Citation
Vertical coordination arrangements

Material Information

Title:
Vertical coordination arrangements some alternatives for the United States dairy subsector
Creator:
Gontijo, Vander, 1947- ( Dissertant )
Kilmer, Richard L. ( Thesis advisor )
Drummond, H. Evan ( Reviewer )
Langham, Max R. ( Reviewer )
McPherson, W. W. ( Woodrow Wilson ) ( Reviewer )
Ward, Ronald W. ( Reviewer )
Denslow, David ( Reviewer )
Fry, Jack L. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1983
Language:
English
Physical Description:
vi, 3, 168 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Derived demand ( jstor )
Manufacturing output ( jstor )
Manufacturing processes ( jstor )
Market demand ( jstor )
Market prices ( jstor )
Milk ( jstor )
Modeling ( jstor )
Production estimates ( jstor )
Supply ( jstor )
Supply and demand ( jstor )
Dairying -- Economic aspects -- United States ( lcsh )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Milk supply -- United States ( lcsh )
Surplus agricultural commodities -- United States ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Milk production in the United States has surpassed commercial consumption. 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 policies. The objective of this study is to examine some alternative arrangements to reduce milk production in the United States. The assumption made is that the sub-sector could, as an alternative to additional government 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-coordinating measures. Within these lines it is suggested that government should anticipate 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.
Thesis:
Thesis (Ph. D.)--University of Florida, 1983.
Bibliography:
Bibliography: leaves 158-167.
Additional Physical Form:
Also available on World Wide Web
Original Version:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Vander Gontijo.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
029296555 ( AlephBibNum )
10034952 ( OCLC )
ACA4940 ( NOTIS )

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VERTICAL COORDINATION ARRANGEMENTS: SOME
ALTERNATIVES FOR THE UNITED STATES DAIRY SUBSECTOR

















BY

VANDER GONTIJO


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


1983













ACKNOWLEDGEMENTS


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

comments.

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

facilities.

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


Page


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

ABSTRACT . . . . . . . . ... . . . . . . vii

CHAPTER

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










Page


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


Users .
Alternative Coor
and Demand of M
Self-Regula
Alternative
Summary . .


. 47

. 47
. 47
S. 48
. 50
. 53


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
. 97
. . 98
. . 99
S. 101
101

. . 101

. . 105
. . 105

. . 110









Page


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

APPENDICES

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

By

Vander Gontijo

April 1933



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-

cies.

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-

coordinating measures.

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.














CHAPTER I
INTRODUCTION


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

necessary.


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








5

arrangements to reduce milk surpluses are ampirically examined with the

estimates obtained in Chapter IV. Summary and conclusions follow in

Chapter VI.














CHAPTER II
LITERATURE REVIEW


Introduction

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 [1967], and its

extensions by Ippolito and Masson [1978] and Dahlgran [1980], 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 [1974], and the Hein

model [1977]. 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.


Kessel Model

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]






























AR


DII


Qi*


QA*


Figure 1. Kessel Model of Regulated Grade A Milk Market


P1 I*










(2.3) QI = DI[PI].

(2.4) QA = QI + QlI.

(2.5) PI = PI .

(2.6) PII = PII

Kwoka [1977] 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"

[p. 380].

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



















SA


U)
< PA'
j Pl, PI'-
O I I


/I I
I I
I I


I I


0 Q1' QA' QA
QI
QII'


Kessel Model of an "Unregulated" Grade A Milk Market


Figure 2.











old statistics since they did not capture new trends and adjustments

in the subsector.


Ippolito-Masson Model

Ippolito and Masson [1978] 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.








12

O
0
















m
0

--- 0


I O

I I
I/ I Io
I I -








--J
I I 1 1











D c













Q_
- I- -- O
*U


I 1

I0 o
I II *


-- - --- S -








- ,J










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 [1978] 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'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

as

(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







15

0)

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0 (-


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o C
-x-"

I ")









-4- I
.^^---------g O





I I







I 'TO
4. /^.


__1 (U



I _







S I
L.











s/v ,7
---4- -- --- 0


17 -0












Sdv1)0] 0o0
0 O0
SHV11O









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a

m










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> OO























rr

Q-Q
O


4-o
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(0




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o




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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-

istrative costs.

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 [1980] 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 [1974] 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

domestic redistribution.










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 [1974] 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























PF*


C)
(n
< PA*

o Ps
0


} $1.00


'DFs


QF*


QMD*


QW*

QS*


The Buxton-Hammond Model for the Price Support Program


QF, QW


III


Figure 6.










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 [1977] 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 [1967], Ippolito and Masson [1978], and

Dahlgran [1980] 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.


Fluid
Differentials
(Pf Pm)


All Milk
Differentials
(Pw Pm)


2.23

2.07

2.15

2.10

2.09

2.05

1 .85

2.14

2.28

2.45

2.24

2.26

2.17


.96

.86

.89

.89

.89

.89

.84

.96

1.02

1 .04

1.01

1.01

1.00


Source: USDA, Dairy Situation, ERS, DS-344, March 1973.


1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972










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,

1964].

Buxton et al. [1981] 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

next.

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






















4o










Do-
0

- C
0 c










0



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-4 I c











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Q
I (





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I 0 0


t-----4-----------------
\g U

---i--------------- ----0 (3 -c~
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-- o .
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0 0


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I I
- 0 L
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ci~










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 [1982] 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

[p. 14].

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

year.

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





















BASE
RESBASE


12 MC


to 11 -----------------4-+-
:5 S SRATC


Q / MR -BPCI

9-

T I I 1 1 I
0 1 2 3 4 5 6 7
Q* Q**


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 [1979] and Gardner [1981].

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

to producers.

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.

















)O





-Q






X~---------- 0 -








I I 0







E I


3 c
0o 0

u
O 0
4-



0




C 0.
IC-







1LL


u
^sO --







n0 0;
S~l~qqo(]










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.


Demand Models

Derived demand functions for fluid and manufacturing milk at the

farm level was estimated by Rojko [1957], Wilson and Thompson [1967],

George and King [1971], Prato [1973], Hallberg and Fallert 11976], and

Dahlgran [1980]. (See Table 2). Regrettably, these studies obtained

estimates that are somewhat inadequate for this study. The reasons are

as follows:

(a) All but Dahlgran's [1980] 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 [1967], Prato 11973] and Hallberg and Fallert

[1976] "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
(1976)
Hein (1977)
Kwoka (1977)
Prato (1973)
Rojko (1957)
Wilson & Thompson
(1967)


U.S.
U.S. Southern

U.S.
Chicago Regionalb
New York-New Jersey
Middle Atlantic
Upper Midwest
New England
Southern Michigan
Eastern Ohio, W. Penns.
Texas
Ohio Valley
North Carolina
Oklahoma Metrop.
Nashville
Quad Cities, Dubuque
Nevada


U.S.

U.S.
U.S.
U.S.
U.S.
U.S.

U.S.


aVia displacement from retail level.
Market orders.












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

where

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 [1980] 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

average elasticity.

However, Dahlgran [1980] 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.















1I














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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 [1953], Halvorson

[1955, 1958], Cochrane [1958], Wipf and Houck [1967], Chen, Courtney,

and Schmitz [1972], Hammond [1974], Novakovic and Thompson [1977], Houck

[1977], and Dahlgran [1980]. 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 [1958] 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 [1972] and Milligan

[1978]. 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

lagged years.

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.








40











Curve I: Polynomial Log
/ Formulation

U-

U-
0


3 Curve 2: "\
0 Geometrically ""'
-.J

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 [1982].

The question that remains is whether Levin's results were due to the

sample used (Mississippi data) or whether the pattern found is concep-

tually sound.

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

relationship.

Three alternative procedures exist that could be used in this

approach: (a) a cross-correlation technique suggested by Haugh [1972,

1976] and Pierce [1977], (b) a one-sided distributed lag approach implied

by Granger [1969] 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 [1979]. 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.


Summary


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.


Coordinating Issues

The coordinating issues are as follows:

(a) The studies by Kessel [1967] and Ippolito and Masson [1978]

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 [1980] did not consider the price

support program as a potential coordinating element in the exchange of

crude milk.











(c) The models by Buxton and Hammond [1974] and Hein [1977] 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.


Empirical Issues

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-

cult.











(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.


Conclusions


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.


Overview


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.














CHAPTER III
VERTICAL COORDINATION IN THE UNITED STATES DAIRY INDUSTRY


Introduction


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

industry.


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.


Graphical Framework

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








49












2
O

0


0)



/ ~4-1






=
") c









L- L_



0 L
7 --------- o



a
-oo
0)
0(








Ca

~------------- a
O




CO <0

-- a- -o
II -

0! 0^
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.


Mathematical Framework

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

processors.

(3.2) QMDt = DM(PMt), derived demand for manufacturing milk

by manufacturers.

(3.3) QAt = SA(PAt), supply of grade A milk by farmers.

(3.4) QBt = SB(PBt), supply of grade B milk by farmers.

Quantity conditions.

(3.5) Qllt E QAt QFt, all grade A milk is used in processing

fluid milk products or in the manufacturing of dairy

products.

(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

milk.

Price conditions.

(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

described above.


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

support program.


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),
C
which is

(3.12) PA = C'(qA), where G is profit.
c

However, PAc is actually computed with values that the individual

farmer does not control. PA is the result of
c
(3.13) PA = (PF' QF* + PM QII )/QA",
c c c c
where

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
c

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

maximize.

(3.14) PROFc = PF QFc + PM Qi l C(QA ),

subject to

(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.
C
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



































BPC


OF*


Figure 13. Blend Price Curve

































PA'


QA)*


Equilibrium Solution in the Grade A Milk Market


BPC


QA


I


Figure 14.


























PF


U)
rr-
_1I
J I
0

PM ----BPC

PM' BPC'





0 QF* QA


Figure 15. Rotation Movement of BPC Due to Changes in PM















SA








- "~ -BPC
g PA' -----------.^

.
BPPCA
SQA QA QBPC'


S I


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

"parity" concept.











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.


Self-Regulation

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

discussed next.








I C-
63


I -^
CD
o




1
4-
I I
C
,,-


L--
I IC



c 0
--C ----- O 4

uI
L---------- O c


0


I I -
I -o
D c 0c







O "--
I



O-1
S031
II < .

r O



I _____ 0.
uO .L





rr o
-I I "-
I I

II .


C

l-- ------- L -
II I O r,

I I
w_11--a- - I11--





CO-
Sdvnnoa












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

and EFG.

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

(Figure 18).








2 65




u c

00
0- E

O 0

._
0 0 0
--- O -0
-_ 0 )



o -o

U te
-C-------- o
I




IO


.4--
. io








0 I a:
01-I

I O
7L
I I z


SO o
I U)











-10
I- )-
I '-
I I l c
---- -+ --
/'y-- --------.0 : I=m

0




S I I 1 I ;




e_ e.. e..
s _-]-____o_
----- j^~
syvnnoG~











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).









i 67







L c1


I
I- u
I0 0


-e
F0 CL
/O o_ -
[---7 ------ a





I o
OZ)






-m u
,.

Q)
1




1 c0





R 4- -
I4




C Cu







Im C
L L







I i I I I





< < < 0 0)
ScL a- 0 aa a-
SV-I-Ol











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

examined next.

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







2 69



I u4

o .




L ^
I 0





I-
I c



CI 0 0
-I "-- -



II ;o





CY--
I ,-
__0 4 _
I I O a


i -
I IO 0
I 0






I L


1 I 1 "-0
a
SI eI I
IL L

-i l .



1 I ,

j i I


J^2

syv, noa











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.






































QIL IQ
QIS


Figure 21. Impact of Temporary or Permanent Decrease in Price
on the Quantities Produced


rC

-j Po
o _
o PI





0











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.


Summary


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








73

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.














CHAPTER IV
FORMULATION OF THE EMPIRICAL MODEL


Introduction


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.












Variable Identification


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.


Demand Functions

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

this approach.

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),

where

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

analysis.

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-

tion is












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(4.3) QMD = DM(PMRr; POM; WM; EM; Y; SI,... ,S4)

where

QMD is the quantity of commercial manufacturing milk purchased

by plants,

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

dairy products,

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.











Supply Functions

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).

where

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

quantities supplied.

As it was also observed in Chapter II, milk supply functions

should include lagged explanatory variables. Recently Levins [1982],

and Chavas and Johnson [1982] 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

model

th
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)

where

QB is the quantity of grade B milk produced and sold to plants,

by state,

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

specified as

(4.6) PB = DB(QB; Y; SI,...,S4; ZDBl,...,ZDB25)

where

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

unit.











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


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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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.











