AN ANALYSIS or MLK mas RELATIONSHIPS
INVOLVED m mun-13mm 5mm AREAS
son MILK MARKETS m LOWER MICHIGAN

Thesis for the Degree of M. 5..
MlCHIGAN STATE UNIVERSITY
William B. Henley“

1961‘”

 

 

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A? AVALYSIS OF MILK PRICE ETLATIOHSHIPS INVOLVED
IN DELINEATING SVTPLY A5733 FOR MILK

MARKETS IV LOVER MITHIGAN

BY

iilliam B. Helleges

A THESIS

Submitted to the School of Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

MASTER or scrapes

Department of Agricultural Economics

1961

Announcements

The euthor wiehee to eXpreee hie eineere gretitude

end eppreoietion to en who eeeieted in en: trey during thie
etudy end preperetion of the eenueoript.

apeoiei recognition ie due to Dr. Glynn nonride who
wee ee helpful in euper'vieins end editing thie theeie.

thenke ie expreeeed te Dr. Willie. L. leten who no

villi we hie tine in en erviei the etetietieel e te
or th‘i‘glIheeie end for minspmsseefiene in ite preperet on.

ippreoietion eiee ie erpreeeed to Dr. Vernon L. Seren-
een who tool: the tine to reed end eeke eusgeetione recerdina

the lenueeript.

to Dr. L. 1.. Boner end the Deperteent of Agriculturei
hone-ice thelte ere expreeeed for the finenoiel eid which
nede the euthor‘e sreduete study peeeible.

eppreoietion ie eiee expreeeed to Hr. George Inine.
lertet Adeinietretor of the Southern Hiehisen llerketing
Order. Ir. 1.11. hemee. Secretery-Keneger of the Michigan
1111: Producer-e ieeocietion Hr. hereon Ii'eel, Director of
‘rreneportetion, niohisen Hill: Producere Aeeooietion. end
, Hr. OJ. Sveneon of the Hiehiaen OoOperetive Crop Reporting
Service, for eekins dete vitel to thin etudy eveilebie end
te e11 thoee eeeeoieted with the Agriculturel Eoononiee
Depertnent end the Depertnent or Econoeioe who here eeeiet-
ed the euthor in oelieetins end prepering the dete tor uee
In thil ”Ci.e

linen? the euthor viehee to then: hie wire. Jeenne.
n

for her eid typing the rough dreft end for her petienoe
end underetendins throughout the euthor'e sreduete etudy.

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en AHALISIB or m ram amrxoasnzrs INVOLVED
III Dummrmc aunt! mes ma um
names In none mum

By

William B. Hellegaa

A THESIS

Submitted to the School of Graduate Studies of
Michigan State University of Agriculture end
‘ Applied Science in partial fulfillment of

the requiremente for the degree 0!

MASTER OF SCIENCE

Department of Agricultural Economics

1961

“

ABSTRACT

This study was concerned with the delineation of milk
supply areas for the Detroit. Jackson, Battle Creek, Kala-
mazoo. Lansing. Grand Rapids, Muskegon, Bay City, Saginaw,
and Flint, Michigan. consuming areas in such a way that
total transport costs would be at a minimum. The nine areas
include ell counties having one or more cities with a pep-
ulation of 40,000 or more and contain 75.65 of the popula-

tion in Lower Michigan.
Based on the per capita consumption in milk equivalents

of 28.603 pounds for November. plus a 153 fluctuation allow-
ence. the total fluid milk requirements for the nine areas
was found to be 135,855,360 pounds.

Total milk production in Lower Michigan for November,
1959. was 363,831,640 pounds, of which 216,498,324 pounds
were available to the marketing areas for fluid use. The
remainder was used for non-fluid purposes and by peeple

living outside the marketing areas.

To minimize total transport costs it was found that
all supply area boundaries had to be defined by points of
price indifference to the receiving stations in reference to

the competing markets. These points of indifference form a
hyperbolic function enclosing the smaller market. The

iv

points on the boundary line were defined by the intersection
of corresponding iso-price lines radiating from the come
noting markets.

The loo-price lines were set at ten mile intervals
representing a change in price of $0.01. This amount re-
flects the added cost of moving a hundred weight of milk ten
miles and is linear with distance.

Through a series of f.o.b. city plant price approxima-
tions the supply areas for the nine marhets were simul-

taneously determined. All supply area boundaries common to
more then one nareet were competitively defined over their

entire range.

the price variation between the markets and the basing
point was found to be influenced by the location of the mar-
ket inreference to the surplus area, density of production,
distance to the basing point and the number and location of
competing markets.

To determine the degree of accuracy with which the
ideal price variation could be predicted the above factors
were quantified as independent Variables in the formula

2': b1x1 e b2!2 + b3x3 e baxh. All the factors more found
to be significant in determining price variation. A correlap

tion coefficient of .99967.was obtained when the estimated
price variations were tested against the observed. indicat-
ing a high degree of association between the desired prices

and the independent variables.
To determine the savings which would result if the

V

supply areas were organized in accordance with the theoret-
ical model. a model was constructed representing the existing
conditions. Price change with distance remained the same
but the price variations among the market was taken to be
equal to the location adjustments provided for in the South-
ern Michigan Marketing Order. When the models were compared
it was found that the variable cost incurred to move the
total market requirements of November, 185,855,360 pounds,
was $120,967.88 in the existing model and $110,030.56 in the
theoretical. The $10,937.32 decrease was the result of a
80.00583 decrease in the average total variable cost asso-
ciated with transporting a hundred weight of milk. The
average length of trip decreased from 65.1 miles in the model
representing the existing conditions to 59.5 miles in the
theoretical model making these savings possible.

The following general conclusions can be drawn from

this study:

1. It is possible within the perfect market concept
to develop s most efficient system of supply areas.

2. The correct price variation among the market will
insure total cost minimization.

3. Price variation is a function of the characteris-
tics of the market in relation to the basing
point.

4. The f.o.b. city plant prices must be greater than
the basing point price minus the variable cost of

transportation between the basing point and the
vi

S.

6.

market if the supply area boundaries are to be

defined.

The fixed costs of transportation must be included

<1n the f.o.b. city plant prices, leaving only the

variable cost to determine a competitive boundary

if supply areas are to reflect minimum cost.
The present system of supply areas does not insure
maximization of the average price paid to all

receiving stations and minimization of total costs

to the city plants.

Total costs can be decreased if the present system
of eupply areas are reorganized through price
variation adjustment in accordance with the model

deveIOped.

711.

CHAPTER

II

III

IV

V

TABLE OF COYTEHTS

Ir§T§ZODEJCTIoNIOOOICCOIOOOOOOOOOOIOOOIOOOOOIOOI.

Objective and PrOblemeeeeeeeeeeeeeeeeeeeeeee
Theorfit1cal Frameworkeeeeeeeeeeeeeeeeeeeeeee
HyPOtheeiseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

REVIEE CF LITERATIRE

IntrOdUCtianpeeeeeeeeeeeoeoeoeeeeeeeeeeeeeee
Literature 39'1eweeeeeeeeeeeeeeeeeeeeeeeeeee

METHODGLOGY A¥D PROCEDURE

Study Settingeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
The Theoratical Hoaeleeeeeeeeeeeeeeeeeeeeeee
Market Requirement3......................ooo

Market supply.eeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Supply Areas and Market Prices.............o

Price Variation Formula.....................
AfiALYSIS

Section I

Panniatloneeeeeeeeeeeeeeeeeeeeeeeeeeoeeeee
Rarket Area RBQUlrementBeeeeeeeeeeeeeeeeee

Milk Available to the Marketing Areas.....
Transportation COStBeeeeeeeeeeeeeeeeeeeeee
Market SUPply Areas...............o.......

Section II 9 Price variationeeeeeeeeeeeeeeee

Factors Affecting Price variation.........
Location in Re erence to the Basing

POlnteeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Relationship with Competing Markete.....
Effects of Density of Production........
Relationship with the Surplus Area......

Pr1ce Variation FOMUla-g.gogggogoooeeeeeee

COMPARISON OF THE PRESENT SUPPLY AREAE EITH
THE THEORETICAL

Section I - The Present Supply Areas........
viii

Page

OHDF‘ 0‘

-q-q

16
18
18

19
19
20

as
25
25
40
49

51
53

53

66
73
77

85

TABLE OF CONTENTS - continued

CHAPTER Page
Section II - Comparison of the two Models.. 91

VI SUMMARY AND CONCLUSIONS.....o................ 104

anDIxA OOODOOOIIOOOCCOC...OOOOOOOOOOOOOOOOOOOOOOOO 109
APPENDIXB00....OIOOOOOOOOCOIOOOOIOOOOOOOOOOOOOOOOOOO 112
APPENDIXC .0...OOOOOOOOOOOOOOOOOIOOOO0.0.00.00.00.00. 114

APPENDIX D OOOOOCOOOOCOOOOQOIOCOOOOOOOCOOOOOOOOOCOOOOO 116
APPENDIX E OOOIOOQOOOOOOOOOOOOOOOOOOOOOOOOIOOOOOOOOOOO 120

APPENDIX?OCOOCCIOCOOCIOOOCQ.OOOOOOOOOOIOOOOOOOOICOCO 124
BIEIOGRAPHY OOOOOOOOOQOOIO0.00.0.0000...OOOOOOOOOO... 131

ix

LIST OF TABLES

Table Page

a-1 Cities in Eichigan with a POpulation of AO,OOO
or more Eased on the 1960 Census............ 24

4-2 Fluid Milk and Cream Requirements in Nilk
E uivalents for the Nine Marketing Areas in
Michigan, November 1959..................... 26

h-B Total Nilk Production in Lower Michigan by
county. 1959......OOOOOOOOUOOI.00.00.00.000. 27

«-4 Fluid Milk Available to the Nine Marketing
Areas in Michigan, November 1959............ 33

4-5 Fluid Milk Imports and Exnorts, Michigan,
NOVQKIber 195900.00000000000000000000eeeeeeee 39

4-6 Price Variation in Units among the Nine
Marketing Areas in Michigan for November
1959 as Determined in the Theoretical

Modeleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeoeeesee 52

4-7 Basing Point Variable for the Nine Marketing
Areas in Michigan. November 1959............ 59

4-8 Location and Competing Market Variable for
the Nine Marketing Areas in Michigan in

unitaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 65

4-9 Area in Square Miles Needed to Fulfill the
Market Requirements of the Nine Marketing
Araafi 1n MIOhigan. November 1959eeeeeeeeeeee 70

4-10 Computation of the Density Variable for the
Nine Michigan Marketing Areas, November

lgsgeeeeeeeeeeeeeeeeeeoeoeeeeeeeeeeeeeeeeeoe 72

4-11 The variable Expressing the Relationship

Between the Markets, the Surplus Areas,
and the Basing Points for Nine Michigan
Marketing Areas. November 1959.q............ 75

LIST OF TABLES - continued

Table
4-12

4-13

5-1

5-2

Price Variation and Variables for the
Nine Marketing Areas in Michigan,
November 19590eeeeeeeeeeeeeeeeeeeeeeeeeeeee

Estimated Price Variation for the Nine
Marketing Areas in Michigan, November 1959..

Price Variations and Corresponding f.o.b.
Plant Prices Based on the Southern Mich-
igan Marketing Order Location Adjustments
for the Nine Marketing Areas in Michigan...

Longest Distance Traveled and Perimeter at
that Radius for the Supply Areas Devised
on the Basis of the Existing Price
Variation for the Nine Marketing Areas in
Michigan, November 1959....................

Total variable Cost of Transportation for
the Nine Marketing Areas in Michigan,
Novomber 1959......OOOOOIIOOIOOOOOOI0.00...

xi

Page

79

82

86

94

100

FIGURE

3-1

4-1

4-2

4-3

4-4

4-5

4-6

5-1

LIST OF FIGURES

Page
Marketing Areas in Michigan 1959............. 17

Theoretical Supply Areas for the Nine
Marketing Areas in Michigan, November

1959....................................... 50

Maximum Distance Factor for Computing the

Basing Point Variable for the Nine Mar-
keting Areas in Michigan (In 10 Mile Units) 60

”x" Axes Used to Estimate the Relationship
of Competing Markets for the Nine Mar-
keting Areas in Michigan, l959............. 52

Pounds of Fluid Milk per Square Mile
Available to the Marketing Areas,
NOVOMber 1959eeeeeeeeeeeeeeeeeeeeeeeeoeeeoo 6?

Estimated Angles Between the Supply Area
Boundaries for the Nine Marketing Areas
for Michigan, November l959................ 59

Distance to Detroit and the Surplus Areas
From the Nine Marketing Areas in Michigan
(In Unite or T9“ M1188)eeeeeeeeeeeeeeeeeeee 76

Location Adjustments Under the Southern
Michigan Marketing Order................... 87

The Supply Areas for Nine Michigan Marketing
Areas, November 1959. Using Location

Differentials Provided-The Southern Mich-
igan Order, Effective February 1, 1960..... 89

Theoretical and Existing Areas for the Nine
Michigan Marketing Areas, November 1959,
Super mposed............................... 92

Average Length of Haul per Tanker Load in
the Theoretical Model for the Nine Mar-
keting Areas in Michigan, November 1959.

(In Units of 10 Miles 101

xii

LIST OF FIGURES - continued

FIGURE Page

5-5 Average Length of Haul per Tanker Load
in the Existing Model for the Nine
Marketing Areas in Michigan, November
1959 (In Units of 10 Miles)................ 10?

xiii

CHAPTER I
INTRODUCTION

The allocation of a given supply of fluid milk among

competing markets is a function of the price offered by
those markets. Transportation costs. density of production,

and market location must be considered in establishing these

prices if the market supplies are to be adequate and secured

in the most efficient manner.1

Objective and Problgg

Southern Michigan. as any area encompassing a number
of markets, is subject to supply area inefficiencies. These
inefficiencies generally come about through a misallocation
of the available supply. A major factor to be considered
in rectifying these inefficiencies is the interrelationship
of prices among the markets.

It is the objective of this study to devise a set of
supply areas for nine Southern Michigan marketing areas
which are consistent with the objective of adequately supply-
ing each market with its fluid milk needs while minimizing

 

chr the purpose of this study efficiency is defined

as securing an adequate supply of milk for all markets at the
lowest total cost for all c ty plants and the highest average

price for all receiving stations (producers). For further
discussion of efficienc refer to Scitovsky. Tiber. Welfare
and Competition. R.D. ruin, Inc.. 1951.

1

total transportation costs.

A further task is to determine the variables affect-
ing price variation and to construct a formula in which they
may be used in a price predicting capacity.

As an ultimate objective it is heped that this study
will be beneficial to all who have a general interest in
orderly milk marketing.

Theoretical Framework

The interaction of the laws of supply and demand de-

termine the market price of a commodity under conditions of
perfect competition.1

If demand exceeds supply price will be bid up and the
supply will tend to increase. Conversely if supply exceeds
demand the price will tend to decrease. Eventually. through
a series of price quantity adjustments. a point of balance
between supply and demand will be reached. This is said to
be the point of equilibrium.

The supply side may be affected by many factors.

