VERTICAL COORDINATION ARRANGEMENTS: SOME
ALTERNATIVES FOR THE UNITED STATES DAIRY SUBSECTOR
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
The author sincerely wishes to express his admiration to
Dr. Richard L. Kilmer, chairman of his supervisory committee. There
was not a moment during this dissertation work in which he was not
available for advice. There is no doubt that much of Dr. Kilmer's
admirable personality and singular way to overcome temporary setbacks
is an example that is worth more than one thousand words of encourage-
ment to the author in the completion of this study.
The author also recognizes the contribution of his supervisory
committee, Dr. H. Evan Drummond, Dr. Max R. Langham, Dr. W. W. McPherson,
Dr. R. Ward, and Dr. D. Denslow, for their comments on the original pro-
posal of this project and for the appropriate answers to the many ques-
tions they were asked. This work would not have been completed without
the help of people that the author does not even know, but will be
looking forward to meeting. They are the government officials from
USDA, USDC, and USDL who so kindly made the data available for this
research. Dr. Levins, Dr. Pagoulatos, Dr. Shonkwiler, Dr. Spreen, and
other faculty members contributed to this dissertation with valuable
The encouraging words from friends and colleagues will never be
forgotten. Thanks go to Mrs. Linda Kilmer for the typing. She did a
very good job, as it can be seen. Thanks go to Rom for his much
requested expertise in SAS; thanks go to Dominique for introducing the
author to the APPLE II; thanks go to the Latin American Studies Center
of the University of Florida for allowing the author to use their
Maria Jose, the author's wife, is directly responsible for his
achievements. His children, Daniela and Alisson, will someday under-
stand that the sacrifice they made during the hours the author should
have been with them and could not, was worthwhile. Without the life
lessons of Conceicao M. Gontijo, his mother, certainly the author would
not have succeeded.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . . . . . . ... . . . ii
ABSTRACT . . . . . . . . ... . . . . . . vii
I INTRODUCTION . . . . . . . . . . . .
Statement of the Problem . . . . . . . . 3
Statement of Objectives . . . . . . . . . 4
Summary and Overview . . . . . . . . . 4
II LITERATURE REVIEW . . . . . . . . . . 6
Introduction . . . . . . . . ... . . 6
Dairy Policy Models . . . . . . . . . . 6
Kessel Model . . . . . . .. . . .. 7
Ippolito-Masson Model . . . . . . . . 11
Dahlgran's Model . . . . . . . . ... .13
Price Support Models . . . . . . . . ... .19
The Buxton-Hammond Model . . . . . . ... .19
The Hein Approach . . . . . . . ... .22
Models for Vertical Coordination . . . . . ... .22
Vertical Coordination through Price Mechanisms . .. 24
Vertical Coordination through Nonprice Mechanisms 29
Demand and Supply Functions for Milk in the
United States . . . . . . ... . . . 32
Demand Models . . . . . . .... .. . 32
Supply Models . . . . . . .... .. . 37
Price Lagged Models . . . . . . . ... .38
Summary . . . . . . . . ... . .. . 43
Coordinating Issues . . . . .... . . 343
Empirical Issues . . . . .... . . . 44
Conclusions . . . . . . . ... . . ..... 45
Overview . . . . . . .. .. . . . . . 46
III VERTICAL COORDINATION IN THE UNITED STATES DAIRY
INDUSTRY . . . . . . . . . . . .
Introduction . . . . . . . . . . .
A Model for the Crude Milk Exchange . . . . .
Graphical Framework . . . . . . . .
Mathematical Framework . . . . . . .
Alternative Exchange Arrangements . . . . ..
Coordination between Cooperatives and Dairy
Farmers . . . . . . . . . . .
Coordination between Cooperatives and First
and Demand of M
Summary . .
dinating Arrangements to Balance Suppl
manufacturing Milk . . . . .
tion . . . . . . . .
Government Controls . . . .
. . . . . . . . . .
IV FORMULATION OF THE EMPIRICAL MODEL . . . .
Introduction . . . . . . . . . .
Variable Identification . . . . . . .
Demand Functions . . . . . . . .
Supply Functions . . . . . . . .
Data . . . . . . . . .
Period of Analysis . . . . . . . .
Unit of Time . . . . . . . . . .
Cross-Sectional Units . . . . . . . .
Model Specification . . . . . . . .
Derived Demand Functions . . . . . .
Supply Function for Grade A Milk . . . .
Supply and Demand Functions for Grade B Milk .
Choice of the Estimators . . . . . . .
Econometric Estimations . . . . . . .
Results for the Fluid Milk Derived Demand
Function . . . . . . .
Results for the Commercial Derived Demand for
Manufacturing Milk . . . . .
Results for the Supply of Fluid Eligible Milk
Results for the Supply and Demand Functions of
Grade B Milk . . . . . . . .
. . 74
. . 75
. . 75
. . 80
. . 84
. . 88
. . 94
. . 95
. . 96
. . 96
. . 98
. . 99
. . 101
. . 105
. . 105
. . 110
Equations for the United States Dairy Industry . . .. 113
Derived Demand Curve for Fluid Milk in the
United States . . . . . . . . .. 113
Derived Demand Curve for Commercial Manufacturing
Milk in the United States . . . . . . 114
Supply Curve for Fluid Eligible Milk in the
United States . . . . . . . . ... 115
Supply Curve for Grade B Milk in the United
States . . . . . .. ... ... . 117
The Blend Price . . . . . . . . . 118
Summary . . . . . . . . .. . . . . 118
Overview . . . . . . . . ... . . . 119
V ALTERNATIVE COORDINATING ARRANGEMENTS TO REDUCE MILK
SURPLUSES IN THE UNITED STATES . . . . . ... .120
Introduction . . . . . . . . ... . . 120
Model Adjustment . . . . . . . . ... . 120
Results . . . . . . . . .. . . . . 122
Simulations .. .. ....... ......... ... 126
Solution for the Basis . . . . . . . 126
Self-Regulation Alternatives . . . . . . 126
Alternative Government Controls . . . . . 129
Summary and Conclusions . . . . . . . . 131
VI SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR
FUTURE RESEARCH . . . . . . . . ... . 132
Summary . . . . . . . . ... .. . . 132
Conclusions .. .. . . . . . . . . . 135
Suggestions for Future Research . . . . . . 135
A DERIVED DEMAND AND SUPPLY FUNCTION DERIVATIONS . . 140
B GLOSSARY . . . . . . . ... .. . . 146
C VARIANCE-COVARIANCE MATRICES FOR ESTIMATED
COEFFICIENTS . . . . . . . . ... . .. 151
REFERENCES . . . . . . . . . . . . . 158
BIOGRAPHICAL SKETCH . . . . . . .... . . . 168
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
VERTICAL COORDINATION ARRANGEMENTS: SOME
ALTERNATIVES FOR THE UNITED STATES DAIRY SUBSECTOR
Chairman: Richard L. Kilmer
Major Department: Food and Resource Economics
Milk production in the United States has surpassed commercial con-
sumption. The government stands ready to buy all excess supply, which
is, conveniently, transformed into cheese, butter, and nonfat dry milk.
Milk is one of the few major farm commodities in the U.S. with a price
support program that has never been subject to production control poli-
The objective of this study is to examine some alternative arrange-
ments to reduce milk production in the United States. The assumption
made is that the subsector could, as an alternative to additional govern-
ment measures, coordinate itself to reduce milk production.
The model constructed contains derived demand equations for fluid
and commercial manufacturing milk, supply equations for fluid eligible
and grade B milk, and quantity and price conditions.
Corresponding equations are estimated using pooling cross-sections
over time series techniques. The sample price elasticities are (a) fluid
milk derived demand, -1.195, (b) commercial manufacturing milk derived
demand, -4.433, (c) supply of fluid eligible milk, .24, and (d) supply
of grade B milk, 1.23. Simulation results are compared to solutions
obtained for the fourth quarter of 1980.
It is calculated that, if self-regulation had been selected, fluid
eligible milk producer's revenue would have decreased .51 percent for
one percent reduction in quantities supplied. However, if government
control had been necessary, then fluid eligible milk producers' revenue
could have decreased by 3.77 percent. In case the government had reduced
the supported price, relatively large percentage decreases in grade B
milk quantities supplied would have occurred. Nevertheless, one percent
decrease in quantities supplied would have decrease grade B farmer's
revenue only 1.74 percent. It was calculated that some of the government
measures could have reduced grade A farmers' revenue by $59 million
(1967 prices) beyond that necessary to reduce milk supply with self-
Within these lines it is suggested that government should antici-
pate its intention to reduce its milk purchases with clear figures.
Dairy cooperatives'importance as a means of coordination should be
better understood and enhanced, and milk producers need to understand
that additional government rules to enforce reductions on quantities
supplied are not their best alternative.
A marketing problem in the U.S. dairy subsector is allocating milk
produced to available outlets. The economic solution of this marketing
problem depends on the structural relationships derived from the objec-
tives pursued by participants in the exchange function of its marketing
segment, and on mechanisms of coordination created by the government.
The government directly sets minimum prices that plants must pay for
milk (Federal and state marketing orders), supports manufactured dairy
products prices, and establishes rules for the exchange of milk between
producers and first handlers (See Glossary in Appendix B). Such mech-
anisms and the unrestricted outlet offered by Commodity Credit Corpora-
tion (CCC) purchases have permitted the allocation, at the supported
prices, of all crude milk produced [Cook and Hayenga, 1981, p. 19;
Boynton and McBride, 1980b, p. 24].
Continuous purchases of cheese, butter, and nonfat dry milk by CCC,
reflecting persistent overproduction of milk, indicate a vertical coordi-
nation problem. According to Boynton and McBride [1980b, p. 6], an
effective coordinating mechanism should facilitate the flow of accurate
information between exchange partners. The subsector coordination prob-
lem seems to be that information generated from transactions between
sellers and buyers of crude milk do not reflect their ex-ante
expectations. The government would like the dairy farmers to produce
according to the commercial demand only [USDA, 1982a]. However, the
actions of milk producers indicate that they have been adjusting their
economic decisions to the total market demand for milk, which includes
commercial demand plus government purchases.