89


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VERTICAL COORDINATION ARRANGEMENTS: SOME ALTERNATIVES FOR THE UNITED STATES DAIRY SUBSECTOR BY VANDER GONTIJO DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY CF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1983

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ACKNOWLEDGEMENTS 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 encouragement 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 proposal of this project and for the appropriate answers to the many questions 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 comments. 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 i i

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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 faci 1 i ties. Maria Jose, the author's wife, is directly responsible for his achievements. His children, Daniela and Alisson, will someday understand 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. i i i

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii ABSTRACT VII CHAPTER I INTRODUCTION , Statement of the Problem 3 Statement of Objectives i, Summary and Overview /, II LITERATURE REVIEW 6 Introduction ^ Dairy Policy Models 5 Kessel Model -j Ippol i to-Masson Model \\ Dahlgran's Model 13 Price Support Models jq The Buxton-Hammond Model ig The Hein Approach 22 Models for Vertical Coordination 22 Vertical Coordination through Price Mechanisms .... 2k 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 ^3 Coordinating Issues ^3 Empirical Issues 4^ Conclusions 45 Overview 1^ 1 v

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Page II VERTICAL COORDINATION IN THE UNITED STATES DAIRY INDUSTRY j, 7 Introduction ^7 A Model for the Crude Milk Exchange 47 Graphical Framework ^3 Mathematical Framework cq Alternative Exchange Arrangements 53 Coordination between Cooperatives and Dairy Farmers Coordination between Cooperatives and First Users Alternative Coordinating Arrangements to Balance Supply and Demand of Manufacturing Milk £,} Self-Regulation £2 Alternative Government Controls 6£ Summary 72 IV FORMULATION OF THE EMPIRICAL MODEL yi, Introduction Variable Identification Demand Functions . Data 53 56 7A 75 75 Supply Functions 80 . . . . 84 Period of Analysis 33 Unit of Time q^ Cross-Sectional Units ac Model Specification o£ Derived Demand Functions g£ Supply Function for Grade A Milk 97 Supply and Demand Functions for Grade B Milk 98 Choice of the Estimators Econometric Estimations Results for the Fluid Milk Derived Demand Function Results for the Commercial Derived Demand for Manufacturing Milk 105 Results for the Supply of Fluid Eligible Milk .... 105 Results for the Supply and Demand Functions of Grade B Milk 110 99 101 101

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Page VI SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FUTURE RESEARCH 113 115 117 Equations for the United States Dairy Industry 113 Derived Demand Curve for Fluid Milk in the United States Derived Demand Curve for Commercial Manufacturing Milk in the United States 1 1 fa Supply Curve for Fluid Eligible Milk in the United States Supply Curve for Grade B Milk in the United States The Blend Price ]ig Summary I lg Overview jjo V ALTERNATIVE COORDINATING ARRANGEMENTS TO REDUCE MILK SURPLUSES IN THE UNITED STATES 120 Introduction 120 Model Adjustment 120 Results )22 Simulations ]2£ Solution for the Basis 126 Self-Regulation Alternatives 126 Alternative Government Controls 129 Summary and Conclusions 131 132 Summary 132 Conclusions I35 Suggestions for Future Research 135 APPENDICES A DERIVED DEMAND AND SUPPLY FUNCTION DERIVATIONS 1 kO B GLOSSARY ]^ C VARIANCE-COVARIANCE MATRICES FOR ESTIMATED COEFFICIENTS 151 REFERENCES 1 58 BIOGRAPHICAL SKETCH 168 VI

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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 By Vander Gontijo April 1933 Chairman: Richard L. Kilmer Major Department: Food and Resource Economics Milk production in the United States has surpassed commercial consumption. 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 policies. The objective of this study is to examine some alternative arrangements to reduce milk production in the United States. The assumption made is that the subsector could, as an alternative to additional government 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

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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 selfcoordinating measures. Within these lines it is suggested that government should anticipate its intention to reduce its milk purchases with clear figures. Dairy cooperat ives' importance as a means of coordination should be better understood and enhanced, and milk producers need to understand

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that additional government rules to enforce reductions on quantities supplied are not their best alternative.

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CHAPTER I INTRODUCTION 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 objectives 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 mechanisms and the unrestricted outlet offered by Commodity Credit Corporation (CCC) purchases have permitted the allocation, at the supported prices, of all crude milk produced [Cook and Hayenga, 1981, p. 19; Boynton and McBride, 1 980b , p. 2k]. Continuous purchases of cheese, butter, and nonfat dry milk by CCC, reflecting persistent overproduction of milk, indicate a vertical coordination 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 problem seems to be that information generated from transactions between sellers and buyers of crude milk do not reflect their ex-ante 1

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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 environment are as follows: (a) from May 1979 through December 1981 there has been increased milk production over the previous year [USDA, 1977198le]; (b) in I98O 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 billion 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 1 983 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 unacceptab1 e . . . , 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

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to reduce the accumulated surpluses. It includes reduction of imports, increase in exports, expansion of domestic consumption through promotion 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 differences 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 necessary. Statement of the Problem The problem to be examined in this study is the impact of alternative exchange arrangements on the supply and demand balance of milk between dairy farmers and manufacturers of dairy products.

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Statement of Objectives Alternative coordinating arrangements that can be used to balance the United States supply and demand for milk will be examined. Comparisons 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 econometr ical ly 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

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arrangements to reduce milk surpluses are ampirically examined with the estimates obtained in Chapter IV. Summary and conclusions follow in Chapter V I .

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CHAPTER I I LITERATURE REVIEW I ntroduct ion 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. Da i ry Pol icy Model s 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 classified pricing, pooling provisions, and the price supports would be, in principle, useful for this analysis. The Kessel model [1967], and its extensions by Ippolito and Masson [1978] and Dahlgran [1980], 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 [ 1 97^] , and the Hein model [1977J. Models that are related to the coordination approach are

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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 provided at the end of the chapter. Kessel Model 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, Ql" would be consumed. The schedule Dl 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 JL class II price Pll 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 JL for manufacturing milk. The blend price function is AR. Finally, PA , V? -k Ql I , and QA , in this regulated grade A milk market, are thus determined by the system (2.1) PA = (PI Ql + PI I Ql l)/(QI + Ql I). (2.2) QA = SA[PA]

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CO rr < o PI I s * Figure 1. Kessel Model of Regulated Grade A Milk Market

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(2.3) Ql = D I [PI]. (2.4) QA = Ql + Ql I . (2.5) PI = PI*. (2.6) PI I = PI |*. Kwoka [1977] used Kessel's model and previously estimated elasticities 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 PI I in the absence of classified pricing, since the blended price, PA = PI Pll (Figure 2). The world price P I I * would determine Ql ' , QA's, and Ql I ' = QA' Ql ' . In moving from this solution to the regulated solution, Kwoka estimated that "several hundred dollars are transferred from consumers to producers. Regulation also causes deadweight losses to the economy totaling $55 to $180 million annually" [p. 380]. 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 shortcomings 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 1 960 and 1970 data, which are now considered

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10 Oil* Figure 2. Kessel Model of an "Unregulated" Grade A Milk Market

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11 old statistics since they did not capture new trends and adjustments in the subsector. I ppol i to-Masson Model Ippolito and Masson [1978] 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 Ippol i to-Masson covers "only price regulations and does not treat the price support system" [p. 3^]. However, the model has some features not incorporated in Kessel's analysis, and so it will be reviewed as well. As in Kessel's model, Dl, 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 DM, 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 introduced 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, PI I is the price determined for the total demand [DM + JL Dl(PI )] and is also the price that will be received by grade B milk JL farmers for each unit of the quantity 0_B produced.

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m o 12 CD O CD O <

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w 13 The unregulated milk market equilibrium would be established hen total demand (Dl + DM) equals SA (Figure 3). At that point, PA' and 0_A' are determined. With PA' = PI', Q|' is obtained, and with PA' = PI I' = PB', Ql I • and QB' are, respectively, determined. The total social costs of moving from the unregulated equilibrium to the regulated equilibrium were estimated by the authors to be around $60 million (including $3** million due to government programs administration) [Ippolito and Masson, 1978, p. 60]. Ippolito and Masson [1978] presented two methodological contributions. The first was the modelling of the relationships between the regulated grade A milk market and the unregulated grade B milk production. 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: "DM is the demand for manufacturing milk out of grade A supplies while manufacturing demand can also be supplied out of grade B production" [1980, p. Gk] . 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 .

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14 Dahlgran's Model Dahlgran added significantly to the previous models by incorporating local interdependence between the grade A and grade B milk production, and by including a much needed manufacturing milk demand function, DM, as in Figure k. 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 Dl, SA, SB, and AR, are the same as defined in the Ippol ito-Masson model. The regulated equilibrium is described in Figure k. Ql is the quantity of grade A milk that, according to Dl, processors will be willing to buy at the minimum price Pi" fixed by the marketing order administration. At the price support PS", both QB", A it Ql I and QS are determined. This last variable represents the amount of CCC removals from the grade A market, which is given by QA" (Ql + DM [PS ]). QA is determined at the blend price PA", calculated as (2.7) PA" = (PI* Ql" + PS" Qll")/(Ql" + Qll"). 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

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o *

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16 Sdvuoa <0 L. 0) 3 i_ c 0) .c o o c o en

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17 price difference is equal to the cost of production difference (C)" [Dahlgran, 1930, pp. 81-82] . Moving from the unregulated equilibrium to the regulated milk market, as in Figure k, the total social cost to society was estimated at $131 million, including $3** million imputed to the programs administrative costs. Note that although the models previously reviewed have all been used to estimate the social costs of deregulation, a purpose that differs from the one pursued in this study, they contain the basic structure that could be helpful in constructing a model to simulate alternative 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 [1 980] is that the equilibrium price for manufacturing milk, in the absence of the price support program, would be determined in the grade A market only, that is, (2.8) PM* = PI |* = DM [QA*], where, PI I 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 = 0J + 0J I, is no longer obtained (AB
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18 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 DM, 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 procedure must be followed in order to separate regulationinduced 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 {Thor 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 0_S" (CCC removals from the grade A market) [Dahlgran, p. 78]. Such shifts were supposed to be captured by introducing Q.S as an explanatory variable in

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19 the demand equation for manufacturing milk. By making QS exogeneous the method used becomes inadequate for this study. Here it is necessary to have QS determined by the model. As a group, the three models reviewed do not consider the vertical 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 assumption will be made to incorporate dairy cooperatives in the exchange of crude milk between producers and processors/manufacturers. These bargaining 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 [197*0 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 domestic redistribution.

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20 According to their model the fluid demand curve DFs and the supply curve for all milk Ss (Figure 6) show the amount of milk demanded as fluid and the total milk supplied, respectively, at each manufacturing milk price with the assumption of a constant fluidmanufacturing 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 production will be QW (Figure 6). The quantity QF will be allocated to the fluid market, QMD to the manufacturing market, and QS = QW (Q_F + 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 = $2.17The 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 $3^0 to $65 million if all government purchases were distributed back to the commun i ty [p. 290] . The contribution of the Buxton and Hammond model [197^] is the treatment of an integrated (grade A and manufacturing) milk market, in which the price support level is the policy variable. The shortcomings of their model are as follows: (a) The model was not estimated

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21 — QF, QW Figure 6. The Buxton-Hammond Model for the Price Support Progra m

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22 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 1). (c) The supply function S contains both fluid eligible and grade B milk. The Hein Approach Hein [1977] 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 1 9^9-73 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 $^02 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 [1967], Ippolito and Masson [1978], and Dahlgran [I98O] 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

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23 Table 1. Selected Milk Price Differentials Prices $1 .00 cwt.

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2k 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, 1964]. Buxton et al. [1981] 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 next. 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 program. At any price support above PE the government acquisition of excess

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25 0) c c > 0) 1_ o Q. D. co i 0) o 1Q. CD C o -o 0) o 4J u u D cn

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26 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 QS I ) , and consumption increases to QDI. Government purchases are reduced from QGO to QG I , as in panel b of Figure 7. The USDA model . Recently, Salathe, Price, and Gadson [1982] presented 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 manufactured dairy products and the costs of government dairy product purchases 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 I983. 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 1 983 [p. 11]. Total milk production would be about 3-0 billion pounds lower in 1 985 [p. 14]. 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.

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27 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 production due to a price variation may take place in periods shorter than a year. 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 I BASE (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 1BASE 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 recognize the effect of surpluses on milk prices, disposal costs, and even

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28 I BASE BPCI Figure 8. Boynton-McBr ide Plan

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29 on the viability of the price support program [1980a, p. 3]. The important cooperative coordinating role would be to "pass on market information 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. *t] . 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 (AR1) (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

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30 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 [1979] and Gardner [1981]. 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 0Y (panel b of Figure 9). At the support price OP, consumers will purchase OQI , according to their demand schedule DD ' . The government will buy (0Y 00.1) units of the product. In contrast to the situation that would prevail without the quotas, the government would have to purchase additional output (0Q3 0Y) to guarantee the price OP to producers. Deficiency payments . In 1973, a plan earlier proposed by President 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 OOJ units of the product. The market will value each unit of the product by only 0P2. The government then issues subsidy checks to farmers to cover the difference between the price they received, 0P2, and the guaranteed target price OP. Compared to the situation that would prevail when the government buys (OQJ OOJ) and stocks the volume purchased, the government costs are reduced by (OP 0P2) (003 " 0Q.1 ) . The alternatives described above have never been the subject of investigation through a simulating model in the dairy industry.

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31 c 03 Q. C o o c o o o L. 0)

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32 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. Demand Models Derived demand functions for fluid and manufacturing milk at the farm level was estimated by Rojko [1957], Wilson and Thompson [1967], George and King [1971], Prato [1973], Hallberg and Fallert [1976], and Dahlgran [1980] . (See Table 2). Regrettably, these studies obtained estimates that are somewhat inadequate for this study. The reasons are as fol lows : (a) All but Dahlgran's [1980] 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 [1967], Prato [1973] and Hallberg and Fallert [1976J "have scant if any theoretical development" and "are econometrically weak," and that the identification of retail products in terms of the farm products are frequently very difficult [I98O, p. 51].