Von Thunen early in the nineteenth century combined
the place and form aspects of the perfect market model in
an attempt to explain agricultural production about an iso-
lated city. In essence his theory states that as one moves

away from the city. production becomes less intensive and
becomes increasingly devoted to production of items that are

h

1For a detailed discussion of the Laws of Suppig and
0

Demand refer to R. H. Leftwich, The Price 3 stem and source
Allocatfigg. Rinehart and Company. InEJ,'HéW York. 1§53 ahaptarB
0

PP e

 

 

 

 

relatively less perishable and whose value is great enough
to bear the cost of transportation.1

Milk being convertible into many forms serves as a
good illustration of his principle. If the principle holds
we would eXpect to find the more perishable and bulky pro-
ducts produced near the centers of pepulation. On the basis
of bulk alone we would eXpect fluid milk to come from the
nearby areas and butter from the most distant. If per-
ishability is the primary concern we would again eXpect to
find fluid milk produced in the nearby areas with condensed
milk coming from the most distant areas. These tendencies
become evident when looking at local markets or the united
States as a whole. The Detroit metropolitan area secures
more than eighty percent of its fluid milk from twelve sur-
rounding counties but relies on the large surplus areas of
the midwest for much of its butter, cheese and condensed
milk. The production on the East Coast is similarly devoted
to fluid production as population in that area is intense
and again relies on the midwest surplus area for most of

its manufactured products.2

Diagrammatically Von Thunen's Principle looks as

follows:3

 

10. Quackenbush. "The Perfect Market, Von Thunen's
Principle, Fetter‘s Law of Markets." Michigan State Univer-

sity, Agricultural Economics Department, mimeograph, 1958.
2lbid” p. 4.

3John M. Casssls, A Stud of Fluid Milk Prices,
Harvard University Press, 1957, p. 20.

s

The boundary line between two
areas is defined by the form-
ula P1 - TIE a P2 - T2R where
P1 equals the price of one
hundred pounds equivalent cf
milk made into product 1.1,:

transportation rate for pro-

 

duct 1.1’2 a city price for one hundred pounds equivalent of
the original product made into product 2 and i'a :- the associ-
ated transportation rate. The equation is solved for R.

when considering the milk industry several modifying
factors must be kept in mind when discussing Von Thunen‘s
thesis:

1) Natural boundaries

2) Overlapping metropolitan areas

3) health regulations

4) Competition of manufactured products from distant

surplus areas.1

In discussing location theory with reference to two
markets Fetter'e Law of lsrkets is useful. In brief
Petter’s Law states that the boundary line between geograph-
ically competing markets or territories is a hyperbolic
curve. At any given point on the boundary line the dif-

 

G. M. Deal and H. H. Bakken. Fluid Milk Marketi .
nimir Publishers Inc... Madison. Macon-In. I553. P99 550

ference in transfer costs is just equal to the difference

in market price.1 From this it can be seen that prices in
different markets determine the location of the boundary
line between them.

When placing the milk industry into Fetter's context
we are confronted with a centripetal market or one that is
characterized by the movement of goods toward the market.2

When considering a single market Fotter's Law says that
price will vary from the base price at the market center only

by the cost of procuring the product.3 fihen two markets are

considered the law would read that the prices received in
either market cannot vary by more than the shot of transporta-

tion between them or, in other words. price differences can be
only less or equal to the differences in transportation costs.4

Based on Potter's analysis it can then be said that
the size of a given supply area is a function of the market
base price relative to its geographical competitors or that
the supply area of competing markets is a function of the ‘
differences in freight costs. base price remaining constant.

The boundary curve will change in location and in shape
with changes in price but will always be curved around the
market with the lower price and away from that with the

 

 
 

1Frank A. Fetter, ‘
Brace and Company. new York. 951. P. 2 3.

2M" Fe 2790
_31b1c.. p. 233.

z“£32.;er Fe 2821-. I

. Harcourt,

 

we‘lnl a l ‘L \s . I -. ,. h..'..“‘b.ul ell 5..
a

higher price.1

It should be noted that even if freight rates are not
constant per unit the concept will hold altering only the

shape of the curve.

'Jans wtm e

Eithin the above framework the basic hypothesis of
this study can be stated: The efficiency with which given
ponulationa acquire their supply of fluid milk is determined
by the interrelationship of the prices existing in the in-
diviiual ma-ket.

Various hypotheses concerning these price relation-
ships and the factors which influen.e than will be stated

in later sections of this study.

 

11bid., p. Efifi.

m)?‘ -\ ‘ ...l 3.‘..-.r..n..,4u
.g

CHAPTER II
REVIEW OF LITERATURE

Introduction

A number of studios havo boon msdo concerning fluid

milk supply cross for various citios. Likowico thoro oro a
numbor of published works concorning oinglo Icrkot and intorb
ncrkot pricing of silk. Works combining thoso two along
with tho applications of gonoral location thoory hovo boon
for. The otudy o! thooo osrlior works. hovovor. givoo tho
broad boois on which this otudy hos boon built.

Litorcturo Roviow

According to Ccosolo. fluctuations in tho sizo of mar-

kot supply cross for s givon commodity can bo diroctly cor-

rolctod with fluctuating supply and donsnd oquilibrium

1

points. rhooo chsnging equilibrium points cro folt to bo

tho rosulto of thooo in tho narkot cooking tho boot possible

Isrkot outlot. thus forcing pricoo that will oquclizo tho
odyuntsgoo ond diocdvsntcgoo of tho dittoront outloto.2

 

1
92' cit., John M. Csssols. p. 19.

2
.IElQ-t p- 18°

. ,
O
1
y u o
. ‘
1 4
L: J
y
u 4
1 o
I I‘ o o?
I
. I I
4
f
o
D O .
. - . t
.
I .
a .
c
o
c . . .
V. t
I
o .
u
a , u
o
‘\
o .
.
girls: I. l! k_ . . . o ‘ll \ : I.‘..'ul.h€l§ ”é

Based on a Von Thuncn typo analysis, Casscls sets up

the following model.1

300
The Relation of the Price of Milk
to Distance from Market in

ifforcnt Product Zones

2°° NW

Milk Cream
Zone Zone Zone

 
 
 
 

100 ‘

isthmusporlhc

ludco

 

 

 

 

 

o""'""'so" """"'""'Io$""' ' I56 200
Distance in Miles

Prics itself doponds on tho interaction of supply and

donand. Tho supply dopondo on tho area snolosod by tho
zcno boundary. On this booio it can bo soon that o chango
in any ono of the factors influencing the equilibrium point
would causo a roadjustncnt of tho markoting arcs.

Cassols' considoration of two markets reverts back to
a Fottor typo analysis. Harkot size. being affected by tho
supply and demand oquilibriun point. will bo equal and the
two markets will bo asparatsd by a straight lino if their
pricos aro oqual. Equal changes in price will bring about
a similar adjustmont in both markets. tho boundary line

 

1John H. Casssls, ngcit.. p. 21.

remaining straight and any point on it will be an equal dis-

tance from tho cantor of oithor market.1

thro prices differ between markets wo have a hyper.

bolls curve as a boundary lino. Each point on tho boundary
will have an a-bax ( x boing constant ) relationship botwoon

tho two markots. Tho market area changes as does tho prico
thus altering tho shapo of tho hyporbola. Tho hyporbcla
always tonds to bo convex toward tho higher priced market
onclosing tho lcwor prico markst.2

RoJko, liko Cancels. whon considering an isolatod mart

kot boliovoo spocializod canon of production arc croatod

based on economics obtainable from shipping concontratod

dairy products long distances.3

Whoro dairy products news botwosn sovoral markots thoir
pricos tond to differ by transfer costs. tho largost being

transportation. Whoro regional covenant occurs, as with
nannfacturod dairy products. pricos sro said to bo dotorcinod

on a national markot and prices among narkots are closely

rolstod.4

RoJko’s nodal illustrating tho above is as follows:5

IJohn H. Cassols. op.cit.. pp. 27-30.
21bid.. p.30.
3Anthony S. RoJko. Tho Demand and Price Structuro f
Daify ngdugtg, (washington. 5.5.: 3.3.5.3.} TocEfiIcaI
O tOs 163. 1953s p.201.

n
“933.. pp. 201.204.

slbldog p.209.

10

Milk in Manufacturing and Fluid OutletszPrice
Premiums in Specified Areas

\fi)
(3

U .

tysanyswmuyenuuua1nusd

 

 

 

 

 

A E
w
0 w # 1 w _... HO
u- ‘ 1 I . s
”Region A Region B _..—_.....”
Distance '

The base lino u n represents any number of producing areas
and consuming centers. The elevation of u w.fron u skis the
amount ever u manufacturing milk is worth at any given point.

Prices of fluid milk are closely related among regions
only when interregicnsl sowenent of fluid silk products can
or could occur. As noted earlier.fluid milk prices are
related directly to manufacturing prices in an isolated mar-
ket. Reiko states that when several consuming centers some
pets with one another for milk from several common producing
areas. prices of milk for fluid use in each.larket may not
be directly related to prices of milk for'nanufscturing cut-
lets. Instead. prices are determined by the supply and de-
mand for fluid milk in the local market and byprices of
silk produced primarily for fluid use in competing or nearby
markets. Based on this. only those markets at the edge of
the surplus area would be directly related to manufacturing
milk prices.1

1Anthony S. RoJko. op, cit.. p. 203.

11

On the previous graph 1 is the point of indifference

between producing mamfacturing milk and fluid milk. and

w . A is the added premium needed to, produce fluid milk.

If there were a close relationship between markets. the price
of fluid milk would take the form of ABC throughout region

B. This is equal to the price at A plus the transportation
cost to other points on the line. If the supply demand re-
lationships between the markets are not interregicnal then

a line such as ABD would represent the prices received}

Hoover. also drawing from Fetter‘s concepts. says that
the res supplying a market will be determined by the pro.
duct cost plus minimum transportation costs.2 He uses the
concentric ring concept to illustrate loci of different
points of equal cost. (product and transportation). When
two markets are considered. the boundary line represents the
locus of all points of equal cost and will be either a straigxt
line or hyperbolic curve depending upon the price rev-
lstionship.

Andes.3 also concerned with market areas and boundaries.
stated that as the amount of fluid milk consumed in a mar-
ket is rather constant while costs of transporting dif-
foront dairy products vary with the product. distance be-

 

Mss p. 201‘s
2mm. Hoover. Locati n Theory and the Shge and Leather
We Cambridge, Stassaghuse s. {am ivers y rose,
19‘8.
3James Andes. Zroblemg in the E232 Sugglug Plan in the
Philadel his Milkshed. University of Pennsyhnia: Un-
SIIsE 5 R 3 E I

p“ O. Q o 68 8. 1937) ppt 11-12.

 

12

comes a factor in determining price. and that price de-
termines the milk shod or supply area.

Hoover describes the bssing point system as estab-
lishing price patterns in which delivered prices of all sell-
ers or buyers grade up or down according to freight rates
from a designated basing point. The basing point is usually

located in a large production area if it's a sellers market

or in a large consumption area if it's a large buying market

such as with fluid milk.1 Reever says that the economies

of long hauls make boundary lines sharper curves than hyper-
bolas and also account for the fact that one market or
supply area may completely surround another.2

One of the first applications of location theory in

developing supply areas for fluid milk for a given area was
done in Connecticut by flames-berg. Parker. and Bresslet'.3
They defined a market as a population or area subject

to the same general economic forces. The most efficient
supply areas for a combination of these markets would be de-
rived ss a result of competitive bidding for the available

milk supply. this in turn would equate supply and demand
and determine the various price relationships between the

 

1
Edgar :4. Hoover o ati n o Ec A
(New York: scores 3111' , . p. . is
2&0. p. 61.
3

mo. Hammerberg. LN. Parker. and mm Bresslerflrn

Efficienc of Milk Marketin in Connection Satorrs.
Writs pm. 1.
mu0‘1n. NOe 2 7' 1942

13

markets.1

It was noted that market pepulation and density of

production will determine the size of the supply area needed

and that in turn these should affect the prevailing market
prices.2

The major conclusion drawn from the study was that it
is possible to allocate producing areas to milk markets in
a manner'that will minimize the costs of moving milk from
farms to markets.

Bredo's and RoJko's study in Massachusetts in 1952

was directed along similar lines.3 Answers were sought to
the following questions: 1) how efficient are price re-
lationships between milk markets. 2) how adequate is the

adjustment in the location of milk supply areas in these
markets. and 3) what is the amount and process of adjust-

ment in milk prices and supply areas among Northeastern mar-

kets under varying economic conditions.4

The results of the study showed interregional and

intermarket movements were hindered by varying quality stand-
ards. This in turn was found to hinder the efficiency of

the resulting milksheds in most of the regions.5 It was

 

11b a.. p. 4-6.

Ibid.. p. 17.
3

e. Bredo and Anthony S. Rojko. Prices and Milksheds
2f Ngggheastern MarketsI Massachusetts gr c ura x-
porimsnt Station, Bulletin No. 470. 1952.

4Ibig... p. 8.

Ibid.. p. 71.

14

found that small deviations in price were all that were

required between cities to insure efficient supply areas.

On this basis it was felt that by eliminating the costs

of price and market uncertainty the theoretical and observed
intermarket prices would be approximately the same and pro-
vide for an efficient supply area.1

Prices in and among markets are often predetermined

by Federal Milk Marketing Orders.2

Federal Orders establish a minimum f.o.b. price at
the basing point of the marketing area. Prices paid or
received in other markets within the marketing area are
then influenced by the location adjustment applicable to
their location. The resulting price in any of the markets
is equal to the f.o.b. basing point price minus the loca-
tion differential.

The purpose of these differentials is to make possible
the procurement of milk throughout the supply area at a
uniform cost to all handlers.3

The location differentials are based primarily on.
transportation costs although convenience, certainty.

seasonal uniformity, etc.. are also considered. The dif-

ferentials fall generally into two categories: 1) those

 

1w. Bredo and Anthony S. RoJko. op,cit.. p. Tl.

2"Regulations Affecting the Movement and Merchandising
of Milk." Market Research Report, No.98. U.S.D.A.

Agricultural Marketing Service. 1955.
31239.. p. 61.

 

r14 .1
.
' g
.
v e e L
n 1
.u n r.
. .
a
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r
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t
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r.
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0
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u .
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.
.

 

15

extending over an infinite area, and 2) those that reach
out only a given radius. The latter in particular. if not

properly adjusted to the supply requirements of the market,

serves as a barrier to milk movements into the market.1

The above studies all represent valuable contributions

toward a better understanding of the problem at hand.

11 kid. . 13. 61s

CHAPTER_III
METHODOLOGY AND PROCEDURE
Study and Setting

Ten cities in Michigan's lower peninsula were selected
for detailed study. These were Bay City, Battle Creek,
Detroit. Flint. Grand Rapids. Jackson, Salamazoo, Lansing.
Huskegon, and Saginaw. These cities and their metropolitan

areas contain 75.6 percent of the pepulation in Lower Mich;

igan and thus provide the primary outlet for fluid milk and

Ofluel

The cities and their metropolitan areas have been com-
bined into nine marketing areas. as shown in Figure 3-1.
In all cases the marketing areas are the same as the metro-
politan areas except for the Bay city and Saginaw areas

which are combined because of theiriproximity.
To achieve the objective of maximizing efficiency

based on the criteria set forth.in the previous chapters.

 

v 1The definition of a metronolitan area as used in this
study is any county within which a city of 40,000 or more

persons is located. Where two or more continuous counties
satisfy this condition they may or'may not be considered as

one metronolitan area depending on the location of the
major population concentration and other characteristics

of the area.

