758 and
196263 that the demand for FCOJ became more elastic between these two
freeze periods. Langham estimated the price elasticity of demand for
FCOJ to be1.23 for 195758 and1.58 for 196263. However, he found
that the two functions gave elasticity estimates of1.62 and1.58 for
195758 and 196263 respectively, when the elasticities were computed
at the mean 196263 prices. In addition to a restructuring of demand,
he showed an increase in the level of demand for FCOJ between the two
freeze periods.
Most earlier studies of the demand for FCOJ have been concerned with
estimating a single linear demand function. A plot of the monthly retail
purchases of FCOJ against monthly average prices paid (as reported in data
obtained from Market Research Corporation of America and adjusted for
sampling bias by the Economic Research Department of the Florida Citrus
Commission) suggested that a single linear function may overstate the
pricequantity relationship in certain ranges of the observations since
1961, and understate it in others.
Results of Analysis
Adjusted monthly purchases of frozen concentrated orange juice in
millions of gallons were regressed on estimated average monthly retail
price of FCOJ per 6 oz. can for the period December 1961 to January 1966.
The estimated price elasticity of demand computed at the means of the price
and quantity series using Equation 1.0 was1.18. Equation 1.0 was estimated
as:
(1.0) Q (in thousands) = 10,458.8 260.06 P
and is presented in graphic form in Figure 1 as Curve I.
5
The plot of monthly retail purchase and price data suggested that
price response breaks may occur in the neighborhood of 19 cents per 6
oz. can and 25 cents per 6 oz. can of FCOJ. The price elasticity of
demand for FCOJ was calculated to be0.90 and1.44 at retail prices and
19 and 25 cents per 6 oz. can, respectively, based on Equation 1.0.
The mean price of observations when price was greater than 25 cents per
6 oz. can was 26.7 cents, for the range 19 cents to 24.9 cents, the
mean was 21.2 and for the observations below 19 cents per 6 oz. can the
mean price was 17.0 cents. The price elasticities of demand computed
at the mean prices for each of these three price ranges using Equation 1.0
were found to be1.93,1.10 and0.73; respectively.
Using Equation 1.0 in Figure 1 we see that the demand for FCOJ is
elastic above a retail price of 20.1 cents per 6 oz. can and inelastic
below that price. A one percent decrease in price in the range 28.2 cents
to 20.1 cents per 6 oz. can is associated with a greater than one percent
increase in monthly quantity purchased. These results suggest that total
sales revenue will increase as the retail price of FCOJ decreases in the
range 28.2 cents to 20.1 cents. The average demand function represented
by Curve I in Figure 1 also suggests that for price decreases below 20.1
cents per 6 oz. can total sales revenue will decrease. A one percent decline
in price is associated with a less than one percent increase in quantity
purchased; or the demand for FCOJ is price inelastic at prices below 20.1
cents.
With no other information than that obtained from the average demand
function in Figure 1, one may conclude that price could be reduced and
revenues increased in the range of prices 28.2 cents to 20.1 cents per
6
6 oz. can. However, it has been observed in the Florida citrus industry
that the price responsiveness of retail purchases is not as continuous
as implied by the average demand curve.
A set of dummy variables was specified in an attempt to determine
whether or not there was a restructuring of the demand for FCOJ as a
result of price movements and to isolate critical price points or regions
as inflection points on the demand curve. The following set of dummy
variables was constructed to test for changes in the intercept or level
of the demand curve.
D, = 1 where retail price is>25.0 cents
= 0 elsewhere
D2 = 1 where retail price is<25.0 cents and 719.0 cents
= 0 elsewhere
D = 1 where retail price is 19.0 cents
= 0 elsewhere
A statistically significant coefficient associated with any of the
variables D1, D2, or D3 suggests a departure from the average intercept
or level of demand for other price conditions associated with a particular
price range. A change in the intercept may reflect a change in the level
of demand if the slope coefficient remains constant.
In addition to changes in the intercept of level of the demand curve
we are interested in changes in the slope of the curve or changes in the
structure of demand. Another set of dummy variables was specified as
follows:
D4 = price for the month when price was 725.0 cents
= 0 elsewhere
D5 = retail price when price was<25.0 cents and 719.0 cents
= 0 elsewhere
D6 = retail price when price was 419.0 cents
= 0 elsewhere
7
A statistically significant coefficient for D4, D5, or D6 suggests a
change in the slope or structure of demand resulting from particular
price conditions. The sign of the variables, D1, D2, ., D,
specifies the direction of the change.