Some of the consequences brought forth by the current dairy envi-
ronment are as follows: (a) from May 1979 through December 1981 there
has been increased milk production over the previous year [USDA, 1977-
1981e]; (b) in 1980 and 1981 CCC net purchases of milk equivalent were
8.8 billion and 12.6 billion pounds, respectively [USDA, 1982b]; (c) the
1982 price support of $13.10 per hundredweight will cost nearly $2 bil-
lion to the government which will buy some nine percent of the Nation's
milk production [USDA, 1982a]; (d) the USDA anticipates it will spend
up to $4 billion between fiscal years 1983 and 1985, up from $46 million
in 1979 [USDA, 1982b], and (e) as of April 9, 1982, the government had
the following in stock: 365 million pounds of butter, 625 million
pounds of cheese, and 975 million pounds of nonfat dry milk [USDA, 1982].
"That's the problem in a nutshell . we have enough surplus to
fill an average-size train stretching from Washington, D.C., to New
York City" [USDA, 1982a]. "This is embarrassing . it's unaccept-
able . it's intolerable! It cannot continue," said John R. Block,
the U.S. Secretary of Agriculture, describing the administration's view
of the current price support program costs [NMPF, 1981].
Two distinct sets of measures have been suggested to alleviate
surplus problem. One set consists of marketing disposal strategies
to reduce the accumulated surpluses. It includes reduction of imports,
increase in exports, expansion of domestic consumption through promo-
tion and advertising, and increasing distribution of surplus dairy
products to needy consumers. The other set consists of measures
directed at controlling production in order to reduce additions to
surpluses. These include producers' input control plans, class I bases,
taxing output, and alternative classified plans.
The first set of measures may be adequate in the short run
[Brandow 1977, p. 266]. Such measures may reduce the stocked surplus,
but they avoid the core of the problem, which is to improve vertical
coordination in order to reduce the formation of the persistent differ-
ences between quantities supplied and demanded of milk.
Milk is one of the few major commodities with a price support
program in the U.S. that has never been subject to production control
policies. Analogies drawn from other agricultural commodity studies are
not adequate because of the unique characteristics of milk production,
distribution, consumption, and regulatory devices. An investigation of
the impacts of production control measures on the subsector is now
Statement of the Problem
The problem to be examined in this study is the impact of alter-
native exchange arrangements on the supply and demand balance of milk
between dairy farmers and manufacturers of dairy products.
Statement of Objectives
Alternative coordinating arrangements that can be used to balance
the United States supply and demand for milk will be examined. Compari-
sons between alternatives will be made by measuring the U.S. farmers'
revenue foregone under each alternative. Four stages will be necessary
to accomplish such a purpose. The objectives of each stage are as
follows: (a) to develop a conceptual framework of the coordinating
process among processors, manufacturers, cooperatives and dairy farmers
in the United States; (b) to describe the derived demand functions for
fluid and manufacturing milk, and supply functions for fluid eligible
and grade B milk, for the United States, which constitute the structural
equations of the model referred to in objective (a) above; (c) to
econometrically estimate these supply and demand functions; (d) to
stimulate, using the model built in objective (a) and estimated in
objective (c), the impact on milk market equilibrium values and on milk
producers' revenue for each alternative coordinating arrangement studied.
Summary and Overview
Having introduced the problem that will be addressed in this
study and delineated the research methodology, Chapter II will be used
to review the studies which provided structural foundation for this
project. Comments will be made on their strengths and weaknesses.
Chapter III will contain the conceptual model in both graphical and
mathematical forms. The empirical model is formulated and estimated
in Chapter IV. In Chapter V the simulations of alternative coordinating
arrangements to reduce milk surpluses are ampirically examined with the
estimates obtained in Chapter IV. Summary and conclusions follow in
The first chapter was used to introduce the research problem and
the major objectives of this study. This chapter provides a review of
the literature that constitutes the foundation of the model that will
be used to measure the impacts of alternative coordinating arrangements
on the balance between supply and demand of milk in the United States.
Dairy Policy Models
The research objective directed the selection of the econometric
models to be investigated as a potential analytical framework for this
study. The coordinating arrangements of interest must be situated in
an environment which considers all the current government regulatory
devices unchanged. Therefore, only the models that include the classi-
fied pricing, pooling provisions, and the price supports would be, in
principle, useful for this analysis. The Kessel model , and its
extensions by Ippolito and Masson  and Dahlgran , have such
characteristics. They were designed to measure the social costs of
regulation. The models specifically related to features of the price
supports program are the Buxton and Hammond model , and the Hein
model . Models that are related to the coordination approach are
also reviewed, as the Boynton and McBride plan [1980a] and the USDA's
Food and Agriculture Policy Simulator (FAPSIM) [Salathe, Price, and
Gadson, 1982]. The shortcomings of these models will be indicated and
will be used to make selective modifications. The literature review
is also extended to supply and demand equations previously estimated for
the U.S. dairy subsector. A summary of the major shortcomings is pro-
vided at the end of the chapter.
In 1967, Kessel designed a model that incorporated some basic
features of the regulated grade A milk market, which are the classified
pricing and pooling provisions.
With the price of fluid milk PI as in Figure 1, QI would be'
consumed. The schedule DI is the demand for fluid milk derived from
the retail level. Producers of grade A adjust production with respect
to the supply function SA. The price farmers receive for grade A milk
is PA which is a weighed average of the class I and class II prices.
The weights are the relative amounts of milk used in each class. The
class II price PII is given to the grade A milk market. It could either
be assumed to be the world price,as did Kessel, or the support price
for manufacturing milk. The blend price function is AR. Finally, PA,
QII and QA in this regulated grade A milk market, are thus determined
by the system
(2.1) PA = (PI QI + PII QII)/(QI + QII).
(2.2) QA = SA[PA]
Figure 1. Kessel Model of Regulated Grade A Milk Market
(2.3) QI = DI[PI].
(2.4) QA = QI + QlI.
(2.5) PI = PI .
(2.6) PII = PII
Kwoka  used Kessel's model and previously estimated elastici-
ties to test the common hypothesis that Federal regulation sets milk
prices so as to benefit producers and to estimate the quantitative
effects of regulation on prices and quantities within markets, on price
patterns among markets, and income distribution and economic efficiency.
With respect to this second objective note that PI would equal to
PII in the absence of classified pricing, since the blended price,
PA = PI = PII (Figure 2). The world price PII' would determine QI',
QA's, and QII' = QA' QI'. In moving from this solution to the regu-
lated solution, Kwoka estimated that "several hundred dollars are
transferred from consumers to producers. Regulation also causes dead-
weight losses to the economy totaling $55 to $180 million annually"
Kessel succeeded in modeling the dairy industry classified pricing
and pooling provisions. Kessel first illustrated the average revenue
curve (AR), which will be used throughout this study. The major short-
comings of Kessel's model are that it does not explicitly include the
entire manufacturing milk market. Also, as pointed out by Dahlgran
[1980, p. 53], Kessel did not empirically estimate his model. Kwoka's
estimations were based on 1960 and 1970 data, which are now considered
j Pl, PI'-
O I I
0 Q1' QA' QA
Kessel Model of an "Unregulated" Grade A Milk Market
old statistics since they did not capture new trends and adjustments
in the subsector.
Ippolito and Masson  developed a model for regulated milk
markets in the United States. They used the model to simulate the
inefficiencies and transfers inherent in regulation.
The analysis performed by Ippolito-Masson covers "only price
regulations and does not treat the price support system" [p. 34]. How-
ever, the model has some features not incorporated in Kessel's analysis,
and so it will be reviewed as well.
As in Kessel's model, DI, SA, and AR (See Figure 3) are the fluid
milk demand derived from retail level, the grade A milk supply, and
the average revenue curve, respectively. But DII, the class II demand
function, now takes a negative slope. The important extension of this
model is the interaction between grade A and grade B milk markets intro-
duced by the authors. A supply curve for grade B milk produced in the
Minnesota-Wisconsin area, SB, was added to their model.
The equilibrium in the regulated market is described in Figure 3.
The quantity, QA of grade A milk, as well as the blend price PA are
determined when AR intercepts SA. Recall that PI is the minimum price
for class I determined by the market order administrator. When QA is
produced, PII is the price determined for the total demand [DII +
DI(PI")] and is also the price that will be received by grade B milk
farmers for each unit of the quantity QB produced.
I/ I Io
I I -
I I 1 1
- I- -- O
I II *
-- - --- S -
The unregulated milk market equilibrium would be established
when total demand (DI + DII) equals SA (Figure 3). At that point, PA'
and QA' are determined. With PA' = PI', QI' is obtained, and with PA' =
PII' = PB', QII' and QB' are, respectively, determined. The total social
costs of moving from the unregulated equilibrium to the regulated equilib-
rium were estimated by the authors to be around $60 million (including
$34 million due to government programs administration) [Ippolito and
Masson, 1978, p. 60].
Ippolito and Masson  presented two methodological contri-
butions. The first was the modelling of the relationships between the
regulated grade A milk market and the unregulated grade B milk produc-
tion. The second was the adoption of a reasonable assumption with
respect to the negative slope of the demand for manufacturing milk (not
totally elastic as in Kessel's model). As pointed out by Dahlgran [1980,
p. 64], the demand for manufacturing milk could be downward sloping for
any quantities demanded above the price support level. Dahlgran also
identified one shortcoming on their model: "DII is the demand for manu-
facturing milk out of grade A supplies while manufacturing demand can
also be supplied out of grade B production" [1980, p. 64]. The major
consequence is that the price of manufacturing milk happens to be
determined by the grade A milk only. This misconception is also present
in Dahlgran's model.
Dahlgran added significantly to the previous models by incorpo-
rating local interdependence between the grade A and grade B milk pro-
duction, and by including a much needed manufacturing milk demand func-
tion, DM, as in Figure 4. Of more importance is Dahlgran's explicit
assumption incorporating features of the price support program. Also,
instead of using retail demand functions, or demand functions derived
from retail levels, as usual, he used a derived demand approach. These
concepts when applied to the first handler level permit the observation
of both supply and demand points for crude milk.