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33 Table 2. Estimated Demand Functions for Dairy Products George & King (1971)

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3h 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 following marketing orders: New York-New Jersey, Chicago Regional, New England, Middle Atlantic, Eastern Ohio-Western Pennsylvania, Upper Midwest, Southern Michigan, Ohio Valley, Texas, Nashville, North Carolina, Quad Ci ties-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 considered 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 correspond geographically to the continental United States.

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35 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, Southeast, 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. = aP b where 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 [1980] 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 average elast ici ty. However, Dahlgran [ 1 980J provided the only study estimating a consistent set of derived demand functions for processors and manufacturers. His demand elasticities estimates are reported in Table 3.

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Q. Q. D CO U1

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37 Note that five markets (Texas, North Carolina, Nashville, Quad Cities Dubuque, and Nevada) have unacceptable signs. Besides, the elasticities 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 [1953], Halvorson [1955, 1958], Cochrane [1958], Wipf and Houck [ 1 967] , Chen, Courtney, and Schmitz [1972], Hammond [197*0, Novakovic and Thompson [1977], Houck [1977], and Dahlgran [1980]. 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 condition 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.

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38 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 production of milk in response to price variations (the nature of the lagged structure); and (b) lack of theoretical reference indicating the appropriate 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 [1958] 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 [1972] and Mill igan [1978]. The argument is that output response to some given price change first increases through time, then decreases. In such a case, only a

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39 flexible lag structure like the polynomial lag formulation is appropriate. 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 justifications 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 lagged years. Very little has been said about what happens in between the shortand the long-run effects. At any period t, new milk cows are being introduced 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.

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ko in Curve I ' Polynomial Lag / Formulation UJ o u_ UJ o o Q UJ O < _i

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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 relatively 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 become negligible" [Levins, 1982, p. 286]. Although the explanations given are not very convincing ones — primarily in regard to the "intermediate term"--the model run for Mississippi generated a pattern quite similar to the one expected by Levins [ 1 982] . The question that remains is whether Levin's results were due to the sample used (Mississippi data) or whether the pattern found is conceptual ly sound. 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.

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42 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 relationship. Three alternative procedures exist that could be used in this approach: (a) a cross-correlation technique suggested by Haugh [1972, 1976] and Pierce [1977], (b) a one-sided distributed lag approach implied by Granger [1969] and formalized by Sargeant Jl 976] and (c) a two-sided distributed lag method advanced by Sims [1972]. The robustness of substantive economic results of all three alternatives was examined by Feige and Pearce [1979]. Studying the relationship between money and income they found that the "Sims procedure 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 fol lowed.

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h3 Since little help could be found in the literature, a search procedure 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. Summary 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 shortcomings. These shortcomings are discussed below. Coordinating Issues The coordinating issues are as follows: (a) The studies by Kessel [ 1 967] and Ippolito and Masson [1978] 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 [1980] did not consider the price support program as a potential coordinating element in the exchange of crude milk.

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kk (c) The models by Buxton and Hammond [197*»] and Hein [1977] 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 [Salathe, Price and Gadson, 1982J does recognize 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 [I980aj only specifies coordination at the production unit, and it did not consider the effects of the price support program. However, it did recognize the presence of cooperatives 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. Empirical Issues 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 mi sspeci f ication. Besides, the identification of retail products in terms of the farm products is frequently very difficult.

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k5 (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 mi sspeci f icat ions 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. Concl us ions 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 including 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 purpose, scope and equilibrium conditions. It was also concluded that a

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^6 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 biological 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 correspondent 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. Overview 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 regulated dairy subsector is an unchangeable reality are made in Chapter V.

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CHAPTER I I I VERTICAL COORDINATION IN THE UNITED STATES DAIRY INDUSTRY Introduction 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 instruments 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 cooperatives, 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 industry. 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/ hi

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i»8 manufacturers (first users). The model is first graphically demonstrated, then it is mathematically developed. Graphical Framework 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 1 1 PS is the equivalent manufacturing milk price supported above the market equilibrium price by government. At PS , QB" is produced 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, OJl". 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 Ql I + 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, Q.S", is given by the difference between QMS" and QMD".

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hS u Q TJ OJ cn a: a> o X) O a)

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50 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, Q. I I , QMD, QS , QB, QMS, PF, PM, and PB. Exogenous variables are Pit, PRt, PSt. Mathematical Framework The model described graphically in the last section can be formulated in terms of mathematics. It is composed of four behavioral equations 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 processors. (3-2) Q_MDt = DM(PMt), derived demand for manufacturing milk by manufacturers. (3-3) QAt = SA(PAt), supply of grade A milk by farmers. (3.M QBt SB(PBt), supply of grade B milk by farmers. Quantity conditions . (3-5) Qllt = QAt QFt, all grade A milk is used in processing fluid milk products or in the manufacturing of dairy products . (3.6) QSt + QMDt E QMSt, total demand for manufacturing milk equals its available supply.

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51 © QMD* ^e QS* Figure 12. Equilibrium Solution for the U.S. Regulated Dairy Industry

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52 (3-7) QMSt = QBt + Q.I 1 1 , the total quantity supplied of manufacturing milk is constituted by grade B and class II milk. Price conditions . (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 S 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 quantities demanded by commercial outlets, QMDt, and government removals from the commercial market, 0_St. 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

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53 the model refers to the national milk market and not to a specific region of the U.S. After the mathematical exposition of the model, and after describing 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 demand of manufacturing milk. The second is to empirically estimate the model, test for its validation, and simulate the alternative coordinating arrangements. The next section takes care of the first step as described above. 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 jointly coordinating roles of two elements present in the model described above. They are the dairy cooperatives' pooling system and the price support program. Coordination between Cooperatives and Dairy Farmers JL Consider that the farmers expect to receive PA c from their coopjJerative. Accordingly, they will be willing to produce QA c = n qA , JL 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

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5h order condition of (3.11) Max G PA* q A C(qA), which is (3-12) PA^ = C'(qA), where G is profit. However, PA^ is actually computed with values that the individual J. farmer does not control. PA" is the result of c -U J. (3.13) PA" = (PF QF"" + PM"" OJI )/QA , *• c c c where JQF c is the quantity of grade A milk sold to processors, PF is the unit price of QF, QM C is the quantity of grade A milk sold to manufacturers, and PM is the unit price of Ql I . These optimal values result from the cooperative marketing activities of assembling the grade A production from n farms and selling in the fluid and in the manufacturing milk market in such quantities that maximize. (3-14) PROF = PF QF^. + PM* (ill C(QA ), L. c c c subject to (3-15) OF :• kOA , < k < 1. It is assumed that any administrative costs incurred by the cooperatives are independent of the quantities traded. No profits are retained 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

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55 perception that it could have enough power to allocate at least a fraction, 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 QA c> and that class I demand is prioritarily met. This problem corresponds to (3.16) Max L(QA c , QF A) = PF* OF + PM*(QA QF ) C(QA ) + A (kOA c QF c ). The first order conditions are (3-17) 9L/3QA = PM* C'(QA ) + Xk = 0, (3.18) 9L/3QF c = PF* PM* X = 0, (3-19) 9L/8X = kQA QF =0. c c Substituting X 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* Q| l*)/QA* c c c which is exactly the right hand side of formula (3.13) used to calculate JL 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.

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56 Now, take 3.21 (which is the blend price curve) and vary Q_A*. The blend price curve, BPC, for given values of PF", 0_f\ 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 \k.) 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 1 . (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

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57 rr < o QA Figure 13. Blend Price Curve

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58 if) a: < o Figure \k. Equilibrium Solution in the Grade A Milk Market

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59 DC < _J _l O o Figure 15Rotation Movement of BPC Due to Changes in PM

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60 QA' QA* Figure 16. Effects of a Decrease in the Manufacturing Milk Pr ice

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61 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 possibilities 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 controlling 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 "parity" concept.

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62 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 manufacturing 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 1 1 . Sel f-Regulat ion Suppose government announces that it would not buy quantities of dairy products in excess of QS" equ i val ent 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 proceedings from pooling (price mechanism). These two alternatives will be discussed next.

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63 CO O 0) c u 3 C 4) C c o o 3 -o o Ia. 3 o 0) c 0) a. 1_ c Q) a: >^ _o 3 Q. 1_ 3 1/5 cn c o 3
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6^ Restricting the quantities produced of grade A milk . Suppose that dairy cooperatives are pressed by the government to reduce the manufacturing milk surplus. The choice could be to impose a quota on each member's production. The grade A milk farmers, organized in cooperatives, must examine the alternatives in order to accomplish the government 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 demand for manufacturing milk, and make only QS available to the government (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, Ql I , PF, QF, PS", QB, QMS, QS, QMTJ) . After allocating QF to the fluid milk, qTT is sold to the manufacturing milk market. When QlT is added to QB, which has been produced at the price support PS, QMS is generated. QMS" is the supply of available manufacturing milk after the quota. The blend price the cooperatives 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 and EFG. 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 QS I , at PSO (Figure 18).

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65

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66 Suppose that cooperatives, being aware of all the schedules in the milk market, project that the government restriction QS I (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 produced, QAI. Revenue losses to producers will be in the order of (QAI PAI QAO PAO). Part of this loss in revenue, (PA c 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 differentiation support prices; (b) deficiency payments; (c) taxing output; and (d) selective price supports. Product differentiation su pport 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 c PAl)QAI. Of course the operat iona 1 izat ion of this alternative would require adjustments in the current administrative mechanisms to allow government to control the price support levels according to the product origin (grade B or fluid eligible milk).

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o

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68 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 alternative would have been (PS~ PMS QMS). Taxing output. Instead of either self-regulation or differentiating 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 QA I (Figure 18). The exact amount of taxes per cwt. is given by (PAO PA I ) in Figure 18. Of course producers may decide to market QAO and be assessed by (PAO PAI) QAO, or to reduce production to QA I and lose (PAO QAO) (PA I QAI) in revenues. Selectiv e 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 reduced. The shortand long-run effects on the dairy farm sector will be examined next. 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 QS I = (QMS I QMD I ) . Total production 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

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69 o

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70 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 shortand long-run supply functions, as defended by Becker [1971, pp. 79-83] are needed here. Figure 21 depicts the shortand long-run supply curves SS and SL, respectively, for grade A milk. Assume that the equilibrium prices and quantities, P0 and Q0 , have been observed for an indefinitely 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, 1 982] 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 shortrun 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 decreasing 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.

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71 QIL J_ Qo QIS Figure 21. Impact of Temporary or Permanent Decrease in Price on the Quantities Produced

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72 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 income 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 shortrun 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 . Summary 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

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73 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.

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CHAPTER IV FORMULATION OF THE EMPIRICAL MODEL Introduct ion In the last chapter, derived demand curves for fluid and manufacturing 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 estimates 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. *75] . 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 estimation 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 chapter 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. 7h

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75 Variable Identification The explanatory variables are, in general, identified from theoretical derivations performed in Appendix A. Explanatory variables not explicitly identified in the derivations are adequately discussed in the next sections. Demand Functions 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 this approach. Market order derived demand function for fluid milk . The processor buys grade A milk and other inputs to produce fluid milk products, a class 1 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. {k. 1) qf = df (pf , po, w, e) , where 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,

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76 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 r ; PO; W; E; Y; S 1§ ...,S ). ' 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 determined, 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 (k.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 premium 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 freedom in two ways. First, by reducing the number of variables that otherwise would be included to isolate the effects of the market size.

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77 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 PFR 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 analysi s . Finally, S , s = (1,...,A) 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 maximization 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 manufacturer demand functions. Some adjustments are introduced to fit the equation into the selected estimation technique. Its final specification is

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78

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79 (k.3) QMD = DM(PMR r ; POM; WM; EM; Y; S,,...^), where QMD is the quantity of commercial manufacturing milk purchased by plants, PM is the unit price of QMD, R r are regional dummies, r = (1 ,2,4, . . . ,9) , POM is an index of prices received from the sales of manufactured da i ry products , WM, EM are prices of nonmilk inputs, labor and energy, respectively, Y is total personal income by marketing order, S 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 manufacturing milk market size (population), and its specifics (per-capita income), on the quantities demanded. PMR r is an interaction between PM , the unit price of QMD in each cross-sectional unit, and R , a dummy variable which assumes the value one if the Federal Order market is included in region r = ( 1 ,2 ,h , . . . ,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.

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80 Supply Functions 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 crosssectional units can be written as (k.k) QA = SA(PA R ; PA .,..., PA ,PA PA t r* t-1 ' ' t-V t-13''--' PA t-l6 ; PB t _,; C; PDF; PMC; S,....^). where QA is the quantity of grade A milk produced and sold to plants by dairy farmers, by state, PA is the unit price of Q.A, R r is a dummy variable which assumes the value one if the crosssection is included in reaion r r = ( l q\ c u region r, r U,...,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

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81 S.,...,S. 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 quant i t ies suppl ied . As it was also observed in Chapter II, milk supply functions should include lagged explanatory variables. Recently Levins [ 1 982] and Chavas and Johnson [1982] 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 beginning 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

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82 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. HI], 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 parameters would certainly be observed. One usual procedure to take care of seasonality is the dummy variables technique. In the present supply model S g = 1 , if data refers to the s th quarter, S g = 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 relationship for all cross-sectional units can be written as (4.5) QB = SB(PB; PA t _ r PA^; PDF, FW; PC; E; S $ ; ZSBj . where QB is the quantity of grade B milk produced and sold to plants, by state, 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,

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83 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, u 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 conversions are not instantaneous because it requires additional investment and the approval of the sanitary authority. Note that all right-hand-side variables of equation h.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 specified as (1».6) PB = DB(QB; Y; S,,...^; ZDB, , . . . .ZDB^) where 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.,...,S, are quarterly seasonal variables, and ZDB , ...,ZDB ,. are intercept shifters for each cross-sectional uni t .