16

 

“i

‘1".‘52

r paufl.‘ , 3.1. figulllnlyuil
r
3
u

    

17

\

CNEsoch

N

J

/

_l/

 
   
 

PRESQUE
ISLE

 

 

 

 

  

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

OTSEco NONTNORENCT ALPENA
{RALKASKA CRAWFORD OSCOOA ALCONA
‘GRAND
TRAVERSE
WEXFORD MISSAUKEE rnoscouHON OGENAW IOSCO
MASON LAKE OSCEOLA CLARE GLAownI ARENAc
HURON
sA
OCEANA NEWAYGO MECOSTA ISABELLA MIDLAND
TUSCOLA SANHAC
AUO" Aw BAY -
NONTCALN GR SAGINAH
APEER
SAINT CLAIR
IONIA CLINTON
O
chfin FLINT
RAPIDS AKLAND
e
LIVINGST N
I GHAM
ALLEGAN BARRY EATON
IANSING
WAYNE
WASHTE Aw
VAN sUREN HOUN DETROI .
. TTLE CREEK
KALAMAZOO JACK§0N
“RR'WCASS SAINT 105er s ANCH NILLscALE LENAWEE
L-
LA PORTE SAINT JOSEPH ELKHART LAGRANGE STEusEN was
/ I - I I I .wuLLIAwS |'U'-'°N \
Figure 3-1

Marketing Areas in Michigan, 1959

Each Marketing Area is composed of one or more Metropolitan

Areas.

A Metropolitan Area is defined as a county containing

one or more cities with a population of 40,000 or more.
POpulation data based upon the 1960 census.

18

certain assumptions concerning the operational characteristics
of the markets must be made.

It is assumed that producers will want to maximize the
price they receive for their product and thus ship to the
market paying the highest price. Handlers will act in a way
which.will minimize their costs of procurement and thus pur»
chase the product as near to the market as possible.

A second necessary assumption is that of absence of

price makers in the market. Under this condition neither
the producer nor dealer can influence prices received for

their products or prices paid for inputs used in producing

the final products.

The Theoretical Model

The model is constructed on the basis of data for 1959.
Supply areas are set up on the basis of supply and demand
data for November of that year. November is chosen as it
is usually the month of lowest total production. Because of
this. supply areas that are applicable during November will
also be of sufficient size to supply the market requirements
during the remainder of the year. As noted in Appendix A,
there is a significant difference in total milk production
between the high production month of June and the low pro-

duction month of November.

Market Requirement

The amount of fluid milk required to fulfill the needs
of a market is a function of the number of peeple in that

19

market and their per capita consumption. In the model 1960
census datazme used to determine the population of the mar—
kets. Consumption is determined on the basis of the 1959
per capita consumption of fluid milk and cream in milk
equivalent. Fifteen percent is added to this amount to

allow for variations in consumption and production.

Market Supply
The available supply of fluid milk for the marketing

areas is based on total milk production data. Total milk
production is determined for each county and is based upon
average production and the number of cows in the county.
Deductions are made from the total to take into account milk
produced which is not of fluid quality, milk used on the
farm for other than human consumption, and that milk which
is consumed by persons living outside the marketing areas.
From the above net figures the total supply of milk of fluid
quality available to the marketing areas is determined by
adjusting the data for net exports or imports and making an

allowance for deficit counties outside the marketing areas.

Supply Areas and Market Prices
With the available supply determined and the market
requirement known, supply areas for the markets are simulta-
neously determined. In essence, the procedure is that of
successive approximations until supply and demand are equated
for all markets. As will be discussed and illustrated in

Chapter IV, these supply areas involve no cross hauling or

20

overlapping and the total transportation costs involved are
minimized.

When the supply areas are determined the exact market
price and price relationships among the markets are also doe
termined as each.must be such as to secure the appropriate
supply. Prices and price variation among the markets are in
relation to a base price f.o.b. city plant, Detroit. The
Detroit market is used because it is the most distant market
from the surplus area of those being considered. It also
contains 67.7 percent of the papulstion under consideration.
and thus has the largest demand. and as will be seen in
Chapter IV, is the market which must travel the greatest dis-

tance to satisfy its requirements.

Price Variation Formula

A formula expressing the price variation found to be
consistent with efficient supply areas is constructed in
Chapter IV. The variables used in the formula are those
found to have been important in determining the supply areas.
They are density of production. papulation. distance to
basing point. and relationship with the surplus area. Co-
efficients for the variables are determined by regression
analysis. The coefficients are then applied to the variables
to obtain estimates of the price variation. By comparing
the estimated price variation with those found in the model

the formula is tested for accuracy. This formula can then

be used to predict the correct price variations for the given

 

llIrLinell ,. I lartilllJIJI-‘ni

,.
.<

Pl

markets, though time as the values of the variables change.
Under the Southern Eishigan marketing Order price
variation among the markets is essentially fixed by the
applicable location adjustments set forth in the order for
the county in which the market is located. In Chapter V a
set of supply areas is constructed using the same procedures
as in the model except market prices are taken to be those
indicated by the Federal order. In section 2 of that chapter

a comparison of the two sets of supply areas is made.

CHAPTER IV

Analysis

The objectives of this thesis, as stated previously.

are to determine the most efficient supply areas for nine

centers of pepulation located in Michigan's lower peninsula
and to construct a formula which will reflect and can be
used to compute price variation among these markets.

The first section of the analysis deals with the con-
struction of a model in which the supply areas for the nine
markets are determined. In deveIOping the model. pepulation,
market requirements. milk production and transportation costs
are taken into account.

In section two the price variation formula is develop-
ed. The variables considered include the density of pro-
duction, the relative size of the population centers. the

relationship between the market and the surplus area. and

the distance to the basing point.

Section 1
Population

According to the 1960 census there were 7,778,200

people bring in Michigan. of which 96 percent were located

in the Lower Peninsula.1

 

fUnited States Department of Commerce, Bureau of the
22

 

.41..

23

Theoretically every source of demand regardless of
size has a corresponding supply area. In the case of a self
sufficient unit, the supply area consists of the area do-
voted to producing the product. In the case of villages.
towns and cities the supply areas consist of the location

from which the product is secured. To make a manageable and

perhaps meaningful analysis of an area. however, the number
of markets to be considered must be limited to those which
are of a dominant size.

As indicated in Table 4-1. there are twenty-two cities
in Lower Michigan with a population of 40.000 or sore.1
Seven of these cities and their respective counties comprise

seven of the marketing areas under study. (See Table 4.1)
Bay City and Saginaw and the counties in which thgy are lo-

cated comprise the eighth area. The ninth area is the De-
troit market which encompasses the remaining thirteen cities
and the counties in which they are located. The exception
to the above is Washtenaw county of which only half is con-
sidered a part of the Detroit marketing area.

The nine areas described above composed of about 13
counties include 75.6 percent of the total pepulation in

the lower peninsula and all areas of pcpulation concentratkn:

of greater than 40,000 persons. They constitute the dominant

demand forces in Lower Michigan. The remaining 24.4 percent

Census re inar Re orts Po ula 1 ns Counts for States
PC (53’ - 5% ingusi. I935. p. l.

l
.cit. Preliminar Re rts Population Counts for
Statehm'pm-g. ’ po ' ‘

 

 

2h

TABLE 4.1

CITIES IN MICHIGAN WITH A POPULATION 0? 40,000
OR MORE BASED Ofl THE 1950 CENSUS

 

 

Population County in Marketing
City 1960 Which City Areas to
is Located Which City
Belongs
Ann Arbor 57.547 Washtenaw Detroit
Warren 88,766 Macomb Detroit
Roseville 50,676 Macomb Detroit
Pontiac 81.651 Oakland Detroit
Detroit 1.654.125 Wayne Detroit'
Dearborn 111,077 Wayne Detroit
East Detroit 45,925 Macomb Detroit
Lincoln Park 53,225 Wayne Detroit
Livonia 68.539 Wayne Detroit
Royal Oak 81.140 Oakland Detroit
St. Clair Shores 77.879 Macomb Detroit
Wyandotte 42.214 Wayne Detroit
Wyoming 45,712 Wayne Detroit
Battle Creek 44,003 Calhoun Battle Creek
Bay City 53.247 Bay Bay City
Saginaw 97.031 Saginaw Saginaw
Flint 19h,958 Oenesee Flint
Muskegon 45,925 Huskegon Muskegon
Grand Rapids 175,3hh Kent Grand Rapids
Lansing 108,128 Ingham Lansing
Jackson 50,2h4 Jackson Jackson
Kalamazoo 81.8?3 Kalamazoo Kalamazoo

_‘_

1/ United States Department of Commerce, Bureau of Census:
Preliminary Reports, Population Counts for States,

August, 1960,

3-5.

 

”=5

lfilfl‘rl,

of the papulation in the state is much less concentrated.

Market Area Requirements
The average per capita consumption of fluid milk and
cream (on a milk equivalent basis) for the United States
is used to determine the market requirements. In 1959 this

1 This is equivalent to 28.603 pounds per

was 348 pounds.

person for the month of November. The market requirements

for the nine areas for Rovember. 1959. are shown in Table 4-2.
To allow for fluctuations in market receipts and con-

sumption fifteen percent of the normal per capita consumption
is added to each.market. This allowance for fluctuations is
consistent with the allowances made under most Federal kar-

keting Orders.

hilk Available to the harket Areas

The amount and location of milk available to the con-
suming centers is derived from total production figures on
a county basis. Table 4-3 shows the computation of the
total available milk supply.

The number of cows and heifers two years old or older
by county are indicated in column 1 of the table. To de-
termine the total number of cows producing milk a deduction
must be made from the number of two yeaerlds and over for
those which are not producing. To make this allowance the

Michigan Crop Reporting Service' data relating to number of

 

1:10:11 5
a gen Department of Agriculture kichi an
‘égricultural Statistics, July. 1960. p. £6.

26

TABLE #-2

FLUID MILK AND CREAM REQUIREMENTS IN MILK EQUIVALENTS
FOR THE NINE MARKETING AREAS IN MICHIGAN
FOR NOVEMBER 1959

Total Market
Fluid Milk a Cream Requirements

. Population Requirements for including 155
;/ Novembgg 1959 g/ allowance 2/
8e

 

Marketing Area 1960 (lbs.)
B.;.1. Creek 138.378 3.953:O26 4.551.730
Bay City-Saginaw 294,831 8,433,051 9.698.009
Flint 370.303 10,591.77? 12,180,544
Muskegon 148,950 4,260,417 4,899,480
Grand Rapids 360,574 10,313,498 11,860,522
Lansing 211.639 6.053.367 6.961.372
Jackson 130.948 3.745.506 4.307.332
Kalamazoo 169.151 4,838,226 5.563.960
Detroit 2,§2§,4§5 ;02,412,482 ;2§.822,41g
Total 5.650.224 161,613.35? 185.855.360

A.

;/ United States Department of Commerce. Bureau of the
Census P l - ar Re 0 Po ation Cou ts for S ates
PC (PI, ugus *

Population of Marketing area times 28.603, the per
capita consumption of fluid milk and cream for November, 1959.

Fluid milk and cream requirements for November. 1959.
plus 151 of that amount.

h. I...“

 

’1‘ I, J N ‘I‘

27

  

 

 

 

 

 

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31

milking cows is used.1 It is assumed that the ratio of

cows two years old and over to the number of milk cows is
constant. The percent of the total cows two years old and
over in each district is determined and that percentage
applied to the number of total milk cows. This approxima-
tion of milk cows per district is shown in column 3 of the
table. In a similar manner the percent of cows two years
old and over in each county is determined and that figure
applied to the total milk cows per district to determine the
milk cow numbers in each county, as shown in column 4 of the
table.

Production per cow was found to vary by district in
1951.2 The variation ranged from 5664 pounds per cow in dis-
trict two to 6973 pounds per cow in district nine. It is
assumed that a similar variation has existed since that time.
Based on the above the percent variation from the overall
average in 1951 is computed for each district and that per-
centage applied to the 1959 average production to determine
the average production per cow in each district. These

figures are shown in column 5, Table a.3. The computations
of the averages are shown in appendix B. Total production

per county can now be computed as in column 6 by multiply-

ing the number of milk cows in each county by the average

 

leptclto. ‘ich 38.“ A cultum S atistica p. 37.

2MiohiganDepartment of Agriculture, Dairy Trends in
Michigan. JUDO. 1955. p. 16.

32

production per cow for the apcrOpriate district.

As discussed earlier, the theoretical model is con-
structed on the basis of the November 1959 supply and de-
mand. As noted in Appendix A based on a ten year average
November production has averaged 7.21 of the yearly pro-
duction. when this percentage is applied to the total
production figures for 1959 the November production per
county is determined. These figures are shown in column 7
of Table 4-3. f

To determine the amount of fluid milk that is available
to the marketing areas certain deductions must be made from
the total milk produced. These deductions are shown in

Table 4-4.
The deduction that is made for milk utilized on the

farm as livestock feed and in producing butter amounts to
3.4% of the total production.1. The net figures on a county
basis are shown in column 2. Table 4-4.

It is also necessary to adjust the production figures
for that milk which is not of fluid quality or for milk
produced for manufacturing purposes only. A study con-
ducted in 1957 indicated that the volume of milk produced
for'manufacturing purposes was decreasing at the rate of

2 A

13.7% per year. more-recent study conducted in October

 

1Michigan Department of Agriculture. Opgcit.. Michigan
Agricultural Statistics. p. 37. '

20. kcBride and W. H. Blanchard. Chances in Michi en's
Manufacturing §'11§ industry, Michigan state finiversity,

Department of Agricultural Economics, Special-Bulletin a?7,
1959. pp. 18'19e

 

 

 

 

 

 

 

 

 

 

 

 

 

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37

of 1960 indicated a continuation of that trend at approx-
imately the same rate.1 When this percentage is applied to
the amount of manufacturing milk produced in 1957 an estimate
of production in November of 1959 is obtained. This estimate
is shown in column 3 of Table 4-4.2

Making the above deductions from the total amount of
milk produced gives us an estimate of the total fluid milk
available in the Lower Peninsula as shown in column 4 of
Table h-h.

To determine the portion of this amount available to
the marketing areas further deduction must be made for per-

sons living in counties other than those included in the

marketing areas. for deficit producing counties, and for the
net difference between exports and imports. The amount of
these deductions are shown in columns 5. 6. and 7 of Table
4-4.

Deductions for those counties outside of the marketing
areas are based on the population of those counties and
their per capita consumption of fluid milk and cream.

The Cleveland, Toledo, South Bend. and Chicago mar-
kets are the sizable markets located near Michigan. The
amount of milk of fluid quality moving to or from the Chicago
and South Bend markets was found to be negligible and thus

iG. McBride and W.B. Hellegas, nger Producers of
‘Mannzanfinzing_flilk, Michigan Farm Economics, No. 21 . Jan-
uar .19616032Eartment of Agricultural Economics. Michigan

Sta e Uni ty.

2Refer to Appendix C for computation of estimate.

 

 

sq..." .~‘

38

is not considered.1 That moving to and from the Cleveland
and Toledo markets. however, is significant and consequently
its effect on the total supply available must be taken into
account.2 As noted in Table 4-5 in both cases exports from
Michigan exceed imports. The excess of exports is deducted
from the total available supply as follows.3 In the case of
Toledo the counties from which the milk originated and the

percent of each county's contribution to the total is pub-
lished in the Market Administrator Report.4 These percent-
ages are used to determine the amount of the not export
which comes from each county and this amount in turn is de-
ducted from the available milk in that county. In the case
of Cleveland no such figures are available. The amount by
which exports exceed imports in this market are allocated
to the area in which the Cleveland receiving stations are
located. The allocation is based on the amount of milk

available in the county in which the station is located and

those surrounding it. The allocations are shown in Appendix

D and the amount is again shown in column 7 of Table 4-4.

