Front Cover
 Title Page
 Table of Contents
 Florida lime industry
 Lime demand
 Empirical demand model
 Lime projections
 Estimates of lime demand
 Policy simulator
 Literature cited

Group Title: Bulletin - University of Florida. Agricultural Experiment Station ; no. 797
Title: The demand for fresh limes
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00027316/00001
 Material Information
Title: The demand for fresh limes implications for prorating
Series Title: Bulletin University of Florida. Agricultural Experiment Station
Physical Description: iv, 26 p. : charts ; 23 cm.
Language: English
Creator: Ward, Ronald W
De, Vo Huu, 1942-
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1978
Subject: Limes -- Marketing -- Florida   ( lcsh )
Cooperative marketing of farm produce -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Bibliography: p. 26.
Statement of Responsibility: Ronald W. Ward and Vo Huu De.
General Note: Cover title.
Funding: Bulletin (University of Florida. Agricultural Experiment Station)
 Record Information
Bibliographic ID: UF00027316
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000929884
oclc - 18435029
notis - AEP0693

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page 1
    Florida lime industry
        Page 2
    Lime demand
        Page 3
    Empirical demand model
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Lime projections
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
    Estimates of lime demand
        Page 20
        Page 21
    Policy simulator
        Page 22
        Page 23
        Page 24
        Page 25
    Literature cited
        Page 26
Full Text
C --

September 1978

Bulletin 797 (technical)

The Demand for Fresh Limes:

Implications for Prorating

Ronald W. Ward and Vo Huu De

Agricultural Experiment Stations Institute of Food and Agricultural Sciences
University of Florida, Gainesville F. A. Wood, Dean for Research


Ronald W. Ward
Vo Huu De

Uivest of Flria

SThis public document was promulgated at an annual cost of
$1631.52 or a cost of 40.8 cents per copy to provide an empir-
ical method for evaluating prorating decisions in the market-
ing of fresh Florida limes.


This research was conducted by Dr. Ronald W. Ward, Asso-
ciate Professor, and Dr. Vo Huu De, Research Associate, both
of the University of Florida.
This study was supported by a grant from the Florida Lime
and Avocado Administrative Committee in conjunction with the
Florida Agricultural Experiment Stations. The research is in-
tended to provide a general understanding of the demand for
fresh limes as well as to develop a direct method for studying
various lime prorate policies. The study is classified under the
Food and Resource Economics Department's research of eco-
nomic structure, conduct, and performance of food and fiber in-
dustries. Thanks to Mrs. Johnette Arnold for typing and ed-
itorial assistance.


PREFACE ........................................ ...... ii
LIST OF TABLES .......................................... iv
LIST OF FIGURES .............. .... .... .......... .. .... iv
INTRODUCTION ......................................... 1
FLORIDA LIME INDUSTRY .......................... ... 2
LIME DEMAND ........................................... 3
EMPIRICAL DEMAND MODEL ............................ 4
Lime Seasonality ............. ............... ........... 5
Demand Growth ........................................ 6
Lemon Effect ..... .............................. ..... 7
Carryover Effect .................................... ........ 7
Price Flexibility ....................................... 10
Lime Demand Model ............................... ....... 11
LIME PROJECTIONS ..................................... 12
The 1976-77 Season ........................ ..... ..... 12
Policy Simulator ......................................... 13
Computer Procedures ..................................... 13
Simulator Examples ...................................... 16
CONCLUSION ........................ .................. 19
APPENDIX B: POLICY SIMULATOR ..................... 22
Example Input of WPLIMPC .............................. 23
Example Input of WDLIMPC .............................. 25
EFERENCES ............................................. 26



Table Page
1 Simulated total revenue from lime shipments for
different prorating policies ......................... 17
2 Simulated weekly revenue from lime shipments ......... 17
3 Simulated weekly lime shipments ..................... 18
4 Simulated weekly lime prices ......................... 18


Figure Page
1 Seasonality of fresh lime demand as compared to
lime shipments ............................... ...... 6
2 Percentage growth in lime demand using April 1976 as
the base with projections made using equation (2) ...... 8
3 Price flexibility for Florida fresh limes as estimated
with equation (2) .................................... 10
4 Actual and estimated FOB lime prices for 1976-77
season with estimates based on the lime demand model
estimated with data from 1972 through 1975 ............. 14
5 Actual and estimated total revenues for 1976-77 season
using tlhe lime demand model estimated with data
from 1972 through 1975 .............................. 15