The functions DI, SA, SB, and AR, are the same as defined in the
Ippolito-Masson model. The regulated equilibrium is described in
Figure 4. QI is the quantity of grade A milk that, according to DI,
processors will be willing to buy at the minimum price PI fixed by the'
marketing order administration. At the price support PS both QB ,
QIl and QS are determined. This last variable represents the amount
of CCC removals from the grade A market, which is given by QA
(QI + DII[PS"]). QA is determined at the blend price PA calculated
(2.7) PA = (PI' QI + PS QII )/(Ql + Q l ).
Dahlgran's model for the unregulated market is depicted in
Figure 5. "The unregulated equilibrium will exist at a point where
fluid demand is satisfied out of grade A production, and manufacturing
demand is satisfied out of grade B production, and the grade A-grade B
---4- -- --- 0
S IV-1-00 L.
Sd .. "-,
price difference is equal to the cost of production difference (C)"
[Dahlgran, 1980, pp. 81-82].
Moving from the unregulated equilibrium to the regulated milk
market, as in Figure 4, the total social cost to society was estimated
at $131 million, including $34 million imputed to the programs admin-
Note that although the models previously reviewed have all been
used to estimate the social costs of deregulation, a purpose that dif-
fers from the one pursued in this study, they contain the basic struc-
ture that could be helpful in constructing a model to simulate alterna-
tive coordinating arrangements to reduce the imbalance between supply
and demand for manufacturing milk. Some modifications will be needed
for correcting shortcomings.
The first shortcoming in Dahlgran  is that the equilibrium
price for manufacturing milk, in the absence of the price support pro-
gram, would be determined in the grade A market only, that is,
(2.8) PM = PII = DII[QA ],
where, PII is the price of class II milk, and PM is the price of
manufacturing grade milk. This approach ignores the participation of
the grade B milk production on the supply side of the manufacturing milk
market. Besides, with the price supports, the definition,
(2.9) QA = QI + QII,
is no longer obtained (AB
depicted in Figure 4a.
Also, Dahlgran did not model a decrease in the price support but
the disruption of the price support program. Moreover, all government
purchases were determined in the grade A market only. The potential
effects of grade B milk production were not considered.
It is interesting to note that the empirical determination of the
regulated equilibrium values would require the empirical estimation of
DII, which was never done by Dahlgran. As a matter of fact, he never
estimated the regulated dairy market model. By never estimating it,
he did not validate his model. It is a usual procedure that subsequent
simulations could conceivably deal with any of a large variety of
assumptions only if the model provides a reasonable simulation of the
"real" (observed) behavior. All simulation results should be compared
with the BASE simulation rather than with actual values. This proce-
dure must be followed in order to separate regulation-induced effects
from simulation-induced errors. Only then can the observed differences
between regulated (BASE) and nonregulated simulation be attributed to
elimination of the government program. Comparisons of unregulated
simulated performance with actual performance (as done by Dahlgran)
would be confounded by the known inability of the simulation algorithm
to reproduce historical behavior exactly even with the regulation in
place fThor and Jesse, 1981, p. 29].
Finally, the incorporation of the effects of the price supports
was done by "shifting the manufacturing demand by the amount QS" (CCC
removals from the grade A market)[Dahlgran, p. 78]. Such shifts were
supposed to be captured by introducing QS as an explanatory variable in
the demand equation for manufacturing milk. By making QS exogeneous
the method used becomes inadequate for this study. Here it is neces-
sary to have QS determined by the model.
As a group, the three models reviewed do not consider the verti-
cal coordination as an alternative approach to balance supply and demand
for manufacturing milk.
The appropriate modifications to correct for the shortcomings
will be described in constructing the model in Chapter III. An assump-
tion will be made to incorporate dairy cooperatives in the exchange of
crude milk between producers and processors/manufacturers. These bar-
gaining entities will be assumed to play a coordinating role in the
vertical organization of the dairy market.
Price Support Models
The models reviewed so far were chosen because they provide the
basic framework for this study. However, they were used for another
purpose, which was to measure the costs incurred by society when moving
from a hypothesized unregulated market equilibrium to the regulated
dairy market. The models that follow are specifically related to the
price support program.
The Buxton-Hammond Model
Buxton and Hammond  developed a method of measuring the net
social cost at alternative levels of price support under condition of
exporting or destroying government purchases and under a condition of
According to their model the fluid demand curve DFs and the
supply curve for all milk Ss (Figure 6) show the amount of milk de-
manded as fluid and the total milk supplied, respectively, at each
manufacturing milk price with the assumption of a constant fluid-
manufacturing price difference. The differential between manufacturing
milk price and class I milk prices was set at $2.17, and the constant
differential between manufacturing milk and whole milk prices was set
at $1.00 [Buxton and Hammond, 1974, p. 287].
When the government sets the price support level for manufacturing
milk PS (most certainly above its equilibrium price), the milk pro-
duction will be QW (Figure 6). The quantity QF will be allocated to
the fluid market, QMD to the manufacturing market, and QS = QW -
(QF + QMD ) will be removed from the market by government programs.
The price received by farmers would be PS + $1.00, and fluid milk
buyers will pay PS = $2.17. The authors, with the above model and
using previous estimated elasticities, concluded that the increase in
social cost of increasing the support price from 85 to 90 percent of
parity would be $107 million [p. 289], and that at 85 percent of parity
the estimated annual social costs would decrease from $340 to $65
million if all government purchases were distributed back to the
community [p. 290].
The contribution of the Buxton and Hammond model  is the
treatment of an integrated (grade A and manufacturing) milk market,
in which the price support level is the policy variable. The short-
comings of their model are as follows: (a) The model was not estimated
The Buxton-Hammond Model for the Price Support Program
by the authors. Previous estimated elasticities were used. (b) The use
of constant differentials between PI and PS, and PW and PS, when the
observed differences are not so constant as they seem to be (see Table I).
(c) The supply function S contains both fluid eligible and grade B milk.
The Hein Approach
Hein  specified and estimated an econometric model of the
U.S. dairy subsector. The model was used to measure the impacts of
milk regulation on consumer prices over the 1949-73 period, and the costs
to consumers of the price support and Federal order program. The total
annual cost of the Price Support Program was found to be $402 million.
The Federal marketing order system was estimated to cost $175 million per
year to consumers. Hein's model for the U.S. dairy industry was estimated
by OLS using annual data from 1950-69. His model, however, was not built
to answer the questions posited for this study.
As a group, the above models do not characterize the price support
program as a potential instrument to vertically coordinate the industry
crude milk exchanges.
Models for Vertical Coordination
The models by Kessel , Ippolito and Masson , and
Dahlgran  were reviewed in the first section because they provide
the basic framework to which extensions will be made for obtaining an
adequate analytical instrument to examine the problem identified in
Chapter I. The models that deal with features of the price support
program were reviewed in the second section. In this section, the
Table 1. Selected Milk Price Differentials
Prices $1.00 cwt.
Source: USDA, Dairy Situation, ERS, DS-344, March 1973.
models for coordinating the exchange of agricultural products under
price supports are reviewed.
Vertical Coordination through Price Mechanisms
Some subsectors in agriculture have demonstrated their preference
for administrative type coordination in part because it leads to a more
stable volume moving through the system and a more homogeneous quality
of the product [Collins, 1959]. However, even in the administratively
coordinated system, the change-inducing role of price is present [Gray,
Buxton et al.  discuss some alternatives to restore balance
between supply and demand and reduce government program costs. The
effectiveness of surplus disposal alternatives is descriptively (no model
was used) questioned by the authors. The supply side alternatives were
called "painful" and most were discarded for difficulties related to
their administration and costs. "The only remaining alternative is to
lower the level of the support price" [Buxton et al. 1981, p. 4], which
is, typically, a proposal to vertically coordinate the subsector through
an administered price mechanism. The spirit of this idea is reviewed
General model. Gardner [1981, p. 13] illustrates the general model
of a price-support program, which is adequate to examine the effects of
price-support controls. Consider Figure 7, where S and D are the supply
and demand curves for an agricultural commodity under price support pro-
gram. At any price support above PE the government acquisition of excess
-4 I c
I 0 0
---i--------------- ----0 (3 -c~
o C 0
I I m
-- o .
- 0 L
1 0- en
supply is given by (QS QD). When the support level is reduced from PO
to PI, as in Figure 7, production reduction is given by (QSO QSI), and
consumption increases to QDI. Government purchases are reduced from QGO
to QGI, as in panel b of Figure 7.
The USDA model. Recently, Salathe, Price, and Gadson  pre-
sented the dairy-sector sub-model contained in the U.S. Department of
Agriculture's Food and Agricultural Policy Simulator (FAPSIM). Among
other things, the model can be used to estimate USDA purchases of manu-
factured dairy products and the costs of government dairy product pur-
chases under alternative dairy price-support options. The authors used
the model to explore the effects of lowering the price-support level on
dairy products from 75 to 65 percent of parity.
The dairy submodel consists of four components: .(a) milk supply;
(b) milk price; (c) milk manufacturing, and (d) commercial demand for
dairy products. Ordinary least squares was used to estimate its equation
parameters. The results suggested that the farm price of milk would fall
by about $0.11 per cwt. in 1981, $0.83 per cwt. in 1982, and $1.26 per
cwt. in 1983. USDA outlays for purchasing butter, cheese, and nonfat
dry milk were estimated to fall $870 million in 1983. Cash receipt to
dairy farmers were estimated to fall by $1.8 million in 1983 [p. Ill.
Total milk production would be about 3.0 billion pounds lower in 1985
The USDA's FAPSIM seems to recognize the price support program as a
mechanism for coordinating the dairy subsector, and first operates with
the concept of commercial demand for manufacturing milk.