Estimated demand functions for the three price ranges, P725 cents,
25.0 >P719.0 cents, and P<419.0 cents, are presented in Table 1. These
functions are expressed graphically in Figure 1 and are labeled II, III
and IV, respectively. Curve II in Figure 1 may provide a more accurate
base for making price decisions when the retail price of FCOJ is above
25 cents per 6 oz. can than Curve I. The level of demand at high prices
is overstated by the aggregate demand curve; however, the elasticity at
the mean of observations where price was above 25 cents is about the
same for Curves I and II, about1.93. The retail demand function for
FCOJ becomes more inelastic and shifts to the right as the retail price
falls below 25 cents as suggested by the relative position of Curve III
in Figure 1. Below 19 cents per 6 oz. can, the demand for FCOJ becomes
slightly more elastic than when the price was between 25 cents and 19
cents.
Table 1. Estimated demand functions for FCOJ for various price conditions;
Quantity in thousands of gallons of FCOJ per month.
Coefficient of
Constant Price (P) Price Condition
10234.5 253.4 (P) P 225.0 cents
9364.2 198.2 (P) 25.0 P 719.0 cents
12099.5 360.6 (P) P Z 19.0 cents
A comparison of the price elasticities of demand for frozen concentrate
7A
30
29
28 Average Curve 196166
27
c
U
o
26
0
w 25 III
U
u
24
I4
22
S 20
o
19IV
18
S17
,4
220
16
2 Mill 3 Mill 4 Mill 5 Mill 6 Mill 7 Mill
Monthly Average Retail Purchases (In Millions Gallons)
Figure 1. Aggregate Demand Functions for FCOJ
8
estimated from each of the four functions represented by Curves I, II,
III, and IV in Figure I is made in Table 2.
Table 2. Comparison of Price Elasticities of Aggregate Demand Functions
Retail Price
(cents per
6 oz. can) Curve I Curve II Curve III Curve IV
26.7 1.93 1.94 
21.2 1.10 0.73
17.0 0.73 1.03
The results in Table 2 suggest that the demand function for FCOJ is
elastic at prices above 25 cents per 6 oz. can. Price reductions in the
28.2 to 25 cent range may be associated with increased sales revenue. A
one percent decrease in retail price could generate about a 1.93 percent
increase in quantities purchased.
The aggregate demand function fit over the entire range of data 1961
to 1966 suggests the price elasticity of demand for FCOJ to be 1.10 at the
mean of the observation when price was between 25 cents and 19 cents per
6 oz. can. The price elasticity of demand estimated from the second
equation in Table 1 at the same mean price and quantity was0.73. Price
decreases in the range from about 23 cents to about 20 cents per 6 oz.
can may actually result in reduced gross sales revenue. Actual observations
in the Florida citrus industry support the estimated inelasticity in the
price range 23 to 20 cents per 6 oz. can.
The price elasticity of demand at the mean of prices below 19 cents
was estimated to be1.03. The demand function for FCOJ was found to be
elastic in the price range 19 cents to about 16.7 cents and inelastic
at prices below 16.7 cents. Consequently, price reductions in the 19
cents to 16.6 cents range may be associated with increased sales revenue
whereas price reductions below 16.7 cents may again result in reduced
sales revenue.
Seasonal Changes and Shifts
Seasonal changes in the structure and level of demand for frozen
concentrated orange juice were estimated by the same procedure used to
estimate changes in the aggregate demand function. The general model
Q = cf lP + P2Zl + P32 + 4Z3 + 5z4
was used to test for slope and intercept changes in the demand functions
for the 1961, 1962, 1963 and 196466 citrus production periods. Q is the
average monthly retail purchases of FCOJ in gallons, P is the monthly
average retail price of FCOJ in cents per 6 oz. can.
Three applications of the general model were made for each crop
season. They were:
1) Q = P + 2Zl + P3Z2
2) Q = a +P + l 2Z + 4 3
3) Q a P P + P 3Z + p
which tested quantity intercept and slope differences for a given season
under conditions when the retail price per 6 oz. can of FCOJ was 725.0
cents, L25.0 cents and L19.0 cents. The coefficient associated with ZI,
2', reflects the direction and magnitude of the quantity intercept or
demand level differences from the mean intercept for the particular year
(denoted byA). The coefficients associated with the dummy variables Z2,
Z3, and Z4 indicate the direction and magnitude of slope differences from
10
the mean slope for a given year, under various price conditions,
Adjusted seasonal demand functions for FCOJ are presented in Table 3.
It is recognized that the estimates presented here may be biased because of
problems of over and under identification.
It is possible to suggest the direction and statistical significance
of changes in the level and structure of the demand for FCOJ under various
price conditions for each the 1961, 1962, 1963 and 196466 production
periods. The 1961 Florida orange crop was one of the largest in history.