Ronald W. Ward and Vo, Huu De

The Code of Federal Regulations (CFR) Title 7, Part 911
provides the Florida lime industry with the legal powers to pro-
rate in an effort to establish an orderly marketing of Florida
fresh limes [2).1 Prorating is defined as the periodic regulation
of the total volume of a commodity that can be shipped where
each shipper is given a pro-rata share of the total. The legal
bases exist for regulating (or prorating) the weekly flow of
limes to the market, but the economic usefulness of imple-
menting the control must be evaluated on a continual basis de-
pending on current and projected supply and demand conditions.
Although projections are not certain for either supplies or de-
mand, producers generally have a better understanding of cur-
rent and projected supplies since supplies are predominantly a
function of tree numbers and seasonal maturity cycles. Ac-
cepting this premise, then the development of an analytical un-
derstanding of lime demand is of major importance for effective
use of the prorate controls.
Demand can be measured at the retail level, in which case a
direct indication of consumer reactions to prices and/or supplies
is noted. The wholesale demand for fresh limes which the
packers face is generally denoted as derived or intermediate
demand [51. For fresh produce such as limes, both the primary
and intermediate (derived) demand are for precisely the same
product. The demands generally differ by at least the cost of
transportation and distribution from the packer to the retailer.
Since the industry marketing decisions are predicated on pricing
at the wholesale level, a measurement of the intermediate de-
mand is of utmost importance. All references to demand in the
remainder of this report will imply that of intermediate or de-
rived demand. The absence of retail price data prevents a direct
measure of primary demand.
The nature of the demand for limes will directly determine
e effectiveness of a supply allocation through prorates. If the
demand is stable and highly responsive to price changes, then

11umbers in brackets refer to Literature Cited.

prorates may be of minimal use. On the other hand, if the de-
mand parameters change over time, then the use of prorates will
have varying effects depending on when the controls are en-
forced. Further, the rate of price transmission from wholesale
to retail will determine the time and duration of consumers' re-
sponses to changes in availability of limes.
Recognizing the importance of demand to prorating, this
study will provide an analysis of lime demand as it relates speci-
fically to potential benefits from prorating. First, the demand for
limes will be estimated, and the results will be used to analyze
the effects from prorating. Second, a forecasting procedure using
the demand estimates will be developed. The results should aid
the industry as it strives to improve its orderly marketing of
fresh limes.

The Florida lime industry is concentrated among a few large
operations with an estimated 75 to 80 percent of the fresh limes
marketed by four packers. There are about 69 lime producers in
Dade County, Florida, but 40 of them are packers, and there are
no packers that are not lime growers. Non-Florida competition
in the lime industry is virtually non-existent, and Dade County
is the only lime producing area of any consequence in the United
States [4].
Lime production differs from that of most other citrus fruits
in that the trees bear continuously throughout the year with the
heaviest harvest occurring during the months of June through
August. The wholesale price is highly volatile. For example, in
1975-76 prices ranged from a high of $35-40 per bushel to a low
of $6-7 per bushel. Prorating efforts are specifically intended to
reduce the large price swings occurring during the summer
While the market order provides the mechanism for reallo-
cating supplies, the physical characteristics of the fruit do not.
On-tree storage is not a viable alternative, and failure to harvest
the summer limes will adversely affect production in the winter
when limes are in short supply. Limes do not store well either
on or off the trees, and most producers strive to pick them over
every 3 to 6 months. Therefore, limes diverted due to prorating
are generally processed. However, growers tend to view pro
cessing as a dumping market since the net average price fo
processed limes has consistently been less than picking ad
hauling cost.

Prorating limes is on a weekly basis; hence the demand for
limes must be considered on a weekly basis. That is, the demand
model used to reflect the effect of a change in supply must be
calculated so that the weekly price response can be estimated.
More aggregative demand models are of little use for analyzing
prorating policies.
Demand based on short time periods can differ substantially
from analyses of longer time intervals. First, for relatively short
periods such as weeks, consumers may be responsive to a price
change and will increase their consumption above their normal
weekly usage. The weekly data may show the market to be more
elastic than what would be measured on a quarterly basis. This
phenomenon is not unique to limes and is generally evident in
a number of perishable products over the short time intervals.
Generally, the storable option is reduced to the packer relative
to the consumer since it is to the packer's economic advantage
to provide the consumer with the highest quality fruit having a
reasonable time period for home use. Delay of shipments at the
packer level reduces the in-store and at-home life of fresh
limes. Second, there appear to be few substitutes for limes. For
some uses lemons serve as a substitute. Yet, limes and lemons
may also be complementary additives in the preparation of a
number of foods and beverages. In either case, lemons are ex-
pected to be the most closely related commodity having an in-
fluence on the consumption of limes. Finally, lime consumption
is expected to be related to the purchasing power of consumers,
where consumption should increase as income increases.
Since this analysis is primarily concerned with pricing pol-
icies at the FOB level in Florida, supply conditions at the FOB
level must be determined. The bulk of the seasonal supplies is
predetermined by the maturing cycles of the fruit with only
minimal storage expected at the packer level. Since supplies are
predetermined, prices are expected to. be dependent upon the
availability of limes at the packer level. FOB prices may also be
influenced by previous lime movements. For example, a change
in supplies in one week will create a direct pressure on the FOB
price in that week. In addition, the full effect of the change at
Sthe packer level may not be realized at the retail level until sub-
sequent weeks. In turn, the lagged retail response may create
pressure on the wholesale market in weeks following the initial
change. If this phenomenon occurs, there will be some carryover
effect from a change in supplies and the full impact of a prorate


