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Group Title: Bulletin - Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Title: Economic implications of an interregional cooperative and processor-retailer integration for the southeast Florida milk market
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 Material Information
Title: Economic implications of an interregional cooperative and processor-retailer integration for the southeast Florida milk market
Series Title: Bulletin - Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Physical Description: v, 51 p. : ill. ; 23 cm.
Language: English
Creator: Prato, Anthony
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Milk trade -- Mathematical models -- Florida   ( lcsh )
Milk -- Cooperative marketing -- Mathematical models   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Bibliography: p. 41-42.
Statement of Responsibility: Anthony A. Prato.
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Bibliographic ID: UF00026821
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: ltuf - ACA0520
oclc - 01708331
alephbibnum - 000362071
lccn - 75624230

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Full Text





HISTORIC NOTE



The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida






Bulletin?70 (technical) May 1975










ECONOMIC IMPLICATIONS OFAN
INTERREGIONAL COOPERATIVE AND
"PROCESSOR-RETAILER INTEGRATION

FOR THE SOUTHEAST FLORIDA

MILK MARKET


Anthony A. Prato






Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J. W. Sites, Dean for Research

















ECONOMIC IMPLICATIONS OF AN
INTERREGIONAL COOPERATIVE AND
PROCESSOR-RETAILER INTEGRATION
FOR THE SOUTHEAST FLORIDA
MILK MARKET

Anthony A. Prato
Former Assistant Professor
Food And Resource Economics
University of Florida



This public document was promulgated at an annual cost of
$2,125.13, or a cost of $1.42 per copy to inform interested
persons of the economic implications of an interregional
cooperative processor-retailer integration on the southeast
Florida milk market.
















i








PREFACE

This study is directed primarily at economists and industry
personnel concerned with the potential impact of structural
change on the southeastern Florida dairy industry. It is assumed
that the reader is familiar with the dairy industry as well as.
the application of simulation models. The basic simulation model
developed in this study should not be judged by how well the
mathematical relationships and parameters correspond to one's
perception of decision-making by milk producers, processors,
and retailers. Rather, the basic model should be judged by how
well it reproduces the behavior of observable system variables.
Likewise, the validity of the results obtained with the coopera-
tive and integration models should be judged by the validity of
the basic model and the reasonableness of the specific assump-
tions underlying these models.




ACKNOWLEDGEMENTS
This study would not have been possible without the aid and encour-
agement of many people. Dallas Fox is to be commended for his con-
tributions to this study during its early phases, particularly in the
conceptualization of the models and the application of the industrial dy-
namics method. I extend my sincere appreciation to Ralph Eastwood for
sharing with the author his invaluable knowledge and understanding of
the Florida dairy industry. Special thanks to R. E. L. Greene, Edna Loeh-
man, Ron Ward, and three other anonymous reviewers for their valuable
suggestions. Finally, I thank Susan Cowels for her assistance in preparing
the manuscript for publication. The author assumes complete responsi-
bility for the content, accuracy, and quality of this report.



















ii








ABSTRACT
The impact of an interregional cooperative and processor-
retailer integration on net returns to milk producers, processors,
and retailers is analyzed with mathematical simulation models.
Three subsystems of the southeastern Florida dairy industry are
modeled: (1) the movement of milk from producers to con-
sumers; (2) the determination of prices at the farm, processor,
and consumer levels; and (3) the level and distribution of re-
turns to retailers, processors, and producers. All models are
based on the industrial dynamics approach and reflect market
conditions during the 1966-69 period in Florida counties cov-
ered by federal milk order 13.
Results indicate that the operation of an interregional co-
operative in southeast Florida would have a negligible effect
on milk production. However, monthly net returns to producers
would on the average be 38 percent or half a million dollars
greater than in the absence of a cooperative. This finding is
based on the assumption that 42 percent of the milk produced
is sold through the cooperative and a Class I premium of 30.5
cents per hundredweight is negotiated. Monthly processor net
returns averaged .26 percent higher and monthly retail returns
2.4 percent greater with a cooperative.
Assuming that independent plants are more inefficient than
integrated plants, the author found that net returns to all proc-
essors are not necessarily greater under a partially integrated
structure than a totally non-integrated structure. Total net re-
turns to processors would be greater if at least 65 percent of
the milk produced is handled by very efficient integrated plants.

















iii








TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS .......................................................................................................... ii

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

LIST OF FIGURES ..... ........................ ..................... ........................................... ...... .. v

INTRODUCTION .... ................................................................................................................... 1
The Problem 2

I. OBJECTIVES AND PLAN OF STUDY .............................................................. 3

II. METHODOLOGY .................................................................. ...................................... 2

III. BASIC MODEL ........................................................................................................................ 4
Description of Model ............... ................ ................................... ................... ........ 5
P rodu action ...................................................... .... .. ... ..................................................... ... .. 8
P processing ............................................................. ................................................... ............. 10
Consumption ................................... ....................................................................... 11
P prices ........... .. ....... .. .... .... ................................................................................................ 13
Revenue and Cost ........................................................................................................... 16
IV. MODEL VALIDATION .......................... ............... ........ ................................ 18

V. ANALYSIS OF INTERREGIONAL COOPERATIVE ...................... 19
R esu lts ................................................................................................................................................... 2 5

VI. ANALYSIS OF PROCESSOR-RETAILER INTEGRATION .............. 30
Results .......................................................... .......................... ........................... 33

VII. SUMMARY AND CONCLUSIONS ...................... ........................ 37
Sum m ary ....................................................... .... .. ... .. ... ....... ............ 37
C conclusions ...................................... ................ .................... ............. ..... ................................. 38
Interregional cooperative .................................................................................... 38
Processor-retailer integration ......................................................................... 39
Concluding Remarks ................................................. ........................................... 39

FOOTNOTES .................... ................ ........................................ ................................ 40

R E F E R E N C E S ........................................................... ......... .......................................................................... 41

APPENDIX A: DYNAMO FUNCTIONS ........ .................................... .............. 43

APPENDIX B: CALCULATION OF CLASS II CONSUMER PRICE ... 44

APPENDIX C: PRODUCTION AND PROCESSING SEGMENTS
OF COOPERATIVE MODEL .............................................. 45

APPENDIX D: PROCESSOR SEGMENTS OF
INTEGRATION MODEL ...........4............................... ....................... 47

GLOSSARY OF VARIABLES ..................................................................................... ........... 49


iv









LIST OF TABLES


Table Page

1 Comparisons of actual and simulated values of six variables,
monthly averages by quarters; southeast Florida, 1966-69 .................. 20
2 Comparison of simulated milk production, processor utiliza-
tion and returns, basic and cooperative models, monthly
averages by quarter, southeast Florida, 1966-69 ..................................... 26
3 Alternative levels of operational efficiency for integrated
and independent milk processing plants ...... ............ 31

4 Per unit costs of processing and distributing Class I and
Class II milk for integrated and independent plants by
m ilk a location ...... ..... .......... ........ ... ................................ ........................................... 34
5 Average monthly and total processor net returns for basic
cooperative and integration models under four milk alloca-
tions, and three efficiency levels 1966-69 ........................................................... ... 35
B-1 Average percentage utilization and retail value of Class II
milk in southeast Florida, 1966, and conversion ratios for
eight dairy products .................. ....... ....... ......................... ................ ......... 44
D-1 Coefficients of COP and GDC for integration model ................................... 48





LIST OF FIGURES



Figure Page


1 D elineation of study area ....... ................................................................. ................ 3

2 Flow diagram of southeast Florida dairy industry ............................... 6

3 Computation sequence for industrial dynamics model .............................. 7

4 Seasonal component of total milk utilization, southeast
Florida, by m months, 1966-69 average ....................................................... ............... 9

5 Seasonal component of fluid milk utilization, southeast
Florida, by months, 1966-69 average ..................................................... ...... 12

6 Relationship between producer and consumer Class I prices
southeast Florida, 1966-69 ............ .......................................................................... 13

7 Condensed flow diagram of milk production and processing
segm ents of cooperative m odel .......... .... ..... .. ... ................................................... 24

8 Alternative allocations of milk between integrated and in-
dependent plants and retailers .................................. ............................................. 32

V










INTRODUCTION
Technical and economic developments over the past two dec-
ades have altered the structure, conduct, and performance of the
United States dairy industry.1 On the production side, milk pro-
ducers have responded to higher production costs by adopting
modern management techniques and by expanding herd size to
capture economies of scale. Milk producers have also attempted
to offset declining profit margins by organizing into local and
interregional cooperatives, i.e. cooperatives with members in
more than one state. Interregional cooperatives in particular
have increased the market power of member producers by bar-
gaining for and obtaining Class I premiums for fluid milk.
Milk processing and distribution have undergone consider-
able structure change. The proportion of milk distributed through
supermarket chains and sold under private label has steadily in-
creased. To gain greater control over their source of supply,
chain stores have developed centralized milk procurement pro-
grams and, in some cases, acquired control of milk processing
plants through backward integration. Significant economies of
scale in milk processing and the increased market power of pro-
ducers and distributors relative to processors have resulted in
fewer and larger processing plants.
Declining per capital consumption of dairy products, on a
milk equivalent basis, has prompted the dairy industry to in-
crease financial support for dairy education and promotional
programs. Milk legislation, particularly as it relates to Class I
base plans and price supports, has attempted to balance demand
and supply for milk products.

The Problem
Although recent organizational changes in the dairy industry,
particularly the spread of interregional cooperatives and growth
of processor-retailer integration, have been confined to other
states, present conditions suggest that may occur in Florida. For
example, leaders of interregional cooperatives consider Florida
a lucrative area for expanding their membership. Florida's high
Class I price, relative to other federal order markets, would in-
crease the pooled returns to non-Florida members, although it
would reduce returns to Florida producers. Higher profits on
milk processed and distributed by corporate food chains coupled
with steady increases in the proportion of state produced milk
utilized in fluid products provide a strong incentive for milk
distributors to integrate into processing. Both prospects raise

1








an important issue. What impact would an interregional cooper-
ative and processor-retailer integration have on the Florida dairy
industry? The answer to this question is of vital importance to
the orderly growth and development of the Florida dairy
industry.
I. OBJECTIVES AND PLAN OF STUDY
The primary objective of this study is to determine the prob-
able impact of an interregional cooperative and various degrees
of processor-retailer integration on prices received by and re-
turns to southeast Florida milk producers, processors, and re-
tailers. Since southeast Florida has been in the Federal Milk
Marketing Order system since 1957, production, utilization, and
price data for this area are more complete and cover a longer
period of time than comparable data for Upper Florida and
Tampa Bay federal order markets. For this reason southeast
Florida (specifically the counties included in Federal Order 13)
was selected as the study area (Figure 1).
The method of analysis chosen for this study involves the
development and application of an industrial dynamics model.2
Reasons for selecting this method are discussed in section II. The
basic industrial dynamics model is developed in section III and
model validation is considered in section IV. Sections V and VI
focus on modifications of the basic model used to analyze the
impact of an interregional cooperative and processor-retailer
integration on net returns to producers, processors, and retailers.
Summary and conclusions are given in section VII.