The shortcomings refer to its annual formulation. Since 1973 the
price support has been readjusted twice in a year. The change in the
regime might have caused a change in the industry behavior. The use of
annual data would aggregate such effects. Also, adjustments in produc-
tion due to a price variation may take place in periods shorter than a
Boynton and McBride model. This model [Boynton and McBride, 1980a]
differs from the other models because of its embodied farm level details,
and because it does not illustrate the effects of their plan on the
entire subsector. The recommended plan is an extension to the blend
price plan with no production base component and to the base-excess plan
with a production base scheme.
Figure 8 depicts the situation for a producer under the proposed
plan. Boynton and McBride assumed that the producer, delivering milk to
a market order, has an IBASE (class I base) of four units and a RESBASE
(reserve base) of one unit. A quantity of five units would be produced
[1980a, p. 6]. The producer's marginal revenue function would be composed
of three linear segments, which would improve the information carried by
the pricing system. Any milk produced by the farmer in excess of IBASE
plus RESBASE would be surplus milk. Surplus milk is priced below the
lowest class price in the order. The capability to discourage surplus
production would be enhanced over the other two common Federal marketing
order producer payment plans.
Boynton and McBride assumed that dairy cooperative managers recog-
nize the effect of surpluses on milk prices, disposal costs, and even
to 11 -----------------4-+-
:5 S SRATC
Q / MR -BPCI
T I I 1 1 I
0 1 2 3 4 5 6 7
Figure 8. Boynton-McBride Plan
on the viability of the price support program [1980a, p. 3]. The impor-
tant cooperative coordinating role would be to "pass on market informa-
tion to keep the members informed. If more aware of market conditions,
members may make production decisions more consistent with the overall
supply-demand environment" [1980a, p. 4].
The difficulty with their plan is that it requires a perfect and
constant update of information not generally available in the market,
like farmers cost structures. Furthermore, the economic assumption of
profit maximization would be critical for the plan's success. If farmers
behave as if to maximize revenue, the plan would not work. However,
in the current regulated environment, the relevant marginal revenue for
the typical farmer is not given by the three horizontal segments, but by
a weighted average revenue curve (ARI) (Figure 8). Accordingly, the
farmer represented in Figure 8 would be willing to produce Q and
receive an average weighted price of $11.00 for each unit of the product.
Vertical Coordination through Nonprice Mechanisms
Coordination between exchange partners sometimes is made through
voluntary agreements that differ from a price guided solution, or through
the use of authority. Production control or marketing allotments on
U.S. milk producers have never been required [Hammond, 1981, p. 8]. If
administrative difficulties (quota establishment, new entrant quota,
input controls, among others) were ignored, the effects of these
production control measures can be illustrated. Some proposals used
for other agricultural commodities will be reviewed in this section.
The illustrations are taken from Mansfield  and Gardner .
Quotas. This scheme specifies that each farm can produce a certain
quota, OX, as in panel a of Figure 9. The total quota for the entire
industry is OY (panel b of Figure 9). At the support price OP, con-
sumers will purchase OQI, according to their demand schedule DD'. The
government will buy (OY OQI) units of the product. In contrast to the
situation that would prevail without the quotas, the government would
have to purchase additional output (0Q3 OY) to guarantee the price OP
Deficiency payments. In 1973, a plan earlier proposed by Presi-
dent Harry Truman's Secretary of Agriculture, Charles Brannan, and
President Dwight Eisenhower's Secretary, Ezra Taft Benson, was adopted.
An illustration of this plan is provided in Figure 9. Suppose that the
government guarantees each farmer a price OP, as in Figure 9, panel b.
At the guaranteed price farmers produce 0Q3 units of the product. The
market will value each unit of the product by only OP2. The government
then issues subsidy checks to farmers to cover the difference between
the price they received, OP2, and the guaranteed target price OP. Com-
pared to the situation that would prevail when the government buys
(0Q3 OQI) and stocks the volume purchased, the government costs are
reduced by (OP OP2) (OQ3 OQI).
The alternatives described above have never been the subject of
investigation through a simulating model in the dairy industry.
X~---------- 0 -
I I 0
Demand and Supply Functions for Milk in the United States
The policy models reviewed consistently contain supply and demand
functions of milk and dairy products. The policy model that will be
developed and estimated for this study will also include demand and
supply functions. A review of recent empirical estimations of these
functions for the U.S. will follow next.
Derived demand functions for fluid and manufacturing milk at the
farm level was estimated by Rojko , Wilson and Thompson ,
George and King , Prato , Hallberg and Fallert 11976], and
Dahlgran . (See Table 2). Regrettably, these studies obtained
estimates that are somewhat inadequate for this study. The reasons are
(a) All but Dahlgran's  estimations are derived from the
demand for dairy products at retail level. The difficulty is that such
displacements require the formulation of a marketing margin model that,
if not correctly specified, causes distortions on the correspondent
derivations. This procedure is judged unsatisfactory.
(b) Furthermore, Dahlgran's criticisms were somewhat convincing
that further work was needed in this area. He reported that the models
by Wilson and Thompson , Prato 11973] and Hallberg and Fallert
 "have scant if any theoretical development" and "are econometri-
cally weak," and that the identification of retail products in terms of
the farm products are frequently very difficult [1980, p. 51].
Table 2. Estimated Demand Functions for Dairy Products
Market(s) of Farm Retail
Author Reference Level Level
Boehm, W.T. (1975)
Brandow, G.E. (1962)
Dahlgran, R.D. (1980)
George & King (1971)
Hallberg & Fallert
Wilson & Thompson
New York-New Jersey
Eastern Ohio, W. Penns.
Quad Cities, Dubuque
aVia displacement from retail level.
For the reasons pointed above, Dahlgran's estimation procedures
will be reviewed with more detail.
Dahlgran's assumption of subsector analysis [Dahlgran 1981, p. 105],
or the representative agent implies perfect substitution between grade B
and grade A milk. This input substitution is not permitted in the fluid
milk processing plant.
Using that assumption, he derived and estimated fourteen sets of
derived demand price elasticities. Each set refers to one of the fol-
lowing marketing orders: New York-New Jersey, Chicago Regional, New
England, Middle Atlantic, Eastern Ohio-Western Pennsylvania, Upper Mid-
west, Southern Michigan, Ohio Valley, Texas, Nashville, North Carolina,
Quad Cities-Dubuque, Oklahoma Metropolitan, and Nevada. These marketing
orders were selected by a sampling procedure specifically designed to
reduce the number of markets to be investigated.
The elasticities for the markets not directly estimated would be
calculated by using a model suggested by Searle [1971, p. 90-91], which
is based on the stratum characteristics of each non-sampled market, and
on the estimated stratum parameters obtained from the sampled markets.
The Oregon, New Jersey, and Massachusetts state orders were combined
with nearby federal order markets and the Hawaii state order was consid-
ered outside the scope of his study.
A milk manufacturing center was assumed to correspond with each
fluid consumption center. The production areas were defined to corres-
pond geographically to the continental United States.
However, after testing and rejecting the hypothesis that regional
or size effects have affected his estimated elasticities, he proposed
that the elasticities for any non-sampled market could be calculated
by averaging the sampled markets estimated elasticities. Next Dahlgran
passed the supply and demand functions through the average quantities
and prices for the following regions: Northeast, Mid-Atlantic, South-
east, Lake States, Corn Belt, South Central, North Plains, Central
Plains, South Plains, North Rockies, Central Rockies, Northwest, and
California. The formulation used was
(2.10) Q = aPb
Q is the average quantity of milk,
P is the average price of milk,
b is the estimated average elasticity, and
a is the implied constant term, so that the above equation is
satisfied for the 1976 average price and quantities of
the respective market.
After Dahlgran  concluded that "all markets have the same
set of structural parameters" [p. 188], the responses of the industry
participants to price variations in any geographical aggregation of
dairy markets in U.S. could then be measured through the estimated
However, Dahlgran  provided the only study estimating a
consistent set of derived demand functions for processors and manu-
facturers. His demand elasticities estimates are reported in Table 3.
>- 1- Q
I C0 \.D0 C
L\ -T Co Co m \, D Or -
Lr -3 f lr 0 0 0
I .O 0
I 0 I
03 .O O
0 0 0
I I I
0 C CDN
0 m 0
oD O co
- o c;
I I I
Note that five markets (Texas, North Carolina, Nashville, Quad Cities -
Dubuque, and Nevada) have unacceptable signs. Besides, the elastici-
ties obtained tend to be highly inelastic.
Supply Models for the Dairy Industry
U.S. dairy farmers' output decisions are hypothesized to depend
on the milk prices. This economic sensibility has long been measured
and tested for various levels of geographical and time aggregations,
under different approaches and methods. Direct estimation of milk
supply response functions has been done by Brandow , Halvorson
[1955, 1958], Cochrane , Wipf and Houck , Chen, Courtney,
and Schmitz , Hammond , Novakovic and Thompson , Houck
, and Dahlgran . Dahlgran estimated a consistent set of
supply functions for grade A and grade B milk at the regional level.
His models will be examined in more detail.
In 1980, Dahlgran, assuming a representative dairy farm (a farm
producing both grade A and grade B milk), derived supply functions from
the farmer profit maximization objective function. Results from that
derivation adequately capture the phenomenon of conversion from grade B
to grade A milk production. However, the "quid pro quo" is that grade
A farms would also reconvert to grade B production (following the con-
dition for symmetry), which is a very dubious action to be taken by
grade A milk farmers. In fact, additional investments are required in
the infrastructure for producing fluid eligible milk.
Dahlgran did not fully account for the advantages of lagged models
in the supply functions. The biological nature of milk production may
preclude rapid adjustments of output to changes in prices. Lagged model
approaches are discussed in the next section.
Price Lagged Models
Supply functions. The biological nature of the underlying milk
production process suggests a lagged response of production to a price
change. Two difficulties have been common to almost all estimations of
milk supply functions with lagged prices: (a) lack of theoretical
reference about the intensity across time which farmers can adjust produc-
tion of milk in response to price variations (the nature of the lagged
structure); and (b) lack of theoretical reference indicating the appro-
priate length of the lags.
Supply functions with lag structures for the milk subsector have
been estimated assuming that the greatest increase is forthcoming in
the first period with declining increases through time. The partial
adjustment model as in Nerlove and Addison  is adequate for this
assumption. It imposes a geometrically declining lag structure to the
coefficients of the lagged prices.