may not be realized within one week. Given that the demand
model reflects this lag, then the full impact of a prorate can be
Limes exhibit a clear and pronounced seasonal variation in
both supplies and demand. This seasonality is expected to be re-
flected by changes in the level of consumption and changes in
consumers' responsiveness to prices. During the months of
largest consumption, a variety of consumers with a number of
uses of limes are in the market. In contrast, during the periods
of lowest demand, the market includes fewer consumers and,
likewise, fewer uses for limes. While data do not differentiate
between institutional and home consumption, a larger portion of
the fall and winter consumption is likely to be in the institu-
tional markets.
Recognizing the possibility of differences in consumer types
during the season, we hypothesized that total demand will be
lower during the fall and winter periods, and the elasticity of
demand will differ throughout the season. In the peak periods,
consumers may be less price responsive because of the needs for
fresh limes. During the off season, consumers may be' more price
responsive since they may readily forego consumption when
prices change. In both periods, however, demand may well be
elastic if limes are not an essential element of the food diet.


The previous section outlined the basic components hypothe-
sized to influence the demand for limes. The price of limes is
expected to be related to both lime shipments and lemon supplies
as well as changes in income levels. Rather than measuring in-
come directly, the model is slightly simplified by incorporating
a growth trend variable which captures the effect of income in
addition to other positive stimulants to growth. The final specifi-
cation of the model for lime demand is given in Equation 1:
log(Pt) = ao + aSt+ at + a3 log(L,) (1)
+ [ ff + y, St-ij log(Qt-)

where Pt = weekly Florida FOB lime price ($/bu),
S, = seasonality index (see Appendix A),
t = time trend (see Appendix A),


L, = weekly shipments of lemons (bu),
Qt- = weekly shipments of limes in week t-i (bu).
Variables St and t measure the seasonality and growth in lime
demand. The parameter as shows the effect of lemons on lime
prices. Finally, the last term in Equation 1 measures the current
and lagged effects of lime shipments on the current FOB price.
In fact, the parameter fi, + ySwhen estimated will give a direct
measure of price flexibility. A priori, the effects of previous
weeks shipments are expected to have less effect on current price
than current shipments, i.e., I Pf I > ] P3 I where i < j. Likewise,
the seasonality in demand should follow where I y I > I I,
letting i < j. The estimates of Equation 1 are given below and
will be used in subsequent discussions (see Appendix A).
log(P,) = 5.39064 + 5.09023 S, + .00277t + .15621 log(Lt) (2)
(.1806 + .1775 S,) log(Q,)
(.1445 + .1420 St,_) log(Q,_,)
(.1084 + .1065S,,) log(Q_2)
(.0723 + .0710 S,_,) log(Qt,3)
(.0361 + .0355 St.4) log(Q'_)

Lime Seasonality
Limes exhibit a strong seasonal demand cycle as evident by
the parameters associated with St in equation (2). The data
shown in Figure 1 are calculated as the percentage adjustment
in demand occurring over the full season relative to the base
period of the first week in April. Demand begins to increase in
early February and continues until a peak is reached by the first
part of June. From this point in early summer, demand declines
to a low in September and then remains at or near this low until
early February. The cycle is then completed by the end of March.
These seasonal shifts in demand are dramatic and can cause
major changes in market prices. Such changes can be especially
evident when supplies are large relative to, the low or declining
portions of the demand curve. For example, the weekly ship-
ments of limes for the 1975 season are overlayed on the season-
ality graph in Figure 1. While supplies generally decrease in the
\late summer and early fall, relatively large shipments occurred
beyond the points where the demand cycle peaks. These large
shipments in conjunction with a declining seasonal demand ex-
plain why lime prices are frequently depressed during the late
summer months.

Demand Supplies
Adj ustment (bu.)

1.75 35000

1.50 I '\ 30000

S1975 Shipments

1.25 / 25000

1.00 \, i o20000

.75 / -15000

.50 I \10000

Seasonal adjustment in demand.
25 5000

SMonth and
10 20 30 40 50 Week #

Figure 1. Seasonality of fresh lime demand as compared to lime

Demand Growth

Even though lime demand exhibits strong seasonal variation,
there is an underlying growth trend. This growth was identified
in Equations 1 and 2 by the variable t and is illustrated in Fig-/
ure 2. Using April 1976 as a base period, the growth in deman4
can be expressed as a percent of this base. For example, if a1ll
other factors remain constant, lime demand for April 1976 to
April 1977 is estimated to increase nearly 15 percent. This

growth does not represent a projection but identifies the under-
lying strength in consumer demand over time. Changing sup-
plies of either lemons or limes would lead to different prices and
any forecast would necessitate projections of such supplies.
The growth trend represents in part the effect from increases
in consumer purchasing power and growth in the population and
is likely capturing the effect of wider product distribution and
in-store space. While the growth trend does confound a number
of important variables, it can be used as an overall norm for
judging economic performance for subsequent seasons.
Comparison of both seasonal and growth trends in demand
shows that the seasonal variation is the predominant variable.
Over time demand increases, but within any season demand may
drop below the base period shown in Figure 2. Hence, the sea-
sonal decline in prices cannot be expected to be offset by a con-
tinual growth in demand.