II. METHODOLOGY
Various methods have been used to study the problems of
food and agricultural industries. Wide use has been made of
economic models that determine the optimal allocation of prod-
uct supplies among alternative markets. An optimal allocation
is usually found by maximizing or minimizing a particular vari-
able, e.g. minimize processing and transfer costs [11], maximize
producer returns [151, or maximize consumer expenditures
[1,12]. While optimization models can readily be solved by math-
ematical techniques, they are somewhat restrictive for analyzing
the impact of changes in economic structure and organization on
industry performance. Specifically, optimization models have a
limited capacity to handle the time-related aspects of industrial
behavior.
As an alternative approach, systems analysis has been suc-

2
























W STUDY AREA










Figure 1.-Delineation of study area.

cessfully used to study the consequences of alternative growth
and development plans [7] and a wide range of economic prob-
lems [8,19]. Systems analysis typically involves the development
of a simulation model. Such models permit a realistic specifica-
tion of decision-making behavior and can be formulated without
reference to optimizing behavior. This study employs the indus-
trial dynamics (simulation) approach developed by Forrester
[31.
Industrial dynamics is an analytical method for studying the
time-related behavior of social and economic systems. An indus-
trial dynamics model consists of a system of deterministic (non-
stochastic) equations which define the levels and rates of change
in the variables of a system. These equations essentially describe
how the decisions made by various economic units such as pro-
ducers, processors, and retailers affect the behavior character-

3








istics of the system as defined by economic variables. A distin-
guishing feature of industrial dynamics models is their use of
information-feedback loops. Such loops exist when the condi-
tions of a system lead to a decision that results in an action
which affects the conditions of the system and hence future
decisions. Closely associated with information-feedback loops
are various amplifications and delays present in the system. Am-
plifications occur when the effect of an initial change in one
variable is magnified at some other point in the system. Delays
occur when the full effect of a particular change is distributed
over several time periods. In general, the industrial dynamics
approach shows how the structure of a system, policy decisions,
and time delays in decisions and actions interact to influence
the variables which affect industrial performance.
III. BASIC MODEL
Simulation involves four basic steps: (1) defining the prob-
lems or issues to be analyzed, (2) constructing a mathematical
model of the system, (3) testing and refining the model, and
(4) applying the model [6]. These steps are by no means inde-
pendent. For example, if the model does not adequately generate
the observed behavior of the system, further refinements become
necessary. Thus, the development of a simulation model is an
iterative process which involves retracing these four basic steps
until a satisfactory mathematical representation of the system
is found. The basic model presented in this section is the out-
come of many such interactions,.
Several criteria guided the development of the basic model.
In view of the objectives of this study, the model was designed
to generate returns to milk producers, processors, and retailers.
Primary emphasis was placed on milk production and utiliza-
tion and the level of prices and costs at production, processing,
and retail levels. Data limitations necessitated a high level of
aggregation. While the model considers separately the behavior
of producers, processors and retailers, it makes no distinction
between types of producers, processors and retailers although
two types of processors were identified in the analysis of inte-
gration. Since the area under investigation is southeast Florida,
the parameters of the model were chosen to represent the con-
ditions in that area whenever possible. To simplify the struc-
ture of the model, no attempt was made to account for the rela-
tively small movement of milk in and out of southeast Florida.
Finally, the initial values and parameters of the model are based
on market conditions during the 1966-69 period.

4








Description of Model

Before proceeding to the basic mathematical model, a verbal
and graphic description of the model is given. Figure 2 is a flow
diagram of the entire model. Solid lines represent the physical
movement of milk from production to consumption. Dashed lines
show information flows and solid lines superimposed with a dol-
lar sign, $, represent money flows. Variables in squares and cir-
cles are levels and the hourglass symbol, X, represents rates of
change in the levels.
The upper portion of Figure 2 depicts the physical move-
ment of milk from production to consumption and the factors
affecting this movement. Milk production is defined in terms of
the rate of milk production. This rate depends on two compo-
nents: expected consumer utilization of milk and the production
incentive. Expected utilization measures the normal pattern of
milk consumption. It is assumed that producers attempt to satis-
fy normal consumption needs by coordinating production with
expected utilization. The second component, or production incen-
tive, measures the effect of changes in the revenue-cost position
of producers on milk production. When producer revenues in-
crease (decrease) relative to production costs, milk production
is assumed to increase (decrease). The rates of processor allo-
cation of milk to Class I and Class II uses are determined by the
proportion of milk allocated to Class I and Class II uses which
in turn depends on Class I and Class II utilization rates.8 Since
Class I products command a higher market price than Class II
products, processing for Class I utilization receives the first
priority. Milk allocated to Class II uses is computed as a resi-
dual, i.e. total production minus the quantity of milk allocated
to Class I uses.
The middle portion of Figure 2 illustrates the determination
of producer, processor, and consumer prices. Minimum Class I
and Class II prices received by producers are determined by
adding a transportation (price) differential to the midwest
basic formula price. Processor allocation rates to Class I and II
uses and the minimum producer prices define the blend price
received by producers. Consumer prices are a specified function
of farm prices. Prices received by processors are derived by
subtracting the retail price margin from the consumer price.
The lower portion of Figure 2 shows the money (revenue-
cost) flows. Consumer utilization and prices determine total
consumer expenditures on milk or equivalently total returns to
retailers. Processor net returns are determined by deducting

5





"Trend

Class I
\ Allocation delay
I Expected Rate Class I /
SMilk Processed Class .
Utilization Inventory Utilization Trend

Produc- Utilization \Expec-ed "
tion R(_ ':Ct / j- ( i-c --Oonnlate \ Class I
i 'I Processor C lss I ass IateE expected -
Production Inventory Allocation ( Allocation Utilization
Process R Proportion Proportion Class I Utilization
Z, Utilization\ Seasonal
Si i Rate Component
// --- r-- Processed I X -- ->( cas,,. 1
/ /^ /Clas -^ Inventory \ \ Utilization
/ \Inventory
Price / Allocation Rate ------ -\
Differen- delay
tia/ Minimum \ delay/ Consumer Class Retail
- -> ClassI -------- Class I -- ----- Price Recd - ---- Class I Price
Price / Price by Processors Margin
Midwest M
Basic Formula
Price

^~\ \ Minimum dela Consumer Class Retail
l Class II ----__ d Caus II
ClassClass II -- Class 1 -- 4-) Price Rec'd -- -- Class II
II | Price Price / by Processors/ \ Price Margin
Price Dji- , 4)
ferential Blend
Price
Rate of net re- Cohs.
turns to produ- I Exp.
Net Returns Total Returns Total Returns Total Returns t Total Consumer
\ To Producers .... to Producers -- --- | to Processor .....=-un o to Retailers --P -= Expenditure
To Produces Rate of total Rate of return to
Returns to Producers processors
\ Trend Produc- Processings Raw Milk .
tion &Distrbu- -- Assembly Retail
\ Costs tion Costs Costs Margns
Production delay Return- --- '--- Returns to -
Incentive -- NetReturns Retailers
Csto Processors


Figure 2.-Flow diagram of southeast Florida dairy industry.









Rates n
the forthcoming
period KL, to be
calculated at time K
Levels
at time J,
already known

be calculated



S -calculated
afConstantter levelsrates over





DT --- DT--- Time

J K L




Figure 3.-Computation sequence for industrial dynamics model.


total producer returns and assembly, processing and distribu-
tion costs from total processor returns. Producer net returns is
the difference between total producer returns and milk pro-
duction costs. The return-cost ratio for producers determines
the production incentive described earlier.
To facilitate the understanding of the basic mathematical
model a brief description of DYNAMO is given. DYNAMO is
the language used to write the mathematical equations of an
industrial dynamics model. These equations should be consistent
with the flow diagram (Figure 2) and should be capable of
generating all the variables of the model. In the DYNAMO for-
mat, the value of a state variable at time K is determined by
the value of that same variable at time J (the previous period)
and changes in other variables from time J to time K. At any
given point in time state variables are independent of one an-
other. For this reason industrial dynamics models are similar
to deterministic recursive models. The "independence" assump-
tion is maintained by selecting a very small solution interval of
equal increments. A solution interval is the elapsed time be-
tween successive solutions of the DYNAMO equations. For the
present study the solution interval, denoted by delta time or DT,
is one-twentieth of a month.

7








Six types of equations are available with the DYNAMO lan-
guage: level (L), rate (R), auxiliary (A), supplementary (vari-
ous designations), initial-value (N) and constant-value (C)
equations. Level and auxiliary equations define the state variables
at time K (designated .K), such as the level of inventories or
prices. Rate equations define the rate of change in variables
which affect the state variables. The suffix .KL refers to the
rate of change in a variable between time K and time L. The
time interval between K and L is of length DT. Rates of change
in a variable are assumed to remain constant within a given DT
but can vary between DT's. Initial-value equations are used to
define the original values of all system variables and constant-
value equations are used to specify the values of parameters ap-
pearing in level and rate equations. The relationship between the
levels and rates of change of variables is illustrated in Figure 3.
An assortment of standard DYNAMO functions can be used
to generate a specific behavior for a variable. Functions applied
in this study include the TABHL, RAMP, PULSE and DELAY
functions. The TABHL function specifies the values of one vari-
able corresponding to a range of values of another variable. A
RAMP function is used to increase or decrease a variable by a
constant amount per DT. The PULSE function permits a vari-
able to change (increase or decrease) periodically by a constant
amount. The DELAY function is used to delay the response of
one variable to changes in another variable. The higher the
order of the delay the more delayed the response. Mathematical
formats for these four DYNAMO functions are given in Ap-
pendix A.


Production
The milk production rate (MPR) is the product of expected
milk utilization (EUU) and the delayed production incentive
(DPI). Expected milk utilization is the sum of a seasonal com-
ponent or total milk utilization (EU) and the secular trend in
Class I utilization (CIUTR) expressed in millions of pounds.
The seasonal component was computed by averaging 1966-69
monthly utilization of all milk after removing secular trend
(Figure 4). Secular trend was removed by subtracting (116.7)
(t), t=1, . 48, from actual monthly utilization where 116.7
is the average monthly increase in total utilization over the 1966-
69 period.4 Separating the seasonal and secular components of
utilization allows one to investigate the effects of changes in one

8








48.8
49-

48

S47 47.1 47.1
z 46.8
o 46 45.3
0-
L 45
0
S44 44.0 43.4
0
43
J 42.5
2 42- 42.3
41 '40.7 40.5

40 40.1

J F M A M J J A S 0 N D
JFMAMJJASOND
MONTHS
Figure 4.-Seasonal component of total milk utilization, southeast Florida, by
months, 1966-69 average.
or both components on the system. The production incentive,
which also affects the milk production rate, is defined in terms
of the ratio of total producer returns to total production costs.
A more detailed explanation of the production incentive appears
in the discussion of the revenue and cost segments of the model.
Equations for milk production are:

R MPR.KL= (DPI.JK) (EUU.K) Monthly production rate
A EUU.K=EU.K+C1UTR.K Expected milk utilization
A C1UTR=RAMP (.1167,1) Class I utilization trend
N C1UTR=0
A EU.K=TABHL (EUT*, MP.K, .75,11.25,.5)
Seasonal milk utilization
C EUT*= 46.8/44.0/44.0/48.8/48.8/47.1/47.1/47.1/47.1/47.1/
42.5/42.5/40.7/40.7/40.1/40.1/40.5/40.5/43.4/43.4/
42.3/42.3/45.3/
L MP.K=MP.J+DT (1-MD.JK)

9








R MD.KL=PULSE (MDP, 11.95, 12)
N MDP=MPY/DT
C MPY=12
N MP=0
N MD=12

Variables MP, MD, MDP and MPY were used in generating the
seasonal component of total milk utilization and have no
substantive interpretation in the model. Notice that the same
seasonal utilization pattern is repeated (via EUT*) in each year.