This expected behavior of the coefficients of the lagged prices
has been rejected by Chen, Courtney, and Schmitz  and Milligan
. The argument is that output response to some given price change
first increases through time, then decreases. In such a case, only a
flexible lag structure like the polynomial lag formulation is appropri-
ate. These two structures can be seen in Figure 10 which depicts the
assumption above mentioned.
The reasons favoring the polynomial lag formulation are that it
allows a greater degree of flexibility in the lag structure, which in
turn may improve supply response estimates. However, none of the justi-
fications backing the two structures clearly indicate why the coefficients
should behave as delineated by Curve 1, or by Curve 2.
The fact that some adjustments can be made in a short period of
time (changing feeding practices and/or culling herds), while others
require more time (raising calves), adds nothing to the cause of the
polynomial lag formulation. The information that "given a price change,"
some output response is realized in the short-run and in the long-run
is suitable for both the partial adjustment and the polynomial lag models.
Milligan [1978, p. 159] indicates that the nature of his lagged
structure model is due to the belief that "some producers result in a
weak aggregate short-run response that may even be the opposite of what
an economist would expect." Consequently, most of the response to
profitability (he did not use prices) could be in the third and fourth
Very little has been said about what happens in between the short-
and the long-run effects. At any period t, new milk cows are being intro-
duced into the herd. It is not clear that a declining response occurs
through time, as is suggested by the Nerlovian partial adjustment model,
or that the intensity of responses will first increase, then decrease.
Curve I: Polynomial Log
3 Curve 2: "\
0 Geometrically ""'
I I I 1 I II
0 1 2 3 4 5 6 7 8
ORDER OF LAGS
In summary, a large set of patterns are possible. A pre-choice of the
nature of the lagged structure is inappropriate since it is sensitive to
the specifics of the sampled data.
This kind of "open guard" in the theoretical approach of the lag
problems led Levins to postulate that "the compromises inherent in
specifying a priori patterns for lagged price parameters can be avoided
if the parameters are estimated directly" [1982, p. 286]. The short-run
and long-run effects of a price change on milk production would be rela-
tively strong compared to the intermediate term "because short-run changes
had already been made and the effects of long-run changes were not yet
felt. After the long-run effects the increases in production would be-
come negligible" [Levins, 1982, p. 286].
Although the explanations given are not very convincing ones--pri-
marily in regard to the "intermediate term"--the model run for Mississippi
generated a pattern quite similar to the one expected by Levins .
The question that remains is whether Levin's results were due to the
sample used (Mississippi data) or whether the pattern found is concep-
With respect to econometric problems, both partial adjustment and
polynomial lag models reduce the number of parameters to be estimated.
However, when the sample is large, losses in degrees of freedom is not a
problem. What remains important for this research are indications that
the "direct approach" could be followed because there will be sufficient
degrees of freedom.
Demand models. The uncertainties related to the length and nature
of the lag structure are more critical on the demand side, in which the
biological characteristics of the milk production do not apply. In cases
where theory and/or observation suggest a distributed lag relationship
between two time series (Xt and Yt), but the exact specifics of the
relationship are rarely known, a data oriented analysis can be adopted
to allow the data itself to reveal the approximate length of the lag
Three alternative procedures exist that could be used in this
approach: (a) a cross-correlation technique suggested by Haugh [1972,
1976] and Pierce , (b) a one-sided distributed lag approach implied
by Granger  and formalized by Sargeant 11976] and (c) a two-sided
distributed lag method advanced by Sims 11972].
The robustness of substantive economic results of all three
alternatives was examined by Feige and Pearce . Studying the
relationship between money and income they found that the "Sims proce-
dure yields substantive results quite different from those uncovered
by use of the Haugh-Pierce procedure or the Granger procedure" [p. 532 .
That is, the nature of an economic conclusion depends on the arbitrary
choice of the test to which "the model must first pass in order for the
estimation and interpretation of the model to be meaningful" [Feige and
Pearce, 1979, p. 521], which does not make sense. Given that the actual
state of art in this case is still not set, the above procedures will
not be followed.
Since little help could be found in the literature, a search pro-
cedure should be used in which the length of the lag is extended until
the contribution of the additional lagged price to the regression sum of
squares is no longer statistically significant. If the lagged prices
were found to be highly correlated, the alternative is to choose that
length of the lag which results in the highest value for the coefficient
of determination corrected for the number of degrees of freedom. If
the differences in that coefficient were found to be so small that a
choice is inappropriate, the expected signs of the various coefficients
may help in choosing the "best" lag for the problem.
The model that will be described in the next chapter is built upon,
or takes advantage of, the studies reviewed in this chapter. Some
modifications are made to include needed detail or to overcome some short-
comings. These shortcomings are discussed below.
The coordinating issues are as follows:
(a) The studies by Kessel  and Ippolito and Masson 
do not include the entire manufacturing milk market and do not explicitly
analyze features related to the price support program.
(b) The study by Dahlgran  did not consider the price
support program as a potential coordinating element in the exchange of
(c) The models by Buxton and Hammond  and Hein  could
be used to study the possibilities of vertical coordination through
the price supports control. However, they were never used for this
purpose. Besides, the Buxton-Hammond model does not consider the pooling
provisions and does not differentiate supply of grade A from grade B. Its
price relationship assumptions seem to be empirically weak across time.
(d) The USDA's FAPSIM ISalathe, Price and Gadson, 1982] does recog-
nize the price support control as a potential element in the subsector
coordination. But that model did not contemplate non-price alternatives,
Besides, the period of time used (year) is inappropriate for this study.
(e) The Boynton and McBride Plan [1980a] only specifies coordina-
tion at the production unit, and it did not consider the effects of the
price support program. However, it did recognize the presence of coop-
eratives in the exchange function of crude milk.
(f) As a group, these studies analyze only problems related to
drastic changes in the regulated structure of the subsector.
(g) Finally, these models have not totally explored the blend price
curve as a potential price coordinating device.
The empirical issues are as follows:
(a) The functions for fluid and manufacturing crude milk at the
farm level derived from demand functions estimated at the retail level
increase the risk of misspecification. Besides, the identification of
retail products in terms of the farm products is frequently very diffi-
(b) The symmetry conditions imposed on the price coefficients of
the supply functions for grade A and grade B milk seem to be unreal.
(c) The inclusion of retail level explanatory variables is a
procedure regularly used in estimating farm level functions. Although
their inclusion is no theoretically required, they may help in correcting
for model misspecifications with respect to the choice of the correct
time response period.
(d) The concept of a commercial demand for manufacturing milk used
in the USDA's FAPSIM [Salathe, Price, and Gadson, 1982] turned out to be
an important idea to this study.
In Chapter II, the recent dairy literature was reviewed to search
for a conceptual model that, if empirically estimated, would respond to
the concerns explicitly described in Chapter I. In reviewing those
previous works, it was concluded that very little would have to be done
with respect to the conceptual model construction. Basically, the main
idea is generated in Kessel's model. Ippolito and Masson, and Dahlgran's
contributions were also valuable. Changes were made in the definition
of the dependent variable in the manufacturing demand function by includ-
ing a version of the manufacturing milk commercial demand concept used
in the FAPSIM [Salathe, Price, and Gadson, 1982], by excluding the demand
for Class 2 milk from those models, and the redefinition of their pur-
pose, scope and equilibrium conditions. It was also concluded that a
complete and coherent set of supply and demand functions would have to
be estimated to make the model empirically manageable.
With respect to the supply side it seems that a lagged structure
is appropriate for estimating the supply functions of milk. The biolog-
ical characteristic of the milk production also helps in defining the
length of the lag and the length of the time period. The time between
short-run adjustments in the farmers' production function and the corres-
pondent variation in output is certainly longer than a month. It is
reasonable to suppose that it takes place within a quarter or within a
year. Long-run responses of milk production to price variation are likely
to occur in periods up to two or three years. Finally, good empirical
adjustments of milk output to lagged prices have been obtained [Tomek
and Robinson, 1977, p. 352], which is a very desirable characteristic
for this study.
No strong reasons were found for specifying the derived demand
functions in lagged structure.
In Chapter III, the models discussed in this chapter will be
modified in order to construct a model in which the concerns about
vertical coordination and U.S. milk surpluses can be answered. The
estimation of the model is discussed in Chapter IV. The simulations of
alternative coordinating mechanisms based on the premise that the regu-
lated dairy subsector is an unchangeable reality are made in Chapter V.
VERTICAL COORDINATION IN THE UNITED STATES DAIRY INDUSTRY
The difficulties in using the current policy models to assess the
vertical coordination in the U.S. dairy industry were identified in
Chapter II. The difficulties were either shortcomings characterized by
lack of needed details, by deficiencies in analyzing the available instru-
ments of coordination, or by imperfections in their estimation procedures.
The conceptual model for the dairy industry that will be developed in
this chapter is built upon the basic structure of the models reviewed.
Some modifications are introduced to overcome the referred shortcomings
in order that the vertical coordination among dairy farmers, dairy coop-
eratives, processors of fluid milk, and manufacturers of dairy products
could be adequately considered. This model will be empirically estimated
and utilized to simulate the impact of alternative exchange arragnements
on the balance between supply and demand of crude milk in the U.S. dairy
A Model for the Crude Milk Exchange
The model formulated in this section explains the regulated
equilibrium for crude milk exchange between producers and processors/
manufacturers (first users). The model is first graphically demonstra-
ted, then it is mathematically developed.
Figure 11 depicts the market equilibrium for crude milk in period
t. The price for fluid milk is PF = PI + PR where PI is the minimum
class I milk price established by the Federal Marketing Order system, and
PR is the cooperatives' announced over order class I price. Given the
derived demand for fluid milk, DF(PF), the quantity QF is determined.