Lemon Effect
Lemons were included in the model and the estimated para-
meter indicates some degree of complementarity between lemons
and limes as evidenced by the positive sign of as in Equation 2.
The estimated parameter shows only a weak degree of comple-
mentarity where for every 10 percent increase in lemon supplies
Florida lime prices are decreased by only 1.5 percent. Also, lemon
estimates showed the lowest level of statistical significance
among all parameters estimated. Given these results, the Florida
lime industry need not be greatly concerned with changing sup-
plies of lemons primarily shipped from California.

Carryover Effect
One of the most important questions regarding the prorating
of limes relates to how fast the effects of prorates are trans-
mitted through the market channels. If reduced supplies lead to
immediate increases in wholesale prices with little subsequent
effects, then the full effectiveness of the prorate can be judged
on that week's price performance. Whereas, if some delay occurs
where pressures on wholesale prices are not immediate, then
\assessment of the prorate must include a longer time span.
Under the situation where the price response is immediate,
ajn evaluation of the optimal prorate is relatively easy. The pro-
rate depends solely on the conditions prevailing or expected to
prevail during the prorate week. In contrast, if there is some

Percentage Growth
1.6 -

Demand Growth
1.4- (April 1976 base)



1.0 -

I, I I III I ItYear and
S 20 40 2 60 80 100 0 120 140 4?160 Week #

Figure 2.- Percentage growth in lime demand using April 1976 as the base with projections made using Equation 2.

delayed response, the optimal prorate depends on current eco-
nomic conditions as well as conditions expected to exist for every
week for which a delayed response is evident. In this latter situa-
tion, prorating decisions must be based on knowledge of previous
supplies as well as future supplies. Since knowledge of future
supplies is needed and is not certain, optimal prorates have an
inherent risk of misallocation. For example, the decision to im-
plement a prorate for one week will cause changes in the fol-
lowing weeks. The future effect from the current policy depends
not only on the predictable seasonal and growth trends identified
in Figures 1 and 2, but also upon the supplies in that future
The demand model specified in Equation 1 includes a measure
of the supply carryover effect. As the number of periods of
the carryover effect increases, the greater the complications of
the prorating decisions. The error from uncertainty in future
periods may be minimal if the carryover parameter is largest
in the first period and declines very rapidly in subsequent pe-
riods. If the decay is slow and/or if the peak effect is beyond the
first period, the risk of misallocation is greater.
The empirical results show a significant carryover effect
where future wholesale prices are influenced by a supply adjust-
ment in the current week. The carryover can be measured up to
four weeks beyond the initial week. That is, implementation of
the prorate in one week will have an impact on wholesale prices
through four subsequent weeks. The model shows that the largest
response to a supply change is realized in the current week.
Prices in subsequent weeks adjust to the current supplies but at
a smaller rate. For example, after one week the price change is
79 percent of that of the initial response. The effect is near zero
after five weeks, and the carryover effect declines at a constant
rate over these weeks. Both the length and rate of the carryover
depend on the estimates shown in Equation 2. The results clearly
establish that supply changes do not generate their total effect
on the market immediately. Hence, the full impact of prorates is
not evident from a simple analysis of the current week's activ-
While the effects of supply adjustments differ throughout
the season, the pattern of carryover as expressed in relative
terms remains the same. As a general rule, 33 percent of the
total price response is expected to, occur in the current week;
26 percent in the second week; 20 percent, the third week; and
13 percent during the fourth week.

Price Flexibilty
Price flexibility measures how sensitive prices are to. cha
in supplies. If a number of substitute products exist, dem
may be expected to be inflexible (i.e., supply changes cause
small price adjustments). Similarily, if the demand is b,
measured over relatively short time periods, the market dem
is generally inflexible (elastic). Also, a market may be less p
flexible as the number of uses of a product increases [5].
The flexibility coefficients estimated in Equation 2 include
seasonal adjustment parameter as well as the carryover eff<
discussed earlier. The seasonal adjustment does show the 1:
flexibility to change considerably depending on the time wit
a season. The seasonal adjustment in the flexibility index is i
trayed in Figure 3 and clearly establishes that consumer resp
siveness to supply adjustments does differ throughout the yo
Again, this difference most likely reflects the changes in
number of users and uses of limes.
As evident from Figure 3, lime demand is consistently cla
fled as a price inflexible market, since the flexibility inde)
always less than one. Generally, flexibility indices less than
imply elastic markets. Elastic markets, in turn, imply that sr


flexibility /



10 20 30 40 50

Figure 3. Price flexibility
Equation 2.