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8k 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 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 Statistics, USDL; and the Bureau of Economic Analysis, USDC. Books, other general publications, special tabulations, tapes, and computer printouts 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 k 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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85 c a Q XI C (0 c o 0) E TO XI TO ro xi ro

PAGE 95

86 c o a 03 3 C o -aa) x X 0) TO E — ro TO 0) c O i o 1_ 03 N T3 03 xi 3 c 1_ 03 -C 4-1 0) X 2 ro . U • X) -3c * — cm c o E Cn E OJ 3 L. XI C < — o o X) a) o 3 Xi o in XI o o en TO XI in 1_ (13 l_ 3 4-1 1_ o ^X X XJ 4-1 03 13 > -* — L. aj ro u z: OJ 11_ 0) 03 X) O L. — O L. a. — TO '— u O aj x> X 03 OJ LiX) c >— XI o Qu 3 o OJ Q. 3 o o flj Q. i —

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87 c o 0) o XI 0) 3 c o -3" 0) X TO 0) X 0) TO E — to iz TO

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88 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 information 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 structure and the frequency per unit of time that price supports are announced. A period in which both variables were kept constant would be better isolated 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.

PAGE 98

89

PAGE 99

90 o to

PAGE 100

91 o L. 3 o OO c o 0) o -o CD 3 C o LTV CO -O TO .-

PAGE 101

92 0) o L. 3 o CO -D C o 0) Q a 0) 3 C C o o LA 03 -Q 03 a) > o -Q 03 (13 > o -Q 03 03 > O X 03 0) > o -Q 03 0) > o 03 0) > O -Q 03 0) > o x 03 > o 03 X>XIX>X>X>X3XIX1 03030)0)0)0)0)0) cccccccc 03 0) •m E 03 03 03 X 03 03 E — 03 1-z. 03 03 in < 03 X> co < 03 X) CO < 0) CO < 03 •a in < 0) X> < 03 a 01 < 0) XI in < 0£ — 3C CL 2 2 — .Q s a. — , o. — lli o a. x an: < o o> U < LJ O. O

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93 o l_ 3 o to

PAGE 103

3h With respect to the stability of the Federal Marketing Order system, it was observed that the number of orders have been changing frequently. The only period of time that it remained relatively unchanged was 1977-1980. However, the period can be extended to l 9 8l because the sole order added to the system can be easily isolated. Two changes in the price support program that are likely to shift the sensitivity of the industry participants occurred in the decade of the 1970's. Starting in 1973, the supporting price level for manufacturing milk became semi-annually adjusted. The second change is that in September 3 0, 1977, the milk marketing year was changed to October 1September 30, instead of April , -March 3 1. The above reasons led to the choice of 1 977 to 1981 . Unit of Time The quarter (one-fourth of a year) was the choice for the unit of time. Two reasons weighed heavily upon this selection. One is the biological and regulated characteristics of the dairy industry. The lag between price changes and production response is certainly larger than a week, or even a month. Milk production is a continuous productive process that cannot be interrupted or altered in a very short period of time. On the other hand, important variations in production (through cow feeding controls), due to short-run movements of prices, would not be captured if annua, data were used. Moreover, quarters are preferred over annual or semestral data due to the necessity of obtaining

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95 sufficient degrees of freedom in the estimation of the models. Recall that the period of analysis covers only five years. The second reason is due to the fact that the frequency of Milk Production issued by the Crop Reporting Board, USDA, as well as some other government statistical reports of interest to the dairy industry, shifter from monthly to quarterly publications in the second quarter of 1982. This gives an advantage for the use of quarterly information if the model were eventually considered for updatings. Cross-Sectional Units The main reason for considering pooling techniques in the estimation of the empirical models was its ability to combine available information from cross section with available time series data in a stat i st ical model . Marketing Order areas fit into the desired patterns for crosssectional units on the demand side. They are delineated to cover important consumer areas and are geographically defined. State marketing orders will not be considered as a cross-sectional unit in the estimation of the demand functions. The reason is that, in general, they also establish a ceiling price for dairy products in addition to the minimum price normally set as in the Federal Order system. The state is considered a natural selection to be the crosssectional unit in the estimations of both supply functions. Statistics are adequately available at this level.

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96 There are kS cross-sectional units in the estimation of the derived demand functions for fluid milk and *1 for manufacturing milk. The Neosho Valley Federal Order statistics were not of acceptable quality. The states of Delaware, Montana, New Hampshire, New Mexico, Nevada, Rhode Island, South Carolina, West Virginia and Wyoming were not included in the supply estimations because statistics with respect to the price of fluid milk were not published. Twenty-five states were grade B milk producers. All entered the estimations. Model Specification Derived Demand Functio ns Difficulties exist, in applied work, in determining the correct functional form of theoretical relationships. The criteria adopted are to select the specification which yields the expected sign for the price coefficients and reasonable levels of significance for the "t" statistics. The derived demands for fluid eligible milk and manufacturing milk in the log-log, or double log, functional form can be written as (*.7) log QF jt log a Q ^ a^log PFjt + a ]Q log P0 jt ~ „ log Wjt a ]2 log E Jt + a ]3 log Y . t i a U S l ± a l 5 S 2± a , 6 S 3 + U j F t

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97 2 9 (k.8) log QMD = log b £ b R log PM . E b R log PM . J ° r=l r r Jt r =k r r Jt + b ]0 log P0M jt b n log WM f b ]2 log EM + b 13 l0g Y jt ^ b l^ S l ± b i5 S 2± b ,6 S 3 + U jf where all variables are defined in Table I. Note that t = (1,2,..., 20) refers to a given quarter, starting with the first quarter of 1977; j = (1,...,A5) refers to a cross-sectional unit (in this case, Federal Order Milk market); s = (1,2,3) refers to the first, second, and third quarters of each year (S^ is not included); r = (l,...,9) refers to the nine U.S. census regions (modified). F M The random errors U and U are assumed to have zero mean and constant variance. All coefficients are assumed to be constant over time, but the price-slope of both functions may differ for each region. Total personal income, Y, was included to shift the intercept across cross-sectional units and across time. Supply Function for Grade A Milk The same criteria adopted in the demand functions with respect to the choice of the functional form of the variables are followed here. Primarily the best adjustment will be chosen when the estimated coefficients of the price variables have the expected sign followed by reasonable levels of significance for the "t" statistics. The supply function for grade A milk specified in the linear form of the variables is

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98 C l^ PA t-13 + ••• +C 17 PA t-l6c ,8 PB t -l + C 19 PMC itC 20 PDF it +C 21 C it± c 22 S , ±c 23 S 2± C 2k S 3 + U it where all the variables are defined in Table 1. Here, i = (l,..., 39 ), refers to a state producing and selling fluid eligible milkt = (1 20) refers to a quarter within the period 1977-1981; S^ is not included to keep the full rank of the matrix formed with observations for the explanatory variables. The random error U^ is assumed to have zero mean and constant variance. Supply and Demand Functions for Grade B Mi lk The supply and demand functions for grade B milk at the farm level, if specified in the linear form of the variables, can be written as equations 4.10 and k.}] below (4.10) ^ ;t = d + d ] P B;t -d 2 PA it . 1 -d 3 PA it . 2 -d 4 PDr it d 5 FW it + d 6 PC itd 7 E it± d 8 S , ±V2± d io S 3± 5 i=ll Z d ZSB + U SB <*•") PB it = e 0e ,Q B it + e 2 Y it± = e s S s , 3 i°eZDB +U DB . s=3 u=6 u lt All variables definitions can be found in Table 1. Here, i = (1.....25) refers to the grade B milk producing state; t = (1 20) refers to each quarter within the period 1977-1981; s = (1,2,3) refers

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99 to the first, second, and third quarters of each year. Again, S. is not included in the model to avoid the "dummy trap." The sub "u" identified the cross-sectional unit that is shifting the intercept. The random error for the i state and t period is U. for the DB supply function and U. for the demand function. it Choice of the Estimators As all coefficients in equations *».7 through k. 11 are assumed to be fixed parameters, the appropriate estimation technique is the "covariance model" [Judge, 1982, p. *»77] . The parameters of the equations k ."] , k.S and k.S do not change across time, but only across groups of individuals. For such cases, it is convenient to write each individual ordinary least squares equation as (A. 12) Y = ZY + WB + e where Y 1 = (Yj, Y'...,Y') is a (lxNT) vector of observations on the dependent variable, Z = is an (NTxR) block diagonal matrix of observations on the explanatory variables. Each block X containing r TK observations and 1 explanatory r

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100 variable. T is the time series length and K r is the number of crossr sectional units included in each region r, and Z K = N J-l j W = [ x r+] >•••,*] is a (NTxG) matrix of observations on the remaining G = m r explanatory variables. 4" = (•',...,•') j s a (lxR) vector of unknown fixed parameters to be estimated 6 ' = (R ' P>) ' P VP r+l*''-'*V is another (lxG) vector of unknown fixed parameters to be estimated. The disturbance vector is the (lxNT) vector e. The least square estimator is used in their estimation. Again, note that all explanatory variables in the right-hand-side of equations 4. 7, 4.8, and 4. 9 are either exogenous or pre-determi ned variables. With respect to the exogeneity of PA in equation 4.9 it can be argued that empirically it seems that every dairy farmer knows, if not exactly, the approximate marketing price for grade A milk. This situation is due to the regulatory devices prevailing in the dairy market. The government directly fixes a minimum price for class 1,11, and III, that plants must pay for grade A milk. This situation is diametrically contrasted with the grade B milk market. There the government fixes no minimum price for crude milk. The price paid by plants is determined by bargaining between plants and producers. The joint dependence between QB and PB therefore arises, and the relationships depicted by equations 4.10 and 4.11 require a simultaneous syst approach. Three stage least squares was chosen as estimator in such cases. em

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101 Econometric Estimations Empirical estimations were performed with the sampled data described earlier using the models discussed in the preceding section. Concerns about serial correlation were raised. Maddala [1977, p. 332] suggests that "in all problems of pooling, it is important to estimate each equation (for each cross-sectional unit) individually by OLS and check whether there is ... a systematic pattern in the residuals." Accordingly, demand and supply equations were estimated for several cross-sectional units, randomly selected from each region. The firstorder autoregressive disturbance coefficients and the Durbin-Watson statistics obtained from these estimations were used to test the null hypothesis of autocorrelation in the residuals. In all but a few cases the Durbin-Watson test was inconclusive and the Rho was not statistically different from zero. In addition it was postulated that the inclusion of size variables in the models, which is supposed to appropriately shift the intercept coefficients, could reduce the mutual correlation across cross-sectional units, if it exists, and by so, lessening the var iance-covariance of the regressors 1 coefficients. Results for the Fluid Milk Derived Demand Function The parameter estimates, their respective standard errors, and the area in both tails of the "t" distribution, are given in Table 6. All estimates have the expected sign and are statistically different from zero.