The level of demand for FCOJ during the last eight months of 1961 was greater
than the average level of demand for the remainder of the study period.
The price elasticity of demand for the period in 1961 when the price of
FCOJ was below 19 cents was0.73, computed at the means.
Table 3. Adjusted Seasonal Demand Functions for FCOJ.a
Price Intercept Slope
Year Conditions Constant Coefficient Change Change
A 1961 P 425 7,504,491 81,454 
B 1961 P<19 10,712,326 271,938 + +
C 1962 P 25 10,233,692 227,727 
D 1962 P 25 10,664,463 269,842 + +
E 1962 P<19 10,296,533 216,644 +
F 1963 P225 5,874,777 92,010 
G 196466 P25 10,404,058 233,138 +
H 196466 P25 10,944,136 300,416 + +
I 196466 P l19 11,319,751 334,540 + +
a There were no observations at prices 25 cents per 6 oz. can in 1961 or
425 cents per 6 oz. can in 1963.
* Represents significant slope and intercept changes for various price
conditions for each season for the 1961 to 1966 season at the 90% level of
confidence.
10A
30
29
28
.F
27
26
.\ I
= 25
o 24
) D
23 G
*4
04
0 22
t 21
> A
20
4
4.1
o 19
H B
18
17
16 C
2 Mill 3 Mill 4 Mill 5 Mill 6 Mill 7 Mill
Monthly Retail Purchases (Million Gallons)
Figure 2. Seasonal Demand Functions for FCOJ
11
A severe freeze occurred in Florida, December of 1962. The price
elasticity of demand for orange concentrate during the first three months
of the 1962 season, the period before the supply was restricted as a result
of the freeze, was about0.50./ The comparison of demand relationships
for the last eight months of the 1961 season and the first three months of
the 1962, B and E in Table 3, suggests that during these two periods the
price responsiveness of retail purchases declined slightly. It is highly
possible that fewer new purchasers entered the market as the retail price
declined at low absolute values and that existing purchasers did not expand
their purchases of FCOJ as rapidly because of a relative satisfaction of their
demand for the product. The price elasticity of demand for the first three
months following the 1962 freeze was about0.83 at a retail price of 22.5
cents per 6 oz. can./ During the last six months of the 1966 season, the
monthly average retail price of FCOJ increased from 25.4 cents to 28.0 cents
per 6 oz. can. The price elasticity of demand for the last six months of
the 1962 season was2.29, a significant increase from the prefreeze estimate
of0.50.
The large increase in price elasticity of demand for FCOJ from pre
freeze to postfreeze periods was to be expected as a result of the price
increases associated with the reduced supply. Consumers who purchased
FCOJ even during large price increases apparently had a much stronger
preference for FCOJ than many of those who purchased FCOJ at prefreeze
price levels. The high price elasticity of demand in the postfreeze
1/ This elasticity estimate was calculated directly from the raw data
because of the low number of observations.
2/ Again, this elasticity estimate was calculated from raw data since
there were insufficient observations for more rigorous estimating procedures.
12
period of 1962 reflects an apparent disloyalty of FCOJ consumers during
the periods of increasing FCOJ prices. No consideration is given to the
income elasticity of demand for FCOJ at this point. It may be, however,
that at higher prices people in lower income classes who purchased FCOJ
were forced out of the market by budget limitations as the price increased.
The level of demand for FCOJ was little different for the three price
conditions which prevailed in 1962 although there was a significant change
in the slope of the function for each of these conditions.
The retail price of frozen concentrated orange juice was above 25 cents
per 6 oz. can for the entire 1963 crop. season. The results in Table 3
suggest that the level of demand during the 1963 season was much lower
than for any other period studied. The price elasticity of demand at the
mean of the prices prevailing in 1963 was estimated to be0.70. The
demand curve not only shifted to the left in the 1963 season, but it became
more inelastic. Consumer purchases responded less to price changes in the
1963 season than any time since the freeze of 1962. Few new consumers
entered the market at the price level prevailing in 1963 and existing
consumers did not significantly expand their purchases of FCOJ. Of course,
the limited availability of the product in retail outlets during the 1963
season confounds the true price responsiveness of purchases during that
period.
The period 1964 to January 1966 is generally considered the major
period of recovery from the 1962 freeze. The results in Table 2 suggest
that the level of demand for FCOJ during the recovery period reached and
perhaps exceeded the level of demand which existed during the prefreeze
period. The price elasticity of demand for FCOJ during the 1964 to 1966
period when the retail price was 225.0 cents, <25.0 cents and <19.0 cents
13
per 6 oz. can was1.39,1.07, and1.08, respectively. The seasonal adjusted
demand functions are plotted in Figure 2. It is not possible to extend
the functions beyond the limits shown because of the absence of observations
necessary for such extension.
