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O

6(7-/3
Agricultural Economics
Research Report EC 67-13
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 67-13


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 price-quantity 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 pre-freeze period (level refers to the

position of the whole demand curve). The level of demand increased from the

low in 1963 to pre-freeze levels or above by January 1966. The retail price

elasticity of demand for FCOJ was-1.03 at a retail price of 16.7 cents per

6 oz. can for the 1964-66 period; slightly more elastic than during the

pre-freeze period at the same price.

Projections of price-quantity relationships were made for the 1966-67

and 1967-68 seasons. Retail sales of 78 million gallons of FCOJ in 1966-67

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 1967-68 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 price-quantity 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 be-1.49 for price increases and-1.75 for price decreases during

a period in 1964. Riggan (6) using time-series data found the price

elasticity of demand for FCOJ to be-1.00. Stout (7) has estimated the

price elasticity of demand for FCOJ to be in the range-2.44 to-3.86.

Recent studies by Polopolus (4) and Minden (3) have yielded price elasticity

estimates for FCOJ of-1.25 and-1.03,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 price-quantity

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 1957-58 and

1962-63 that the demand for FCOJ became more elastic between these two

freeze periods. Langham estimated the price elasticity of demand for

FCOJ to be-1.23 for 1957-58 and-1.58 for 1962-63. However, he found

that the two functions gave elasticity estimates of-1.62 and-1.58 for

1957-58 and 1962-63 respectively, when the elasticities were computed

at the mean 1962-63 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

price-quantity 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 was-1.18. 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 be-0.90 and-1.44 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 be-1.93,-1.10 and-0.73; 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, about-1.93. 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










7-A


30



29


28 Average Curve 1961-66



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 was-0.73. 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 be-1.03. 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 1964-66 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 1964-66 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 was-0.73, 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 1964-66 P25 10,404,058 -233,138 +
H 1964-66 P-25 10,944,136 -300,416 + +
I 1964-66 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.










10-A



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 about-0.50.-/ 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 about-0.83 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 was-2.29, a significant increase from the pre-freeze estimate

of-0.50.

The large increase in price elasticity of demand for FCOJ from pre-

freeze to post-freeze 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 pre-freeze

price levels. The high price elasticity of demand in the post-freeze



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 be-0.70. 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 pre-freeze

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 was-1.39,-1.07, and-1.08, 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 pre-freeze periods. The level of demand increased from

a low in 1963 to pre-freeze levels or above during the period 1964 to 1966.

The retail price elasticity of demand for FCOJ was-1.03 at a price of 16.7

cents per 6 oz. can for the 1964 to 1966 period; slightly more elastic

than during the pre-freeze 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 (1957-59 = 100).









14

3. per capital personal income deflated by the consumer price
index (1957-59 = 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 price-quantity 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 1965-66 crop season was

111.0 and is projected to 112.0 and 113.0 in the 1966-67 and 1967-68 crop

seasons respectively.

Projections of price-quantity relationships were made for the 1966-67

and 1967-68 seasons using the prediction equation, 1.2. If the 1966-67

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 1967-68 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 1967-68 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 1966-67 and 1967-68 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, On-Tree and In-Store 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.




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