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Table 6. Derived Demand for Fluid Milk 102

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103 The derived demand price elasticity for the entire sample, £ ALL , is calculated by weighing the elasticities estimated for each region, which can be calculated with Table 6 estimates, by the relative quantities of milk sold by each region. Consider equation *4 . 1 3 • 9 (A. 13) Q = £ QF r=l r where OF is total fluid milk sold to plants and dealers in region r, r = (1,...,9); deriving both terms with respect to PF, and post-multiplying them by PF/Q, it follows that K ' ^F 3PF Q , 3PF Q \ 8PF Q QF r=l r=l r 9 3^. p^QF^ 9 QF^ r t, 3PF QF r Q " ^ ^ Q which is the elasticity for all the regions considered. The regional elasticities, £ F > are directly derived from Table 1, and the participation of each region in total milk sold to plants, by category, can be found in Table 7The calculated elasticity for fluid milk derived demand is -1.195As expected, this value seems higher than the ones obtained in general from time-series estimations. Coherence for this value can be found by comparing it with the elasticity for manufacturing milk demand. It has been found, in empirical estimations, that the demand functions for

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04 Table 7. Regional Participation in the Total Sales of Fluid and Manufacturing Milk Region Federal Milk Orders Q F r /QF QMD /QM Middle Atlantic New England New York-New Jersey .2561 177 Louis. -Lex. -Evans. Memphi s Nashvi 1 le Paducah Tennessee Valley .0551 _ 03u Georgia Southeastern Florida Tampa Bay Upper Florida .0768 Central Arkansas Greater Louisiana Lubbock-Plainview Oklahoma Metrop. Red River Va I 1 ey Texas Panhandle Texas .1242 .065 Central Illinois Eastern Ohio-W. Pa. I ndiana Ohio Valley Southern I 1 I inoi s Southern Michigan .I960 m Chicago Regional Michigan Upper Peninsula Upper Midwest . M 28 i, 1 Black Hi Ms Eastern South Dakota Greater Kansas City Iowa Nebr. -Western Iowa St. Louis-Ozarks Wichita .0826 .103 Central Arizona Eastern Colorado Great Basin Lake Mead Rio Grande Val ley Western Colorado .0536 n/)8 Inland Empire Oregon-Washington Puget Sound ok2 8 .045

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105 manufactured dairy products are, in general, more elastic than the demand for fluid milk. Results for the Commercial Derived Demand for Manufactu ring Milk A summary of statistics related to the estimation of the manufacturing milk derived demand function can be found in Table 8. The sample generated estimates have the expected signs. The own-price elasticity for all regions entered the sample is -h.kj,!, which confirms earlier studies suggesting that the demand for manufacturing milk is more elastic than the demand for fluid. The same procedure used to compute the price-elasticity for the derived demand of fluid milk is followed. The value of ^t A 3 3 is found by the formula ALL 9 r QMD r M r = 1,2.4 M QMD where £ are the respective regional elasticities, as in Table 8, and QMD /QMD is the share of each regional in the total manufacturing milk marketed (See Table 7). Results for the Supply of Fluid Eligible Milk Direct estimations of the supply model for fluid eligible milk generated the coefficients shown in Table 9. All estimates, but one, have the expected sign. The short-run elasticity for the sample is .2k, which compares with previous studies. The sample elasticity is calculated by weighing the regional elasticities with the share of each region in the total milk marketed. Consider the equation

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106 Table 8. Derived Demand for Commercial Manufacturing Milk

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107 Table 9. Results for the Supply Function of Fluid Eligib e Milk Variabl e

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108 9 (A. 16) QA = Z QA p , r = (1,..., 9 ) r=l ows The elasticity for all regions can be calculated as foil Ik 17) f ALL 3QA PA I 3QA r PA PA 9 ^ A r 'A 3PA QA r :, 3PA" QA QA ^ 9pa~ where PA is the quarterly average price of QA; QA is the quarterly average quantity of fluid milk produced 9 during the period, QA = £ QA , and r=l r r ~ (1,..., 9) designates a region. 3QA p The slope, ^, for region r, is given by taking the derivative of the aggregate quantity of region r with respect to the price PA. The equation for each region is given by m Ct.18) S QA. = QA = mCO + mC,PA + ... + v m A i=l ,Z r «t * u it where m is the number of states i in region r, and C Q , C lf ...,C 24 , are estimates for c Q , c,,...,^. (See equation 4.9). 9QA r SmCe ' 3PAJT = mC r' for re 9' on r Usin 9 data from the sample and the estimated coefficients from Table 9, the elasticity for all regions can be calculated

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109 ALL 5 45 C A = 24731 [8 x 23J3 + k x 1] k 1 + 3 X 17.18 + 5 X 17.86 + 4 X 29.28 + 3 X 22.89 + 5 X 29.52 + 3 X 34.08 + 4 x 60.99] = 0.24 Notice that responses of production throughout time seems to confirm the hypothesis that: (a) short-run adjustments are important in milk production; (b) the effects of a price increase tend to deteriorate after a certain span in time; and (c) in the long-run, the effects of price increase are still present, perhaps due to motivated increase in the number of calves. The elasticity of grade A milk supply with respect to a price change in year t-i are Year Elasticity t .240 t-i .010 t-2 .130 t-3 .118 t-4 .002 t-13 .013 t-14 -.004 t-15 .018 t-16 .063 The elasticity for the entire period is .59This elasticity is within the range of results obtained by Halvorson (1958) and Wilson-Thompson (1967).

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110 Results for the Supp ly and Demand Functions of Grade B Milk The results of the three stage least squares estimation for the supply and demand functions of grade B milk at the farm level are shown in Tables 10 and 11. | n the estimated demand equation, all variables have the expected sign. In the supply side, the coefficient of WF, (farm wage rate) has the wrong sign. However, statistically, it is not different from zero if 9 percent of confidence is desired. (Kwoka, [1977, P373] had a similar problem.) Family labor seems to be largely involved in the grade B milk activity. Tradition, or even religious concerns, could isolate production decisions from wage rate variations. The price elasticity for the supply function of grade B milk is 1.23, which can be computed by a process similar to the one used in the grade A milk supply case, or "•' 9) E B -WT t Q57= Hd,=fe25x52.316 ^ . , , 23 where M is the number of states; dj is the estimated coefficient for PB i t ' PB t and QB t are quarterly average price and quantities for all states in the sample. This value seems reasonable in view of the estimation techniqu used which tends, itself, to capture some long-run reactions. Note, meanwhile, that besides difficulties usually found in the estimation of the grade B supply function the sample used revealed that grade B que

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Ill Table 10. Demand Function for Grade B Milk

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112 Table 11. Supply Function for Grade B Milk

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113 production has been shrinking, ceteris paribus, due to increases in grade A milk lagged prices. Equations for the United States Dairy Industry Equations 4.7, 4.8, 4.9 and 4.10, estimated with data generated by pooling cross-section over time-series, are now converted to represent the behavior of the entire United States dairy industry. Derived Demand Curve for Fluid Milk in the United States The equation for the derived demand curve for fluid milk in the United States was assumed to be (4.20) QF US = A. PF AI EXP ( Z A n S ), s=2 ' S where US Q_F is total fluid milk demanded by processors in the United States, by quarter; A Q is a constant term for the equation; PF is the price of fluid milk, by quarter; Al is the price elasticity of -1.195 as derived previously. The value, A, is determined in order that equation 4.20 is satisfied for the fourth quarter of 1980. Recall that the intercept coefficient for the equations 4.7 through 4.11 are the intercept coefficients (constant terms) for the fourth quarter. Seasonal shifters S. , S„ , and S_, for the first, second, and third quarter, respectively, are explicitly introduced. Therefore, (4.21) A Q == OjypT 1 ) = 13097/(5.77)''' 195 = IO636O, and

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114 Vl =A e '° 4 ° = "0,700; A o, 2 = A o e "*° 50= '0'.'72; A )3 =A o e "-° 50 =10M72; where .04, -.05, and -.05 are the estimated coefficients for S . S , and S 3 , respectively, as in equation 4. 7 . The derived demand curve for fluid milk in the U.S. can, therefore, by represented by (4.22) QF US = ,06360 PF"'-^ exp ( . Qi| S] . Qt . ^ _ ^ Deri ved Demand Curve for Commercial Ma nufacturing Milk in the United States ~~ The derived demand curve for commercial manufacturing milk in the United States is assumed to have the following specifications (4.23) QMD^ S = B0 PM®' EXP ( E B S ) C «9 °> s s s=2 where .US QMD t is total commercial manufacturing milk demanded by manufacturers in the United States, in period t; PM t is the price of manufacturing milk in the United States, in period t; Bl is the elasticity of -4.438, as estimated earlier; B0 is a constant term for the equation. Its value is determined in order that equation 4.2 3 is satisfied for the fourth quarter of 1980. S s are seasonal intercept shifters, and B are the coefficients for S . 5 s

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115 S ince, (k.2k) BO = QMD t /(PM^) = 15192/( i +-82)" Z+ 1 * 33 = 16,201,770. The constant terms B0,1, BO, 2, and BO, 3, for the first, second, and third quarters, respectively, are BO, 1 = BO e'° 32 16728611 , BO, 2 BO e -097 = 17852089, 1 0? BO, 3 = BO e" ,U * = 179^573, where .032, .097, and .102 are the estimated coefficients for S. , S„ , and S_, respectively, as in equation 4.8. The equation for the derived demand curve of commercial manufacturing milk in the United States can therefore be written as (4.25) QMD^ S = 16201770 PM ^ 33 EXP (.032S, + .097S 2 + .102S-). Supply Curve for Fluid Eligible Milk in the United States The supply curve for fluid eligible milk in the United States is assumed to have the following equation (4.26) QA^ S = CIPA, + E C n S t t s=2 0,s s where QA is the quantity of fluid eligible milk supplied in the United States, by quarter; PA is the price received by farmers for fluid eligible milk sold in the United States, by quarter;

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116 CI is the value for the U.S. price coefficient. It is calculated by multiplying the number of states entering each region, by its respective estimated price coefficient, that is 3QA^ S 9 3QA r {h 27) WK~ = Z WT = [11 X 23J 3 + * X 21.47 + 4 X 17.18 t r=l t + 5 X 17.86 + 5 X 29.28 + 3 X 22.89 + 5 X 29.52 + 7 x 34.08 + 4 X 60.99] = 1684. C Q is the intercept for the above equation. Its value is determined so that the fluid eligible milk supply curve for U.S. is solved for the fourth quarter of I98O. Since, (4.28) CO, 4 = QA^ S ciPA t = 25276 1684 X 5-39 = 16200. The above intercept is shifted by the seasonal variable S , as included in equation 4.9. The intercepts C0,1, CO, 2, and CO, 3, for the first, second, and third quarters, respectively, are C0,1 = CO, 4 + n CIO = 16200 + 48 X 26.37 = 17466; CO, 2 = CO, 4 + n Cll = 16200 + 48 X 80.30 = 20055; CO, 3 = CO, 4 + n C12 = 16200 + 48 X 33.79 = 17822 where 26.37, 80.30, and 33-79 are the estimated coefficients for S , S 2 , and S 3 , respectively, as in equation 4.9. The equation for the United States supply curve of fluid eligible milk can thus be written as (4.29) QA^ S = 1684 PA t + 17^66 S, + 20055 S 2 + 17822 S 3 + 16200 S^.

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117 Supply Curve for Grade B Milk in the United States Assume that the equation for the grade B milk supply curve in the Uni ted States i s US 5 (4.30) QB^ DIPB^ + I D n S t t _ 0,s s s=2 where US QB is grade B milk sold to plants and dealers in the United States, by quarters; PB is manufacturing grade milk price, United States, by quarters; Dl is the estimated value of 1413, as derived previously; D-. is the intercept for the above equation, where value is derived by solving that equation for the average quantity and price values for the fourth quarter of 1980. The solution is (4.31) DO = QB Dl PB = 48.5 25 + 52.32 X 4.92 = -1620. The intercepts for the first, second, and third quarters, D0,1, DO, 2, and DO, 3, respectively, are DO, 1 = DO + n dg = -1620 + 25 X 38.87 = -649; DO, 2 = DO + n d = -1620 + 25 X 62.41 = -60; DO, 3 = DO + n d = -1620 + 25 X 30.22 = -865; where 38.87, 62.41, and 30.22, are the estimated coefficients for S. , S„ , and S.., respectively, as in equation 4.10. The equation for the supply curve of grade B milk for the United States can therefore be written as (4.32) QB^ S = 1308 PB t 649 S, 60 S 2 865 S 3 1620 S^.

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118 The Blend Price Curve A simplified way of writing the blend price formula is (*»-33) PA t = f ' t + f, /QA t , where f = Prl , and o,t t ' ,t = (PF t " P V * F t Setting this equation for the values of f and f when t is the o , t l , t fourth quarter of 1980, results (if. 3k) PA = 4.82 + 12^2/QA, because f . = k.BZ, and o,t f l,t = (4 77 " 4 82) 13 ° 97 = ]2kk2 Summary All the equations necessary to describe the interface between dairy plants and milk producers are estimated. Adjustments were made to conform the estimated price slope coefficient to the national level. The technique used in the estimations, "pooling" cross-sections over time-series, seems to have compensating results. In general, the estimated equations show adequate explanatory power and the level of significance of most of the coefficients is high. The elasticities may seem larger than normal standards. However, it should be recalled that the "pooling" technique may implicitly be capturing some long-run adjustments. "Given that cross-section data tend to show the long-run, static equilibrium behavior and that time-series data tend to show short-run, it is not at all clear what pooled cross-section and time series data will represent" [Cassidy, I98I, p. 83].

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19 Overview The estimated equations for (a) derived demand function for fluid milk; (b) derived demand function for commercial manufacturing milk; (c) supply function for grade B milk; and (d) supply function for fluid eligible milk, described in this chapter were used to derive respective equations for the United States, which, in turn, will be used to solve, under certain conditions, the model formulated in Chapter III. Chapter V details the phases of such solutions, the adjustment of the estimated equations for the period, 1979"8l, and its application to the research's primary problem which is the simulation of alternative coordinating arrangements to reduce surpluses of milk in the United States.

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CHAPTER V ALTERNATIVE COORDINATING ARRANGEMENTS TO REDUCE MILK SURPLUSES IN THE UNITED STATES Introduct ion The subject of this chapter is centered on simulation of alternative coordinating arrangements to reduce milk surpluses in the United States. It is expected that results from these simulations may diminish uncertainties in the dairy subsector if the simulated changes were, eventually, considered by policy makers or dairy producers organizations. The fourth quarter of 1 9 80 is selected as the simulations' ba s i s . The derived demand curves for fluid and manufacturing milk and the supply curves for grade A and grade B milk obtained from "pooling cross-section over time-series" data, are used in this chapter to solve the model described in Chapter III. The adjustment of the equations are checked by comparing predicted variables against actual values for the period 1 979-1981 . Model Adjustment The derived demand for fluid and manufacturing milk curves, as well as the supply for grade A and grade B milk curves, obtained in 120

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121 Chapter IV, compose the simulator, which, along with the quantity and price conditions, are rewritten below. Demand functions . (5.1) QF = 106360 PF" 1 195 EXP (.Oh S, .050 S £ .050 S ): Equation for the derived demand curve for fluid milk in the United States; (5.2) QMD = 16201770 PH~ k k33 EXP (.032 S ] + .097 S 2 + .102 S ) Equation for the derived demand curve for commercial manufacturing milk in the United States. Supply functions . (5-3) QA = 1681* PA + 17^66 S, + 20055 S 2 + 17822 S + 16200 S^: Equation for the supply curve of fluid eligible milk in the United States. (5.4) QB = 1308 PB 649 S, 60 S 2 865 S 3 1620 S^: Equation for the supply curve of grade B milk in the United States. Quantity conditions . (5-5) Ql 1 = QA QF: Grade A milk not used in the processing of fluid products and is used in the manufacturing of da i ry products ; (5.6) QMS = QB + Ql I : The available supply of manufacturing milk is composed of grade B and class II milk. (5-7) QS = QMS QMD: Government removes all excess supply of manufacturing milk from commercial markets.