 

1Based on discussions with Mr. G. A Swanson, Michigan
Cooperative Crop Reporting Service and information received

from plants which ship to these markets from time to time.

2 1
Data obtained from the Toledo. Detroit, and Cleveland
Market Administrators and the plans which are involved in
exporting_and importing of milk of fluid quality.

3See Appendix D for allocation to counties.

Toledo. Ohio Marketing area, Analysis of Producers
Receipts, for months of January. June. and December, 1959.

39
TABLE 4-5

FLUID MILK IHPORTS AND EXPORTS,
MICHIGAN, NOVEMBER. 1959

Milk Milk Exports from

 

imported e orted Hichigan in excess

to Michigan to he area of imports to

from the area from Michigan Michigan
Market- in November 1959 November 1959 November 1959
ing Area (pounds) (pounds) (pounds) ;/
Cleveland 387,142 2,413,982 2,026,840
TOIOdO ‘ ‘ 301.775 366.575 54.800
South Bend 2/ 2/ I as
Chicago 2/ _2/ .

 

'l/ For allocations of deductions see Appendix D.

3/ Negligible

Source: Personal interview with Mr. G.A. Swanson of the
Michigan Cooperative Crop Reporting Service, September. 1960.
Personal letters from Mr. George Irvine, Market Administraton
Southern Michigan Marketing Order, September 30, 1960,

Fr. R. J. Quaintance Deput rarket Administrator Toledo Milk
Marketing Area. September . 1960, Mr. A. w. Jolgm

Manager. Constantine Gosperative Creamery Campany, September.
30. 1960, and mr. A. Wiersma, Manager, Head Johnson and '
Company, September 30. 1960. ,

40

A final adjustment must be made for those counties
which do not produce enough milk to cover the above de-
ductions. It is assumed that these counties will obtain
milk from neighboring counties to take care of their def-
icits. The allocation of the deficit to neighboring coun-
ties is shown in appendix D. These counties as noted in
column 8 of Table A-h have no excess milk from which the
marketing area may draw. .

Column 8 of Table 4-4 indicates the amount of fluid
milk by county available to the market areas being examined.
In column 9 of that table the relative density per square

mile is shown.

Transportation Costs

To determine the most efficient supply areas for the
nine markets. it is necessary to again set forth the assump-
tions upon which this analysis is being made. It is assumed
that the receiving stations (representing the producers) will
sell to the point of highest return and that the city plants
will purchase from the points of lowest procurement cost.
Under the perfect market concept the cost of moving milk
from one point to another then becomes the logical basis on
which competitive choice is made.

Maxi-um efficiency is reached when the total costs of
transportation for all markets is minimized. It should be
noted that this is not necessarily consistent with minimiz-

ing the transportation costs of any one of the markets. Wifli

a1

transportation costs minimized the receiving station in
total will receive the highest average price for their milk.
and the city plants when all_markets are considered will be
paying a minimum amount to secure the milk.

To minimize the cost of transportation it is necessary
to determine how total transportation costs vary with dis-
tance. Total costs. or costs per mile times miles traveled,
are relevant for our purposes at it is these costs which
must be minimized.

The total cost of transportation is broken down into
three classes. fixed costs, fixed costs of Operation and
variable costs.

Fixed Costs - Fixed costs are those which cannot be
varied within the time period being considered. They 8P0
composed of costs such as depreciation allowances. licenses.
insurance, etc.

Fixed Costs of Operation - These are the costs which
can be varied within a given time period but which are fixed
and do not vary if the unit is utilized. The coat of load-

ing and unloading compose this cost item. This cost does

not vary with miles traveled and thus cannot be considered
a variable cost.

Variable Costs - The variable costs of transportation
are composed of costs incurred by drivers' wages. repairs.
fuel. etc.. which Vill vary within the given time period

based on the number of miles the means of transport travels.

The variable costs associated with milk hauling are

42

assumed to be linear in nature.1 That is. fuel costs, labor
costs. etc.. increase at a constant rate with miles traveled.

The following figure shows a general graphical rep-
resentation of these cost functions for a given size load

carried any number of miles.

Costs of Transportation

if:

TC

D / VC
0 /
s ///////

FCO ‘

FC

 

 

 

 

 

 

 

~— A

 

 

 

Miles (per unit of time)

As depicted in the figure price varies with miles traveled

by the increase in variable cost. The variable cost being

linear with distance. indicate a constant rate of increase

in cost with miles traveled or a constant marginal cost in-

dicating the addition to total cost of moving one more mile

is constant.

0n the basis of the above the concentric ring analysis

 

1
This assumption appears Justified and is based on
data examined by the author and on discussion with
Dr. E.w. Smykay, Associate Professor, Department of Mar-

keting and Transportation Administration. Michigan State
University. -

a:

used in constructing the model will consist of rings which

move out from the market origin at a constant rate. The

rings represent a constant increase in cost or miles. These
increases are equal to the increase in cost incurred by
moving a given number of miles or the number of miles that
can he traveled at a given cost.

The above does not suggest that the fixed costs of
transportation are unimportant or foregone. It does. however;
indicate that they are not functionally distributed on the
basis of miles traveled. but rather included on a cost per
unit basis in the f.o.b. plant prices.

Theoretically all milk consumed in a market must be
relocated from its point of production or collection. The
fixed cost incurred to move this milk will then represent a
portion of the value of that milk regardless of its source.
For this reason it should be included in the quoted f.o.b.
price.

The following example further exemplified the above.

In a concentric ring analysis with the rings varying
in radius by a constant number of units the lines of indif-
ference between the two markets or the lines defining the
market boundaries will take on the form of a hyperbolic

function. This function by definition will satisfy the con-
dition of A - B = K where A and B are the distances from

the two markets to the point on the boundary line. The con-
stant. K. is important as it relates the distance from B to-
ward A (the basing point) at which the hyperbolic function

44

will cross the x axis. In case 1, K is considered the units
from A to 8 either based on miles or the variable cost of

transportation.

Market Prices Based on Total Variable Cost

 

The basing point, or Market A, price is equal to the

surplus price (83.00) plus the fixed cost of transportation
(30.50) plus the variable cost of transportation, 30.10 per
10 mile unit ($2.00). The f.o.b. price offered by A will be
equal to this total cost of 35.50 minus an allowance per
hundred weight to cover the fixed cost of transportation for
thl Milk Purchased ($0.50) or $5.00. The f.o.b. price at
B is equal to the basing point f.o.b. price minus the var-
iable cost of moving milk between A and B or 35.00-7 $0.10 =
fi#.30.

At one unit from B towards A, A will offer its f.o.b.

price minus the variable cost incurred by moving six units
or $5.00 - $0.60 = 3#.40. B will offer its f.o.b. price
minus the variable cost associated with one unit of dis-
tance or 3¢.30 - $0.10 = $4.20. From this we can see that
A will offer a higher price at all points between A and B

and thus secure all the milk in that area. As we move to-
ward C. A and B will offer the same price in the checked

y
.
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45

area. For example at point D each will offer their market
f.o.b. price minus the apprOpriate variable cost:
A a 85.00 - 80.90 a $4.10: B = 84.30 ~ 80.20 2 $4.10.

As a result of the above we can see that when the
f.o.b. prices vary only and exactly by the variable cost of
transportation it is not economically profitable for a pro-
ducer in an area such as indicated above to sell to one
market in preference to the other. thus the market-supply
area is indeterminate. '

The above illustrates the importance of X. If X is
equal to the total number of units by which the two markets
differ the supply area becomes indeterminate. If X is less
than the total number of units it reflects the amount by
which the f.o.b. price in market B is above the base price
minus the variable cost of transportation between the two
points and thus the distance which the supply area for B
will project toward A.

In case 2 we examine what will result if the f.o.b.

prices vary by the total cost of transportation (fixed plus

variable).

Market f.o.b. Prices Based on Total
Transportation Costs (adjusted)

 

 

as

The costs are assumed to be the same as in case 1. In this
analysis, however. the f.o.b. price at B is increased by

30.10 so that the supply area boundary will not be indeter-
Elna“.

The basing point. or Earket A. price will than equal
the surplus price plus the total cost of transportation to
A or 05.50. The Price at B would be equal to the basing
point price minus the total cost of transportation between
the two points e 30.10 or £5.50 «- 3.0.50 - $0.70 + $0.10 net-MD.
The following prices will be offered at point C a D based
on the above f.o.b. prices and the total cost of moving milk

between those points and the markets.

F.o.b. prices 1": vs Price
Price at C for A.= $5.50 . .50 - .90 a 84.10

Prico .t C for B 3:24.40 . .50 - .30 3 33.60

Price at D for A
Price at D for B

35e50 ‘ e50 ‘ e80 3 ?Q.20
324.110 " e50 . em =3 ?3e7o

fl

Although mileage unite indicate a market boundary is
defined as A - B a K in neither case do the two markets pay
an equal price at the common points. From this it is con.
cluded that competitive market supply areas are not defined
if prices differ by the total cost of transportation.

In case 3 the fixed costs of transportation are in.
eluded in the f.o.b. prices and thus contribute nothing to I

the price variation among points in the market. In this
case the f.o.b. price at B will again be increased by $0.10

47
so that the supply ares will be defined. ‘The costeof trans-

portetion are assumed the same as in the previous cases.

Market f.o.b. Prices Based on Total
Virishle cost (adjusted)

  

 

$5.50 ' r 7 Ufiits‘ ' ;4'

As in case 1 where the f.o.b. price makes allowance
to cover fixed costs the f.o.b. price at A is equal to
85.00. The f.o.b. price at B is then equml to the market
A price minus the variable cost of transporting milk from
A to B plus 80.10 or 85.00 e 30.10 + $0.10 or %#.40.

The following ere the prices that will be offered at
points 0 and D‘by markets A and B assuming Just the variable
cost is deducted free the f.e.b. price.

Vhrisble
§§253° Price
Price at c for A 35.00 30.90 34.10

":0. ‘t C for ’ 8‘s” $0.30 84.10
PPIOI at D for A 35.00 $0.50 $0.20
Price at D for B $4.40 30.20 8A.?O

In both cases the conditions of A - B n X are satisfied
using either cost or mileage unite. At both c and D each
sortet offers the same price. From this it is concluded

that to competitively define market supply sress the f.o.b.
prices must include the fixed cost of transportatien end

48

must be somewhat less than the variable cost of transporting
milk between the two points.
The above three cases are summarized as follows:
1) the fixed costs of transportation must be in-

cluded in the f.o.b. prices if competitive

supply areas are to be defined

2) the f.o.b. basing point price must be greater
than that which would result from subtracting
the total cost variation from one point to
another.

3) the net prices offered to receiving stations
(Producers) are less than the f.o.b. market
prices in two competing markets by an amount
equal to the variable cost of transportation

and are equal on the market boundary.

In deveIOping the theoretical model the concentric

rings will vary in radius by a constant number of miles and
cost as discussed earlier in the chapter. Based on pre-
viously published data and other data examined by the author
a variable cost of approximately $0.001 per hundredweight
per mile is applicable for tankers with a capacity of 50,000
to 55,000 pounds per trip.1 The concentric rings in the

model will be approximately ten miles apart and thus repre-

sent a cost change of approximately 20.01 per zone.

 

1A mile in this study refers to trip mile or the cost
incurred e.g.. one mile round trip.

[:9

Karket Supply Areas
The market supply areas are determined simultaneously
for all the markets considered. This is done essentially
by a series or approximations varying the amount by which

the f.o.b. market price exceeds the base price minus the

cost of transporting milk from the base point to the mar»
kets. When all the market demands are exactly satisfied and
each decreasing price line represented by the concentric
rings moving away from the basing point are continuous over
the entire area the most efficient supply areas are defined.
The supply areas for the markets are illustrated in Figure
4-1. It can be noted that each decrease in price is con-
tinuous over the whole area under consideration. In this
case. 12.8 units is the maximum deviation from the basing
point f.o.b. price. share a price line is not continuous
it represents an increase in prices for the market in which
it is located. These increases come about in areas such as
Grand Rapids where price actually increases with distance
from the basing point over a given range. In the case of
Grand Rapids this range is between A and B_as indicated on
the map. These increases in price are the result of less
competition in the immediate area. Again using Grand Rapids
as an example we can see on the map that it can radiate out
using almost full rings as the requirements of the other*mar-
kets are satisfied before reaching the Grand Rapids area.

In determining the correct price variation the f.o.b.

prices will not necessarily be expressed in even dollars and

_..- _.. .wan “_..-1

50

 
   
 

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Figure.a-l

Theoretical Surety dress for the Nine Nerketing
Areas in Michigen, November 1959

51

cents but in general will involve fractions of a cent. This
results from the fact that the initial ring moving away from
the city determines the eize of the area included for that
market. In.moet caeee this ring is not a full ten miles
and thus represents only a fraction or the cost of moving
ten miles or a fraction of a cent. The radius or the initial
ringie influenced by factors such as the density or pro-
duction in the area in which the market is located and the
effects of other competing markets. These factore will be
discussed in more detail in Section II or this chapter which
deal: with the factors affecting price variation.

The price variation among the markets ae computed on
the basic of Figure 4.1 are shown in the Table 4-6. Each
supply area covere an area which will supply exactly the

amount of milk required by that market. The amount of’milk
included in the supply areas are determined geometrically.

Eheh.county'e contribution in square milee ie determined and
then.multiplied by the density of available production per
square mile for that county. The total or all the county

contributions are equal to the market requiremente.
Section 11

Price Variation
As shown in the preceding section when supply areas

are determined for a act of markets the price variation
among theee market. are also determined. Table 4-6 shove

the price variation among markets based on the theoretical

52

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o aw. ma.. ma. 0a., mo.~ om.4 mayo

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cu; mgmaa

53

model.
In this section a price variation formula is con-

structed. With this formula the price variation that must

exist among the markets to insure minimum transfer costs
for the whole area under consideration can be estimated.

For such a formula to be useful through time and have

general applicability, the variables included must represent
the relevant factors which affect the size, shape and thus

the price in the markets and be capable of doing so as the
market characteristics change.

The market characteristics or variables after being
defined and quantified are put into the general formula de-
scribed above and tested statistically for accuracy in com-
puting price variation. The resulting formula, within its
statistical limits. can then be used to determine the price
variation which would insure a system of supply areas or-
ganized in accordance with the criteria set forth in this

study.
Factors Affecting Price Variation

Location in Reference to the Basing Point

As previously stated this study is concerned only with
the derivation of a most efficient set of supply areas based
upon milk transport cost. In constructing the model in this
manner we are assuming that labor costs. land costs. feed
costs, eto.. are constant throughout the area and consequenflur

have no affect on price variation.