Processing
The milk production rate regulates the flow of milk into
processor inventory of raw milk (PIR) and milk allocated to
Class I and Class II products regulates the flow of milk out of
processor inventory. Rates of allocation to Class I uses (RAC1)
and Class II uses (RAC2) are determined by the Class I (P)
and Class II (1-P) allocation proportions. The Class I allocation
proportion varies with respect to the adjustment ratio (AR) of
Class I allocation (RAC1) to Class I utilization (C1UR). Using
the average Class I allocation proportion in 1966 as a base
(.877), the Class I proportion increases above the base when the
ratio is less than one and falls below the base when the ratio
exceeds one. Rates of increase or decrease in P are specified by
the PT* table function. Equations describing processor utiliza-
tion of milk are:

L PIR.K=PIR.J+DT(MPR.JK-RAC1.JK-RAC2.JK)
Processor raw
milk inventory
N PIR=50
R RAC1.KL= (MPR.JK) (P.K) Rate of allocation
N RAC1=41.1 to Class I uses
R RAC2.KL= (MPR.JK) (1-P.K) Rate of allocation
N RAC2= 5.7 to Class II uses
A P.K=TABHL (PT*,AR.K,0,2,.2) Class I allocation
proportion

10








C PT*=1.0/1.0/1.0/.95/.95/.877/.85/.80/.75/.70/.70
A AR.K= RAC1.JK/C1UR.JK Allocation-Utilization
adjustment ratio
L C1PI.K=CIPI.J+DT (RAC1.JK- CIUR.JK)
N C1PI=80 Class I
processed inventory
L C2PI.K=C2PI.J+DT (RAC2.JK-C2UR.JK)
N C2PI=15 Class II
processed inventory
Initial values for PIR, C1PI and C2PI are not critical since
these inventories do not enter into the decision concerning the
rate of allocation to Class I and II uses or consumer utilization
rates. Attempts to make these inventories an integral part of
the allocation decision were not successful. Initial values for
RAC1 and RAC2 were computed by multiplying the base Class I
allocation proportion (.877) by MPR and the base Claos II al-
location proportion (1-.877) by MPR, respectively. Simulations
were run using alternative PT* values. The values chosen gave
a simulated allocation proportion (P) that most nearly re-
sembled the observed proportion.

Consumption
The Class I utilization rate (C1UR) was defined by applying
a third-order delay (DELAY 3) to expected utilization of Class
I milk (EEUC1) with a delay constant (DC1) of .25 months
or approximately one week. EEUC1 was determined in the same
manner as EUU. The seasonal component of EEUC1 is EUC1
(Figure 5) which is defined by table function EUC1T*.5 The
secular trend component is CIUTR. Class II utilization rate
(C2UR) was defined by applying a third-order delay (DELAY
3) to the rate of allocation to Class II uses (RAC2) with a delay
constant (DC2) of .5 months or two weeks. Equations for con-
sumer utilization of Class I and II milk are:
R C1UR.KL=DELAY 3 (EEUC1.K, DC1) Class I
utilization rate
A EEUC1.K=EUC1.K+C1UTR.K Expected Class I
utilization
A EUC1.K=TABHL (EUCIT*, MP.K,.75,11.25,.5)
Seasonal Class I
utilization

11







C EUCIT*="41.0/39.1/39.1/43.2/43.2/40.6/40.6/39.2/39.2/34.1
34.1/34.7/34.7/35.2/35.2/36.5/36.5/38.3/38.3/37.0
37.0/40.2
R C2UR.KL=DELAY 3 (RAC2.JK, DP2) Class II
C DC1 =.25 utilization rate
C DC2=.5 Delay constants
Class I and II utilization rates are independent of retail
prices. The main reason for not permitting retail prices to af-
fect C1UR and C2UR is the lack of conclusive empirical evi-
dence concerning consumer purchase response to changes in milk
prices in southeast Florida and other areas. For example, recent
estimates of the own price elasticities of consumer demand for
Class I and Class II products in the U.S. were found to be sta-
tistically insignificant [16]. Other determinants of consumer


43.2
43

42

S41 41.0
41
D 40.6 40.2
0 40-

S. 39 39.2
0 39.1 38.3
n 38

- 37
J 36.5 37.0
2 36
35 35.2
34 1 34.7
34.1

J F M A M J J A S O N D
MONTHS

Figure 5.-Seasonal component of fluid milk utilization, southeast Florida, by
months, 1966-69 average.

12












"15


ICL
S14-




S13
0





o

6.0 6.4 6.8 7.2 7.6 8.0
Producer Class I Price ( /cwt.)





Figure 6.-Relationship between producer and consumer Class I prices, south-
east Florida, 1966-69.

utilization, such as the seasonal component and population
changes are accounted for in EEUC1.
Prices
The model specifies the prices received by producers (paid
by processors), prices received by processors (paid by retailers),
and prices received by retailers (paid by consumers) expressed
in dollars per hundredweight. Class I and Class II prices re-
ceived by producers (C1P and C2P) are the sum of the one-
month lagged price per hundredweight paid for 3.5 percent milk
by Minnesota-Wisconsin manufacturing plants (referred to as
the basic formula price, BFP) and the corresponding Class I and
Class II price differentials (C1PD, C2PD) [5]. The Class I price
differential represents the cost of transporting raw milk from
Minnesota-Wisconsin to federal order 13. The Class II price dif-
ferential was computed by taking the difference between the 1966

13







minimum Class II price in southeast Florida and the basic for-
mula price. Both differentials were assumed to be constant over
the simulation period. The observed basic formula price was
included in the model by means of a table function (BFPT*).
Blend price received by producers equals total producer returns
(TPR) divided by total milk allocated to Class I and II uses
(RAC1 +RAC2).
An examination of prices paid by consumers and received by
producers for Class I milk shows that the relationship between
these two prices can be closely approximated by a step function
(C1CST, Figure 6). For example, when producer prices vary
between $6.40 and $6.85 per hundredweight, the consumer price
remains fairly constant at $14.2 per hundredweight. Consumer
prices of Class I milk (C1C) used to compute consumer expendi-
tures were determined by geometric smoothing of the Class I
consumer prices generated by the table function (C1C*). Geo-
metric smoothing permits consumer prices to adjust gradually
to changes in producer prices.
Consumer prices of Class II products involved more elaborate
computations. During the 1966-69 period Florida milk was allo-
cated to nine major Class II uses: buttermilk, flavored milk
drinks, half and half, table cream, sour cream, cottage cheese,
ice cream, ice milk, and sherbert. Since Class II uses constitute
a secondary outlet for producer milk, Class II products were
treated as a single-use category. Since consumer prices are used
to compute consumer expenditures on milk, the aggregation of
Class II products into a single category necessitated a weighted
average consumer price for Class II products in terms of whole
milk equivalents. A whole milk equivalent price was needed since
the Class II utilization rate (C2UR) is measured in whole milk
equivalents (3.5% milk). Computation of the Class II consumer
price is explained in Appendix B. The initial (computed) Class II
consumer price for January 1966 (IC2C=$14.75) was increased
by five cents per month by adding the Class II price trend (C2T
which is a Ramp function) to the initial price. This gave the
Class II consumer price (C2C) used to compute consumer ex-
penditures.
Prices received by processors for Class I and Class II products
(PRPC1, PRPC2) were defined, since no data were available on
these prices, by multiplying one minus the gross retail price
margins (RMARG1, RMARG2) by consumer prices. Since data
on retail milk margins are not published for Florida, the margins
were based on price margin data for 50 Midwestern supermar-

14








kets [14]. The gross retail margin for Class I products is about
15 percent and the Class II margin about 18 percent of the cor-
responding consumer price.
Farm, processor and consumer price equations are:
A BFP.K=TABHL (BFPT*, TME.K, 0, 48, 1)
Basic formula price
C BFPT*=3.47/3.47/3.58/3.68/3.64/3.65/3.82/4.05/4.26/4.34/
4.26/4.15/4.14/4.08/4.02/4.01/3.98/3.96/3.96/3.95/
3.97/3.97/3.98/4.00/4.04/4.01/4.00/4.02/4.18/4.19/
4.18/4.18/4.20/4.23/4.28/4.27/4.30,/4.27/4.23/4.28/
4.34/4.37/4.39/4.41/4.42/4.49/4.58/4.62/4.63
L TME.K=TME.J+DT Time counter
N TME=0
A C1P.K=BFP.K+C1PD Class I
C C1PD=3.10 producer price
A C2P.K=BFP.K+C2PD Class II
producer price
C C2PD=1.04
"A BP.K=TPR.K/ (RAC1.JK+RAC2.JK) Blend price
"A TPR.K= (C1P.K) (RAC1.JK) + (C2P.K) (RAC2.JK)
Total producer
returns
L C1C.K=C1C.J+ (DT/CPC) (C1CS.J-C1C.J)
Class I
Consumer Price
C CPC= .5
A CICS.K=TABHL (C1CS*, C1P.K, 6.40, 7.80, .05)
C C1CS* = 14.2/14.2/14.2/14.2/14.2/14.2/14.2 /14.2/14.2/14.2/
14.4/144.4/14.4/14.4/14.4/14.4/14./14.4/14.4/14.9/14.9/14.9/
14.9/15.3/15.3/15.3/15.3/15.3/15.3 /15.3/15.3/15.3/
N C1C=14.2
A C2C.K= IC2C+ C2T.K Class II consumer price
A C2T.K=RAMP (.05, 1.0)
C IC2C=14.75
A PRPC1.K= (1-RMARG1) (C1C.K) Class I processor price
C RMARG1=.15 Class I price margin
A PRPC2.K= (1-RMARG2) (C2C.K) Class II processor price
C RMARG2=.18 Class II price margin