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122 Price conditions . (5.8) PF = PI + PR: p r ; C e Q f fluid milk is composed of the minimum order price plus cooperative announced premium. (5-9) PA = 4.82 + 12442/QA: Blend price function for the (f o> ( V fourth quarter of 1980. The values for the coefficients of equation 5-9 for all quarters in the period 1977-1981 are given in Table 12. Resul ts The simulator described in the last section is now used to predict the values for GF t : Quantities purchased by processors of fluid eligible milk in the United States, by quarters, in the period 1979-1981; QMD t : Quantities of milk purchased by manufacturers in the United States, by quarters, in the period 1979-1981; QA t : Quantities of fluid eligible milk sold by plants and dealers in the United States, by quarters, in the period 1979-1981; PA t : Price received by farmers for fluid eligible milk, in the United States, by quarters of 1979-1981; and QB t : Quantities of grade B milk sold to plants and dealers in the United States, by quarters of the period 1979-1981. The predicted values for the above variables, as well as their actual values, are shown in Table 13.

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123 Table 12. Quarter Coefficients for the Blend Price Curve: 1977-81

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124 Note that QA t and PA t are derived by the solution of equations (5.10) QA t = 1684 PA t + 17466 S, + 20055 S £ + 1 7 822 S + 16200 S^, and (5-11) PA t =f 0>t+ f 1>t / Q A t , where f Q ^ and f^ assume the values given in Table 12 for each quarter. It was observed that the estimated seasonal coefficients for the grade B milk supply curve were performing poorly when compared to the other equations. The equation written as (5.12) QB t 1308 PB t 1651 S, 1462 Sj 1 1 58 83 1620 S^ improves the adjustments of the curve. The seasonal coefficients are here estimated by solving for the correspondent quantity and price values for the first, second, third and fourth quarters of 1 9 80. Since, applying D^ = OJ3°' 5 . c , PB] , for , = (,,...,4) of 1 9 80. The coefficients D 0J ,D 0>2 , D 0J , and D Q ^ were obtained D 0,l = k85 ° ~ '308 X 4.97 = -1651, D 0,2 = 5287 = ,308 X 5.16 = -1462, D 0,3 = 5003 1308 X 4.71 = -1158, and D 0,4 = 48, 5 " 1308 X 4.92 = -1620. Notice that although the demand and supply curves have been set to solve only for the fourth quarter of 1 98O values, the model seems to have a reasonable ability in tracking actual values for other quarters within the period 1979-81. The simulator was even able to generate the expected excess supply of manufacturing milk, which, being a residual value, incorporates the errors committed in the estimation of all

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1_ 3 OO I a o a. in 3 •u O < in 3 in L. 0) > -a 25 <7\ *o o — S = ° ^ D I © £ £ T ©Or*. * * 1A 1« ^ ^ ^ S | •» c %l 5 — o o O^ t/% Q> >4> © o o — ° <2 ^) r^ »\ © «-* ° £ ^ w\ «*»».» r^ ^ vf, J -. o «1 m f. *" *• O O a r«» -» O O O W% n o o"n
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126 functions in the model. The diversity of data sources used, errors in proxying the variables, and errors committed in adjusting the estimated functions to the national level are the primary causes of the observed divergences. However, predicting is not the model's primary objective, but rather the simulation of alternatives to reduce milk surpluses. For this purpose, the fourth quarter of I98O is selected as the simulator basis. Simulat ions Solution for the Basis The model is first solved for the fourth quarter of I98O, the "basis", to which results of subsequent simulations will be compared (Table ]k) . Self-Regulation Alternatives The following alternatives assume that the dairy industry captures the signals with respect to the amount of purchases of equivalent milk the government is desiring th cut off. No further action is taken by the government. The dairy subsector coordinates itself to produce the quantities of milk just sufficient and necessary to meet the commercial demand and government announced removals. The options for the subsector reside on either the use of authoritative or comprehensive coordination, or price control mechanisms.

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127 vD — — *j O « O Q. > . . . v vD — — § — r-. i/\ — r^» — i/\ j§ — O r— O J" — — -X s § D c O — -9 vD — — .CO** DO. OC d cy o— — o — — o — -» -T — rco l/\ \© nd — — 3 E § — o c — — — o — T> — 03 •o — — V W— T3 J£ I — C — o ~ 2 => 3 E * — C— C — >£ — V W .— «0 — A3 — O 1) l ID Q. 4) C — V «-> — — l-

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28 Non-price mechanism: rest ricting milk production . Suppose that through authoritative coordination a production quota is imposed upon grade A dairy farmers in such a way that the government intended cut offs in equivalent milk purchases is accomplished. Suppose that government wants to reduce its purchases by one-fourth. That is, the government announces it will not buy quantities in excess of 11 58 million pounds of equivalent milk at the announced support price of $4.82. The corresponding quota on the grade A milk production is 24763 million pounds, since a reduction of 386 million pounds is necessary. The price received by farmers for each hundred pounds of grade A milk will be $5,322 which is higher than the price before the quota. Even so grade A farmers would see their revenue being reduced by $18. 78 million, in 1967 values, which corresponds to a loss of $47.86 million in terms of 1980 values. This solution is shown in the second column of Table 14. Price-mechanism: coo perative price control . Producer cooperatives are responsible for marketing most (92 percent) of the milk sold to processors who are regulated by milk marketing orders [Cook and Hayenga, 1981, p. 16]. Suppose that these organizations are eligible to retain, at least temporarily, part of the returns obtained from milk sales. The cooperatives self-coordination rule is to pay producers only the price that will generate a volume of production to satisfy commercial demands and limited government purchases. Assume, again, for further comparative purpose, that the government is limiting its purchases of equivalent milk to QS2 = 1 1 58 million

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129 pounds. The price that cooperatives should pay grade A farmers is PA2 = $5,085 per hundredweight, which is the solution of the equation (5.13) PA2 = (QA2 16200/1684) for QA2, which is 24763. The remaining equilibrium values for this solution can be seen in the third column of Table 14. Note that the cooperatives existence allows a new element of coordination to enter the model, without needing government direct control. The cooperatives would retain cash values, in this case around $58,688 million (PA1 PA2) QA2. Alternative Government Controls If the dairy subsector is not able to coordinate itself in order to reduce milk production, the route is open for additional government regulations. Alternative policies are searched to enforce the supply side of the dairy subsector to adjust with the desired situation. Product differentiation support price . Suppose that government is convinced that milk surpluses are due to excess supply of grade A milk and thus decides that products manufactured with grade A milk would have a lower price support. The problem here is to find which price support would be necessary and sufficient to make grade A farmers produce only the amount required by commercial and government outlets. Mathematically, the problem is to find the solution for PM3 in the equat ion (5.14) PA3 = PM3 + (PF3 PM3) QF3/0.A3, for the value of PM3, that is, (5.15) PM3 = (PA3 X QA3)/0_A3 QF3) = 4.32,

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130 where PA3 = 5-085 is given by the solution of (5.16) PA3 = (QA3 16200)/ 1684, for QA3 = 24763. In this case, if grade A farmers had chosen to reduce production through any of the self-regulation alternatives, they would have saved $58,688 million (1967 prices) because $77-^71 would be the reduction in revenue if the presented alternative were chosen, and only $18. 611 would be the revenue reduction due to the quota sel fimpos i t ion (Table 14). It is assumed that the differences between the two supported prices would be collected by the government from the manufacturing plants . Taxing output . Suppose that a $0.23 checkoff had been levied on every hundred pounds of grade A milk produced. If the checkoff had been previously announced it would be effective only if quantities exceeded 24763 million pounds, an alternative open to grade A milk farmers would be to reduce production to that level. In this case, total loss in revenue would be (PAO QAO) (PA4 QA4) = 1878, that is, $18.78 mill ion. However, if QA4 = QAO is produced anyway, revenue losses with the checkoffs are $57,843 million (Table 14). Selective price support levels. Suppose the price support had been set ten cents of a dollar below its fourth quarter of 1 980 level. The solution to this alternative which can be seen in Table 14, is more drastic than the former because it involves indiscriminately grade A

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131 and grade B milk production. Revenue losses to the dairy sector would be $10.39 million. Grade A farmers revenue reduction would have been $6,116 mi 1 1 ion. Summary and Conclusions Estimates obtained from "pooling cross-sections over time-series" techniques were used to calculate derived demand curves for fluid and manufacturing milk and supply curves for grade A and grade B milk in the United States. These four equations plus quantity and price conditions identities were the components of an empirical model used to simulate alternative coordinating arrangements to reduce milk surplus in the United States. The transformed equations demonstrate a reasonable predicting power for the period 1979-1981. The fourth quarter of 1980 is selected as the "basis" for the simulations. Results seem to indicate that it would be better for both the government and the private dairy subsector that alternatives labeled as "self-regulations" be selected. Substantial savings in revenue would be realized by farmers if they coordinate themselves to reduce milk surpluses, avoiding additional government supply side regulations.

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CHAPTER VI SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FUTURE RESEARCH Summary Milk production in the United States has exceeded commercial consumption. The consequent volume of milk to be removed, at the prevailing support prices, seems to be above acceptable levels. Three broad strategies to solve this problem are (a) increase commercial consumption, (b) reduce milk production, and (c) increase consumption and reduce product ion. Most of the measures designed to increase consumption of domestic milk, such as reduction of imports, increase in exports, promotion and advertising, may reduce stocked surpluses in the short-run, but formation of surplus, the core of the problem, is likely to persist. The objective of this study was to examine alternative supply side arrangements to reduce milk surpluses in the United States. The model developed in Chapter l.lwas based on the model initially formulated by Kessel [l 9 6 7 ] and extended by I ppol i to-Masson [l 97 8], and Dahlgran [1980] (see Chapter ||). Model modifications included (a) defining the manufacturing milk demand function to include commercial quantities, excluding government purchases, and (b) redefining the purpose, scope, and some equilibrium conditions. 32

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133 Using information collected from the United States Departments of Agriculture, Labor, and Commerce, derived demand equations for fluid and commercial manufacturing milk (at the Federal Milk Marketing Order level) and grade A and grade B supply equations (at the state level) were estimated using "pooling" techniques. The estimated coefficients were used to compute correspondent equations for the United States. The model, composed of the supply and demand equations plus quantity and price conditions, was used to simulate alternative arrangements that would reduce milk surpluses. The fourth quarter of 1980 was selected as a "basis." Alternatives to reduce milk production require changes and/or improvements in the coordination between participants in the exchange function, including government. These alternatives can be classified as (a) self-regulation alternatives, and (b) government control alternatives. The first set is so labeled because it is assumed that the private sector of the dairy industry would maintain the volume of milk removals at acceptable levels by controlling milk production. The second set of alternatives assumes that government needs to enforce milk production reductions . These alternatives were simulated using the model developed in Chapter 111, with coefficients calculated from equations estimated in Chapter IV. Equations for derived demand for fluid and manufacturing milk, and for grade A and grade B milk supply were estimated by pooling sections over time-series data. The price elasticities computed from

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134 the estimated equations are as follows: (a) fluid milk derived demand: -1.195; (b) commercial manufacturing milk derived demand: -4.^33; (c) grade A milk supply: .24; and (d) grade B milk supply: 1.23. Regional elasticities can be calculated for all functions. Supply and demand elasticities appear to be different among regions. In particular, previous studies have reported systematic lack of response of manufacturing milk demand at regional level. This hypothesis was not consistent with the results of this study. The commercial derived demand for manufacturing milk seems to respond to prices at the regional level. Results from the simulations performed in Chapter V indicate that "self-regulation" should be preferred by milk producers. Government intervention with additional controlling rules would cause further reductions in dairy farmers revenue. It was found that if self-regulation is selected, for every one percent reduction in quantities supplied of grade A milk, dairy farmers' revenue may decrease .51 percent, but if government control is necessary, then for every one percent decrease in quantities marketed of grade A milk, dairy farmers' revenue could decrease by 3.77 percent. If indiscriminate measures are taken by government, that is, measures affecting both grade A and grade B milk farmers, relatively large decreases in production of grade B milk can be expected. However, for every one percent decrease in quantities supplied of grade B milk, farmers' revenue may decrease only 1.74 percent.