54

Based on the above we can see that price variation
among the markets will be the same regardless of the basing
point used. This is true since there is only one geometric
combination of supply areas that will minimize total trans-
portation costs for all markets. this does not say that
the formula being developed will not change if the basing
point is other than Detroit. The variables will remain the
same but their quantitative values will change and since we

are using a mathematical solution. so will their coefficients.
Detroit is used as the basing point because it has the

largest market requirement and thus will have the largest

supply area. Because of this it must have the greatest
price at its origin relative to other markets to enable it

to compete at distant locations. All price deviations will
then result in f.o.b. prices which are less than Detroit's.
If another market was used the variation would result in
f.o.b. prices higher and lower than that of the basing point.
the variations empressed in units would remain the same but

they would be more difficult to handle mathematically.
in using Detroit as the basing point the concentric

rings or iso-prieelines moving out from its origin represent

the maximum amount by which price can vary between the base

‘point and a market located on a given radius if the supply
area for that market is to be defined.

As discussed earlier if the variation is greater the

supply area will not be defined in any manner and if it is
exactly equal to that variation the supply area boundaries,

L
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55

although indicated, will not be exactly defined. For this
reason a variable expressing the relationship of the basing
point to the individual markets must be included in m for-
mula.

The Importance of distance I“ the basins point is
illustrated in the following enamels.

the density of available milk supply is assumed cone
etant throughout the area in which the markets compete for
milk. The requirements of A and D are also constant thus
the geometric area in the respective supply area will be the

same in all three cases.

Effects of Market Location in Reference
to the Basing Point

 

dass‘D

 

 

 

 

 

 

J

 

Case 2

 

 

 

 

A a Basing Point

In case 1. market I is located relatively close to

56

the basing point. are satisfy the requirements of effi-
ciency, B's market boundary is a line of indifference ex-
tending out as far as the two must move to satisfy their'
total requirements. As a result B's market takes the form
of a long narrow hyperbole. In order to define such a hyper»
bola the price at B is Just slightly above the base price
minus transportation cost. The extent of this increase can
be measured either by the distance CD or BF. If its devise
tion from the base price minus transportation cost were
greater than this amount the market would secure its supply
in a more circular manner and inefficiencies of cross haul
would result.

in case 2, B is more distant from A. It can be noted
in the example that most of A's market requirement is sat-
isfied before A and B compete for the available supply. Be-
cause of this the relative price variation with distance
from the basing point decreases from that found in the first
case. As discussed in the previous section the concentric
ring representing the lowest price or greatest differential
from the base point must be the lowest for all markets. Be.
cause of this, market B's f.o.b. price is increasing with
distance from the basing point between points OH. this in.
crease represents the amount by whimh the f.o.b. price at B

is greater than the f.o.b. base point price minus trans-
portation costs. It can be seen even though B's require-

ments are the same this deviation is greater than in the
earlier case. The amount of deviation is proportional to

57

the distance the market is located from the basing point.

Case 3 represents a situation wherein A and B secure
their supply independent of direct competition. With A
representing the basing point its outer concentric ring sets
a price limit subject to transportation costs. which sets a
maxhnum limit on the price variation at B or the minimum
price that B can pay.

From the above it may be concluded that distance from
the basing point does affect price variation among the-mar-
hats.

In constructing a quantitative value for this variable
the maximum amount of deviation due to distance is fixed by
the distance between the two points. The relative market
requirements .m then determine the amount of the axioms
variation that is relevant. if the markets were of equal
size each would have an equal price and the area would be
divided equally between then. is one market increases rel-
ative to the other. price variation appears. the variable
expressing the relationship with the basing point is based
on this principle of relative market size in determining the
amount by which price variation will differ from the varia-
tion resulting from distance alone. ,

Each.msrket as shown in the model has an f.o.b. price

which is greater than the f.o.b. base point price minus
transportation costs. The hyperbolic function defining the

supply area boundaries determines this deviation. The dis-
tance from B that the hyperbola intersects the X axis going

58

from B to A indicates this deviation in price variation

from the total transportation costs. From this we can see
that if the population or market requirements of B increases
or decreases relative to A the distance and thus the amount
of deviation will increase or decrease as the hyperbole will
change. This deviation then represents the push.of B back

on a and is termed the power effect. the ratio of 3's pop-
ulation to A's being termed the power factor. is shown in

Table A-7, the power factor applied to the total distance A
to B estimates the number of miles or units that B's market

will move toward A. Column 4 of the Table shows the net
effect on variation or the total distance minus the power
effect due to the market relationship with the basing point.
This is variable x: used in the formula.

is noted in column 2 of Table 4-7, the distance used
for Grand Rapids and Muskegon is 13.8 units. Figure s—é
shows that a 13.8 unit radius from Detroit encompasses
enough fluid.nilk and cream to supply all the requirements
of the included area snd.earkets. this is then taken tore the
maximum variation for'nankets located outside the 13.8 unit
distance as discussed in case 3 of the above example.

In summary the variable is quantified by the following

forlula:

x1 2. distance A to B - (W .. distance A to B)
Opu a on

Relationship With Competing Markets
the number, location, and size of competing markets

in relation to a given market also will affect price varia-

C‘

‘Q

59

TABLE 4-?

seams POINT VARIABLE FOR ms NINE MARKETING
AREAS m MICHIGAN, NOVEMBER 1959

“4—.

_r v f w— _.1 v 1 Y W

Distance from

 

mm simiy manta 335w Ifi’fiifizy
5;, Cit; .0362 11.03 .399 W 16.841
Saginaw .0771 9.15 .705 8.#45
Flint .0968 5.65 .547 ‘ 5.103
Muskegon .0389 13.80 .537 13.263
Grand Rapids .0943 13.80 1.336 12.464
Lansing .0553 8.00 .443 7.557
Jackson ~.0342 6.87 .235 6.635
maeazco .0442 _ 12.78 .565 12.215
Detroit 0 o 0 O

The power factor reflects the push of the individual _
Ierkets back on the basing point market. It is equal to the
population of a marketing area divided by the population
of the basins po nt market as area.

‘3/ One unit equals 10 eiles.
£4; the power effect is the power factor tines the dis-
'ce in units from Detroit to the market.

3/ The variable is equal to the total distance minus the
power effect.

’ .5 mh..ai“-=Kllv ~A..1
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sENzIa GRANB‘v
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TUSCOLA SANILAC
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LIVINGSTON
ALLEGAN BARRY EATON INGHA
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. BAlTLE CREEK
KALAHAZOO JACKéON
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“Rm“ AINT JOSEPH BRANCH HILLSOALE LENAWI.E \
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, I IWILLIAMS |FULT°" \
Figure 4-2

Maximum Distance Factor for Computing the Basing
Point Variable for the Nine Marketing Areas in

Michigan. (In Units of 10 Miles)

61

tion. If we refer to Figure 4-1. the model developed in
the last section, it is easy to see that changes due to the
above would cause price changes among the markets. If for

example the requirements for Battle Creek were doubled, the

size. shape and amount of price variation from the basing
point would change for all the markets located near Battle
Creek to enable it to satisfy its greater requirement.

The amount by which price variation will differ from
that of transportation cost from the basing point can again
be measured by the distortion of the concentric rings moving
out from Detroit. To quantify an estimate of this distor-
tion the following rationale is used.

As discussed earlier a line from Detroit through a
given market center represents the x axis used in forming
the hyperbolic function representing the market boundaries.
Since a hyperbole is symmetric to this line the location in
which the supply area will be formed is determined by the
angle or direction of the x axis. is noted in Figure A-3,
if X axes are constructed for all the markets we have three
groups of axes with similar angles from the basing point.
This indicates that supply areas formed on these axes will
come into contact over a large portion of their boundary.
For purposes of computing variable x2 the markets in each
of these groups are considered as the primary source of dis-
tortion. This does not say that other markets will not in-
fluence price variation but rather that for estimating purb

poses the affects from other markets are not measured. The

   
   
  

 

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a mass:
_..—_.—
\ 'ONIA cumon 5"““55”
GRAfiD\ rim
RAPID \ o“ A
NGSTON
ALLEGAN BARRY EATON I on? 'V'
E 8 NC
VAN suasu KALAM CALHOUN JACKSON WASHTENW
_..-fi-AfiLE.CREEK
KALANAZOO JACK§ON
“Rm“ BRANCH HILLLD'ALE 1“qu "°’"’°‘
roar: SAINT JOSEPH ELKHART LAGRANGE srtussu was
I I I l 'WILLIAMS FULTON ‘
Figure 4-3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SANILAC

SAINT CLAW

MACON.

"X" Axes Used to Estimate the Relationship of Competing
Markets for the Nine Marketing Areas in Michigan, 1959

63

reason for this is that these markets not competing over
wile areas of their boundary will have little effect on the

market price and that without constructing a model as used
in the last section the number and importance of affecting
markets other than those with like 1: axes «not be estimat-
ed accurately.

the following steeple illustrates the aocmulative

nature of the distortion among markets with similar x axes.

Affects of Interrelated Marketa

\\\ .

'-

,ie..,_.. _mwmw—I—m—v—q
.________.....-_-_—rm
0 l

I I“... .

a is the basing point. As discussed in reference to the
x! variable. B's deviation from the maximum variation can be
measured by If. The axes represented by an. Ac, and AD used

 

‘

 
  

in dates-minim the hyperbol is functions have approximately

the same angle in reference to A. As shown in the emample
this causes 0's market to be constructed on concentric rings

moving out from B and D's from rings moving out from 6. Thus

the x axes for c and D are actually lines originating from
B and C respectively. The amount of deviation from trans-
portation costs from B to c for market C is thus measured
by on. with the total deviation from the basing point being
on 4 EF. The same is true for market D with its total varia-
tion equal to I: + OH + EF. From the above we can see that
the price variation is influenced by the accumulated effects
moving away from the basing point.

As mentioned in discussing the Xi variable the dis-

tance between any two markets influences the concentric ring

distortion. Based on this the accumulative distances are
used in quantifying the X2 variable. The quantified vari-
ables as shown in Table 4-8 represent the total distance in

units such as from the basing point to market 3 plusthe dis-
tance from market B to 0. etc.. for all markets affected.

The variables are negative because they will have a price
increasing, or price variation decreasing affect in relation-
ship to the base price. ‘

As will be shown later, the resulting variable is high-
ly correlated with the variation found in the theoretical
model.

The general equation for this variable would be as

follows:

x: a distance to market being considered from the basing

point plus the distance from that market to all other’mar-
kets located between the two points which compete directly

65

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El

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>.

 

o omn.o~ 05.0 Oco.w omooap 0m0.n~ omocm oapsmp ooo.~— \mednewhmp

 

named :25 . eschew
30.5mm comma—mama momxoen wounds nomad momexoax 05.3 eauasm 1.33 had

I,

\m mama; 2H UEWUHUH... 3H mammal mmrmhuuufix mag mg. mum gmzmfiw usummqu m2 my...e...ma.._.u 92 mowefiooan

004 Rams...

66
with the market being considered.

Effects of Density of Production
Figure 4-4 shows the density of available fluid milk
per square mile for November, 1959. in the area under study.

As can be noticed the density varies widely over the area

being considered. Because of this variation two markets
with identical requirements may have supply areas which dif-

fer in total area included.
To the extent that price or price variation is a func-

tion of the size of the supply area an allowance must be made
for this variation in density in reference to the average
density of the basing point supply area. variable X is in-

3
eluded for this purpose.

Even though we know that the boundaries separating
supply areas will take a form based on hyperbolic functions
it is difficult to visualize these boundaries without ac-
tually constructing a model. This is due to the accumula-
tive effects of distortion discussed in reference to the x2
variable. It thus becomes impossible to determine the exact
average density that a supply area will have without going
through the type analysis discussed in section 1.

To get a quantitative value for this variable it is
necessary to form an estimate for the density which.will
exist in the supply areas.

When looking at the supply areas devised in the model
we can see that two straight lines intersecting at a point

67'

    
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
  

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

  
  
 

 

 

   
 
    
       
    
 

 

17* \ ~ \. rx /
K g" ‘z \ in}; \.—/'
i _) CHEBOYGAN
p (m ’7
T)\\ \\“v) 1 s 298 7:550”:
/‘ v
\ ,I/CHARLgvgz 2 ’ 3 79
r? orszco NONTNORENCY ALPEHA
_/ .( ANTRIM '
/ >3
,\1f 4 A 520 1,259 1,094 2,656
412:1” ,7
7 ,"XfKALKASKA CRAWFORD oscoDA ALCONA
GRAND
TRAVERSE
0 S3 0 880 1,823
WETFORD NISSAUKEE RDSCDNNDN DGENAVV IOSCO
1,210
75 1,671 0 3,796
HASON LAKE OSCEOLA CLARE GLADWIN AREHAC
6 342 . 4 , 4 7 1
’ 1,185 2,756 1,302 1,983 “mm.
BAY
OCEANA NEWAYGO .1 MECOSTA ISABELLA HIDLAND 8 s 541
to OLA
3,113 4,864 3,175 3,625 o 97
NUSKEGON ‘ NONICALN GRATIO" SAG'Ngx'Ggazw ° 7 ’ 572
4,270 3 386 .
’ 6%KEGON KENT ' 7 ,436
GENESEE
onAIng8 10’ 155 IONIA CLINTON 5 "”55“ 1 1 , 013 15 ’437
7’ cams 10. 882 . HINT
RAPIDS 10,948 11,863 E”
ALLEGAN ‘BARRY EATON INGHAN L'V'NGSTO" ‘
MNSING
7.203 7,935 11,073 13.121
VAN BURENWAMAZOO CALHOUN JACKSON WASHTEMW
2 . 675 5:035 BA’I‘TLE CREEK 9 113
KAIAHAZDO JACK§0N ,
- 9,047 8,930 '
CASS SAINT JOSEPH BRANCH HILLSDALE ENAVIEE
.1,511 4,564 9,196 11,051 8,289
LA PORTEISAINT JOSEPH IELKHART [LAGRANGE . |STEUBEN 'WMMHS FULTON ‘LUCAS L.~
’Figure 4-4

Pounds of Fluid Milk Per Square Mile Available

to the Marketing Areas, November 1959

68

between the market being considered and the basing point'
gives a fairly good representation of the general shape of
the supply area boundary. If we construct a set of these
as done in Figure 4-5, taking into account the market re-
quirement and the available supply located in the area be-
tween the lines, we can get an indication of the counties
that will be included in the supply area. By using these
counties, an approximation of the density in the supply area
can be derived. Appendix E shows the computation of the
estimated average densities as shown in column 2 of Table
449. It is emphasized that in constructing those estimated
boundaries that the location of other markets, density of
available production and market requirements must be kept
in mind because the angle formed by the intersection of the
two lines is important in quantifying the variable.

As the price variation is put in terms of deviation
from the bassxpcint f.o.b. price the estimated density of
the Detroit market is used as a basis cf comparison for the
other markets. If the estimated density for a given market
is the same as Detroit's the x3 variable has a value of zero
as both.markets secure the same amount of milk from a given
unit of area. If a market‘s estimated density is higher
than Detroit's the variable is positive as the Detroit mar»
ket procures less on the average from a given area than the
market being considered. As a result Detroit would have to
have a higher price to enable it to move farther stay from its
origin to get an equal amount of’milk. It is the same as a

69

/

\./

CHEBOYGAN

PRESOUE
ISLE

 

 

OTSEGO ’MONTMOIiNCY ‘ ALPENA

    
      

_l KALKASKA CRAWFORD OSCODA ALCONA

GRAND
TRAVERSE

 

 

—.‘ W
WEXFORD MISSAUKEE FROSCOMMON OGEHAW I O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

oscsou cue: GLAowm ARENAC
HURON
BA
uscosu ISABE mouuo
“‘0 w gamut
.. emaw BAY "
sun on no SAGINAH
‘1. SAINT Cl.“n
”nomA' cumon 5“ "l E
\ FLINT
95,, no “cows
e
———- STON
ALLEGAN var" anon ‘ | cam “W“;
LANSING
>\ waves
acxsou means“
VAN suasn ..-.. CALHHJ DETROI
3 )mc ON
L———-1 s
CASS .sn cu HIL..SDALE LENAWEE "0W0
art'sum JOSEPH IELKHART |ucnmcs Isrtuszn ‘Lucas L“

.wuums FUUO"

Figure 4-5

Estimated Angles Between the Supply Area Boundaries
for the Nine Marketing Areas for Michigan, November 1959

70

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at: mqm<a

71

decrease in the other market price, or an increase in varia-
tion between the two. If the supply area's density is less
than Detroit's the reverse is true.