In Figure 11 PS is the equivalent manufacturing milk price supported
above the market equilibrium price by government. At PS QB is pro-
duced by grade B milk farmers. Given derived demand for manufacturing
crude milk, DM, QMD will be acquired by the manufacturers to meet the
dairy products' commercial outlets. The blended price for grade A milk,
when PF QF and PS are given, becomes a function of the volume of
grade A milk placed in the manufacturing market, QII As QF + Qll =
QA PA is also a function of the total volume produced. Grade A
farmer's optimum volume of production is determined when the blended
price curve BPC, intercepts SA, the supply function of grade A milk. The
volume of manufacturing milk available in the market, QMS is thus given
by QII + QB. All of it is bought by manufacturers, but part of it is
not sold to commercial users. The government purchases of equivalent
manufacturing milk in period t, QS is given by the difference between
QMS and QMD
7 --------- o
-- a- -o
Sd ^ \ *lOG
The diagram on Figure 12 shows stepwise how the equilibrium solution
values can be achieved with the above model. The endogenous variables
in the model are PA, QA, QF, QII, QMD, QS, QB, QMS, PF, PM, and PB.
Exogenous variables are Pit, PRt,'PSt.
The model described graphically in the last section can be formu-
lated in terms of mathematics. It is composed of four behavioral equa-
tions plus price and quantity identities. The behavioral equations do
not include all the explanatory variables for expository convenience
only. These variab les will be properly discussed later.
Supply and demand relations.
(3.1) QFt = DF(PFt), derived demand for grade A milk by
(3.2) QMDt = DM(PMt), derived demand for manufacturing milk
(3.3) QAt = SA(PAt), supply of grade A milk by farmers.
(3.4) QBt = SB(PBt), supply of grade B milk by farmers.
(3.5) Qllt E QAt QFt, all grade A milk is used in processing
fluid milk products or in the manufacturing of dairy
(3.6) QSt + QMDt E QMSt, total demand for manufacturing milk
equals its available supply.
Figure 12. Equilibrium Solution for the U.S. Regulated Dairy Industry
(3.7) QMSt E QBt + QIlt, the total quantity supplied of
manufacturing milk is constituted by grade B and class II
(3.8) PFt = Pit + PRt, the price processors pay for fluid milk
is composed by the minimum market order price added by
the cooperatives announced premium.
(3.9) PAt = PMt + (PFt PMt) QFt/QAt, formula for the blended
price. The price received by farmers for the grade A
produced, PAt, is a weighed average price. The weights
being the quantities respectively allocated to the fluid
and to the manufacturing market.
(3.10) PMt = PBt = PSt, identity between (a) priced paid by
plants for manufactured milk products, PMt, (b) price
received by farmers for grade B milk, PBt, and (c)
price support by government, PSt.
Note that total demand for manufacturing milk is composed of quanti-
ties demanded by commercial outlets, QMDt, and government removals from
the commercial market, QSt. This definition differs from the demand for
manufacturing milk used in the studies reviewed in Chapter II. The other
change in modelling the dairy market introduced in the above model is that
a demand for class II milk is not included. As an excess of production
over quantities consumed, class II milk is appropriately considered as
part of the supply of milk available for manufacturing uses. Note that
the model refers to the national milk market and not to a specific re-
gion of the U.S.
After the mathematical exposition of the model, and after describ-
ing how equilibrium is obtained, two important steps must be taken. The
first is to show that the model could be used to design alternative
coordinating arrangements to reduce the imbalance between supply and de-
mand of manufacturing milk. The second is to empirically estimate the
model, test for its validation, and simulate the alternative coordina-
ting arrangements. The next section takes care of the first step as
Alternative Exchange Arrangements
This section will show how the model developed in the preceding
section could be used to simulate alternative coordinating arrangements
to bring the manufacturing milk market to a desirable institutional
equilibrium. Before that, however, it is convenient to detail the joint-
ly coordinating roles of two elements present in the model described
above. They are the dairy cooperatives' pooling system and the price
Coordination between Cooperatives and Dairy Farmers
Consider that the farmers expect to receive PAc from their coop-
erative. Accordingly, they will be willing to produce QAc = n qA ,
where n is the number of grade A milk farmers, and qA the quantity
produced by an individual farmer which is determined from the first
order condition of
(3.11) Max G PA qA C(qA),
(3.12) PA = C'(qA), where G is profit.
However, PAc is actually computed with values that the individual
farmer does not control. PA is the result of
(3.13) PA = (PF' QF* + PM QII )/QA",
c c c c
QFc is the quantity of grade A milk sold to processors,
PF is the unit price of QF,
QllI is the quantity of grade A milk sold to manufacturers, and
PM is the unit price of QII.
These optimal values result from the cooperative marketing activ-
ities of assembling the grade A production from n farms and selling in
the fluid and in the manufacturing milk market in such quantities that
(3.14) PROFc = PF QFc + PM Qi l C(QA ),
(3.15) QF > kQA, 0 < k < 1.
It is assumed that any administrative costs incurred by the coop-
eratives are independent of the quantities traded. No profits are re-
tained and information from producers and buyers is available. The
class I milk price PF is pre-announced, PF and PM is supposed to be
given as PM The constraint reflects the marketing cooperative
perception that it could have enough power to allocate at least a frac-
tion, k, of all grade A milk produced by its members in the class 1 milk
market. Other implicit assumptions are that the marketing cooperative
has control over QAc, and that class I demand is prioritarily met. This
problem corresponds to
(3.16) Max L(QAc, QF ) = PF QFc + PM(QAc QF ) C(QA ) +
c c c c c c
X (kQAc QFc)*
The first order conditions are
(3.17) L/aQAc = PM C'(QAc) + Xk = 0,
(3.18) LL/QFc = PF PM X = 0,
(3.19) L/9X = kQAc QF = 0.
Substituting A and k into 3.17, from their solution in 3.18 and
3.19, respectively results in
(3.20) PM + (PF* PM") QF /QA = C'(QA ),
c c c
which is the profit condition for the cooperative firm. Notice that the
left hand side of equation 3.20 is equal to
(3.21) PF QF + PM QII)/QA
which is exactly the right hand side of formula (3.13) used to calculate
the blend price (PA") for grade A milk.
This result reveals that the assumptions imposed upon the behavior
of the marketing cooperative are consistent with the current blend price
formula used in the subsector for computing the grade A milk price. It
is also the explicit condition for a coordinated equilibrium between
grade A farmers and dairy cooperatives.
Now, take 3.21 (which is the blend price curve) and vary QA .
The blend price curve, BPC, for given values of PF QF and PM is
generated (See Figure 13). As it was shown above, the best of these
optimum marketing values is determined only when cooperative members
reveal their aggregate supply schedule, SA. (See Figure 14.) At the
intersection of BPC with SA, the equilibrium between the marketing and
the production segments is established.
Coordination between Cooperatives and First Users
Note that anytime PM changes, some adjustments are necessary in
the BPC curve just derived. Suppose PM' < PM is discovered to be the
relevant price in the market this period. The BPC curve would then
rotate downward around (PF QF ) as in Figure 15 below. BPC' would
be the new blend price curve, derived with PM = PM'. The new marketing
signal is supposed to be immediately perceived by farmers in the form
of the new calculated blend price PA'. (See Figure 16.)
At this point, uncertainties that would exist with respect to the
price of the manufacturing milk are drastically reduced when the price
support level is pre-announced. The expected price for manufacturing
milk in period t is equivalent to the prevailing support level previously
established for that period. The instrument to transmit to grade A milk
farmers the marketing alternatives at every price support level is the
BPC curve. The BPC curve just derived will be used as an instrument to
coordinate the exchange of crude milk between farmers and cooperatives
and between farmers and the first users of crude milk. Basically, it
Figure 13. Blend Price Curve
Equilibrium Solution in the Grade A Milk Market
0 QF* QA
Figure 15. Rotation Movement of BPC Due to Changes in PM
- "~ -BPC
g PA' -----------.^
SQA QA QBPC'
0 QA' QA* QA
Figure 16. Effects of a Decrease in the Manufacturing Milk Price
plays the role of a "regulated total demand function for grade A milk."
To cooperatives, BPC represents a set of marketing opportunities. To
farmers, it reflects the prevailing demand conditions. Optimum prices
and quantities can be derived. The BPC curve incorporates the possi-
bilities of coordinating the responses of farmers because it is sensitive
to the levels of a series of parameters including the level of the price
supports. Since it establishes the coordinating linkage between partners
that exchange crude milk in the dairy subsector, the BPC curve will be
extensively used in the section that will deal with the simulations.
Alternative Coordinating Arrangements to Balance
Supply and Demand of Manufacturing Milk
The Dairy Price Support Program has had four economic roles. The
first three are interrelated and are primarily concerned with welfare
of the dairy farm sector. The fourth role reflects concerns with con-
trolling the physical production level. These economic roles are (a) in
the short-run, to avoid income losses to dairy farmers in the spring
season by holding possible breakdown in the milk prices, (b) in the
long-run, to support dairy farmers income, and (c) stabilization of milk
and dairy products prices. Recently, the price support program has
assumed its new role as a coordinating mechanism to reduce surplus of
milk. The provisions of the program were changed to conform it to this
new function. The price support level is not as closely tied to its
The model developed in this chapter will be used to examine how the
price support program, as a coordinating instrument, can accomplish the
objective of reducing the unbalance between supply and demand for manu-
facturing milk. All the alternatives of balancing supply and demand for
manufacturing milk contemplate the production side of the milk market
only. Advertising and promotions, as well as other disposal features,
are excluded from the analysis.
As farmers and cooperatives become the focus of attention of the
coordinating measures, preferences will be measured in terms of the
total net revenue that would be foregone by milk producers under each
set of alternatives. All the simulations start with, and are compared
to, the dairy subsector in estimated "regulated equilibrium" as depicted
in Figure 11.
Suppose government announces that it would not buy quantities of
dairy products in excess of QS equivalent milk, at the prevailing price
PS (Figure 17). The dairy farmers, organized in cooperatives, have at
least two options to accomplish this demand restriction. One is to
impose a production quota on themselves (a nonprice type mechanism of
coordination). The other is to block distribution of part of the pro-
ceedings from pooling (price mechanism). These two alternatives will be
--C ----- O 4
L---------- O c
I I -
D c 0c
II < .