for Florida fresh limes as estimated with

adjustments in wholesale prices lead to relatively large adjust-
ments in the quantity demanded. Similarly, large adjustments in
supplies cause only minor changes in prices with inflexible de-
Given that the market is inflexible (elastic) at any time
during the season, it is doubtful that prorating supplies to the
degree that has been exercised in the past can have any major
stabilizing effect on the market. Prices respond most to supply
adjustments during the periods from March to June, as shown
by the higher flexibility rates in Figure 3. While the market is
always elastic, the seasonal pattern of demand indicates that the
current prorate weeks correspond to those periods where the
greatest price response occurs.
Figure 3 in conjunction with Figure 1 suggests that earlier
shipments of limes can lead to increased returns. However, the
physical restrictions on production may in fact prevent signifi-
cant adjustments in the flow of supplies. Second, efforts to pre-
vent the drastic decline in lime demand during the late summer
and fall months could greatly improve returns. While additional
research would be needed to support specific advertising and
promotional programs, such efforts provide one possibility for
changing the demand parameters illustrated in these figures.
The flexibility index in Figure 3 shows the immediate price
response to a change in supplies. Equation 2 also indicated a
significant carryover effect, in which case the price changes in
Figure 3 represent only a portion of the total price adjustment
that will eventually be realized. As a general rule, the immediate
price adjustment represents approximately 33 percent of the
total price change that can be expected. The total price flexibility
can be easily approximated by dividing the values in Figure 3
by 0.33.

Lime Demand Model
The previous discussions identify the components affecting
the demand for limes. Changes in supplies and seasonality in the
demand for limes are the major factors causing the instability
in lime prices. During early April lime demand is relatively
large, and hence prices remain high even with large levels of
shipments. As the season progresses beyond June, the demand
curve shifts downward and prices become depressed, especially
when large shipments extend into these periods. During the
early fall, demand decreases to the lowest levels and prices are
depressed. Demand again increases in the winter and early

spring months while supplies are still relatively low. During
these months prices are generally very high.
As apparent from these discussions, efforts to reduce the
drastic seasonal decline in demand during the late summer when
supplies are still large is probably the most effective way to
reduce price instability. While advertising and promotions are
one way of influencing the seasonal declines, it is doubtful at
such marketing efforts could in a short span of a few marketing
seasons completely reduce the instability. Efforts to reduce the
seasonality should be preceded by a study to identify what
causes such strong seasonal adjustments.

The previous section quantified the basic economic compo-
nents leading to variations in the demand for Florida fresh
limes. When these components are considered in the aggregate
they can be used to provide projections for the future under if-
ferent prorating policies. Second, the model can be used to as ess
a current season's performance relative to what would be Iro-
jected based on past data. The latter alternative will be con-
sidered first.
The 1976-77 Season
The demand model developed in Appendix A was based on
weekly data for the production seasons 1972-73 through 1975t76.
The 1976-77 season was purposely excluded in order to compare
how well the model would project prices for data not used in the
estimation of the demand equation. Further, the latter months
of 1976-77 were unique in that a severe freeze occurred w ich
caused considerable damage to limes. Hence, the performance
of the model can be further assessed for those unusual su ly
periods [33.
Both the actual and estimated weekly wholesale lime pr ces
are shown in Figure 4. The model generally captured the price
responses that occurred in the 1976-77 season where the raid
price decline and relative flatness of prices in the late summer
and fall are evident. Prices generally began to increase by
October and continued upward for the remainder of the se on.
A severe freeze occurred in late January, and shipments decli ed.
The model indicated a major rise in prices but generally o er-
estimated the actual price during the first few weeks follow ing
the freeze. However, in late February actual prices began ris ng,
and by March the actual and estimated values were nearly eal.

The freeze represents a unique occurrence not accounted for
in the model and, hence, the forecast error would be expected to
be larger than normal. Given sufficient time for the full impact
of the freeze to be transmitted from wholesale to retail levels,
then the predicted and actual values should be more in line.
The demand model immediately reflects shortages when
smaller shipments are included in the model. In contrast, during
and following the freeze, some supplies were already in the mar-
keting channels, and pressures on retail supplies may not have
been immediate. Once the supplies in the trade channels were
depleted, actual prices rose rapidly. The phenomenon explains
at least in part why the actual prices remained relatively flat for
a few weeks following the freeze.
The revenues generated from the prices shown in Figure 4
are graphed in Figure 5. The actual and estimated values are
close and generally reflect the instability in weekly revenues.
Note specifically that returns dropped considerably during the
freeze period. Unlike that of a number of citrus products, the
lime industry was adversely affected by large freeze damages.

Policy Simulator
The demand model can be used to stimulate various supply
policies. Given that prorating controls are to be implemented,
the model can be used to estimate the price and total returns for
each policy considered. Further, the effectiveness of the same
supply policy implemented at different times during the season
can be directly measured. The effects of changes in the total
harvesting patterns can also be shown.
Given that the demand model does reasonably well at esti-
mating prices as shown in Figure 4, then it can be a useful tool
for evaluating the economic effects of programs designed to
change demand. For example, promotion and/or advertising pro-
grams designed to reduce the rapid seasonal decline should lead
to increased prices for the same shipments. If the model con-
sistently underestimated prices following periods of strong pro-
motions, then at least part of the difference between actual and
estimated values may be judged as resulting from the promo-
tional effort.
Computer Procedures
The procedures for exploring various prorating policies are
included in Appendix B along with the computer program. As-
suming that the simulator is on-line through a remote terminal,

FOB Lime Price

80 1


Estimated N
I /

*\ \ .--. /

Estimated s I

\-. I- |.