Column 1 of Table 4-10 shows the angles formed by the

estimated market boundary. The density variable is based
on the distance a given market will have to go to secure
its supply, based on its estimated density in comparison
with the distance it would have to go if the Detroit supply
area density prevailed. We are interested in a comparison
of radii of the most distant concentric rings under the two
circumstances. To derive this, the angles in column 1 of
Table 4-10 are put in terms of a full circle as shown in
column 2. Columns 3 and 4 designate the number of square
miles needed to fulfill the requirements of the markets, as
calculated in Table 4-9. based on the two market densities.
It is these areas that would have to be included within the
angles given in column 1. To put these in terms of a com-
plete circle as shown in columns 5 and 6, they are multiplied

by column 2. Columns 5 and 6 then represent the areas of

two circles. one determined on the basis of the estimated
Detroit supply area density and the other on the basis of
the given market's estimated density. To determine the dif-

ference in radii of these circles the areas are put into the

formula r2 z -¢- . The radii for the two circles are shown

in columns 9 and 10 and their differences in column 11. The

X5 variables. as shown in column 12, are in terms of unit

differences in radii. or column 11 divided by 10.

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73

The variable camputed above gives us a relative
measure among the markets of the effects of variation in
density on price variation with reference to the basing
point. In other words. it is an estimate of the amount and

direction of price change needed to discount the variations

in density from the non-basing point markets in reference

to the basing point.

Relationship With the Surplus Area

In theory. prices in all markets are influenced by
that market’s distance from the surplus area. the surplus
price plus the cost of transportation determine the lininum
and maximum prices in the market. The maximum f.o.b. basing
point price and thus the saxisum price that the basing point
earket will offer at any point is based en the surplus price
plus cost of transportation to the basing point. In turn,
the mininun price that is acceptable at any point is based
on the surplus price plus the cost of transportation. In

our case the Detroit (basing psint) market is the major buy-
ing narket.'points located distant from Detroit can be

thought of primarily as selling markets. The maximum price
offered by the basing point is then determined by the sur-

plus price plus transportation cost to Detroit minus the
transportation cost to the point being considered. In terms

or the selling markets the surplus area. in effect. sets

the maximum value that their product is worth. The devia-
. tion between the two is the basis of the xp variable. The

C‘

.5 v
.

V
r .
. .
‘.
-ra'.
,1
- 4
I
O O
. e
f
‘
.x-
‘.
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.
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t
C I

‘v C
l ' I
->. | ' .41".
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‘.
l l s

 

 

74

following example illustrates the above:

The ”Basing Point-Surgltga Area-Karlzet" Relationship

 

$3.00 ' 20 vim. 33.20

The basing point price equals 33.20. or the surplus
price plus the cost of transportation. The price 3 will
offer at C equals $3.90 - .14 e 33.06. or the basing point
f.o.b. price minus the cost of transportation to C. in
turn. the value Oplsces on its produce a 33.00 4 .10. or
the surplus price 4 cost of transportation. Thus at point
c, c values product at four units or 30.04 above that which
E is willing to pay.

In quantifying the XA variable the price discrepancies
described above for the markets are shown in column 3 of
Table #«ll. They are equal to the distance is 9 CB . AB.
or column 1 sinus column 2. Figure 4-6 shows these dice
tances for'the individual markets. The distance from the
surplus area is taken from point A on the map. Although
this is not in the surplus area of Wisconsin. it is the
point of entry into Michigan and thus can be used. The

price assigned to that point represents the surplus price

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76

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n? OTSEGO HONTNORENCY
(’\ /(‘
K t
\chJ ,/ a
//
\ ,1 ‘4 :?
LEELANAU A
zjé/‘L‘anALxASNA CRAWFORD osconA ALCONA
BENZIE GRAND
TRAVERSE
ANISTEE waxr'OR'o' ' 'ms'SAu'xr: fiiosCONNON OGENAW Iosco
NAsON LAKE osczou CLARE GLAowm ARENAC
HURON
BAY
OCEANA NEWAYGO i'fcosrA ISABELLA NIDLAND
TU OLA sANILAc
M -
HUSKEGON HONICALN GRATIO" “G'N‘WGI
I
s KENT
MU RECON GENES ”Pm
SAINT CLAIR
OTTAWA ll IONIA CLINT N 5’" “”55“
OSSE:;:: FL
PID \‘. nAKLA I ”ACO!!!
_C__.———
flLIVINGSTON
ALLEGAN BARRY EATON I HAN
“mlfi'f-u
3* I ‘
0
§ ‘
Q
WA ,
v BUREN AH 200 ALHOUN JACKSON WASWENW E
N “ --
& KAIA ZOO JACIaON
MONROE
‘9'“ CA SAINT JOSEPH RANCH ILLSDALE LENAWEE
{1-
H-
L PORT: nu EPH K AR EN (1“
|SAN 05 .El. H T ILAGRANGE Isrzua MLUAMS ‘ruuon ‘LUCAS
I
Figure 4-6

Distance to Detroit and the Surplus Area from the

Nine Marketing Areas in Michigan
In ten mile units)

77
plus transportation costs to that point. For price varia-
tion purposes we are thus subtracting a constant from all
markets which will not affect variation in price among the

markets. the deviation from the price variation as determin-

ed by distance alone is taken to equal the price discrep-
ancy. or column 3 tines the relative power factor derived
earlier as shown in column A. In effect. this states that
the price variation is influenced by the competitive power
of the market. the net effects are shown in column 5 of the
table. The I; variable will be either positive or negative
depending upon whether A0 or GB is greater. Where A0 is the

larger. the variable is negative representing an increase-
in price variation or a decrease in price. this results be-

cause the basing point is closer to the market than the sure
plus area and thus represents the primary influence. Where

on is greater'the variable is positive representing a dew

crease in price variation or an increase in price. this is

due to the delinant influence of the surplus area. The above
reflects the decreasing possibility of using the surplus area

rather than the basing point outlet as distance free the sur-

plus area increases. ' }

Price Variation Formula
The variables to be used in.predicting the price varia»

tion between the nine f.o.b. aarket prices and the basing

point price were discussed and quantified above.
The general foreula that is used to predict the price

78

A

variations is I = blxl + hex2 + b3)!3 + bAXa, where I is the
estimated price variation between the market being consider-
ed and the base market. X1. 12. x3. and In are the indepen-
dent variables; distance tc the basing point. location and
number of competing markets, density of production and re-
lationship with the surplus area. and the b's represent the
partial regression coefficients.

It is of interest to see which of these variables can

be directly related to the actual price variation found in
the theoretical nodal. To determine this relationship the
predictor variables are correlated with the observed I
values. Table t-l2 lists these variables as deterained
earlier in the section. The results of the analysis show
that both the x1 and x2 variables are directly related to
price variation as they have correlation coefficients of

.97 and -.92 respectively.1 Variables x3 and 2:4 with
correlation coefficients of c.39 and +.81 cannot be directly

related as indicated by their low coefficients. these re-
sults suggest that the price variation say be closely asso-

ciated with.distance to the basing point and competing sar-
keta but not with density of production and location in ref-
erence to the surplus area. They do not, however, tell us
anything about the combined effects of using these variables

to predict the price variation.
To determine the weight (b1) that should be given to

A; h— _ L

1All statistical computations for this-section are
shown in Appendix F.

V.

 

 

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N we: magma.

80

each of the variables to obtain a "best estimate” of the
price variation a multiple regression analysis is used.
The "best estimate” is then tested for its accuracy in pre-
dicting‘i'by a correlation analysis between §'and I.

The regression coefficients. or the ”1 values and

their standard errors are:

D 4' e b ‘0' e 3139
1' }.335§) 2' (.0396)

b g Q' e235} b g ’ e8180
3 (.0828) 4 (.1038)

these coefficients indicate the relative weights of their
respective variables in determining the price varieties.
the standard errors show that all the coefficients are sig-
nificantly different from zero.

To test these variables for significance in detersin~
ing the estimated price variation a I test is used. the
standard errors are divided into the regression coefficients

and compared with the 1 distribution It the 95% end 99%

levels. The resulting i values are:
bl' 1‘g%££,= e 15.446 be. .3139 2.4 7.920

b .2353 8 9 2.840 b“. .e8180 3 - 7.884

73655 , .1033

these results show that bl’ b2, and b# are significant at
"the 99% level and that b3 is significant at the 951 level.
It is thus concluded that all the variables are significant

50

l

in determining price variation.
xx
The general fornule then becomes Y = 1.36777!1 + .3139Xé

81

+..2353X3 + (-.8130X4).. Using this equation the estimated
price variations are computed. The resulting estimates are
shown in column 5 of Table 4-13. The standard error of
estimate is .0479.

To determine the reliability of these estimates
in determining the appropriate price variations they are test-
ed for correlation with the observed Y values. As indicated
in Appendix F they are found to be highly correlated. with a
coefficient of .9996?. indicating that the estimated Y's are

very close to the actual Y's found in the theoretical model.
The equation giving the exact value of the estimated
variation is:
§ -.-.- E + b1(X1 - 5'1) + b2(X2 - i2) + b3(x3 - 3(3)
+ DAD!4 - it) + E, f being the mean of the

observed I values.
The formula for the standard deviation of Y is:

Q... -"2
my - «[1 + %' e (xllj Xi) Sb

 

2 + (X -.i )2 Sb 2?
1 213 2 2

 

-§ 2 - 2 24
x - x Sb X - x Sb 8 .
’ ( 311 3) 3 + ( 413 a) 4 yx
S = the standard error of estimate.

yx
Using the Lansing Market as an example we find that

A

Y = 7.888 + .53. or 7.835 <§< 7.941. Referring back to

Table 4-13 we find that the predicted value for Lansing was
7.99. The estimated value is .05 greater than the upper limit

This amount can be attributed to rounding in the computation.

In summary, it was found that all the variables signif-

82

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n7... 3mg

ona<Hm4> monm quequhwm

83

icantly influenced the price variation. It was also shown
that the price variation estimated by the formula was close
to the observed price variation. Based on the above it is

concluded that the price variation formula can be used to
predict the correct price variation which.must exist if the

market supply areas are to be organised in accordance with

the criteria set forth in this study.

CHAPTER V

COMPARISON OF THE PRESENT SUPPLY AREAS
WITH THE TfiEORETICAL

In the preceding chapter supply areas for the nine
markets being examined were constructed on the basis of

November. 1959. production and consumption data. The per-
fectly competitive model developed. even though it is based
on current data. cannot be considered consistent with
reality as the conditions of a perfect market are seldom

encountered in today's world. Using this framework. however.

has enabled the development of a system which serves not

only as an ideal for comparative purposes but also as the
desired end insofar as minimum costs of transfer are con-

corned.

In section one of this chapter a set of supply areas

are derived on the basis of current production. consumption.

and transportation cost figures. The price structure among

the markets. however. is determined by the present govern-
mental regulations in the area being considered. 1

In section two the resulting set of supply areas from
section one are compared with the supply areas as determined

in Chapter 4. Section 1.

1In this thesis the present governmental regulation
refers to the Southern Michigan Markets Order which became
effective February 1. 1960.

84

85

Section 1
The Present Supply Areas

Under the present Southern Michigan Marketing Order
the Detroit price is subject to location adjustments.1
These adjustments determine the amount by which the min-
imum price received in any area can be less than the Detroit
price.' Figure 5-1 shows the area under consideration and
the apprOpriate adjustments. by county. as prescribed in
the Southern Michigan Order.

The set of supply areas derived in this section are

based on the price variation determined by the location

adjustments. The price variation and the f.o.b. city plant
prices are shown in Table 5-1. The prices are based on a
85.50 base price in Detroit minus the applicable adjustment
for the county in which the market is located.
I With the f.o.b. prices fixed the markets will again
secure their supplies by moving away from their origin in
a concentric manner. The units between each ring are e-
qual due to the linearity of transportation costs as dis-
cussed in Chapter 4.

Figure 5-2 illustrates the resulting supply areas. It

will be noted that the areas take on a variety of shapes.
These variations form a general pattern as was found to re-

 

iUnited States Department of Agriculture. 1 ricultural
.msrketing Service. Order No. 24 as Amended Effect ve
February 1. 1960. T. 7. Ch. 11. Code of Federal Register

Marketing Order - Part 924. Section 924.54. p. 6.

86

TABLE 5.1

PRICE VARIATIONS AND CORPE SPONDIHG F. 0.3. PLKNT PRICES
BASED ON THE SOUTHERN MICHIGAN MARKETING ORDER
LOCATION ADJUSTMENTS FOR THE NINEIMARKETING
AREAS IN MICHIGAN

A _._._._. _A

_v_ W

Location adjustment for

 

county in which market Assumed f.o.b.
Market is(::§::;d plant price
Detroit 0 38.50
Flint O 5.50
Bay Oity~$aginaw O 5.50
2...... 7 5.43
Grand Rapids 15 5.35
Muskegon 20 5.30
Jackson 7 5.“)
Battle Creek 12 5.38
Kalamazoo 15 5.35

 

m. base rice in Detroit 1. the same as um. used in
examples 3agger1 IV. It is equal to a rice in the
surplus area of plus the fixed and varia le costs of

transportation or 33.W 4 .50 e .01 x 200 a 83.50.

 

 

87

  
      
 
 
 
 
 
 

 

  

 

 

 

 

 

 

 
 
 
  
 

 

 

 

 

      
    

A» VF? r~\\ ‘K K" \\ (/
IL, 4" < \ xfilEMMET \\'/ Legend-
\‘ I) ( HEBOYGAN
ex\ \ \ U = No Adjustment
Sf‘l :: 7c -
\ ’- \\7,“ .1] _j VA I ‘ 10¢
\V K 5 3 ll " '
,VILEEICANAur .4" ‘ , . .
.> 5:: ' 12¢

1,,I.
.'/
\//{
‘t,

  
  
 

AVERSE

 

 

FLINT

  
  
  

 

’ -.; NAM u sen
xgx x 8 xx ‘t ‘
“Xxx h““‘“"
ex 3
, KKKIXKXX XXX
' :hE'FcC’fE,‘ ' 5A€K§xNx x “ I
. .0...".e.‘e.. ‘ ‘ x x“ 'x‘
. “XXX X I
xxx xx xx:

"." «.0
xkaKYX"
xx! xx)!“ '

  

  
    
     
 

  

 
  
  

W
DETROI

 
 

     
 
   
   

      
  
  

 
  
 

  

                
    
   
   
 

  
 
 

 

 

 

TON ‘LUCAS

  

MS

     

I
Figure 5-1
Location Adjustments Under the Southern Michigan
Marketing Order

Source: USDA-ANS, Order No. 24. as amended effective February 1, 1960, T. 7,
Ch. IX, Code of Fed. Regs. Marketing Order Part 924, pg.6.