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135 Concl us ions In view of results obtained in Chapter V, it seems that some strategies should be designed by dairy policy makers, from either the government or private sector, in order to motivate dairy farmers to reduce milk production. Additional government rules would further increase dairy farmers' losses in revenue. (Comparisons were made taking fourth quarter of 1 980 as basis.) Within these lines it is suggested that immediate actions by government should not be taken. Farmers may need more time to be motivated and to internalize the government restrictions. However, (a) government should demonstrate and reinforce its position with clear figures about the volume of intended purchases, well in advance; and (b) dairy cooperatives' importance as a means of coordination in the dairy subsector should be understood and enhanced. These organizations may be the best channel for communicating the government restrictions to dairy farmers. Dairy cooperatives should help farmers understand the current situation, making clear to dairy farmers that they would be worse off if additional government rules were created to enforce production reductions. Suggestions for Future Research Unfortunately, tests for the irreversibility hypothesis in the supply functions of both grade A and grade B did not reveal satisfactory results. Approaches by Tweeten and Quance [1969], Wolffram [1971], Houck [1977], and Traill, Colman, and Young [1978] were unsuccessfully

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136 tried. Even though it is strongly believed that if more time were dedicated to this specific subject, some important results would be obtained. The analysis of a short-run decrease in the price of milk would be enhanced with a non-reversible supply function. This research could also be empirically extended by simulating the impact of the alternatives examined in this study at the regional level in the context of a regional equilibrium model. The "pooling" technique seems a reasonable estimation procedure. However, it is suggested that more investigation be dedicated to the seasonality problem and to the price-lagged response of the derived demand functions. A recent phenomenon in the dairy industry is the utilization of some processing plant facilities for fruit (orange in most cases) price packaging. Derivations of fluid milk demand functions should eventually consider this complementary activity in the processor's profit function. Another suggestion would be to bring dynamics into the model. The effects over time of alternative arrangements to reduce milk surpluses would bring additional insights into the problem. Independent cooperatives, as well as "free-riders" (noncooperativated milk producers) could modify the simplified analysis conducted in this study. The extension of their influence could be investigated in further research. However, the government alternatives, analyzed in this study, would, in principle, be imposed upon all milk producers, free-riders, or not. Note that in the current regulated environment (guaranteed milk purchases at the price support level), reduction in

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137 cooperative members' production would not create, itself, any incentive for free-riders to increase theirs. Finally, the effects of interstate trade of milk cows should be modeled in order that its influence on the lagged price responses could be better understood.

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APPENDICES

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APPENDIX A DERIVED DEMAND AND SUPPLY FUNCTION DERIVATIONS

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Theoretical Approach This Appendix has two purposes. The first is to derive, mathematically, using assumptions about the economic behavior of dairy farmers, milk processors and manufacturers, the functions needed to solve the model described in Chapter III. The sec ond objective is to identify explanatory variables for each equation considered in that model. What follows is based on procedures suggested by Varian [1978, pp. 8-34]. Traditionally, the economic behavior of a perfectly competitive firm can be described from its profit maximization objective (Al ) ir(p) = max p.y s. t. y is in Y where p is a vector of prices for inputs and outputs of the firms; y is either input or output quantities, and Y is the firm's technological possibi 1 ities. The first-order conditions for the single output profit maximization problem when all inputs are used is (A2) pDf(x") = w or where f(x ) summarizes a production function at the levels x* and /' These conditions say that the value marginal product of each factor must be equal to its price. 40

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Ii»l The second-order condition for profit maximization is that the matrix of second derivatives of the production function must be negative semi-definite at the optimum set values, that is, the matrix 2w *, _ 3 2 f(x") (A*.) DV(x") = P dX.dX. ' J must satisfy the condition that hD 2 f(x*) h £ for all vectors h, which is the same to say that the production function must be locally concave in the neighborhood of an optimum. For each vector of prices (p.w) there will in general be some optimal choice of factors x" . The function (A5) x(p,w) gives the optimal choice of inputs as a function of the prices. This relation is called derived demand function of the firm. Similarly, (A6) y(p,w) = f(x(p,w)) is called the supply function of the firm. There is an alternative way of finding demand and supply functions which allows an easier discussion of their properties. Let y(p,w) be the firm's supply function and let xi(p,w) be the firm's demand function for factor i. Then it can be proved [Varian, 1978, pp. 31-32] that ( A7 ) y( P ,w) = **kj»L • and 9p (A8) xi( P ,w) .-Z^XL, i d,...,n), when the derivatives exist, and when w > 0, p > 0. Now, let xi(w,y) be the firm's conditional factor demand for input i. Then, if c is d i f ferent iabl e at (w,y) and w > 0, it can be proved [Varian, 1978, p. 32] that

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]k2 (A9) xi(w,y) = 3c ^: y) , i = 0,...,n), dW I Equation (A9) means that the cost-minimizing input vector is just given by the vector of price derivatives of the cost function. Using equations (A7) through (A9) it can be shown that (Aio) (a): 9y(P,w) 3 ( 3tt( P ,w) ) , 3 2 tt(p,w) dp dp dp ,. Z dp which is non-negative since i is a convex function. Therefore, the supply function slopes upward. 2 (Al 1 ) (b) • 5xi (P' w ) ~ 9 / dTT(p,w) v = _ 3 (tt(p,w) ) 3xi 3wi 3wu .2 dwi which is non-positive since it i s a convex function, hence, the demand functions slope downward. ( A , 2 ) ( c ). 3xj(p,w) m 5 ( . 3tt( P ,w) ) = 3 ( _ 3;( P> w) } , dWI dWI dWJ dWJ dWI 3xi (p,w) 3wj That is, the cross-price effects are symmetric, and 2 (A 1 3 ) (d) : D tt(p,w) is positive semi -de( in i te , since it i s a convex function. Derived Demand Function for Fluid Milk Using the theoretical framework of the last section, the processor derived demand function for crude milk would be (Al 4) q f = df (pol , . . . ,pox; pwl , . . . ,pwz;pf ) where

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1*3 QF is the quantity of crude milk used in the processing of fluid milk products ; pf i s the price of qf ; poi is the price received for the i t fluid milk product; pwj is the price of the j -t nonmilk input. It is assumed that the processor is a profit maximizer economic agent in a perfect competitive environment. Equation (A14) gives the quantities of milk demanded at each price, pf, in such a way that the processor could maintain itself at the optimum solution domain. The curve for fluid milk derived demand is downward sloping (equation All). Derived Demand Function for Manufacturing Milk The difference in the profit function between the fluid milk processing plant and the manufacturing milk plant is that the latter may use either fluid eligible or grade B milk, or both, on its productive process. Its restricted profit function is defined as 9 h (A15) it = Z poi qoi £ pwj qwj pm qm 1-1 J-1 Subject to: F(-) = F(qO;qw;qm) > 0, pm = (pcqc + pBqB)/(qc + qB) , qm = qc + qB, qo, qw, qc , qB >_ 0. The corresponding derived demand function for manufacturing milk is

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(A 1 6) q m = qc + qB = dm (po;pw;pm), where qm is the quantity of manufacturing milk used in the production process ; qc is the quantity of fluid eligible milk used in the production of dairy products; qB is the quantity of grade B milk used in the production process; po is the vector of prices received for manufactured dairy goods; pw is the vector of prices paid for the inputs fw, and pm is the average price of manufacturing milk. According to equation (All), the function (A16) is downward sloping. Supply Functions for Fluid Eligible and Grade B Milk Assume that a representative dairy farmer produces both fluid eligible and grade B milk. Its restricted profit function can be given by (A 17) tt = pAqA + pBqB pwjqwj subject to: F ( • ) = F(qA; qB; qw) = 0, and qA > 0; qB > 0; and qw > 0, from where the corresponding supply functions would be derived as (A18) q*A = h(pA; pB; pw) . (Al 9) q"B = g(pA; pB; pw) . Using equation (Al 0) it can be concluded that equations (Al 8) and (Al 9) are upward sloping functions of their respective prices.

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APPENDIX B GLOSSARY

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BLEND PRICE: Is an average of the fluid milk price and manufacturing milk price, weighed by the proportion of milk sold for fluid use and that sold for manufacturing purposes, respectively. CCC: The Commodity Credit Corporation is the government agency that implements commodity programs. CLASS I MILK: Is fluid eligible milk processed into fluid milk products such as whole milk (bottled milk), lowfat milk, flavored milk drinks, buttermi 1 k, etc. . . CLASS II MILK: Is, in this study, assumed to be any utilization for the fluid eligible milk other than class I use. As such class II milk includes the milk used to manufacture ice cream, sour cream, cottage cheese, yogurt, hard cheeses, butter, evaporated or condensed milk, and dry mi 1 k powder. CLASSIFIED PRICE: Means that the fluid eligible milk is priced according to its utilization (class I, class II, or class III). CWT: Hundred weight, a measure that corresponds to one hundred pounds. DAIRY SUBSECTOR: Includes the individuals and firms engaged in milk production, handling, manufacturing, processing, distribution and retailing, as well as the suppliers of needed inputs. 146

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I*»7 FEDERAL MILK MARKETING ORDERS: This is a legal instrument issued by the Secretary of Agriculture, as authorized by the Agricultural Marketing Agreement Act of 1937 as amended, which regulates the handling of milk in specific marketing areas. Each milk marketing order sets forth minimum prices that handlers must pay producers or assocations of producers according to the way the milk is used. FIRST HANDLERS: First recipient of grade A milk from producers regulated under Federal Milk Order Markets. FLUID ELIGIBLE MILK: Is the milk that can be used for consumption in fluid form (most grade A milk). FLUID MILK PROCESSING PLANT: This is a plant which processes fluid milk products . GRADE A MILK: Is fluid eligible milk. This grade of milk is produced under conditions which meet sanitary and health requirements of state and local authorities for consumption in fluid form. Grade A milk can also be used in manufactured products. GRADE B MILK: This grade of milk does not meet grade A requirements, but does meet the requirements for use in manufactured products. It cannot be used for fluid products. HANDLER: A handler refers to a plant or marketing organization which is regulated under the terms of an order.

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U8 HARD MANUFACTURING PRODUCTS: Cheese, butter, nonfat dry milk, and canned milk. MANUFACTURERS: Refers to a concern primarily engaged in making so-called hard dairy products such as butter, nonfat dry milk, or American, Italian, or semi-soft cheeses (Muenster and the like), and evaporated milk. In this study this concept is widened to include also the producers of soft dairy products. MANUFACTURING: Is here defined as the conversion of grade A or B milk to dairy products other than those defined as class I use. MANUFACTURING MILK PRICE: is the price paid by manufacturers. MANUFACTURING PLANTS: These plants process storable manufactured dairy products . NMPF: National Milk Producers Federation. POOLING PRICE: Mechanism which insures that grade A milk producers receive the blend price. The dairy cooperative associations marketing their members' milk under Federal orders are entitled to blend the net proceeds from sales of milk. PRICE SUPPORT: The government stands ready to purchase butter, nonfat dry milk, and cheese at prices sufficient to support the manufacturing milk price at the level established under the support program.

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149 PROCESSING: Is, here, the conversion of grade A milk to fluid dairy products . PROCESSORS: Is, here referred to a concern that bottles, or packages grade A milk for drinking purposes. SOFT MANUFACTURED PRODUCTS: Yogurt, ice cream, and cottage cheese. VERTICAL COORDINATION: When all transactions in a subsector are taken together, involving hundreds of different kinds of firms at different stages in the subsector, their synchronization is called vertical coordi nation. Vertical coordination is a process by which the various functions in a subsector are brought into harmony with respect to a single managerial control.