15








Revenue and Cost
Revenues received by retailers, processors, and producers
are ultimately derived from total consumer expenditures. Con-
sumer expenditures equal Class I retail price times Class I util-
ization (C1R x C1UR) plus Class II retail price times Class II
utilization (C2R x C2UR). Total returns to retailers (TRR) is
the product of the retail margin on Class I products (RMARG1)
times consumer expenditures on Class I products plus the retail
margin on Class II products (RMARG2) times consumer ex-
penditures on Class II products. Note that TRR is equivalent to
gross returns to retailers after payments to processors but be-
fore deducting retail handling costs. Since data on retail costs
of handling milk were not available, it was not possible to com-
pute net returns to retailers.
Total returns to processors (TRP) equal total consumer ex-
penditures minus total returns to retailers. To obtain net returns
to processors (PCNR), costs of milk assembly, processing, and
distribution are deducted from total processor returns. Proces-
sors are assumed to incure assembly (from producers to proces-
sors) and milk distribution (from processors to retailers) costs.
This is the typical arrangement in southeast Florida.
Raw milk assembly cost (RAC) is the product of the milk
production rate (MPR) and per unit assembly costs (PAC).
The value of PAC in 1965 [20], namely 22 cents per hundred-
weight, was used. Packaged milk distribution costs (GDC) is the
product of total milk utilization (C1UR+C2UR) and per unit
distribution costs (PDC). Packaged milk distribution costs (for
a 20% home delivery-80% wholesale distribution) were com-
puted to be $2.50 per hundredweight based on cost figures de-
veloped by Stennis et al. [20].
Costs of processing Class I milk products (CCOP1) and Class
II products (CCOP2) are set at $1.50 and $.50 per hundred-
weight, respectively. The Class I figure reflects 1965 cost con-
ditions in Miami [20]. Class II processing costs are not available
for Florida. The figure used here pertains to dry whey and cheese
plans in Minnesota in 1965 [10]. Assembly, processing and dis-
tribution costs were held constant throughout the analysis.
Producer net returns (PRNR) equal total producer returns
(TPR) minus total milk production costs (TPC). Total produc-
tion cost is the product of the milk production rate and the aver-
age cost of milk production (ACP). Greene [6] estimated the
average cost of milk production in 1965 for each of four groups
of dairy farms in southeast Florida. The weighted average cost

16








of production for the four groups (using annual milk sales for
each group as weights) is $6.30 per hundredweight. Starting
from the $6.30 level in January 1966, production costs were al-
lowed to increase at an annual rate of two percent per year.
This pattern of costs was generated by a table function (AC*).
Initially a 5 percent annual increase in production costs was
simulated but rejected because it yielded negative net returns
to producers. A value of 2 percent was chosen because it yielded
quite reasonable results.
The production incentive (PI), which allows the milk pro-
duction rate to deviate from expected milk utilization, varies
with respect to the return-cost comparison (RCR) or ratio of
total producer returns to total milk production costs. When this
ratio is less than 1.05, milk production decreases and when it is
equal to or greater than 1.05, production increases from the level
of expected utilization. The complete relationship between the
RCR ratio and the production incentive is defined by a table
function (PI*). Since milk production is not expected to adjust
instantaneously to changes in the revenue-cost ratio, a third-
order delay with a delay constant (PDQ) of three months was
applied to the production incentive. The product of the delayed
production incentive (DPI) and total milk utilization deter-
mines the milk production rate.
Revenue and cost equations are:

A TCE.K= (C1R.K) (C1UR.JK) + (C2R.K) (C2UR.JK)
Total consumer expenditures
A TRR.K= (RMARG1) (C1R.K) (C1UR.JK) +
(RMARG2) (C2R.K) (C2UR.K) Total retail returns
A TRP.K=TCE.K-TRR.K Total processor returns
A PCNR.K=TRP.K-TPR.K-COP.K-RAC.JK-GDC.JK
Processor net returns
A COP.K= (RAC1.JK) (CCOP1) + (RAC2.JK) (CCOP2)
I Costs of processing
C CCOP1=1.50 Per unit Class I
processing costs
C CCOP2= .50 Per unit Class II
processing costs
R RAC.KL= (PAC) (MPR.JK) Raw milk
assembly costs

17








C PAC= 0.22 Per unit raw milk
assembly costs
R GDC.KL= (PDC) (C1UR.JK+C2UR.JK)
Packaged milk
distribution costs
C PDC=2.50 Per unit milk
distribution costs
A PRNR.K=TPR.K-TPC.JK Producer net returns
R TPC.KL= (MPR.JK) (ACP.K) Total production costs
A ACP.K=TABHL (AC*,TME.K, 0, 48, 1)
Average cost per
hundredweight
C AC* = 6.30/6.310/6.321/6.331/6.342/6.352/6.363/6.373/
6.384/6.394/6.405/6.415/6.426/6.437/ 6.447/6.458/
6.469/6.480/6.491/6.502/6.512/6.523/6.534/6.545/
6.556/6.566/6.577/6.588/6.598/6.609/6.620/6.631/
6.642/6.653/6.664/6.675/6.686/6.697/6.708/6.719/
6.731/6.742/6.753/6.764/6.776/6.787/6.798/6.808/6.820
A PI.K=TABHL (PI*,RCR.K,.95,1.25,.05)
Production incentive
C PI*= .96/.98/1.00/1.02/1.04/1.06/1.08
A RCR.K=TPR.K/TPC.JK Revenue/cost ratio
R DPI.KL= DELAY 3 (PI.K, PDQ) Delay production
incentive
C PDQ=3
N DPI=1

IV. MODEL VALIDATION
Model validation refers to the consistency between simulated
and real system behavior. Consistency is judged here by the
degree of similarity between the variables generated by the sim-
ulation model and the real system. The model developed in sec-
tion III was checked for consistency several times, particularly
when modifications of the model were made. In this section the
overall consistency of the basic model is discussed.
Data are not available on many of the variables generated by
the simulation model. Published data were available on six vari-
ables: producer milk utilized in Class I products (RAC1),

18







producer milk utilized in Class II products (RAC2), producer
milk deliveries to handlers (approximately equivalent to the
monthly production rate, MPR), blend price (BP), proportion
of producer milk used in Class I products (P), and total pro-
ducer returns (TPR= MPR BP).
Since all simulations were based on a solution interval (DT)
of one-twentieth of a month, 20 values per month can be gener-
ated on each variable. In actual runs the variables were printed
at intervals of 10 DT's, i.e. approximately mid-month and end-
of-month. A monthly value was constructed by averaging the
mid-month and end-of-month values. Consistency was checked
by comparing the simulated and observed values of the six vari-
ables on a quarterly basis, i.e. the average of the three monthly
values in each quarter (Jan.-Feb.-Mar., Apr.-May-June, July-
Aug.-Sept., Oct.-Nov.-Dec.).6 Table 1 gives the simulated and ac-
tual values of the six variables, the difference between the simu-
lated and actual value, and the difference as a percentage of the
actual value. For example, the first quarter 1966 figures for
RAC1 show that simulated Class I utilization is 1,089 million
pounds or 2.62 percent below actual utilization. Absolute per-
centage differences- are smallest for blend price (1.51%), fol-
lowed by MPR (1.80%), RAC1 (2.16%), P (2.53%) and TPR
(2.55%). For RAC2 the percentage differences are quite large
with an average absolute percentage difference of 17.56 percent.
Apparently, the model is least accurate in determining RAC2. This
inaccuracy may be due in part to the importation of milk for Class
II uses which is not accounted for by the model. However, since
Class II utilization is small relative to Class I utilization, the
in accuracies in RAC2 have only a minor effect on the consis-
tency of other variables. The direction of the differences (posi-
tive or negative) between the simulated and actual values of
the six variables does not exhibit a systematic pattern. In gen-
eral, the comparisons indicate that the basic model accurately
generates milk production, utilization, and farm prices in the
southeast Florida milk market. For this reason the basic model
is judged to be an acceptable mathematical representation of the
real system.
V. ANALYSIS OF INTERREGIONAL COOPERATIVE
The interregional cooperative analysis is primarily concerned
with investigating the changes in net returns to producers, proc-
essors, and retailers that would occur if some Florida producers
become associated with an interregional dairy cooperative. As
viewed here the dairy cooperative's primary objective would be

19











0 m t o t C a co C-4,w
SC c 0 C CT 1
C1 N1 M^ 1 C N 4 N N t

t I I 1 1 .
IL

cu c



So *-



"c
'C 8








- rom ( 0) CD 0D o 0 0 0))
m m 0 Itc N -d r mo(
M' U - 0P) N -N -
0 :



o 0
e 0 )I, a COCto m LO Lrco) m cto m D)No
t S 0 -(D 0 rco 0 ro ) C C CN4
m Cto)(OCO 0 0 C4O -o0)C- 0) LO 0
SE U mLO i (d(1m e 1(6101 (6 (60L6








CY rg coi~i~o > O)











oE
N O0 t; :- 0 4





00 C
- C.D D
cn Sr, c S~ m ( rco o c,,Or(o rcO mp^T r r0*c-4
t S : rcic, Omlo ItR (M
o 4












0



( r-1'( c0Cco 0 ) 100)N
0 0
0 2
- .0 o-c (or" (OCDOCT -r-Lmf 0)(0)0)






co 0









Table 1.-Comparison of actual and simulated values of six variables, monthly averages by quarters, southeast Florida, 1966-69.
(Continued)

Variable Monthly Production Rate (MPR) Blend Price (BP)
Year, Differ- Percentage Differ- Percentage
quarter Simulated Actual ence" difference Simulated Actual ence" difference

-------- 1000 Ibs. -------- Percent -------- $/cwt. -------- Percent

1966 1 45,795 45,863 68 .15 6.42 6.22 .20 3.22
2 44,849 46,332 -1,483 -3.20 6.53 6.19 .34 5.49
3 41,252 40,872 380 9.30 7.02 6.98 .04 .57
4 45,944 45,227 717 1.59 7.04 7.11 .07 .98

1967 1 48,876 49,288 412 .84 6.89 6.93 .04 .58
S2 47,267 47,762 495 -1.04 6.81 6.76 .05 .74
" 3 42,901 44,013 -1,112 -2.53 6.81 6.73 .08 1.19
4 46,564 48,210 -1,646 -3.41 6.85 6.74 .11 1.63

1968 1 49,390 50,672 -1,282 -2.53 6.86 6.84 .02 .29
2 48,237 49,762 -1,525 3.16 7.01 6.67 .34 5.10
3 44,384 43,835 549 1.25 7.05 7.14 .09 -1.26
4 48,259 45,907 2,352 5.12 7.13 7.21 .08 -1.11

1969 1 51,173 49,891 282 2.57 7.11 7.19 .08 -1.11
2 49,935 49,227 708 1.44 7.19 7.14 .05 .70
3 45,969 45,613 356 .78 7.28 7.28 0 0
4 49,955 49,042 913 1.86 7.45 7.47 .02 .27

"Simulated minus actual.
"bDifference as a percent of actual.
Source: For actual values [22]. Continued









Table 1.-Comparison of actual and simulated values of six variable 3, monthly averages by quarters, southeast Florida, 1966-69.
(Continued).