88

cult in the theoretical model which are due primarily to
the price relationships among the markets.

The Detroit. Flint. and Bay City-Saginaw markets have
equal f.o.b. prices. As a result of this price equality
the area between the markets should be equally divided as
discussed in Chapter 1. Due to different market require-
ments and densities of production. however. the Flint and
Bay City-Saginaw market requirements are satisfied without
competing with each other or with Detroit price-wise. Be-
cause of this the market boundaries do not define points of
indifference between the markets.

The above situation results because as Detroit moves
toward the other two markets it is forced to offer a contin-
ually decreasing price due to the increasing total cost of
transportation. Bay City-Saginaw and Flint having a fixed
f.o.b. price equal to that of Detroit will offer a higher
price over’the area which is needed to fulfill their re-
quirements. ?3. and 18 miles respectively. For a similar
reason the Bay City-Saginaw and Flint markets do not com-
pete price-wise.

The Lansing Market takes on a resemblance to the
theoretical market develoned in the previous chapter. This
is due to the fact that the f.o.b. price in Lansing is just
slightly above the Detroit price minus the transportation
cost between the two points. As will be noted in Figure 5-2

the supply area takes on a hyperbolic form signifying price
competition for the twenty miles it extends to satisfy its

89

rx’\ ._,(w\ /
("7 2" It \ \, ‘ I ‘\_/
. <, ' EMMET \ g
\ , ) / CHEBOYGAN W

\ PRESOUE
\ ‘ -' ISLE

 

\. [CHARLEVOIX

/
.1,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

. orssco womuonencv ALPENA
. , K .
\ ‘ ' '_ \ANTRIM
\“ “ ’
,LEELANALJF h"
n 7" ---"'-\TI/KALKASKA cmwrono OSCODA ALCONA
/
BENZIE W5 »‘
TRAVERSE
[MANISTEE WEXFORD MISSAUKEE noscomuou OGEMAW Iosco
"‘50“ LAKE OSCEOLA CLARE GLADW N ARENAC
HURON
v
NEWAYGO uccosu ISABELLA mo 0
scou SANILAC
BAY ' \l
MONTCALM Imor SAGINA‘W ‘
SA INAH
MUSKEGO NT
/
"4 ccwsszz PE“
SAINT CLAR
TTA I I 7 CLINYON 5"“ ‘55
D
mums FLINT
RAPII‘s 0A mo MACON
ALL W1?" mecsr N
NSING
AW WA NE
VAN BUREN J xsou wssmtu
I DETROI e \
CRL’ K "x
. ’0‘ I fiCKéON
\
BERR'E HILLiDALE LENAWIIE ”0"“ \K
I
K
‘w
.. LA Pomclssmr JOSEPH ELKHAR‘I’ ILAGRANGE STEUBEN l LUCAS L.“
l WILLIAMS FULTON ‘
l I
Figure 5-2

The Supply Areas for Nine Michigan Marketing Areas,
November 1959, Using Location Differentials
Provided-The South Michigan Order,
Effective February 1, 1960.

90

requirements.

The Jackson supply area is indeterminate due to the
fixed f.o.b. price which differs from the Detroit price
only by the cost of transportation between the two Points.
The checked areas in Figure 5-2 are the areas in which both
markets offer the same price. w

The Battle Creek and Kalamazoo supply areas do not
encompass the centers of population for which they are con-

”structed because of their price relationship with Detroit.
In both cases the adjustment is larger than the cost of

transportation between the two points. This results in
relatively low f.o.b. prices in the two markets. As the
f.o.b. prices are fixed the receiving stations located near
the two markets find it more profitable to ship to Detroit
than to the nearby markets. Because of this the Kalamazoo
and Battle Creek supply areas are not defined until the
Detroit requirements are satisfied. As can be noted in
Figure 5-? Battle Creek secures its supply first and then
Kalamazoo for the same reason. The exception in the above
case is the small area in which Kalamazoo can compete with

Battle Creek in Battle Creek's most distant zone.

The Kalamazoo supply area is again pushed further away

from its origin because of its relatively low price in com-
parison to that of Grand Rapids with whom it comes into con-

tact on its northern boundary.
The Grand Rapids and Muskegon supply areas are some-

what similar to those of Bay City-Saginaw and Flint primarily

91

because of their distance from Detroit. The Detroit mar-
ket and those which It encompasses have satisfied their

requirements before reaching the Grand Rapids area and thus

are discontinued. As a result. Grand Rapids can radiate out

and encompass those areas not included in the previously dis-
cussed marketa. As shown in Figure 5-2. because of its
price relationships Grand Rapids does not have a competitive
boundary with the markds south or east of it. Likewise.
Muskegon does not have a competitive boundary with Grand
Rapids.

In summary we can say that when a set of markets have
fixed f.o.b. prices the size. shape. and location of their
supply areas will be determined by the relationship of the
fixed price to the base price. the density of production.

and the location of competing markets.

Section II
Comparison
For comparative purposes the two sets of supply areas

are superimposed as shown in Figure 5-3.
The total area included in the theoretical model is

slightly larger than that of the existing supply area model
as can be seen in Figure 5-3. We may conclude however that

this does not signify a greater total transportation cost
and thus a less efficient system. This is because of the

fact that the areas in which the theoretical model extends”

beyond the existing are areas of low average density per

92!

m , LEGEND

(. «x .\ /

L < \ 'EMMEI C./

\. } / cssaovon
PRESOUE

\ \\- “I ISLE

\ ,, CHARLEVOIX

--- Based on location
differentials in
use on February 1,
1960

___ Based on differ-

entials as com-

    
  
  
 

 

 

 

 

  

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 
 
 
   
  
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

? OTSEGO sosrsosEsCY1ALPEsA
\ ll //-) \ANTRIM ' pulled in Chi.
g , x study
\ "'\.I ; '
.,,L£ELAsAur' __ ,-
\ / f‘Lg’KALKAsxA anwroao OSCODA ALcosA
// ,/
GRANO"
TRAVERSE
{NANISTEE wexroso MISSAUKEE Roscossos OGEMAW IOSCO
{fr
1; ,/
sAsos LAKE OSCEOLA CLARE fipow s ARENAC
susos
BAY
# I
NEWAYGO ssCosIA ISABELLA MIDL’AN ’1'
I' / / Tl‘SCOLA SAMLAC
I l
/ ' BAY '
c T y SAG'NA-W -
MOMCALM / GRA IO bAGI ]
I \ w ’
/ \ ' LAPEER
\\ SAINT CLMR
IOsTA CLINTON \ J ‘
\ ’ \ L T I
’ ‘ sAcosa
l\ \ oAsLAsO/
I ‘ J“ leuscstos ,
EATON Is s‘w \ ’
I Assxsu
7‘ I
\ ‘D’
‘r”
I I I ‘l‘ ‘ w wuss
L ' ' WASHTENA
VAs UREN' KALAMAIOO CALsL s, ' JACKSON DETROI .
O
' . BAT4tJ'CREEK ',
‘ mum-00 | ‘ ‘0 JACK s
| I |\
\ \\ \
.5 sossoc

 

  
 

 

 

\ a
BERR'E" CASS ‘ SAINT JO 59s 8 mm I‘ILLSD LE
‘\ ‘ \ \ ‘
\\ \ \

\\_/ x \\ \k 4

 

 

 

 

 

\
E ass I Li.
. LA PORTEISAINT JOSEPH IELKHART ILAGRANGE IST U 'WILUAMS ‘FULYON ‘LUCAS
Figure 5-3

Theoretical and Existing Areas for the Nine Michigan
Marketing Areas, November 1959. Superimposed

93

square mile while the reverse is true in those areas in ‘
which the existing model extends beyond the theoretical.
Since total transportation costs are a function of the number
of loads carried as well as distance it cannot be concluded
that the theoretical model represents a greater total cost.

Table 5-2 shows the longest distance each market must
travel and the length of the perimeter it must cover at
that distance to satisfy its requirement.

The Bay City-Saginaw. Flint. Lansing. Grand Rapids.
and Detroit markets all extend further in the theoretical
model than in the existing model. This would tend to in-
dicate a greater total transportation cost. when we con-
sider the length of the perhmeter covered at this distance
the above indication becomes less evident. In all cases
the perimeter in the existing model ie_greater at the most
distant points than in the theoretical ma. Detroit.
being the extreme. has to cover 104 miles at a distance of
125 miles in the existing model as compared with.having to
cover 11 miles at a distance of 128 miles in the theoretical
model. From this we can see that the length of the average
trip and the total cost will be greater in the existing mod.
el even though the most distant point is greater in the
theoretical model. In the case of Flint we do find a lower
total cost of transportation in the existing model than in

the theoretical because of the extreme variation in density
of production. The area included in the existing supply

area. as can be noted on the density map (Figure 4-5). is

.
I . ’
l ‘ I s . ‘ ‘
.
‘ .
I ‘ ' I I‘ .
4 ' ' | - --
V v '
O
l I .
‘ .
. ,
I . ‘
‘ I
A _ -
. ' '
. .
,
‘ . v > ’
. - 0
\
e I I
, .
‘ ' s 'I
C
. Q

. s- . .
. ‘
, a .
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1 . . ' A . .
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| f s e ‘» ' '
’ . .1 . f,
t
,.
e 4 ‘ -. ‘ ‘
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. h
. .
. . .
l‘ ‘ l e I ’ .
V f '
-_ - -
. .
- e 1‘ ‘ 'u '
1 r T
- .
I

U
l
.
s
a; '
I U
A‘.\
e'
. .
. 9
I
. .
l I
. 1 ‘
4
J
9
‘ . ‘
fl
.
..

94

TABLE 5-2

LONGEST DISTANCE TRAVELED AED PEEIHETER AT THAI RADIUS
FOR THE SUPPLY AREAS DEVISED OH THE BASIS OF
THE EXISTING PRICE VARIATION FOR THE
fiIHE MICHIGAS MARKETIHG AREAS
NOVEEBEIR 1959

A

Length of Length of
longest radius Perimeter'longest radius Perimeter

in theoretical at that in existing at that

 

Marketing model radius nodal radius
area units y units 1] units g/ units 9’
Detroit 12.80 1.100 12.50 10.467
Flint 7.70 2.000 1.80 5.652
$133,- 5.30 3.054 2.30 6.078
Lansing 5.00 .100 2.00 -2.215
Grand Rapids 2.55 2.557 2.20 4.202
Muskegon 2.40 2.007 2.4 2.721
Jackson 5.40 .100 y y
Battle Greek 3.40 3.853 3.8 4.540
Kalamazoo 2.85 .#00 3.8 ' 3.314

 

.1/ Derived tron Figure 5-2, One Unit equals 10 niles.
3/ Derived free Figure 0.2.
1/ Indeterminate.

95

high in available fluid milk whereas the area covered in

the theoretical model is low and in some cases zero. Be-

cause of the variation in density the area included in the
existing model is enough smaller than that in the theoret-

ical to make the average length of trip smaller and thus
the total cost less. It must be remembered that we are in-
terested in total cost of all the markets and not in min.
imizing them for any one market in particular.

In the Muskegon market the greatest length of trip is
equal in both.models. The perimeter covered at that dis-
tance is slightly larger in the existing model which would
seem to indicate a greater total cost.

The remaining defined markets of Battle Creek and
Kalamazoo quite obviously involve a greater total cost in
the existing model than in the theoretical model. In both_
cases the most distant point is farther and the perimeter
covered is greater.

The above comparisons, although primarily visual in
nature. indicate that the total cost of transportation on
the individual market basis is not always less in the theoret-
ically more efficient model. than we consider all markets
as a unit. however. the indication is that the total cost
is less in the theoretical model. I

The following geometrical example is evidence of the

above. The total area under consideration is taken to be

equal to that included in the rectangular figures. The

96

Cost of transportation with Different
Harket Structures

 

Transportation Costs

 

 

 

 

 

 

 

 

 

(Units)
2234 A 4:19.:
I .5...L_ w 4.1.
a 2 2
b 3 3
c . I. 1.8
d 2 3.6
'0 3 .e
f 5 1
Ԥ_ 5 ' l
TOtfll 15 6 21 3.8
Total
I 9 y 21 ”e8

 

production within them is Just equal to the requirements of
the two markets x and y. x requires four units and is the
basing point. 2 requires three units. The units are rep-
resented by s‘- g. In case 1. y's supply area takes on
the form of a hyperbolic function as a result of satisfy-
inglthe conditions discussed in Chapter IV.

In case 2. the f.o.b. prices are fixed and equal.
this is similar to the case of Flint and Bay City-Saginaw

in the second model develoned.
The costs of transportation are summarised next to

the example. In both cases the transportation cost of x
exceeds that of y. In case i. the cost is less for x than

:\- rm. \‘ea :0 0.5;.

" :"-.- i

 

.. /""'r';“;‘7"'7 s/‘fls

 

‘l
-- - ...-. c /' i \ \ “1
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e
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1
w":£v'. *1 ct“) :. .’.".:'- Li}, 3! ." l 31 JL‘I ’NIJ‘N ’1'."
1:. 231-2' '1'“ ' W.‘ ' .5 ‘ .; ..' a x sinks": on! -‘~"
o"' sJ'v. in: ..1. - a; ..{-, an i ..:i3- 3,. .
u e ' - .s ‘s y . r .
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i. -i '1') ,f s 3 3 to?“ H". at?!" u l 1 "do! v~.-:’,'
.‘3. °c.f"'-r ct 51".“ L} "’:";‘-V" :5? ".‘i
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. . . . e .
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51-1.: in: " a - " .‘.. - --. J '16 rises cg"?
‘ a? “' "OI. 2. r'.‘ (:s; 'e 's‘ I ' ' ”If m.I-n'-“.X‘ '. ..
. m m f... m
9 H . I : ' h 1‘ ': 9 0,: ' e‘u- Q ‘I "L: B" '

 

97

in case 2. The reverse is true for y.

To evaluate the efficiency of the total system we
must compare total costs. In our example we find that case 1
has the least total cost indicating a more efficient system.
Case 1. from the above illustration, can be directly related
to our theoretical model in that the market boundaries take
their form because of being hyperbolic functions. Khan exam-
ining the theoretical supply areas we find that where two or
more markets come together they are divided by a hyperbolic
function. In price terms it is shown by a line that divides
the area such that all markets will be offering the same
price at a common point.

In the case of Jackson. Lansing, and Flint the outside
boundaries are determined by an interrelationship with the
Detroit price. In the remaining markets more than one mar-
ket influences the shapes of the boundaries. the extreme
being Grand Rapids which is influenced by all eight other
markets. Because of this complete system of competitively
defined market boundaries each enclosing exactly the required
amount of fluid milk and cream to satisfy its requirement
we have a system which minimizes total transportation costs.

0n the contrary in the model deveIOped based on exist-
ing f.o.b. prices the supply area boundaries are not a func-
tion of competitive bidding. As a result of this supply
areas are defined that involve cross-hauling which increases

the total costs of transportation when all markets are con-

sidered.

98

It is therefore concluded that. given the assumptions

set forth in the theoretical model. the supply areas de-
veloped illustrate the most efficient manner in which.the
nine marketing areas under study can secure their given re-
quirements of fluid milk and cream.

The increase in efficiency can best be measured in
terms of dollars saved when the supply is secured as indicat-
ed in the theoretical model.