\ period
.-._ ,--.
"*.**-- .-- Jan. 22,
April 2, 1976 Augut 7, 1976 -Oct. 16, 1976
-A"-i:_2_:>19767 7, 1977 ct"16 196I

60 +

40 +

lb -0 36 40 50 60
- Actual and estimated FOB lime prices for 1976-77 season with estimates based on the lime demand model
estimated with data from 1972 through 1975.

arch 5, 1977

Revenue ($)


500000. I, Estimated

1/ V7

; / \'/ ,/

300000.. '

l t* A

100000 ,
'// \'

April 2, 1976 August 7, 1976 October 16, 1976
S 1 January 22, 1977 March 5, 1977
10 20 30 40 50 60
Figure 5. -Actual and estimated total revenues for 1976-77 season using the lime demand model estimated with data
from 1972 through 1975.

the following procedures can be used. First, an input data
file allowing up to three different lime supply policies must be
developed and saved. For example, the excerpt on page 23,
Appendix B, represents the type of data needed. If additional
data are accumulated or other policies are to be evaluated, the
new file using the same name must be created. The variable,
Policy Q, is always reserved for actual shipments as long as the
information exists. Hence, any updating as the season pro-
gresses requires replacing Policy Q with the actual information.
Once the input and policy simulator are run, the program
then provides the estimated prices and total returns for each
week included in the input file and for each supply policy. While
the simulator does not necessarily provide the optimal solution,
it does provide the essential information for determining the
desirability of one prorate policy over another. The revenues
and prices resulting from each policy are printed and can be
directly compared. Appendix B outlines the exact procedures for
implementing the simulator.

Simulator Examples
While the number of alternative policies are unlimited, the
three examples below should illustrate the program capabilities.
The example is based on data for 18 weeks starting with the
first week in March. The first output from the simulator is
always started with the fifth observation of the inputed data.
This occurs because the first four observations are required to
calculate the lagged effect from prior shipments.
The three policies in the following example include the actual
shipments occurring in 1976 (Policy Q) ; a 10 percent reduction
in shipments during weeks 6 through 13 (Policy W) ; and a re-
allocation of supplies within the weeks (Policy Z). Tables 1
through 4 show the computer output for each policy. Table 1
reports the total revenue realized for the 14 weeks being simu-
lated, and only minimal differences in FOB revenues are evident.
Of course, these values would differ depending on the policies
being evaluated. Table 2 gives a week by week accounting of the
revenues generated from each supply policy. Shipments gen-
erally increase over the weeks simulated but revenues decline.
For elastic (inflexible) markets such as limes, increased ship-
ments should lead to greater returns even though prices gen-
erally become depressed with the greater shipments. Lime re-
turns decline in the examples because of the rapid seasonal de-
cline in demand as initially illustrated in Figure 1.

Table 1. Simulated total revenues from
prorating policies.

lime shipments for different

Policy Total Revenue

Q 4,294,747.66
W 4,310,510.18
Z 4,260,000.83

Table 2. Simulated weekly revenue from lime shipments.

Total Revenuea
Obs. Week
Policy Q Policy W Policy Z

1 Ib 441379 441379 441379
2 2 436009 436009 436009
3 3 458020 458020 458020
4 4 405569 405569 405569
5 5 399783 399783 399783
6 6 268650 251038 232181
7 7 356147 342776 351817
8 8 341871 336153 350969
9 9 286106 285047 295663
10 10 183058 183258 208441
11 11 181613 181181 193766
12 12 225845 224363 229355
13 13 191656 189492 192731
14 14 119042 125933 114829
policy Q represents actual shipments during 1976 starting with the 1st
week of April. Policy W represents a 10 percent prorate reduction in weeks 6
through 13, while Policy Z is a reallocation of 8,000 bushels from weeks 6-9
to weeks 10-13 where each week is adjusted by 2,000 bushels.
')This example starts simulating with the 1st week of April, 1976.

Tables 3 and 4 provide the shipment data and estimated
prices. Comparison of the effects of different shipments in any
week can be readily made. For example, in week six a realloca-
tion of supplies where 2,000 more bushels were assumed shipped
led to a price reduction of approximately two dollars. Again, the
full price response not only depends on this current policy but
also on previous supply policies. Any number of prorate policies
can be evaluated in a similar manner.

Table 3. Simulated weekly lime shipments.
Total Lime Shipmentsa
SObs. Week
Policy Q Policy W Policy Z
1 1 7076 7076 7076
2 2 7466 7466 7466
3 3 9214 9214 9214
4 4 9977 9977 9977
5 5 12969 12969 12969
6 6 9860 8874 7860
7 7 17886 16097 15886
8 8 24591 22131 22591
9 9 28776 25898 26776
10 10 21514 19362 23514
11 11 24965 22468 26965
12 12 38033 34228 40033
13 13 36560 32904 38560
14 14 21539 21385 21539
aSee footnote a, Table 2 for policies.