I _____ 0.
-I I "-
l-- ------- L -
II I O r,
w_11--a- - I11--
Restricting the quantities produced of grade A milk. Suppose that
dairy cooperatives are pressed by the government to reduce the manu-
facturing milk surplus. The choice could be to impose a quota on each
member's production. The grade A milk farmers, organized in coopera-
tives, must examine the alternatives in order to accomplish the govern-
ment demand restrictions. The alternative which generates the least loss
in revenue should be preferred by producers. One of the ways to satisfy
both the demand schedule for fluid milk, and the commercial derived de-
mand for manufacturing milk, and make only QS available to the govern-
ment (Figure 17) is a self imposed limit on the farmer's production of
fluid eligible milk. The equilibrium values for the milk market with
the classified pricing, pooling, and price supports are given by the
vector (PA, QA, QII, PF, QF, PS, QB, QMS, QS, QMD).
After allocating QF to the fluid milk, QlI is sold to the manu-
facturing milk market. When QII is added to QB, which has been produced
at the price support PS, QMS is generated. QMS is the supply of avail-
able manufacturing milk after the quota. The blend price the coopera-
tives will be able to pay their member producers is PA, which is above
the equilibrium price PA The change in revenue for the grade A dairy
farmers can be measured by the difference between the rectangles ABC
Cooperatives blend price control. The cooperative board [USDA,
1981, p. 26] may choose to pay a blend price that would induce producers
to generate exactly the amount limited by the government QSI, at PSO
0 0 0
--- O -0
-_ 0 )
0 I a:
I I z
I I l c
---- -+ --
/'y-- --------.0 : I=m
S I I 1 I ;
e_ e.. e..
Suppose that cooperatives, being aware of all the schedules in the
milk market, project that the government restriction QSI (Figure 18),
could be met if the proceedings from the marketing of the crude milk
were computed at the price PSI instead of PSO. According to the BPC
schedule, PAI would be paid to producers for each unit of grade A pro-
duced, QAI. Revenue losses to producers will be in the order of
(QAI PAI QAO PAO). Part of this loss in revenue, (PAc PAI)QAI
would be retained by cooperatives.
Alternative Government Controls
The next four alternatives assume increasing government's role
with additional coordinating measures. They are: (a) product differ-
entiation support prices; (b) deficiency payments; (c) taxing output;
and (d) selective price supports.
Product differentiation support prices. Suppose the government
finds enough reasons to assert that surpluses are due to excess supply
of grade A milk and thus decides to impose a lower price support to
products manufactured with grade A milk. With the same objective of
former alternatives, the price support to be imposed on grade A farmers
will be PSI, as in Figure 19. In this case, besides the decrease in
gross revenue of about (PAO QAO PAI QAI), the cooperatives would not
be able to retain (PA PAI)QAI. Of course the operationalization of
this alternative would require adjustments in the current administra-
tive mechanisms to allow government to control the price support levels
according to the product origin (grade B or fluid eligible milk).
/O o_ -
[---7 ------ a
R 4- -
I i I I I
< < < 0 0)
ScL a- 0 aa a-
Deficiency payments. If government decides that all milk produced
should be sold to commercial markets, the price of manufacturing milk
would drop to PMS (Figure 17). Government expenses with this alterna-
tive would have been (PS- PMS QMS).
Taxing output. Instead of either self-regulation or differen-
tiating support prices according to milk classification, the alternative
may reside in taxing. The government with the objective of reducing
its total purchases decides to collect a once-for-all dollar tax on
every hundred pounds of marketed milk, if quantities exceed QAI (Figure
18). The exact amount of taxes per cwt. is given by (PAO PAI) in
Figure 18. Of course producers may decide to market QAO and be assessed
by (PAO PAl) QAO, or to reduce production to QAI and lose (PAO QAO) -
(PAl QAI) in revenues.
Selective price support levels. Suppose the government decides to
use its discretionary power over the price supports level to signal to
farmers its intention in seeing the formation of the milk surplus re-
duced. The short- and long-run effects on the dairy farm sector will be
The long-run effects (Figure 20) shows that a permanent reduction
in the level of the price support from PSO to PSI will reduce government
purchases of manufacturing milk to QSI = (QMSI QMDI). Total produc-
tion of grade A milk will be reduced to QAI, and farmers will receive
PAI for each unit produced. The reduction on the government purchases
is drastic. Grade B production decreases along with a reduction in
CI 0 0
-I "-- -
__0 4 _
I I O a
I IO 0
1 I 1 "-0
SI eI I
-i l .
1 I ,
j i I
class 2 and 3 quantities. The commercial demanders now take more at
the lower price.
The short-run analysis is important because it introduces aspects
that are similar to policies recently proposed. The concepts of short-
and long-run supply functions, as defended by Becker [1971, pp. 79-83]
are needed here. Figure 21 depicts the short- and long-run supply
curves SS and SL, respectively, for grade A milk. Assume that the equi-
librium prices and quantities, PO and QO, have been observed for an in-
definitely long period. A price decrease to PI would have a different
impact on the quantities of milk produced depending on the way farmers
interpret that movement of prices. In the analysis of the preceding
alternative it was assumed that farmers understood that the price support
decrease was a permanent move taken by CCC.
However, News for Dairy Co-ops [NMPF, 1982] indicates that the
price freeze at $13.10 (current dollars) would be suspended by 1984,
when it would be again corrected to follow its parity concept. To the
extent that farmers become aware of this "news," it is very likely that
the response to the price (real) decrease would be made along their short-
run supply curve. The return to the "parity" concept after a short
period of time may indicate to farmers that the price decrease will be a
temporary measure. Adjustments would then be made mostly through de-
creasing the use of variable factors. Farmers would not dispose of their
fixed factors, but would reduce their utilization, waiting until prices
returned to original levels.
Figure 21. Impact of Temporary or Permanent Decrease in Price
on the Quantities Produced
Currently, the House of Representatives has established that the
temporary freeze of the manufacturing milk price supports would end by
1984, but that the real price would not go back to its original level
(1982). It would rather be kept at its real value of October 1, 1983,
estimated at 63 percent of parity. Note that no reasons are given for
this decision. It seems that by coming back to the parity level, "a
concept that the Federation (NMPF) considers an absolute necessity in
the support program," will again link the program objective to its in-
come support issue. Becker's analysis of short-run equilibrium is
suitable for this situation and may be used to simulate the effects of
the current freeze under some special circumstances. Bringing his
analytical framework into the model for the dairy industry, the short-
run equilibrium values after a temporary decrease in the price support
level can be obtained.
Note that as a result of the above analysis the availability of
manufacturing milk for government uses will be larger than if the
farmers had believed that price would have been permanently frozen at
some given level.
After having introduced the problem of this study in Chapter I,
and having reviewed the relevant literature in Chapter II, the model and
what can be conceptually done with it to assess the problem was just
addressed in this chapter. The empirical estimations will be discussed
in Chapter IV. In Chapter V the estimated relationships will be used
to validate the conceptual model and to execute the simulations
discussed in this chapter.
FORMULATION OF THE EMPIRICAL MODEL
In the last chapter, derived demand curves for fluid and manufac-
turing milk, supply curves for grade A and grade B milk for the United
States were identified as the basic components of the conceptual model.
Their empirical estimation will be essential since the available esti-
mates were considered inadequate for the purpose of this study. A
decision was made that the national functions would be obtained by using
"pooling" cross-sections over time series techniques. This procedure
makes the maximum use of available information and enriches the sample
basis [Judge, 1982, p. 475]. The Federal Milk Marketing Order market is
chosen as the cross-sectional unit on the demand side and the state is
judged to be a natural choice for the cross-sectional unit for the esti-
mation of the supply functions. The availability of information oriented
toward these selections. The explanatory variables to be included in the
empirical estimation of the above functions can be identified from a
theoretical derivation, which will be included in Appendix A. This chap-
ter reports the selected specifications, the variables that will be used
in their empirical estimation, as well as the data sources. Results are
presented after a brief discussion of the respective estimators.
The explanatory variables are, in general, identified from theo-
retical derivations performed in Appendix A. Explanatory variables not
explicitly identified in the derivations are adequately discussed in
the next sections.
The concept of a derived demand function is used in this study
for two basic reasons. First, the market stage under investigation is
an intermediate market. Second, it would be very difficult to estimate
the final demand for crude milk. Besides, given the objectives of this
study, there are no major theoretical or practical reasons for not using
Market order derived demand function for fluid milk. The processor
buys grade A milk and other inputs to produce fluid milk products, a
class I use. A unique relationship between purchases of raw milk and
its price is found (See Appendix A) to be like equation (4.1) if profit
maximization is assumed and if perfect competition is the environment
in which trade takes place.
(4.1) qf = df(pf, po, w, e),
qf is the quantity of raw grade A milk purchased by the processor,
pf is the unit price of qf,
po is price received by processor for output sales,
w and e are prices paid by processors for nomilk inputs--wage
and energy, respectively.
A market order derived demand function is assumed to be a horizontal
summation of individual processor derived demand functions, and all the
derived demand functions, for all market orders, can be written as
(4.2) QF = DF(PFR ; PO; W; E; Y; Sl, .. ,Sr)
Given the regulated milk market and the assumptions of perfect
competition, all the explanatory variables in the demand equation for
fluid milk are considered exogeneous variables. PO, W, and E are assumed
to be given since perfect competitive output and input markets are
assumed for all nonmilk inputs.
In general, when price and quantities in a market are jointly de-
termined, both price and quantity variables are considered endogeneous
to the model. Administrative price discovery techniques change the
econometric nature of price as an explanatory variable. The price of
fluid milk, PF, becomes exogenous in the equation (4.2). The Federal
Milk Order Marketing system establishes a minimum unit price that the
processor must pay for QF, PI Very often, PR a pre-announced pre-
mium over class I prices, are added to PI
The variable Y is introduced to capture the effects of the market
size on the total quantities demanded in each cross-sectional unit. Y
is total personal income by Federal Milk Order markets. The advantage
in using Y instead of dummy variables is that it saves degrees of free-
dom in two ways. First, by reducing the number of variables that other-
wise would be included to isolate the effects of the market size.