Variable Proportion of Milk in Class I (P) Total Producer Returns (TPR)

Year Differ- Percentage Simulated Actual Differ- Percentage
quarter Simulated Actual encea difference ence" difference

-------- 1000 Ibs. -------- Percent -------- $1,000 -------- Percent

1966 1 88.32 90.55 -2.23 -2.46 2,938 2,852 86 3.02
2 87.40 83.60 3.80 4.55 2,941 2,870 71 2.47
3 87.84 87.41 .43 .49 2,888 2,854 34 1.19
4 87.57 87.05 .52 .60 3,211 3,212 1 .03

S1967 1 87.63 87.57 .06 .07 3,368 3,413 45 -1.32
2 87.18 83.91 3.90 3,232 3,231 1 .03
3 87.83 16.64 1.19 1.37 2,916 2,961 45 -1.52
4 87.97 87.44 .53 .61 3,169 3,251 82 -2.52

1968 1 88.08 87.22 .86 .99 3,389 3,465 76 -2.19
2 87.36 81.47 5.89 7.23 3,395 3,318 77 2.32
3 87.87 88.81 -1.01 -1.14 3,621 3,131 490 15.65
4 87.89 90.67 -2.78 -3.07 3,416 3,309 107 3.23

1969 1 87.98 90.15 -2.20 -2.44 3,638 3,587 51 1.42
2 87.35 87.58 .23 .26 3,608 3,515 93 2.65
3 87.87 90.60 -2.73 -3.01 3,339 3,332 17 .51
4 87.87 91.71 -3.84 -4.19 3,695 3,667 28 .76

"Simulated minus actual.
bDifference as a percent of actual.
Source: For actual values [22].







to negotiate producer prices for the purpose of obtaining higher
net returns for member producers. Anyone of a number of ex-
isting interregional dairy cooperatives would fit this description.
Florida membership in an interregional cooperative was sim-
ulated using a modified version of the basic model. The pro-
cedure involved specifying the adjustments that were likely to
result from the activities of an interregional cooperative and in-
corporating these adjustments into the basic model. The adjust-
ments, which are the key assumptions underlying the interre-
gional cooperative analysis, were based on market changes in
the north central states that resulted from the activities of inter-
regional cooperatives [9]. The experience in the north central
states was felt to be representative of the changes that would
occur if an interregional cooperative operated in Florida. The
following adjustments were specified:
a. Forty-two percent of the milk produced is marketed
through the interregional cooperative (PMC=.42). The
remaining 58 percent is sold by independent producers.
b. Processor-oriented services provided by the cooperative
enable the cooperative to negotiate a Class I premium
(C1PR) of 30.5 cents per hundredweight on all milk.
c. Processor-oriented services provided by the cooperative
permit milk producers to reduce distribution costs (RDC)
on member produced milk.by 11.6 cents per hundredweight.
d. To finance the producer-oriented services rendered by the
cooperative, coop-member producers pay a service fee
(retained by the cooperative) of 10 cents per hundred-
weight.
e. Coop-member producers sell all their milk through the
cooperative and independent producers sell all their milk
independently of the cooperative.
Values in a through d reflect average adjustments on the north
central region. Although there is little basis for selecting dif-
ferent values for Florida, market conditions in Florida could
lead to different premiums, service fees and reduction in milk
handling costs.
A condensed flow diagram of the milk production and proc-
essing segments of the cooperative model appears in Figure 7.
"The mathematical formulation is given in Appendix C. Symbols
appearing in Figure 7 are the same as those in Figure 1
with the addition of the dashed line (- -). The latter
signifies that other variables in addition to the one from which
the line originates affect the variable at which the line termi-

23





PC COP


Costs of
Processing
Costs of
production



S MONTHLY MEMBER
Ct PRODUCTION RATE

-\MMPR PCNR
Member
Net Service 1
Returns / Fees j Processor
lR f \ Net Returns
MPRNR
\SF I RDC


\ I Reduction in
Production
Production Handling costs
BP 1

NPRNR

Non-Member Price Processor Total
Net Returns P Cooperative Inventor Returns


k\V Premium I C1PI

NMPR C1PR

--- NON-MEMBER MONTHLY
cost of PRODUCTION RATE ALLOCATION TO CLASS I AND
Productio L USES- RAC1, RAC2



PC Figure 7.--Condensed flow diagram of milk production and processing segments of cooperative model.








nates. The distinguished feature of the cooperative model is the
separation of milk produced by cooperative-member producers
from milk produced by independent producers. This separation
was required to account for the service fee and reduction in
handling costs on member produced milk. Note that all produc-
ers receive the Class I premium. The distinction between mem-
ber and non-member produced milk is not carried over to the
processor segment of the model. That is, the same proportion of
member and non-member produced milk is allocated to each use.
Since remaining segments of the cooperative model are essential-
ly the same as in the basic model, they are omitted from Figure 6.
A question arises concerning the evaluation of the coopera-
tive model. Should the behavior of the cooperative model be
compared with the behavior of the real system or the basic
model? Since the cooperative model is essentially a modification
of the basic model and the latter adequately represents the real
system, comparisons are made between the cooperative and basic
models. Six variables are selected for comparison: monthly pro-
duction rate (MPR), rate of allocation to Class I (RAC1) and
Class II (RAC2), producer net returns (PRNR), processor net
returns (PCNR) and total retail returns (TRR).



Results
Table 2 contains the values of six selected variables gener-
ated by the basic and cooperative models and the differences be-
tween these values expressed in actual and percentage terms.
Tabled values are monthly averages for the three months in each
quarter. Except for processor net returns, variables for the co-
operative model exceed those for the basic model in every quar-
ter. The differences in milk production rates for the two models
exhibit a systematic pattern. The largest differences occur in the
second quarter followed in descending order of magnitude by
the first, third, and fourth quarters. The average percentage
difference for MPR over the entire period is quite small at 1.18
percent. Percentage differences in RAC1 are also small ranging
from .93 to .99 in the first, third, and fourth quarters and 1.30
to 1.39 in the second quarter with an average difference of 1.06
percent. Differences in RAC2 are also quite small averaging 3.07
percent.
Despite minor differences in MPR, RAC1, and RAC2, pro-
ducer net returns under the cooperative model are 26 to 68 per-

25








Table 2.-Comparison of simulated milk production, processor utilization and returns, basic and cooperative models, monthly averages
by quarters, southeast Florida, 1966-69.

Variable Monthly production rate (MPR) Rate of allocation to Class I (RAC1)
Year, Cooperative Basic Differ- Percentage Cooperative Basic Differ- Percentage
quarter Model Model encea Differenceb Model Model encea Difference"

........... 1,000 1 b................. Percent ........... 1,000 Ib ............. Percent

1966 1 46,359 45,795 564 1.22 40,843 40,437 406 .99
2 45,581 44,849 732 1.61 39,838 39,286 552 1.39
3 41,761 41,252 509 1.22 36,539 36,181 358 .98
4 46,261 45,944 317 .69 40,394 39,969 425 1.05

S1967 1 49,534 48,876 658 1.33 43,307 42,825 482 1.11
2 48,020 47,267 753 1.57 41,880 41,309 571 1.36
3 43,434 42,901 533 1.23 38,015 37,637 378 .99
4 46,904 46,564 340 .72 41,092 40,713 379 .92

1968 1 50,044 49,390 654 1.31 43,909 43,496 413 .94
2 48,982 48,237 745 1.52 42,798 42,230 568 1.33
3 44,919 44,384 535 1.19 39,329 38,954 355 .90
4 48,691 48,259 342 .70 42,562 42,175 387 .91

1969 1 51,834 51,173 661 1.28 45,446 45,014 4?2 .95
2 50,689 49,935 754 1.49 44,284 43,709 575 1.30
3 46,512 45,969 543 1.17 40,727 40,347 380 .93
4 50,298 49,955 343 .68 44,031 43,621 410 .93


Continued









Table 2.-Comparison of simulated milk production, processor utilization and returns, basic and cooperative models, monthly averages
by quarters, southeast Florida, 1966-69. (Continued)

Variable Rate of Allocation to Class II (RAC2) Producer Net Returns (PRNR)
Year, Cooperative Basic Differ- Percentage Cooperative Basic Differ- Percentage
quarter Model Model encea Differenceb Model Model encea Differenceb

...... 1,000 Ib ...... Percent ......... 1,000 Ib ........ Percent

1966 1 5,596 5,348 248 4.43 149 48 101 67.79
2 5,839 5,657 182 3.12 183 82 101 55.19
3 5,158 5,007 151 2.93 360 265 95 26.39
4 5,816 5,670 146 2.51 394 287 107 27.16

b 1967 1 6,222 6,046 176 2.83 331 219 112 33.84
2 6,205 6,066 139 2.24 265 157 108 40.75
3 5,371 5,216 155 2.89 227 130 97 42.73
4 5,775 5,565 210 3.64 249 144 105 42.17

1968 1 6,125 5,885 240 3.92 256 144 112 43.75
2 6,283 6,105 178 2.83 306 196 110 35.95
3 5,536 5,377 159 2.87 283 186 97 34.28
4 6,000 5,793 207 3.45 329 219 110 33.43

1969 1 6,377 6,148 229 3.59 326 209 117 35.89
2 6,418 6,326 92 1.43 344 230 114 33.14
3 5,732 5,569 163 2.84 339 234 105 30.97
4 6,223 6,002 221 3.55 439 319 120 27.33


aValue for cooperative model minus value for basic model. Continued
"bAs a percentage of value for cooperative model.