Table 4. Simulated weekly lime price.
Lime Pricea
Obs. Week
Policy Q Policy W Policy Z
1 1 62.3769 62.3769 62.3769
2 2 58.3992 58.3992 58.3992
3 3 49.7092 49.7092 49.7092
4 4 40.6504 40.6504 40.6504
5 5 30.8260 30.8260 30.8260
6 6 27.2465 28.2892 29.5396
7 7 19.9120 21.2944 22.1464
8 8 13.9023 15.1892 15.5358
9 9 9.9425 11.0065 11.0421
10 10 8.5088 9.4648 8.8645
11 11 7.2747 8.0640 7.1858
12 12 5.9381 6.5550 5.7291
13 13 5.2422 5.7589 4.9982
14 14 5.5268 5.8889 5.3312
aSee footnote a, Table 2 for policies.

The demand for fresh limes has been shown to be highly
seasonal, with large declines occurring during the late summer
and fall months. Likewise, the supplies are seasonal, even though
some Florida limes are harvested year around. When large vol-
umes of shipments enter the market after the peak demand
weeks, prices become depressed and highly unstable.
Changes in weekly lime supplies have a carryover effect on
the wholesale market, where shipment prorates will influence
wholesale prices up to four weeks after the initial supply change.
Once the impact of the supply adjustment is realized at the re-
tail level, this again creates additional pressure on the whole-
sale market in later weeks. Throughout these changes, however,
the fresh lime market remains price elastic.
The lime demand model has been used in a policy simulation
procedure which provides an easily accessible means for ex-
ploring various prorating policies. The examples simulated gen-
erally indicate that large prorates would be required to generate
relatively small revenue changes. While only a few examples
were included, the studies do indicate that prorates alone cannot
be expected to be a major factor in stabilizing prices. The anal-
ysis shows that shipments earlier in the season can improve re-
turns by coordinating the lime supplies with the peak demand
periods. Also, efforts to reduce the large seasonal decline in
demand during the late summer months could substantially im-
prove producer returns. Advertising and promotions in July and
August may be an effective means for changing this seasonality.

Estimates of Lime Demand

The demand function shown in Equation 2 is a nonlinear
model having two distributive lag variables and a sine function
to account for seasonality. Further, preliminary estimates indi-
cated the presence of serial correlation problems. The model was
then estimated using polynomial lag procedures with corrections
for a first order autoregressive process. Additional estimates
further showed that a first degree polynomial model constrained
to zero values after four lagged periods gave the most desirable
statistical results. The demand equation was estimated as shown

Demand estimates for Equation 2
Symbol Parameters SE t-statistic
Constant ao 5.3906 1.13929 4.731
Lemons a .1562 .07953 1.964
Seasonality aL 5.0902 .99356 5.123
Time a2 .0027 .00113 2.445
Limes(t) Po -.1806 .02925 6.177
Limes(t-1) P, -.1445 .02340 6.177
Limes (t-2) P2 -.1084 .01755 6.177
Limes (t-3) P, -.0723 .01170 6.177
Limes (t-4) 14 -.0361 .00585 6.177
Seasonality*Limes(t) o7 -.1775 .03496 5.078
Seasonality*Limes(t-l) 71 -.1420 .02797 5.078
Seasonality*Limes(t-2) 2, -.1065 .02098 5.078
Seasonality*Limes (t-3) 7, -.0710 .01399 5.078
Seasonality*Limes (t-4) 4y -.0355 .00699 5.078
R2 = .9343
F (5.197) = 560.455
DW = 1.5079
RHO correction = .85911
No. of obs. = 203

The seasonal variable was developed such that a complete
cycle is completed over a 52-week period. The phase of the cycle
was determined by estimating the complete model assuming dif-
ferent phase adjustments and then comparing the error sums of

squares for each phase. Using this procedure the seasonal vari-
able (S) follows as:
St = sin (.1231994* (WEEK-1) + 1.0995565) where WEEK
is an index of the week during the season. Note that when 1 <
WEEK < 52, 0 < .1231994*WEEK-1 < 27, the sine function
completes a cycle within 52 weeks. The sine in the first week is
zero without the phase adjustment. The phase may and in fact
does differ by the adjustment 1.0995565. This adjustment is pre-
cisely what determines the peak shown in Figure 1.
Price flexibility of demand is easily calculated from the model
since it is in log form:
f--i Pt /=3i + yist-i.
Letting i = 0 gives the immediate price response while the total
flexibility from a change in supplies in period t is derived as:
4 4
I f,= 2 (P + 7,,).
i= 0 i=0

Policy Simulator
Using the demand model estimated in Appendix A, a simple
policy simulator using SAS computer software has been devel-
oped (1). The basic principle for the design is that policy makers
who make prorating decisions need to, have some guidelines as
to the economic consequences from setting upper limits on
weekly supplies entering the market. The simulator will allow
up to three policies (supply levels) to be considered in one run.
Given the supply data, output then includes both printed and
plotted values of weekly shipments, prices, and total revenues
for each policy. If more than three policies are to, be analyzed,
then additional computer runs are required.
The program is shown on the following page and the imple-
mentation procedures below. The user needs to be aware that
since the regression model included a first order autoregressive
process, forecasts of today are related to errors made in the
previous period. The forecast in Figure 4 was made using these
errors. However, often during analysis of different policies,
actual data are not available and errors cannot be calculated.
Hence, the policy simulator ignores previous errors when esti-
mating price responses.
The policy simulator can be accessed as follows assuming
that an on-line terminal is available.