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APPENDIX C VARIANCE-COVARIANCE MATRICES FOR ESTIMATED COEFFICIENTS

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REFERENCES Amemiya, T. "A Note on a Fair and Jaffee Model." Econometrica kl (\37k) : 759-762. Babb, E.M., and Arlo J. Minden, "A Total Marketing System for U.S. Dairy Cooperatives." Amer. J. Agr. Econ. 5k (1972): 2~l\-~lk. Babb, E.M., D. E. Banker, 0. Goldman, D.R. Martella, and J.E. Prott. Economic Model of Federal Milk Marketing Order Policy Simulator Model A . Indiana Agr. Exp. Sta. Bull. No. 158, Purdue University, 1977. Babb, E.M., D. E. Banker, and G. L. Nelson. Price Relationships Among Federal Milk Marketing Orders . Indiana Agr. Exp. Sta. Bull. No. 146, Purdue University, 1 976. Babb, E.M., D. A. Bessler, and J.W. Pheasant. Analysis of Over-Order Payments in Federal Milk Marketing Orders . Indiana Agr. Exp. Sta. Bull. No. 235, 1979Babb, E.M. and W. T. Boehm. "Consumer Response to Changing Fluid Milk and Ice Cream Prices." Unpublished paper for MIF/IAICM Convention, Dallas, Texas, 22 Oct. 197^. Babb, E.M., R. D. Boynton, W. D. Dobson, and A. M. Novakovic. "Alternatives for Federal Marketing Programs: Milk Marketing Orders." Paper presented at the Farm Foundation Meeting, Chicago, 15-17 Mar. 1982. Beck, Robert L. "Kentucky's Manufacturing Milk Industry: Structure, Trends, Issues." Dept. Agr. Econ. Progress Report 263, University of Kentucky, June 1S&2. Becker, Gary S. Economic Theory . New York, N.Y.: Alfred A. Knopf, Inc., 1971. Blakley, L., and D. W. Kloth. "Price Alignment and Movements of Class I Milk between Markets." Amer. J. Agr. Econ. 5^ (1972): ^96-502. Boehm, W. "The Household Demand for Major Dairy Products in the Southern Region." Southern J. Agr. Econ. No. 2 (Dec. 1975), PP187-196. 58

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162 Houck, J. P. "An Approach to Specifying and Estimating Nonreversible Functions." Amer. J. Agr. Econ . 59(1977): 570-72. Huang, D. S. Regression and Econometric Methods . 2nd ed . Huntington, N.Y.: Robert E. Krieger Publishing Co., 1980. Intril igator, M. D. Econometric Models, Techniques and App lications. Englewood CI iffs, N.J. : Prentice-Hall, 1978. Ippolito, R. A., and R. T. Masson. "The Social Cost of Government Regulation of Milk." J. Law and Econ . No. 21, Vol. 1 (1978) pp. 33-65. Ito, Takatoshi. "Methods of Estimating for Multi-Market Disequilibrium Models." Econometrica , 48(1980); 97-125. Jesse, E. V., and A. C. Johnson, Jr. "Defining and Idnetifying Undue Price Enhancement." Antitrust Treatment of Agricultural Marketing Cooperatives, ed. E. V. Jesse. Seminar on Section 2 of the CapperVolstead Act, Washington, D.C.: 15 Apr., I98O. • Farmer Cooperatives and Undue Price Enhancement . Dept. of Agr. Econ. Issue No. 62, University of Wisconsin, Sept. I98I Jones, W. W. Milk Processor, Distributor's Sales, Costs, and Ma rgins. '979 . Washington, D.C.: USDA ERS, Oct. 1 98 1 . Judge, G. G., W. E. Griffiths, R. Carter Hill, and Tsoung-Chao Lee. The Theory and Practice of Econometrics . New York, N.Y.: John Wi ley and Sons, I98O. Judge, G. G., R. C. Hill, W. E. Griffiths, H. Lutkepohl , and Tsoung-Chao Lee. Introduction to the Theory and Practice of Econo metrics. New York, N.Y. : John Wiley and Sons, 1982. ~ Kelley, P. L., and D. A. Knight. "Short Run Elasticities of Supply of Milk." J. Farm Econ . 47(1965): 93-104. Kennedy, P. A Guide to Econometrics . Cambridge: The MIT Press, 1979. Kessel, R. A. "Economic Effects of Federal Regulation of Milk Markets." J. Law and Econ . , No. 10 (I967), pp. 51-78. Kmenta, J. Elements of Econometrics . New York, N.Y.: Macmillan Publ ishing Co. , 1971 .

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163 Knutson, R. D. "The Impact of Cooperatives on Market Performance, Subsector Coordination, and the Organization of Agriculture." Agricultural Cooperatives and the Public Interest , ed . B. W. Marion. NC Regional Research Committee 117. St. Louis, Mo. : Sponsored Workshop, 6-8 June 1977. Kwoka, J. E., Jr. "Pricing Under Federal Milk Market Regulation." Economic Inquiry , 15(1977): 367-84. Levins, R. A. "Price Specification in Milk Supply Response Analysis." Amer. J. Agr. Econ . 64(1982): 286-88. Ling, K. C. Pricing Plans for Managing Seasonal Deliveries by Dairy Cooperatives . Washington, D.C.: USDA ACS Res. Report No. 22 Aug. 1982. MacAvoy, P. W., ed. Federal Milk Marketing Orders and Price Supports . Washington, D.C.I American Enterprise Institute for Public Policy Research, 1977. Maddala, G. S. "The Use of Variance Components Models in Pooling Cross Section and Time Series Data." Econometrica 39(1971): 341-58. . Econometrics . New York, N.Y.: McGraw-Hill, 1977. Manchester, A. C. "Agricultural Marketing Cooperatives and Antitrust Law." Antitrust Treatment of Agricultural Marketing Cooperatives , ed . E . V. Jesse, Seminar on Section 2 of the Capper-Vol stead Act. Washington, D.C., 15 Apr. 1980. Mansfield, E. Microeconomics: Theory and Application , 3rd ed . New York, N.Y.: W. W. Norton, 1979. Milligan, R. A. An Economic Analysis of the Factors Affecting the California Dairy Industry . Giannini Foundation Research Report No. 325, California Agric. Exp. Sta., Feb. 1978a. "Milk Supply Response in California: Effects of Profitability Variables and Regional Characteristics." West. J. Agr. Econ . 3 (1978b): 157-64. Morigouchi, J. "Aggregation over Time in Macroeconomic Relations." International Econ. Review , 11(1970): 427-40. National Milk Producers Federation. News for Dairy Co-ops . Washington, D.C., selected issues, I98I. Nerlove, M., and W. Addison. "Statistical Estimation of Long Run Elasticities of Supply and Demand." J. Farm Econ. 40(1958): 861-80.

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164 "^ZiVurt M : i\ 3 p d !" U Th ° mpson " The lm P^t of Imports of Manufactured Mi Ik Products on the U.S. dairy Industry." Amer J Aqr |con. 59(1977): 507-519. Aqr Ofek Halm "Is Perfect Competition an Empirically Inadequate Model?" Economic Inquiry , 20(1982): 21-39. Pierce, D. A._ "Relationships and the Lack Thereof between Economic Time Series with Special Reference to Money and Interest Rate." J. of the Amer. Stat. Assoc . 72(1977): 11-12. Prato A. A "Milk Demand, Supply and Price Relationships, 1950-1968 " Amer. J. Agr. Econ . 55(1973): 217-222. Purcell, J.C. Ana lysis of Demand for Fluid Milk and F luid Milk Substitutes in the Urban bouth. Georgia A q r Fv p §ti Pnll. No 12 University of Georgia, Oct. 1957. R ° jk0 : A S ' The Demand and Price Structure for Dairy Products Washington, n 7c7: USDA Technical Bulleti n 1168, 1957 " . ' Salat rn;,l' P E i' V" ,' riCe ' ^ K E GadSOn " The Food and Agricultural Pol ,cy S.mulator: The Da i ry-Sector Submodel ." Aqr Econ Research , Vol. 34, No. 3 (July 1982), pp. 1-14. 9 Sargeant T J. "A Classical Econometric Model of the United States." J. of Pol . Econ . 84(1976): 207-37. Searle.^S. R. Linear Models . New York, N.Y.: John Wiley and Sons, Inc., SimS '540-52. " MOneY ' ' nCOme and Causalit Y-" Amer. Econ. Review . 62(1972): Song, D. H., and M. C. Hallberg. Are Dairy Programs Biased Toward Producers or Consumers? Agr. Econ. and Ru ral Sociol. Dept Staff Paper No. 38, The Pennsylvania State University, Nov. I98O. ^'Z'^;' ^n I!' V Jesse Economic Effects of Terminating Fp Hp^I u!u i'" q | S Pi Ca1ifnrnia Arizona ° rann ^^hTnftoK -DTc USDA ERS Technical Bulletin No. l664, Nov. 1981. TOmek ionk ""/<' ^ L R f inS0n "Agricultural Price Analysis and Outl° 0k /. A Sur vey of Agricultural Economics Literature . ed . L R ^ m ' PP325-409. Minneapolis: University of Minnesota Press, Agricultural Product Prices. 2nd ed . Ithaca, N.Y.: Cornell University Press, 1 98 1

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165 Traill, B., D. Colman, and T. Young. "Estimating Irreversible Supply Functions." Amer. J. Agr. Econ . 60 ( 1 978) : 528-31. Tweeten, L. G., C. L. Quance. Foundation of Farm Policy , 2nd ed . Lincoln: University of Nebraska Press, 1970. "Positivistic Measures of Aggregate Supply Elasticities: Some New Approaches." Amer. J. Agr. Econ . 51(1969): 3^2-52 . • "Techniques for Segmenting Independent Variables in Regression Analysis: Reply." Amer. J. Agr. Econ . 53(1971)359-60. U.S. Department of Agriculture. Crop Reporting Board. Farm Labor. Washington, D.C.: Selected monthly issues, 1 9771 98 1 a . _. Crop Reporting Board. Agricultural Prices . Washington, D.C.: Selected monthly and annual summaries, 1 977 1 98 1 b . Agricultural Marketing Service. Dairy Market Statistics. Washington, D.C.: Selected annual summaries, 1 9771 98 1 c . • Agricultural Marketing Service. Federal Milk Order Market Statist ics . Washington, D.C.: Selected annual summaries, 19771 98 1 d . Crop Reporting Board. Milk Production. Washington, D.C.: Selected issues, 1 9771 98 1 e . . Econ. Res. Service. Dairy: Outlook and Situation, Washington, D.C.: Selected monthly issues, 1 9771 982a . Economic Reporting Service. Da i ry Si tuat ion. Washington, D.C.: Selected monthly issues, 1 977~ 1 982b . . "Cooperatives in Federal Milk Order Markets." Federal Milk Order Market Statistics , No. 250, Oct. 1980a. . Costs of Producing Milk in the United States Final 1978, Preliminary 1979, and Projections for I98O . Washington, D.C, ESCS for the Committee on Agriculture, Nutrition, and Forestry United States Senate, July 1 S30b . . "How Federal Milk Order Market Statistics Are Developed and What They Mean." Federal Milk Order Market Statistics No. 241, Apr. 1980e.

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66 . "Producer Milk Marketed Under Federal Milk Orders by State of Origin." Federal Milk Order Market Statistics No. 240, Feb I 9o0d . ~ The Federal Milk Marketi ng Order Program . Wash! ngton , D.C . : AMS Marketing Bull. No. 27. Revised, June 1 96 1 "Emergency Dairy Adjustment Act of 1982." Adendum to a Statement by Secretary of Agriculture, May 5," 1982a. • "1931 Milk Manufacturing A Record." Dairy: Outlook and Situation . DS-389, ERS, June 1982b. *— News_. Washington, D.C: Office of Government and Public Affairs, May 5, 1982c. Statement by Secretary of Agriculture John R. Block. Washington, D.C: E.D.T., May 5, 19$2d. U.S. Department of Commerce, Bureau of Economic Analysis. Survey of 1 977-82. BU5ineSS Washin 9ton, D.C: Selected monthly issues, U.S. Department of Labor, Bureau of Labor Statistics. Employmen t and Earn,n g 5 Washington, D.C: Selected monthly iss ues, 1977-1981 . Varian, H. R. Microeconomic Analysis . New York, N.Y.: W. W. Norton Vitaliano, P "The US. Dairy Price Support Program: Past, Present and Future. V . rg . n . a Coop. Ext. Serv. Bull. No. 325. Virginia Polytechnic Institute and State University, 1981. Wilson R. R and R. G. Thompson. "Demand, Supply and Price Relationships for the Dairy Subsector, Post-World War II Period." Amer. J. Agr. Econ . ^9(1967): 360-71. Windall P. M and D. L. Weiss. "An Iterative GLS Procedure for Estimating the Parameters of Models with Autocorrelated Errors Using Data^Aggregated over Time." The Journal of Business . 5M1980): Wipf, L. J., and J. P. Houck. Milk Supply Responses in the United States an Aggregate Analys.s . Dept. of Agr. Eco n. Report No . t>U, University of Minnesota, I967. Wolff ram, R. "Positivist Measures of Aggregate Supply Elasticities: 530970356-59 " ^^ Critica ' Notes: Amer. J. Agr. Econ ..

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167 Young, T. "Modeling Asymmetric Responses, with an Example." J Aqr Econ . 31(1980): 175-86. — ~ Zellner, A. "An Efficient Method of Estimating Seemingly Unrelated Regression and Test for Aggregation Bias." Jour nal of the Amer Stat. Assoc, 57(1962): 3^8-68. '

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BIOGRAPHICAL SKETCH Vander Gontijo was born in Divinopolis, Minas Gerais, Brazil, on February 22, 1947. After graduating in Economics from the "Uni vers idade Federal de Minas Gerais (UFMG) ," Belo Horizonte, in 1969. he entered the "CEDEPLAR-UFMG (Centro de Desenvol v imento e Planejamento Regional)" where he obtained his master's degree in 1975. While completing his degree requirements, he taught Economics in the "UFMG," and in the "Fundacao Universidade de Itauna." In 197* he was nominated undergraduate coordinator for the Department of Economics of the "UFMG." From 1970 to 197^ he held a research position in "CEDEPLAR-UFMG." In October of 197** he moved to Brasilia, D.F., where he coordinated perspective studies for national agricultural plans. In January 1979 he initiated studies pursuing a doctorate degree in agricultural economics at the University of Florida, awarded a scholarship from the "Empresa Brasileira de Pesquisa Agropecuaria EMBRAPA." 168

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Richard L. Kilmer, Chairman Assistant Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is ful adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ~. H. Evan Drummond Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. 77] oy <^> f?_!3^! Max R. Lanqham £/ Professor of Food and Resource Economi cs I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Woodrow W. McPherson Graduate Research Professor of Food and Resource Economics

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ISaoaJj) m^ ^v>^ Ronald W. Ward Professor of Food and Resource Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully aaequate, in scope and quality, as a dissertation for the degree of Doctor of Phi losophy. ? yf 1_ David Denslow, Jr. // Associate Professor of Economics This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate Council, and was accepted as Partial fulfillment of the requirements for the degree of Doctor of Ph i losophy . April, 1983 uk cL ^ W Dean// Col lege of Agriculture Dean for Graduate Studies and Research