In summary, the results in Table 3 and Figure 2 suggest that the price
responsiveness of the demand for frozen concentrated orange juice increased
during the few months immediately following the 1962 freeze. During the
1963 season, because of price and availability conditions, the level of
demand was lower than any other period studied and the price elasticity
was lower than the months immediately following the freeze but about the
same as for the prefreeze periods. The level of demand increased from
a low in 1963 to prefreeze levels or above during the period 1964 to 1966.
The retail price elasticity of demand for FCOJ was1.03 at a price of 16.7
cents per 6 oz. can for the 1964 to 1966 period; slightly more elastic
than during the prefreeze period at the same price.
Projections for Periods of Low Prices
Rapid increases are expected in Florida citrus production in the five
years 1966 to 1971. Larger crops suggest lower retail prices for frozen
concentrated orange juice. To provide a basis for projecting future price
quantity relationships for FCOJ, a demand function was estimated using
monthly observations when the retail price of FCOJ was below 18.5 cents
per 6 oz. can for the period 1952 to 1966.
Variables considered in the analysis were:
1. adjusted monthly retail purchases of FCOJ as reported by
Market Research Corporation of America.
2. retail price per 6 oz. can of FCOJ deflated by the consumer
price index (195759 = 100).
14
3. per capital personal income deflated by the consumer price
index (195759 = 100).
The estimated function was:
(1.2) Q = 4762.3 261.21P + 18.42PPI
where Q is quantity or retail purchases of FCOJ in thousands of gallons
per month, P is the deflated monthly average retail price per 6 oz. can
and PPI is the deflated monthly per capital personal income measured in tens
of hundreds of dollars.
Given the prediction equation above, the following assumptions were
made when projecting future pricequantity relationships. Per capital
personal income was assumed to increase at the same rate from 1965 to 1967
as during the past five years, 3.96 percent per year. In 1965 the deflated
per capital income level was $2500. Per capital personal income was projected
to be $2599 and $2702 in 1966 and 1967 respectively. These income pro
jections incorporate a growth in per capital personal income of 3.96 per
cent per year and an increase in the consumer price index of one percentage
point per year. The consumer price index for the 196566 crop season was
111.0 and is projected to 112.0 and 113.0 in the 196667 and 196768 crop
seasons respectively.
Projections of pricequantity relationships were made for the 196667
and 196768 seasons using the prediction equation, 1.2. If the 196667
retail movement of frozen concentrated orange juice were to be 78 million
gallons, or about 6 million gallons per month, the equation suggests an
annual average retail price of 15.2 cents per 6 oz. can, in current dollars.
A retail pack of 86.7 million gallons in the 196768 crop season would
result in an average annual retail price of 13.3 cents per 6 oz. can, in
current dollars.
15
The projection procedure used assumes that all relationships between
the variables in the prediction equation will be the same during the 1966
67 and 196768 seasons as they were during past periods when the annual
average retail price of frozen concentrated orange juice fell below 18.5
cents per 6 oz. can. The monthly average retail purchases are in terms
of a 41.80 brix concentrate. A 44.80 brix concentrate will be marketed
during the 196667 and 196768 crop seasons.
BIBLIOGRAPHY
1. Henderson, Kenneth Robert. Demand and Substitution Relationships
for Frozen Orange Concentrate. Unpublished thesis. Department
of Agricultural Economics, University of Florida, Gainesville,
Florida, 1965.
2. Langham, Max R, OnTree and InStore Citrus Price Relationships.
Unpublished paper. Department of Agricultural Economics,
University of Florida. Gainesville, Florida, 1965.
3. Minden, Arlo J. Quadratic Programming: A Tool for Estimating
Optimal Final Product Combinations. Forthcoming in the
Southern Journal of Business.
4. Polopolus, Leo and Black, W..E. Synthetics and Substitutes and
the Florida Citrus Industry. Economic Research Department,
Florida Citrus Commission, Lakeland, Florida, 1966.
5. Rice, T. G., Williams, F. W. and Godwin, M. R. Demand and
Substitution Relationships for Florida Orange Juice in Drug
Stores. Department of Agricultural Economics, Agricultural
Experiment Stations, University of Florida, Gainesville,
Florida, 1966.
6. Riggan, Wilson B. Demand for Florida Oranges. Unpublished thesis,
Department of Agricultural Economics, University of Florida,
Gainesville, Florida, 1965.
7. Stout, Roy G. Use of Price Elasticities by Firms or Commodity
Association in Planning Special Price Promotional Activities.
Unpublished paper.