Create input data /S WDLIMPC

If new policies are needed or if the data are to be updated
simply, fetch WDLIMPC, make the appropriate changes, and
resave. Likewise, new lines of data can be directly typed onto
the fetched input file. The data are entered under free format
where one space is an adequate delimitor. However, the infor-
mation in WDLIMPC must be entered in the sequence shown in
the column headings on page 25.

Example Input of WPLIMPC
0003 // EXEC SAS
0004 //SYSIN DD *
0005 DATA;
0006 INPUT T P L Q W Z;
0008 OUTPUT;
0009 QLAG4=QLAG3;
0010 QLAG3=QLAG2;
0011 QLAG2=QLAG1;
0012 QLAG1=Q;
0013 ZLAG4=ZLAG3;
0014 ZLAG3=ZLAG2;
0015 ZLAG2=ZLAG1;
0016 ZLAG1=Z;
0017 WLAG4=WLAG3;
0018 WLAG3=-WLAG2;
0019 WLAG2=,WLAG1;
0020 WLAG1=W;
0021 CARDS;
0024 SET DATA1;
0025 IF T>=5;
0026 A=.1231994;
0027 B=1.0995565;
0028 T1=SIN(A* (T5) +B);
0029 T2=SIN(A* (T-6) +B);
0030 T3=SIN(A*(T-7)+B);
0031 T4=SIN(A*(T-8)+B);
0032 T5=SIN(A* (T-9) +B);
0035 1976-77 ADJUSTMENT TO T=308
0036 1977-78 ADJUSTMENT TO T=360
0037 1978-79 ADJUSTMENT TO T=412

TO 308;
0040 BO= 5.39064+ 5.09023*T1+.002772* (308+ T);
0041 B1=LOG(L)*.156209;
0042 C1=-.1807 -.1776*T1;
0043 C2=-.1445 -.1420*T2;
0044 C3= -.1084 -.1065*T3;
0045 C4= -.07226 -.07102*T4;
0046 C5=-.03613 -.0355*T5;
0047 IF T>=5;
0048 PQ =EXP(BO+B1)*Q**C1*QLAG1**C2*QLAG2**C3
0049 *QLAG3**C4*QLAG4**C5;
0050 PZ =EXP(BO+B1)*Z**C1*ZLAG1**C2*ZLAG2**C3
0051 *ZLAG3**C4*ZLAG4**C5;
0052 PW =EXP(BO+B1)*W**C1*WLAG1**C2*WLAG2**C3
0053 *WLAG3**C4*WLAG4**C5;
0054 TQ=PQ*Q;
0055 TZ=PZ*Z;
0056 TW=PW*W;
0057 WEEK=T-4;
0068 PLOT WEEK*Q='*' WEEK*Z='+' WEEK*W
0070 /*

Example Input of WDLIMPC

5 E-4 N
d o

02 A4 PL 0Lq
1 9 9 8960 8960 8960
2 9 9 9826 9826 9826
3 9 9 6773 6773 6773
4 9 9 5367 5367 5367
5 46.25 160000 7076 7076 7076
6 46.25 160000 7466 7466 9466
7 47.50 160000 9214 9214 11214
8 47.50 160000 9977 9977 11977
9 42.50 160000 12969 12969 14969
10 37.50 160000 9860 8874 7860
11 30.00 160000 17886 16097 15886
12 15.00 160000 24591 22131 22591
13 11.25 160000 28776 25898 26776
14 11.00 160000 21514 19362 21514
15 10.62 160000 24965 22468 23965
16 10.62 160000 38033 34228 37033
17 10.62 160000 36560 32904 35560
18 10.62 160000 21539 19385 20539


[1] Barr, Anthony, et al. A User's Gude to SAS. SAS Institute, Inc.
Raleigh, N. C. 1976. pp. 34-54.
[2] Code of Federal Regulations. "Limes Grown in Florida-Part 911".
Washington, D.C. January 1, 1969. pp. 138-151.
[3] Florida Lime and Avocado Administrative Committee. "Price and
Quantity of Limes Seasonal Data." Homestead, Florida. 1972-73
to 1976-77 Seasons.
[4] Manley, William T. "Characteristics and Potentialities of the Con-
sumer Market for Florida Limes." University of Florida Agri-
cultural Experiment Station. February 1962. pp. 32-36.
[5] Tomek, William G. and Kenneth L. Robinson. Agricultural Product
Prices. Cornell University Press. Ithaca, N. Y. 1972. pp.

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