Table 2.-Comparison of simulated milk production, processor utilization and returns, basic and cooperative models, monthly averages
by quarters, southeast Florida, 1966-69. (Continued)

Variable Processor Net Returns (PNR) Total Returns to Retailers (TRR)
Year, Cooperative Basic Differ- Percentage Cooperative Basic Differ- Percentage
quarter Model Model encea difference Model Model encea Differenceb

....... 1,000 lb.................. Percent ........1,000 lb.......... Percent
1966 1 722 782 60 -8.31 1,033 1,019 14 1.36
2 532 580 48 9.02 994 973 21 2.11
3 595 554 41 6.89 962 932 30 3.12
4 651 642 9 1.38 1,063 1,036 27 2.54
1967 1 774 632 142 18.35 1,141 1,090 51 4.47
00 2 586 525 61 10.41 1,071 1,034 37 3.45
3 669 612 57 8.52 995 962 33 3.32
4 736 656 80 10.87 1,079 1,041 38 3.52
1968 1 844 720 124 14.69 1,149 1,117 32 2.79
2 699 632 67 9.59 1,130 1,091 39 3.45
3 753 727 26 3.45 1,060 1,031 29 2.74
4 617 749 -132 -21.39 1,146 1,115 31 2.71
1969 1 858 829 29 3.38 1,228 1,195 33 2.69
2 669 739 70 -10.46 1,178 1,163 15 1.27
3 702 812 -110 -15.67 1,104 1,098 6 .54
4 664 787 -123 -18.52 1,190 1,185 5 .42

aValue for cooperative model minus value for basic model.
"bAs a percentage of value for cooperative model.








cent greater than under the basic model with an average differ-
ence of 38 percent. This result is not too surprising, since all
producers receive a Class I premium of 30.5 cents per hundred-
weight under the cooperative structure. Comparing total pro-
ducer net returns under both models shows that over the entire
period producers receive $514.3 thousand more under the co-
operative arrangement. Of this amount, member producers
receive about 38 percent or $195.4 thousand and independent
producers receive 62 percent or $318.9 thousand, even though
member producers account for 42 percent and independent pro-
ducers account for 58 percent of milk sales. This seemingly un-
equitable distribution of net revenue between member and
independent producers occurs because member producers pay a
service fee of 11.6 cents per hundredweight while all producers
receive the Class I premium.
Processor net returns are greater under the cooperative
arrangement in ten quarters and lower in six quarters. For the
entire period processor net returns are $76.8 thousand more than
in the absence of a cooperative. The gain in total processor net
returns is substantially smaller than the gain in producer net
returns.
Total returns to retailers (after payments to processors) are
slightly greater under the cooperative arrangement. Monthly
differences range from $5 to $51 thousand with an average of
2.34 percent. While the differences do not exhibit a quarterly
pattern, they decrease substantially during the last three quar-
ters of 1969. Total retail returns for the entire period are $136
thousand higher with a cooperative.
Since the Class I farm price in the cooperative model con-
tains a premium, the Class I retail (C1R) price in the cooperative
model is on the average greater than the C1R price in the basic
model. This occurs because C1R is a step function of Class I farm
price (see Figure 6). The maximum Class I price permitted by
the step function ($15.30 per hundredweight) was attained
sooner in the cooperative model than in the basic model; July
1968 vs. August 1969. Since Class I utilization and retail prices
are both greater under the cooperative arrangement, total con-
sumer expenditures are also larger. Total consumer expenditures
over the entire period are $34.1 million for the cooperative model
and $33.2 million for the basic model.
Compared to the basic structure, a cooperative arrangement
yields greater returns to producers, processors and retailers.



29








Admittedly, returns under the cooperative model, or for that
matter any arrangement that increases farm prices, would be
greater as long as the Class I premium is passed on to consumers
in the form of higher consumer prices for Class I milk. However,
it is unlikely that the entire increase in Class I producer prices
could be passed on to consumers. Specifically, higher Class I con-
sumer prices may reduce Class I utilization. Provided consumer
demand was inelastic, total consumer expenditures would in-
crease. As previoulsy mentioned, there have been no time series
studies on consumer demand for fluid milk in Florida. Moreover,
several demand studies at the national level show that milk
consumption is not significantly related to milk prices. For these
reasons, the basic model assumes that consumer milk purchases
are not responsive to changes in milk prices at least over the
range of Class I prices permitted in the models, i.e. $1.22 to
$1.31 per gallon.



VI.-ANALYSIS OF PROCESSOR-RETAILER INTEGRATION
The effects of processor-retailer integration on returns to
processors and distributors were analyzed using a modification
of the basic model referred to as the integration model. The in-
tegration model is based on several assumptions regarding
changes in milk processing and distribution costs (cost adjust-
ments) associated with processor-retailer integration. Unlike
the case with the cooperative model, there was no previous ex-
perience on which to base the cost adjustments assumed for the
integration model. Cost adjustments were expressed in terms of
the relative operational efficiency of integrated and independent
plants.
Integration is most likely to occur by large retail food chains
acquiring control of processing plants. Accordingly, the larger
more efficient plants are more likely to integrate into retail dis-
tribution. Small retail food chains would therefore have to obtain
the bulk of their milk from smaller, less efficient plants. For
these reasons, integrated processors were assumed to have lower
per unit processing and distribution costs than independent
processors. Due to lack of information concerning per unit costs
of operating integrated versus independent plants, costs reduc-
tions were defined in terms of percentage deviation from the
costs specified in the basic model.
Three alternative cost adjustments were simulated with the

30








Table 3.-Alternative levels of operational efficiency for integrated and inde-
pendent milk processing plants.

Efficiency level

Activity I II III I II ll

Integrated Independent

percent-
Processing -5 -10 -15 +15 +10 +5
Distribution -2 5 -8 +8 +5 +2





integration model (Table 3). Efficiency level I is the least ef-
ficient, level II is moderately efficient and level III is the most
efficient of the three in terms of operational costs of integrated
plants relative to independent plants.
The presence of integrated processor-retailers was assumed
to have no effect on producer and consumer prices. Class I and
II producer prices are determined by federal market orders
and premiums established by cooperatives. Hence, producer
prices are unlikely to change as a result of integration. Blend
prices depend on producer prices and the allocation of milk to
Class I and II uses. Processors do affect this allocation; however,
there is no reason to expect the allocation to differ between in-
tegrated and independent plants since both face the same milk
consumption pattern. The (assumed) independence of retail
margins and consumer prices from processor-retailer integra-
tion is perhaps more difficult to accept since private label milk'
(which is likely to account for a significant share of sales of
integrated processor-retailers) is likely to have different gross
retail margins and consumer prices than processor label milk.
However, the magnitude of these margin and price differences
would be small relative to their absolute levels.
Thus far the proportion of producer milk allocated to inte-
grated and independent plants has not been specified. This allo-
cation has an important effect on processor net returns due to
the assumed differences in processing and distribution costs for
integrated versus independent plants. Four allocations were
simulated (Figure 8). Under allocation one, 10 percent of the
milk is handled by integrated plants and 90 percent by inde-

31









Allocation I
i--------------------- _------,

I0%0/ Integrated I0% ^ Integrated :35%
Plants Retailers
Milk L ------ ---------- ----------- ---------- --- Consumption
Production 25/
Independent Independent I '
90% plants 65%/ Retasler 65%


Allocation 2
------ -- -- --- -

35% Integraed 35% Integrated 35%
i ^ Plants
Milk L----------------------------1 Consumption
Production
Independent Independent
65% Plants 65% Retal 65%


Allocation 3
Large 35% Large
Integrated Integrated
350% Pnts Plants 35%
15% 25%/
Mik Small 15% Medium & Small
Production Integrated 3P5 Integrated Consumption
Plants Retailers

10Y
50% I O% 40%
Independent Independent
Plants 40% Retailers


Allocation 4
Large 35% Large
Integrated Integrated
35% Plants Retailers 35%
15% 5% --
Small 25% Medium& & f
Product Integrated Small Integrated Consumption
Plants Retailers


40% 40%
"40 "Independent Independent
Plants 40% Retailers




Figure 8.-Alternative allocations of milk between integrated and independent
plants and retailers.

32








pendent plants. Twenty-five percent of the milk processed by
independent plants is sold to integrated retailers and 65 percent
to independent retailers. Allocation two is similar to one except
that only 65 percent of the milk produced is handled by inde-
pendent plants all of which is sold to independent retailers. In
allocation three a distinction is made between large and medium-
to-small integrated processor-retailers. Allocation four is simi-
lar to three except that only 40 percent of the milk produced is
handled by independent plants all of which is sold to independent
retailers. Table 4 gives the per unit costs of processing and
distributing Class I and II milk under each product allocation
and efficiency level. These costs were used in the processing
segment of the integration model. The mathematical formulation
of the integration model is discussed in Appendix D.



Results
Since the cost adjustments and product allocations specified
for the integration model do not affect the producer and retail
segments of the basic model, returns to producer and retailers
do not vary with the allocation or efficiency level. However, the
rate of production and farm prices do affect the level of net
returns to processors. The processor segment for each of the
four allocations and three levels of efficiency was run with the
producer and retail segments of the basic and cooperative models.
Processor net returns for these runs are reported in Table 5.
Processor net returns under all four allocations and three
efficiency levels are greater for the cooperative-integration than
the basic-integration model. This result reflects the higher milk
production rate in the cooperative model than in the basic model.
For the basic and cooperative integration models, processor net
returns increase from allocation one to allocation four and from
efficiency I to III. This illustrates two points. First, as the pro-
portion of milk handled by integrated plants increases, total
processor net returns increase for every level of efficiency.
Second, the greater the cost reductions due to integration, the
greater the increase in processor net returns. Changes in net
returns are quite sensitive to product allocation and the level
of efficiency. Table 5 shows the trade-offs for increasing proces-
sor net returns by increasing the extent of integration (moving
from structure one to structure four) versus increasing the
efficiency of integrated plants (moving from efficiency I to III).

33










Table 4.-Per unit costs of processing and distributing Class I and Class II milk for integrated and independent plants by milk allocation.

Integrated Plants Independent Plants
Efficiency
Level: Processinga Distributionb Processinga Distributionb
Allocation
Class I Class II Class I & II Class I Class 11 Class I & II
Value Percente Value Percente Value Percente Value Percentc Value Percentc Value Percentc
S/cwt. S/cwt. S/cwt. S/cwt. $/cwt. $/cwt.

Efficiency
Level 1:
1 & 2 1.425 95 .475 95 2.45 985 1 2
3 & 4 1.425 95a .475 95' 2.45 98 2875 5 575 5 270
1.470 98e .49 98e 2.55 102e 2.875 115 .575 115 2.70 108
Efficiency
Level 11:
1 & 2 1.350 90 .450 90 2.375 95625 105
3 & 4 1.350 90' .450 90' 2.375 95d 2.750 110 .55 110 2.625 105
1.425 95e .475 95e 2.500 100e 2.750 110 .55 110 2.625 105
Efficiency
Level III:
1 & 2 1.275 85 .425 85 2.30 92
3 & 4 1.275 85d .425 85d 2.30 92 2.625 105 .525 105 255 102
1.380 92e .460 92e 2.45 98 e 2.625 105 .525 105 255 102
aExcludes milk assembly costs from farm to plant and cost of raw milk.
includess only cost of distributing milk from plant to retailer.
cAs a percent of corresponding value for basic model.
"dFor large integrated retailer. eFor small and medium integrated retailer.









Table 5.-Average monthly and total processor net returns for basic, cooperative and integration models under four milk allocation and
three efficiency levels, 1966-69.

Integration-Efficiency I

Period Model Basica Cooperativeb
Basic Cooperative 1 2 3 4 1 2 3 4

...................... .................. $1,000.......................................
Monthly
Average 684 700 521 583 605 623 535 597 624 636

Total (1966-69) 3,285 3,362 2,490 2,786 2,915 3,001 2,591 2,859 2,989 2,561
co
CA Integration-Efficiency II

Monthly Average 589 650 674 689 602 664 688 704

Total (1966-69) 2,813 3,108 3,219 3,294 2,886 3,183 3,296 3,371

Integration-Efficiency III

Monthly Average 656 717 737 750 670 733 752 765

Total (1966-69) 3,136 3,431 3,525 3,587 3,211 3,509 3,603 3,667

aUsing production and retail segments of basic model.
bUsing production and retail segments of cooperative model.