Second, because it jointly captures the effects of population (the market
size) and per-capita personal income (the specifics of each market).
Furthermore it has the advantage over "zero-one" variables because X
could also shift the intercept across time.
The variables PFRr are the price of fluid milk in all marketing
orders included in region r, r = (1,...,9). R are defined as variables
that assume the value one when the cross section unit is included in
region r, and zero otherwise. The regions considered are the nine
census regions (modified) defined for the United States (Figure 22).
The hypothesis is that the response of the dependent variable to PF is
different for different regions, but it is constant over the period of
Finally, Ss, s = (1,...,4) are dummy variables to account for
seasonality in the derived demand for fluid milk by processors.
Market order derived demand function for manufacturing milk. The
manufacturer buys milk, either grade B or grade A, to produce nonfluid
dairy products such as ice cream, sour cream, cottage cheese, cheese,
butter, nonfat dry milk, and condensed milk. Assuming profit maxi-
mization as an objective, and perfect competition in both input and
output markets, a demand function for crude manufacturing milk is
derived (See Appendix A). The demand for all manufacturers in the U.S.
is assumed to be just a horizontal summation of the individual manu-
facturer demand functions. Some adjustments are introduced to fit the
equation into the selected estimation technique. Its final specifica-
(4.3) QMD = DM(PMRr; POM; WM; EM; Y; SI,... ,S4)
QMD is the quantity of commercial manufacturing milk purchased
PM is the unit price of QMD,
Rr are regional dummies, r = (1,2,4,...,9),
POM is an index of prices received from the sales of manufactured
WM, EM are prices of nonmilk inputs, labor and energy, respectively,
Y is total personal income by marketing order,
Ss are quarterly seasonal variables, s = (1,...,4).
For the same reasons as the ones related in the derived demand for
fluid milk, all the right-hand-side variables of equation (4.3) are
exogenous variables. Y is included to capture the effects of the manu-
facturing milk market size (population), and its specifics (per-capita
income), on the quantities demanded.
PMR is an interaction between PM, the unit price of QMD in each
cross-sectional unit, and Rr, a dummy variable which assumes the value
one if the Federal Order market is included in region r = (1,2,4,...,9).
Such regions are based on the modified nine U.S. census regions (Figure
22). The region composed by Alabama, South Carolina, Georgia and Florida
is left out. It accounts for only one percent of the manufacturing milk
marketed in the U.S.
In Appendix A it was assumed that a typical dairy farmer produces
either grade A, grade B, or both types of milk. In that Appendix, the
reasons behind this assumption and the corresponding derivations of the
respective supply functions can be found.
Supply function for fluid eligible milk. The supply function for
all producers of grade A milk in any cross-sectional unit would be the
horizontal summation of the supply function derived for the individual
farmer. The general form a supply function representing all cross-
sectional units can be written as
(4.4) QA = SA(PA Rr; PAt-_,...,PAt-4; PAt_3 .PAt_16;
PBt_ ; C; PDF; PMC; SI,...,S4).
QA is the quantity of grade A milk produced and sold to plants
by dairy farmers, by state,
PA is the unit price of QA,
R is a dummy variable which assumes the value one if the cross-
section is included in region r, r = (1,...,9). Such regions are based
on the nine U.S. census regions (modified) as shown in Figure 22.
PB is the price received by dairy farmers for grade B milk
sold to plants,
C is the number of milk cows in the state,
PDF is the price of dairy feed with sixteen percent proteins,
PMC is the price of milk cows, and
Sl,...,S4 are quarterly seasonal variables.
The price of grade B milk, lagged one period, is introduced to
capture the conversion of grade B milk to grade A milk. Milk cows are
an asset to the dairy farmers. As the value of cows (PMC) increases,
farmers expand their herd size which increases milk production
[Novakovic and Thompson, 1977, p. 514]. The number of milk cows in the
state, C, captures the effect of the cross-sectional unit size on the
As it was also observed in Chapter II, milk supply functions
should include lagged explanatory variables. Recently Levins ,
and Chavas and Johnson  have suggested that the lagged structure
should follow the biological characteristics of the industry to which
supply estimations are referred to. Accordingly, the responses of
dairy farmers to price variations would be more intensive in the be-
ginning and end of a period defined between the instant the milk price
is changed and the production of milk by calves raised because of that
price increased motivation.
Milk produced by U.S. farmers shows a very definite seasonal
pattern. Spring and summer volumes are always greater than the output
obtained in the fall and winter. Some exceptions are observed for some
of the southern states. Seasonality in milk production has been observed
extensively in the dairy literature. Rojko, for example, noted that
"consumption of milk was at a minimum during June, July, and August,
when supplies were in a relatively surplus position, whereas production
of milk tends to be the least in November and December, when sales in
most markets are above their annual average." [1957, p. 12]. Recently,
in a study about seasonal deliveries by cooperatives, Ling observed
that "milk production peaks in spring and bottoms out in fall. Fluid
demand is higher in early spring and fall than in summer and winter."
[1982, p. iii].
The econometric implications of such patterns are that other
reasons than economic ones are influencing variations in production.
Such exogenous and perhaps uncontrollable factors should be adequately
treated. Elimination of the variations would improve the efficiency
of the estimator, since reductions of variances of the estimated para-
meters would certainly be observed. One usual procedure to take care
of seasonality is the dummy variables technique. In the present supply
S = 1, if data refers to the s quarter,
Ss = 0, otherwise; s = (1,2,3,4).
Supply function for grade B milk. The dairy farmer supply function
for grade B milk is derived in Appendix A. A quantity dependent relation-
ship for all cross-sectional units can be written as
(4.5) QB = SB(PB; PAt-_, PAt-2; PDF, FW; PC; E; Ss; ZSBu)
QB is the quantity of grade B milk produced and sold to plants,
PB is the unit price of QB,
PA is the unit price of grade A milk,
PDF is the price of sixteen percent dairy feed,
FW is farm wage rate,
PC is the price of beef cows,
S are quarterly seasonal variables,
ZSB is the intercept shifters for each cross-sectional unit.
Lagged fluid eligible milk prices were introduced in the above
specifications to isolate the effects on the supply response of grade B
milk caused by conversions to the grade A milk activities. Such con-
versions are not instantaneous because it requires additional investment
and the approval of the sanitary authority.
Note that all right-hand-side variables of equation 4.5 are
exogenous except the price of grade B milk. The government guarantees
the price of cheese, butter and nonfat dry milk, not the price of the
crude milk input. Fixing a floor the manufacturer's output prices only
limit the input price variations. At the farmer-manufacturer interface,
the variation in price is still a function of the quantity produced of
grade B milk. Therefore, the demand function for crude grade B milk is
(4.6) PB = DB(QB; Y; SI,...,S4; ZDBl,...,ZDB25)
PB is the price paid by plants for grade B milk,
QB is the quantity of grade B milk sold to plants,
Y is total personal income,
S, ... S4 are quarterly seasonal variables, and
ZDB,,...,ZDB25 are intercept shifters for each cross-sectional
The joint dependence configuration between PB and QB in the above
relationships requires that a simultaneous system approach be used in
their estimation [Kennedy, 1979, p. 37].
Data for empirical estimation of the supply and demand functions
described in the last section are needed. The major sources are the
Dairy Division, Agricultural Marketing Service, USDA; Crop Reporting
Board, and Economic Division, Statistical Reporting Service, USDA; the
Commodity Credit Corporation, ASCS, USDA; the Bureau of Labor Statis-
tics, USDL; and the Bureau of Economic Analysis, USDC. Books, other
general publications, special tabulations, tapes, and computer print-
outs were the most frequent forms in which the data were obtained.
Telephone calls and letters were the means of communication used in the
contacts with respective officials from those government agencies.
Table 4 contains a summary of all the variables used in the model
estimation. Most of them are constructed variables because of needed
adjustments in either the period or the geographical unit in which the
primary statistics were obtained. Each state's manufacturing grade
milk (grade B) is divided among the Federal Marketing Orders in the
same proportion as each state's grade A milk production. Also, when
the explanatory variables for the Federal Order demand equation are
available only at the state level, an average value was constructed
by weighing the values of each state by the proportion of the Federal
Order's population coming from each state.
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) O 4
L- L- 0 C >,
a ( a) -(
- Ll -
a) a a.
-C L -
---' 2 T
0) - TO 0 "
a) C 1
2 O O-- C c a
- 0 4-) a)
4- U COU L >
C -U T 0
-N UZ -O O U
a o*- L-
a)- LL- a) >-
-'La C a
CU a) (
(U a- LD L U)
>C (U a) U L l
0 4-L 4-J 4-j ( a)
>-- 0- ) 0 U
20) -0 1 T >
E )a u 0) 1- -
C C >- (U >. C L 0
L. 0 S
S- 3 e UJ >-
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- OU C C
/ N N
LI e C
a9 d 0
a a a
Finally, all data should preferably refer to a quarterly basis.
Some aggregation of monthly, as well as disaggregation of yearly, issued
information will be necessary Also, note that it is implicitly assumed
that all regulated grade A milk delivered to a handler regulated under
Federal Order j, is sold to a processor or to a manufacturer in that
Federal Marketing Order.
Table 5 contains all the variables used in the estimations, the
variables used in their construction, and respective sources.
Period of Analysis
The upper limit of the time series was set at the fourth quarter
of 1981, which was the most recent period that a complete set of informa-
tion was available. Beginning in 1982, some important modifications were
introduced into the legislation of the price support program, altering
the observed homogeneity. This is the very reason why the lower limit of
the time series was set at 1977. Homogeneity was basically looked upon
with respect to the industry structure. Two variables that may alter the
industry structure are changes in the Federal Order milk marketing struc-
ture and the frequency per unit of time that price supports are announced.
A period in which both variables were kept constant would be better iso-
lated from external and undesirable shocks. Besides, the choice of a
homogeneous period would minimize aggregation problems if aggregation
were required, or at least would improve comparability of data.
n n 0.
U U -- O
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