For example, moving from structure one to two under basic in-
tegration, efficiency I increases processor net returns from $521
to $523 thousand, or 12 percent, whereas moving from efficiency
I to II under structure one increases net returns from $521 to
$589 thousand or 13 percent. In this trade-off comparison, ap-
proximately the same increase in net returns can be achieved
under two different arrangements. Comparisons such as these
give insight into the structural alternatives for improving re-
turns by integration.
Total net returns over the 1966-69 period were slightly
greater when independent plants sold all their milk to inde-
pendent retailers than when sales were divided between inte-
grated and independent retailers. This is supported by the
higher returns under allocation four than allocation three.
Returns under the simple basic model ($684 thousand month-
ly average, $3,285 thousand in total) are greater than returns
for all allocations under efficiency I; for allocations one, two and
three with basic integration and allocations one and two with
cooperative integration under efficiency II; and for allocation
one under efficiency III. This suggests that processor-retailer
integration might result in no gain in total net revenue to
processors if only efficiency I can be reached, minor gains under
efficiency II and significant gaips under efficiency III. Returns
under the simple cooperative model ($700 thousand monthly,
$3,362 thousand in total) are greater than returns for all allo-
cations under efficiency I; for allocations one through four with
basic integration under efficiency II; and for allocation one with
basic or cooperative integration under efficiency III. Hence, in
going from a cooperative structure to an integrated structure, net
returns do not increase until at least 10 percent of the milk
moves through efficient integrated plants or at least 65 percent
moves through moderately efficient integrated plants.
In general, integration of processing and retailing activities
does not necessarily increase net returns to all processors. It
appears that net returns to processors would increase if integra-
tion was widespread and/or the cost efficiencies of integrated
plants relative to independent plants are substantial. From the
standpoint of individual processors and retailers there probably
exists a strong incentive to integrate, namely more .stable
product supplies and perhaps greater profits. Hence, while in-
tegration may not be profitable from a total industry viewpoint,
the movement toward integration may still be quite strong.

36








VII. SUMMARY AND CONCLUSIONS


Summary
This study analyzes the probable impact of an interregional
cooperative and various degrees of processor-retailer integration
on prices received by and returns to milk producers, processors
and retailers in southeast Florida. The analysis was based on a
mathematical model which describes the basic decisions affecting
the movement of milk from producers to consumers; the deter-
mination of prices at the farm, processor, and consumer levels;
and the level and distribution of returns to retailers, processors,
and producers. Changes in industry performance were measured
by the level and distribution of returns to retailers, processors,
and producers.
The mathematical simulation model was based on the indus-
trial dynamics approach. Model parameters reflect conditions in
the southeast Florida milk market during the 1966-69 period.
Results obtained with the models are conditional in nature. They
depend on the validity of the basic mathematical model and as-
sumptions made concerning the changes in milk pricing and
milk processing-distribution costs associated with an interregion-
al cooperative and processor-retailer integration. Tests of model
validity showed that the basic model adequately described the
behavior of the real system.
The simulation models used in the interregional and proces-
sor-retailer integration analyses were based on several key as-
sumptions. They are as follows:
Interregional cooperative:
a. Forty-two percent of the milk produced is marketed
through the interregional cooperative. The remaining 58
percent is sold by independent producers.
b. Processor-oriented services provided by the cooperative
enable the cooperative to negotiate a Class I premium of
30.5 cents per hundredweight on all milk.
c. Processor-oriented services provided by the cooperative
permit milk processors to reduce distribution costs for
member produced milk by 11.6 cents per hundredweight.
d. To finance the producer-oriented services rendered by the
cooperative, all coop-member producers pay a service fee
(retained by the cooperative) of 10 cents per hundred-
weight.
e. Coop-member producers sell all their milk through the

37








cooperative and independent producers sell all their milk
independently of the cooperative.
Processor-retailer integration:
a. Integration of milk processing and retailing increases the
efficiency of performing these functions. Hence, per unit
processing and distribution costs for integrated plants are
lower than for independent plants.
b. Integration of processing and retailing activities does not
affect the pricing of milk at the farm and retail levels.
Assumption a under processor-retailer integration was im-
plemented by simulating three levels of efficiency. In addition,
four milk allocations, which define the proportion of milk handled
by integrated and independent plants, were simulated.


Conclusions
Results obtained with the simulation models support several
conclusions. All conclusions are based on market conditions dur-
ing the 1966-69 period.

Interregional Cooperative
Operation of an interregional cooperative in southeast Flori-
da would have a negligible effect on the production of milk.
Monthly milk production would be only 1 percent greater, Class I
utilization between 1 and 1.4 percent greater, and Class II utili-
zation about 3 percent greater than under a non-cooperative
structure. Despite minor changes in milk production and utiliza-
tion, net returns to producers would be on the average 38 per-
cent per month or half a million dollars greater in the presence
of a cooperative. Of this amount, member producers receive 38
percent or $195 thousand and independent producers receive 62
percent or $319 thousand. Considering that (by assumption)
member producers account for 42 percent and independent pro-
ducers account for 58 percent of total milk production, the above
distribution of net returns seems inequitable. This occurs because
all producers receive the Class I premium while only member
producers pay a service fee to the cooperative.
Processor net returns would increase by about $77 thousand
over the entire 1966-69 period. However, net returns in six of the
16 quarters from 1966 to 1969 would be lower than in the ab-
sence of a cooperative. Monthly returns to retailers would be
from $5 to $51 thousand or on the average 2.4 percent greater.

38








Processor-Retailer Integration
Changes in processor net returns associated with processor-
retailer integration vary with respect to the proportion of milk
handled by integrated plants and the relative operational effi-
cency of integrated versus independent plants. For each of the
three levels of efficiency analyzed in this study, total net returns
to processors increased with the proportion of milk handled by
integrated plants. Likewise, for a fixed proportion of milk han-
dled by integrated plants, total net returns to processors in-
creased with respect to the relative efficiency of integrated
plants. Processor-retailer integration would not increase net
returns over the levels in a non-integrated structure unless at
least 65 percent of the milk produced is moved through moder-
ately efficient integrated plants or at least 35 percent of the milk
is moved through highly efficient integrated plants. Apparently,
when an interregional cooperative already exists, the gains in
total net returns to processors from processor-retailer integration
are meager.
Concluding Remarks
The models developed and applied in this study are at a high
level of aggregation. Hence, the impact of an interregional co-
operative or processor-retailer integration on specific producers,
processors and retailers was not analyzed. While a disaggregated
model would be preferable, data limitations preclude its develop-
ment. Milk consumption was not allowed to vary with consumer
price because significant estimates of the own price elasticity of
milk demand are lacking. This property of the model could in-
validate the results and conclusions when consumer prices vary
substantially. Fortunately, the relative variation in consumer
milk prices in southeast Florida was small during the 1966-69
period. Assumptions made concerning price and cost adjustments
associated with an interregional cooperative and processor-re-
tailer integration had a direct effect on the results. Alternative
assumptions would undoubtedly lead to somewhat different re-
sults and conclusions. However, the implications of alternative
assumptions can be investigated by making minor changes in the
parameters of the models.
For these reasons care should be exercised in applying the
results of this study to the formulation of policies and market
strategies. Results should be viewed in light of the underlying
models and periodically updated to account for emerging changes
in the structure and behavior of the southeast Florida milk mar-
ket.


39









FOOTNOTES

1. Market structure refers to the number and size distribution of firms, the
nature of the products sold, and the conditions of entry. Market conduct
refers to the behavior of firms within a market structure particularly
the nature and types of decisions that are made. Market performance
refers to the effect of market structure and conduct on prices, costs, out-
put and other economic variables. See [2, pp. 408-410].
2. An industrial dynamics model is essentially a set of deterministic mathe-
matical equations which describe the operation of an economic or social
system. Such models are generally used to improve the understanding
of the behavior characteristics of a system and to simulate the impact
of a particular course of action on the system. See section II, Forrester
[3], Pugh [17] and Raulerson [18] for further details.
3. Class I products include whole milk, skim milk, low-fat milk, and choco-
late milk. Class II products include buttermilk, flavored drinks, half and
half, table cream, sour cream, ice cream, ice milk, and sherbet. This
classification applied during the 1966-69 period. Current Class I and II
products are somewhat different,
4. The seasonal component of total milk utilization (EU) was fairly uni-
form from 1966 to 1969. The coefficients of variation for monthly milk
utilization were quite small, namely: Jan. 3.5, Feb. 3.0, Mar. 1.9, April
2.2, May 5.5, June 2.8, July 1.5, Aug. 2.7, Sept. 7.2, Oct. 3.1, Nov. 4.1,
and Dec. 4.0.
5. The seasonal component of Class I milk utilization (EUC1) was fairly
uniform from 1966 to 1969. The coefficients of variation for monthly
Class I milk utilization were quite small, namely: Jan. 2.0, Feb. 1.0, Mar.
1.6, April 1.6, May 1.7, June 2.2, July 2.2, Aug. 2.4, Sept. 3.3, Oct. 1.9,
Nov. 3.3, and Dec. 4.2.
6. Consistency could have been checked on a monthly basis; however, the
month was considered too short a time interval to expect good correspon-
dence between actual and simulated movements in the variables.























40









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41








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the South, 1965 and 1975, Sou. Coop. Ser. Bull. No. 163, Jan. 1971.

[21] United States Department of Agriculture, Bureau of Labor Statis-
tics, Retail Prices of Food, Govt. Printing Office, Wash., D.C.,
1966.

[22] Consumer Marketing Service,
Federal Milk Order Statistics, annual summaries, 1966-69.

[23] Economic Research Service,
Conversion Factors and Weights and Measures for Agricultural
Commodities and their Products, Stat. Bull. No. 362, June 1965.
























42








APPENDICES

APPENDIX A
DYNAMO FUNCTIONS
The TABHL, RAMP, PULSE and DELAY functions are
written in the following mathematical format [17].
TABHL (TAB, X, XLOW, HIGH, XINCR)
TAB = name of table
X= independent variable
XLOW = lowest value of range of independent variable
XHIGH= highest value of range of independent variable
XINCR= increment of independent variable
RAMP (SLP, STRT)
RAMP= 0 if TIME = STRT
TIME
RAMP= x SLP DT if TIME> STRT
STRT
PULSE (HGHT, FIRST, INTVL)
HGHT = pulse height
FRST = TIME of first pulse
INTVL= interval between pulses
DELAY 3 (IN, DEL)
IN= input to the delay
DEL= magnitude of the delay












43








APPENDIX B


CALCULATION OF CLASS II CONSUMER PRICE

Consumer prices for Class II products were generated by
adding the Class II trend (C2T) to the initial Class II consumer
price (IC2C). The latter was derived by taking a weighted aver-
age of Miami consumer prices for buttermilk, flavored drink,
half and half, table cream, sour cream, ice cream, ice milk, and
sherbet in 1966. The weights are the average percentage utiliza-
tion of raw milk in each product during the 1967-69 period.
Since the percentage utilization is in terms of raw milk, the
consumer price of each product had to be expressed on a raw
milk equivalent basis. This was done by dividing the 1966
Bureau of Labor Statistics (BLS) estimated retail price of each
dairy product in Miami by the corresponding conversion ratio
(quantity of raw milk required to produce 100 pounds of finished
product). Weighting these retail prices by the corresponding
percentage utilization gives an average retail value (consumer
price) of Class II milk per hundredweight of raw milk of $14.75
in 1966. Table B-1 gives the average percentage utilization of
raw milk, the retail value of raw milk, and the conversion ratio
for each product.


Table B-1-Average percentage utilization and retail value of Class II milk in
southeast Florida, 1966, and conversion ratios for eight dairy
products
Product Percent Utilizationa Retail Valueb Conversion Ratioc
Percent S/cwt. Pounds
Buttermilk 13.11 11.75 102.09
Flavored Drink 9.88 17.69 101.73
Half and Half 12.18 5.10 333.33
Table Cream 4.51 9.99 540.54
Sour Cream 2.07 7.00 500.00
Ice Cream 35.19 10.79 324.31
Ice Milk 20.46 25.14 139.20
Sherbet 2.60 49.91 54.10
aAnnual percentage utilization, 1967-69 average [4,13].
bRetail value per hundredweight of raw milk used in each product. Obtained by
dividing the BLS retail price of each product in Miami [21] by the conversion
ratio.
cPounds of raw milk required to produce 100 pounds of finished product [23].



44








APPENDIX C


PRODUCTION AND PROCESSING SEGMENTS
OF COOPERATIVE MODEL

Equations for the production and processing segments of the
cooperative model are as follows :

Monthly Production
A MPR.K=MMPR.JK+NMPR.JK
R MMPR.KL= (MDPI.JK) (MEUU.K)
R NMPR.KL= (NDPI.JK) (NEUU.K)
A MEUU.K= (MS) (EUU.K)
A NEUU.K=(1-MS) (EUU.K)
A EUU.K=EU.K+C1UTR.K
C MS= 0.42

Class I Allocation
R RAC1.KL=MRAC1.JK+NRAC1.JK
R MRAC1.KL= (MMPR.JK) (P.K)
R NRAC1.KL= (NMPR.JK) (P.K)
N MRAC1=(41.1) (MS)
N NRAC1=(41.1) (1-MS)

Class 2 Allocation
R RAC2.KL=MRAC2.JK+NRAC2.JK
R MRAC2.KL= (MMPR.JK) (1-P.K)
N NRAC2.KL= (NMPR.JK) (1-P.K)
N MRAC2= (5.7) (MS)
N NRAC2= (5.7) (1-MS)

Minimum Class 1 Producer Price
A C1P.K=BFP.K+C1PD+ C1PR
C C1PD=3.10
C C1PR=0.305


10nly those segments of the coop model that differ from the basic model
are given.



45








Blend Price Received by Producers
"A TPR.K= NTPR.K+MTPR.K
"A MTPR.K= (C1P.K) (MRAC1.JK) + (C2P.K) (MRAC2.JK)
(MRAC1.JK MRAC2.JK) (SF)
"A NTPR.K= (C1P.K) (NRAC1.JK) + (C2P.K) (NRAC2.JK)
"N SF=0.10
"A BP.K=TPR.K/(RAC1.JK+RAC2.JK)


Net Returns to Processors
A APCNR.K=PCNR.K+ (MRAC1.JK+MRAC2.JK) (RAF)
C RAF=0.116


Return-Cost Comparison
A MRCC.K=MTPR.K/MPC.JK
A NRCC.K=NTPR.K/NPC.JK
R MPC.KL= (MMPR.JK) (ACP.K)
R NPC.KL= (NMPR.JK) (ACP.K)


Net Returns to Producers
"A MPRNR.K=MTPR.K-MPC.JK
"A NPRNR.K=NTPR.K-NPC.JK
"A PRNR.K=MPRNR.K+NPRNR.K


Production Incentive
A MPI.K=TABHL (PCT*, MRCC.K, .95, 1.25, .05)
A NPI.K=TABHL (PCT*, NRCC.K, .95, 1.25, .05)
R MDPI.KL=DELAYS (MPI.K, PDQ)
R NDPI.KL=DELAY3 (NPI.K, PDQ)
N MDPI=1
N NDPI=1


Variables appearing in the above equations are defined in
the glossary. An M prefix indicates that the variable refers to
member producers and an N prefix indicates that the variable
refers to independent producers.



46








APPENDIX D

PROCESSOR SEGMENTS OF INTEGRATION MODEL
The processor segments of the integration model essentially
define processor net returns (PCNR) under each of the four al-
locations and three efficiency levels discussed in section VI.
GPCNR and IPCNR represent net returns to integrated (G)
and independent (I) plants, respectively. APCNR is total proc-
essor net returns over the entire 1966-69 period and PCR is
processor net return before deducting processing and packaged
milk distribution costs. All other variables are defined in the
glossary. The equations for efficiency level II are as follows:

Allocation 1
A PCR.K=TCE.K- (TRR.K+TPR.K--RAC.JK)
A GPCNR1.K=.10 (PCR.K+RDC.K) (.09 COP.K) -
(.095 GDC.JK)
A IPCNR1.K-.90 (PCR.K+RDC.K) (.99 COP.K) -
(.945 GDC.JK)
A PCNR1.K=GPCNR1.K+IPCNR1.K
L APCNR1.K=APCNR1.J+DT (PCNR1.J)
N APCNR1=0

Allocation 2
A GPCNR2.K=.35 (PCR.K+RDC.K) (.315 COP.K) -
(.3325 GDC.JK)
A IPCNR2.K=.65 (PCR.K+RDC.K) (.715 COP.K) -
(.6825 GDC.JK)
A PCNR2.K= GPCNR2.K +IPCNR2.K
L APCNR2.K=APCNR2.J+-DT (PCNR2.J)
N APCNR2=0

Allocation 3
A SPCNR3.K=.15 (PCR.K+RDC.K) (.1425 COP.K) -
(.15 GDC.JK)
A IPCNR3.K=.50 (PCR.K+RDC.K) (.550 COP.K) -
(.525 GDC.JK)
A PCNR3.K=GPCNR2.K+SPCNR3.K+IPCNR3.K
L APCNR3.K=APCNR3.J+DT (PCNR3.J)
N APCNR3=0



47








Allocation 4
"A SPCNR4.K=.25 (PCR.K+RDC.K) (.2375 COP.K) -
(.25 GDC.JK)
"A IPCNR4.K=.40 (PCR.K+RDC.K) (.440 COP.K) -
(.420 GDC.JK)
A PCNR4.K= GPCNR2.K+SPCNR4.K+IPCNR4.K
"A APCNR4.K=APCNR4.J+DT (PCNR4.J)
"A APCNR4=0


Numerical coefficients in the above equations are derived
from the proportion of milk moving through integrated and in-
dependent plants and the amounts by which various processing
and distribution costs deviate from those used in the basic
model (see Table 3 through 6). For example, under allocation
1, 10 percent of the milk is handled by integrated plants so they
receive 10 percent of net returns before deducting processing
and distribution costs (PCR) plus 10 percent of the reduction
in costs of product distribution (RDC) which is counted as an
addition to revenue. Processing costs (COP) for integrated
plants are 90 percent of the cost of processing specified in the
basic model and integrated plants handle 10 percent of the milk
under allocation 1. Hence, processing costs are (.90) (.10) of
COP or .09 COP. Coefficients of COP and GDC under the four
milk allocations and three efficiency levels are given in Table
D-1. The equations for efficiency levels I and III were defined
using these coefficients.



Table D-1-Coefficients of COP and GDC for integration model
Efficiency Allocation
level: Plant
type I II II IV
COP GDC COP GDC COP GDC COP GDC
Integrated .095 .098 .3325 .3430 .147 .153 .2450 .2250
Independent 1.035 .972 .7475 .702 .575 .540 .460 .432
II:
Integrated .09 .095 .315 .3325 .1425 .15 .2375 .25
Independent .99 .945 .715 .6825 .550 .525 .440 .420
III.
Integrated .085 .092 .2975 .322 .138 .147 .230 .245
Independent .945 .918 .6825 .663 .525 .510 .420 .408




48








GLOSSARY OF VARIABLES

AC* =Table values for average per unit cost of producing
milk

ACP =Average per unit costs of producing milk

APCNR =Accumulated (1966-69) net returns to processors
AR =Adjustment ratio (RAC1/C1UR)
BFP = Basic formula price for raw milk
BFPT* = Table values of basic formula price
BP = Blend price received by producers
CCOP1 = Per unit cost of processing Class I products
CCOP2 =Per unit cost of processing Class II products
COP = Total cost of processing all milk
CPC = Consumer price constant
C1C = Consumer price of Class I milk
C1C* = Table values of consumer price of Class I milk
C1CS = Consumer price of Class I milk, smoothed
C2C = Consumer price of Class II milk
C1P = Producer price of Class I milk
C1PR = Class I price premium
C2P = Producer price of Class II milk
C1PD = Class I price differential
C2PD = Class II price differential
C1PI = Class I processed milk inventory
C2PI =Class II processed milk inventory
C2T = Class II consumer price trend
C1UR = Class I consumer utilization rate
C2UR = Class II consumer utilization rate
C1UTR = Class I consumer utilization trend



49








DC1 = Delay constant for expected Class I utilization
DC2 = Delay constant for expected Class II utilization
DPI = Delayed milk production incentive
EEUC1 =Expected utilization of Class I milk with trend
EU = Expected utilization of all milk
EUC1 =Expected utilization of Class I milk
EUC1T* =Table values of expected utilization of Class I milk
EUT* =-Table values of expected utilization of all milk
EUU = Expected utilization of Class I milk with trend
GDC = Packaged milk distribution costs
GPCNP =Integrated processors' net returns
IC2C = Initial Class II consumer prices
IPCNP = Independent processors' net returns
MD = Months discarded
MP = Months passed
MPR = Monthly production rate
MPY =Months per year
P =Class I allocation proportion
PAC = Per unit cost of raw milk assembly
PCNR = Processor net returns
PCR =Processor net returns before deducting processing
and distribution costs
PDC =Per unit cost of packaged milk distribution
PDQ = Production delay constant
PMC =Percentage of milk sold through cooperative
PIR = Processor inventory of raw milk
PI = Production incentive
PI* =Table values of production incentive



50







PRNR = Producer net returns
PRPC1 = Price received by processors for Class I milk
PRPC2 = Price received by processors for Class II milk
PT* = Table values for allocation proportion
RAC =Raw milk assembly costs
RAC1 =Rate of allocation to Class I uses
RAC2 = Rate of allocation to Class II uses
RCR = Return-cost ratio
RDC = Reduction in milk distribution costs
RMARG1 =Retail margin on Class I products
RMARG2= Retail margin on Class II products
TCE = Total consumer expenditures
TME =Time variable
TPC = Total milk production costs
TPR = Total processor returns
TRR =Total retail returns
TRP = Total returns to producers




















51




































SSmrng Mankin4
co 1875 1975

mn COi





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