.In making a comparison between the two models total
fixed costs are assumed to be the same. The fixed costs of
operation will obviously be the same in both cases. There
may however be a decrease in the fixed costs associated with
truck ownership. repair parts. etc.. in the theoretical
model due to a decrease in the total number of miles travel-
ed. Since this study does not go into a detailed analysis
of truck capacities or'maxinum distances each unit can be
driven within a given time period the possibility of a de-
crease in fixed cost is recognised but not estimated. .It
should be noted. however. that a decrease in fixed costs .
would indicate additional savings resulting from supply areas
organized as in the theoretical model.

Assuming the total fixed costs equal in both.sodele
we can then determine the savings which would result from
using one of the models by comparing the variable cost in-

curred to secure the supply.
It will be remembered from the earlier discussion that
the variable cost is a function of the number of miles

99

traveled. The model with the lowest total variable cost

for all markets thus has the lowest total cost and is. on
this basis, the more efficient of the two. Table 5-3 shows
the computation of total variable costs for the two models.
Column 1 of the table shows the fluid milk and cream re-
quirements for each market. These requirements divided by
the average size tanker load determine the total trips nec-
essary to secure the market requirements. These figures are

shown in column 3 of the table. The average distance of
haul is then taken to be equal to the radius from the maru

ket center which encloses one-half of the market requirement.
With the pounds of milk hauled per tanker per load being
equal the number of loads hauled less than this distance is
equal to the number hauled greater than this distance.
Figures 5-4 and 5-5 indicate the areas that are closest to
the market center which includes one-half of the market
requirements. The cases where the geometric areas are not
equally divided indicates variations in the density of avail-
able milk in the supply area. Columns 5 and 6 of Table 5-3

show the average length of trip determined in the above
manner. The total miles traveled as shown in column 7 and
8 are determined by multiplying the average length of trip
by the total trips made.

Having found the total number of miles traveled for

each market we can then determine the total variable cost
by multiplying the total units (ten miles) traveled by 35.25,

This is the cost of moving 52.500 pounds of milk one unit

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TRAVERSE
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L
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I
_ / L
LA PORTE'SAINT JOSEPH 'ELKHART ILAGRANGE 'STEUBEN FULTON ‘LUCAS ~\
'WILLIAMS |
Figure 5-4

Average Length of Raul per Tinker Load in the
Theoretical Model for the Nine Marketing Areas in

Michigan, November 1959.

(In Units of 10 Miles)

 

1132

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TRAVERSE
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NASON LAKE OSCEOLA CLARE GLADW
HURON
NEWAYGO NECOSTA ISABELLA MIDLAND
SCOLA SANILAC
I
7
., SAGINAW 3’” '
NONTCALN GRATIO SAG INAH
MUS‘KE ‘0 Em GENE PEER
SAINT CLIUR
OT” IONIA CLINTON 5"“ ‘5 E 'J
’fimm ’ FLINT
RAPIDS ND IIIACOMB
EATON '6 M LIVING N
ALL A BA v a
l'“ Nsmc I):
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I l
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‘ \\ J LENAWI'E MONROE .\
' IL D LE . .\
35“ EN‘CAS \SAIN JO PH BRANCH \\ I‘ b5
\ \ \
\\ \a
. ‘K
(-\
LA PORTE SAINT JOSEPH ELKHART LAGRANGE STEusEN l LUCAS
’/ I I l I .WILLIAMS 1“”70" ‘
Figure 5-5

Average Length of Raul per Tanker Load in the
Existing Model for the Nine Marketing Areas in

Michigan, NOvember 1959.

(In Units of 10 Miles)

103

or ten.miles. It should be noted that the transportation
cost is in terms of a round trip and not one way.

when comparing the total variable costs incurred in
the individual markets we can see. as earlier noted. that
minimizing total cost for all the markets is not necessarily
consistent with minimizing costs in the individual markets.

In summarizing the comparison we can see that the
total variable cost in the theoretical “4.1 1. $10,937.32
less than that in the model based on the existing conditions
forIthe month of'chember 1959. .This represents a decrease
in cost per hundred-weight hauled of 80.00588. ‘

~ In examining these savings in a somewhat different

manner we can see that the savings in the month of November
would more than cover the cost of securing the market re-
quire-ants of milk in the Battle Creek. hay City-Saginaw,
Flint. Nuakegon. Grand Rapids, Lansing, and Kalamazoo mar-

tets combined for the same month.
In summary we have seen that the supply areas defined

by competitive boundaries derived from hyperbolic functions
minimize total transportation costs. ;In turn the model de-
veloped on the above basis was found to be more efficient

than the model representing the existing conditions by
810,937.32 in November 1959.

CHAPTER VI
Summary and Conclusions

This study was concerned with the delineation of milk
supply areas for the Detroit. Jackson. Battle Creek.
Kalamazoo. Lansing. Grand Rapids, huskegpn. Bay City-5aginaw,
and Flint. Hichigan consmsing areas in such a way that total
‘transport costs would be at a minimum. The nine areas in-
clude all counties having one or more cities with a pop. -
ulation of “1.000 or more and contain 75.6 percent of the
population in Lower Michigan.

Most of the basic data used in the study were from
secondary sources. In most cases the data used were those
relating to November 1959. the time period upon which the
analysis is based.

The fluid milk and cream requirements. in milk equiv-
alents. for the nine marketing areas was found to be
185,855,360 pounds. This was based on the per capita con-

sumption of 28.603 pounds, the number of oonmxmers in the
marketing areas and a 15 percent allowance for variations

in production and consumption.
It was found, based on the average number of milk cows

in each eounty and the average production per cow. that
“3.831.640 pounds of milk were produced in Lower Michigan

10h

105

in November 1959. Of this. 215.498.3216 pounds were avail-
able to the marketing areas for’fluid use. The remainder
was milk not of fluid quality. milk fed on the farm where
produced and milk consumed outside the marketing areas.
Adjustments were made for net exports or imports of silk
and for that milk shipped into deficit milk producing
counties outside the marketing areas.

.In satisfying the criteria of efficiency established
for the study. it was found that all supply area boundaries
Vcomnon to more than one market were defined by points of
price indifference to the receiving stations in reference
to the competing markets. The resulting boundary lines were
hyperbolic functions with the points of indifference defined
by the intersection of corresponding iscuprice lines radiat-
ing from the ocnpeting.markets.

The increase in the cost of moving milk as distance
traveled increased was found to be equal to the increase in
the variable cost incurred. The variable cost was found to
be 80.001 per'mile per’hundred weight and linear with dis-
tance. The lac-price lines used to define the supply area
boundaries were separated by ten mile intervals represent-

ing an increase in transportation cost of $0.01 perlhundred
VOtShte
A model of the most efficient supply areas for the

nine markets based on the market requirements and the avail-
able supply of fluid milk was developed in Chapter IV, In

essence it was the result of a series of approximations of

106

the f.o.b. city plant prices for all markets.
The price variations that were found to exist between

the markets and the basing point were found to be less than
the cost of transportation between the two points. The die-
tortion of the appropriate ice-price line moving out from
the basing point determined the amount of variation from
that of transportation costs. This variation was found to
be influenced by the location of the market in relation to
the surplus area. distance to the basing point. density of
production and the number and location of competing markets.
The above factors were quantified and used as indepen-
dent variables in the formula I“: bIXi + bzx2 + b325 + bhxh
to determine the degree of accuracy with which the price
variation (2) could be predicted. The regression co-
efficients which resulted from a regression analysis were
found to be significantly different from zero indicating
that all the independent variables were significant in de-
termining the price variation. A correlation coefficient
of .9996? was obtained when the predicted price variations
were tested against those observed in the theoretical model.
In Chapter v an approximation of the size. shape and
location of the present supply areas was made. This approx»
imation was based on the price variations suggested by the
location differentials in the present Southern Hichigan Ear»
keting Order. The variation for the individual markets was
taken to be equal to the location adjustment applicable to

the county or counties in which the marketing area was

107

located.an

when comparing the two models it was found that the
variable cost incurred to move the total market requirements
of ‘Rovember. 185.855.360 pounds. was $120,967.83 in the
model representing the existing conditions and 3110.030.56
in the theoretical model. The $10,937.32 decrease was the

result of a 30.00538 decrease in the average total variable
cost associated with transporting a hundred weight of milk.

The average length of trip decreased from 65.1 miles in the
model representing the existing conditions to 59.5 miles in
the theoretical model making these savings possible.

The following general conclusions can be drawn from

this study.
1. It is possible within the perfect market con-

cept to devolup a most efficient system of
supply areas.

2. The correct price variation among the market
will insure a minimization of total cost of
transfer.

3. Price variation is a function of the char»
acteristics of the market in relation to the

basing point.
4. The f.o.b. city plant prices must be greater

than the basing point price minus the varia-

ble cost of transportation between the basing
point and the market if the supply area

5.

6.

T.

108

boundaries are to be defined.

The fixed costs of transportation must be
included in the f.o.b. city plant prices,
leaving only the variable cost to determine

a competitive boundary if supply areas are to
be efficient.

The present system of supply areas does not
insure minimisation of the transfer costs in
meeting the silk requirements of the designated

markets.

Total costs can be decreased if the present
system of supply areas are reorganized through
price variation adjustment.in accordance with
the model deve10ped.

APPENDIX A

110

Appendix A, page 1 - AVERAGE MILK PRODUCTION PER cow
FOR HIGH AND Low MONTH AED THAT monru's PERCENTAGE
OF THE TOTAL annuat rnocucron. MICHIGAN.

 

 

1950 - 1959

prgfiztion 5333331.” .312? 533.3 :f gogg‘ggt‘é

per cow per cow per cow total annual total annual
Year (pounds (pounds (pound production productim
1950 651 432 6 . 280 10. 37 6. 88
1951 654 435 6.340 10.32 6.86
1952 667 #52 6,470 10.31 6.97
1953 660 450 6.500 10.15 6.92
1954 666 455 6.510 10.23 6.99
1955 675 l$80 6.670 10.12 7.20
1956 670 485 6.820 9.82 7.11
1957 691 539 7.090 9.75 7.60
1953 692 560 7.200 9.61 7.78
1959 696 556 7.270 _g‘fizl _I&§2
Average 10.03 7.20

“_...A

Hichigen Departs-eat of Agriculture. Michigan Agricultural
StatiatIOI. 1956. p. ‘5. 195?. ps 43’ 1959. p0 4no

.9

111.

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APPENDIX I

113

Appendix 3 - ESTItATIon 0? THE AVERAGE PRODUCTION ”ER
00% BY DISTRICT, MICHIGAH, 1959

 

District
average
production
as a percent Average
of the State Average production
Production average production per cow by
per cow production per cow district
District 1951 y 1951 1959 3/ 1959 2/
pounds pounds pounds
1 5.790 83.9 7270 69453
2 5,664 87.0 ” 6,3?5
3 5.793 83.0 I. 6.398
4 6.124 9a.1 " 6,841
5 6.119 94.0 " 5.834
6 6,54‘“ 102.1 I! 7.422
7 6.3“ 2 102.2 " 7.430
8 6.8%} 105.1 " 7,5hl
9 6.973 107.1 " 7.736

 

%/ Michigan Department of Agriculture, Dairy Trends in
.ichigan. June 1955. p. 16.

g/ Michigan Department of Agriculture, Hichigan Agricultural
Statistics, July 1960, p. 37.
2/ Column 2 applied to column 3.

0"]!!! O

115

Appendix 3 - r“O‘J"TIOW 0e V'"uracmr“1'
”ILK BY DISTRICT, “I" 1131“, 1957

 

 

A‘. 2311. .uT; 1959
Estimated Average Projected Projected
yearly rate of 1953 1959 Estimate-i
production decrease production production November
by district of by by frciucthga
District _1_/p1 04101.10?! 9/ district 1/ dis tricth a/g/
(W‘llicn (percentI‘ (million (2 illion (mi ion
pounds) pounds) pounds pounds)
Column 1 Column 2 Column 3 Column Column 5
9 153.4 13.3 % 136.5 117.7 8.5
3 23.° " 23.3 $0.9 1.5
4 25.3 " 99.? 19.1 1.3
5 370.8 " 319.5 275.5 19.8
6 231.0 " 199.1 171.6 12.4
7 131.8 " 155.7 135.1 9.7
3 973.6 " 935.3 903.3 14.6
9 52.3 " 45.5 39.2 2.8

 

1/ The estimated 1957 receipts by district: the total 1957

production (footnote 9, pageixa times the percent of cows
2 years and over in each district.

3/ G. TcBrile, 1!. Blanchard. Chnnfies in Vichircn’e Ven-
ufactzring ‘11” In‘xct rv. Elichigun 3tate Lnifiersifyo Ue-
partnent 01 A ricuItural Economics, Special Eulletin 427,
19599 DD. 13:19.
2/ Column ? applied to column 1
[5/ Column 2 applied to column 3
‘é/ Rover ber production taken to equa.l 7.9. percent

appendix B) of the total.
g/ The percentage of cows two years and over in each county

is applied to these district fi~ures for ”ovenber to
arrive at the county figures in column 3 of Table L-a.

APPENDIX D

117

Appendix D, page 1 - ADJUSTMENT FOR EXPORTS IN EXCESS
OF IMPORTS FROM MICHIGAN AND FOR DEFICIT
PRODUCING COUNTIES, NOVEMBER 1959

 

Source and Amount Source and Amount Total Amount

 

of net eXport to of net export to of

Toledo market Cleveland net export
“7323:3595” “:22:an “Isms?”
Calhoun 253.355 253.355
Hillsdale 10.886 253.355 264.241
St. Joseph 253.355 253.355
Kalamazoo 253.355 253.355
Branch 4,406 1,013,420 1,017,826
Lenawee 36.029 36,026
Monroe 8,100 8.100
Jackson 1.620 1.620
Wastenaw 3,758 3.758

 

‘1/ Based on percentages given in Analysis of Producers

Recei ts, Toledo. Ohio marketing area, January, June. and
DEcemEer. 1959. Branch County 6.8%, Hillsdale County 16.8%.
Jackson County 2.5%. Lenawee County 55.6%, Monroe County 12.5%.
Washtenaw County 5.8%.

g/ One-half allocated to Branch county where plant is

located and 1/8th to each of the remaining counties as
indicated.

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119

Appcndix D. page 3 - SUMMARY OF DEDUCTIONS
FOR NET EXPORTS AND CONTRIBUTION TO DEFICIT
PRODUCING COUNTIES BY COUNTIES

_A.‘ w Vfi—

Amount deducted due Amount deducted Total

 

to contribution due to net enount of
to deficit exports deduction
Counties (pounds) (pounds) (pounds)
Antrin 78.327 78.327
Bay 72.955 2.955
Branch 1. 017 . 826 1.017 . 826
Calhoun 253. 355 253. 355
Case 681.135 681.135
Clare 9.974 9:974
Gladwin 155.883 12533 .883
Gratiot #8.636
Billadale 264.241 264: 2&1
Isabella 194.545 198: 585
Jackson 1.620 1. 620
Kalamazoo 253.355 253.355
Kalkaaka 177.107 177.107
Lake 15.971 15. 971
Leelanau 131.456 131.456
yang" 5 36.026 6.026
a
Hissaukee {9:323 , &:§EO
“on”. 8 . 100 8. .100
Osenau 19.360 19.360
Decode 20.452 20. 452
Oteegc 21.073 21.073
Saginaw 28.318 24.318
St. Joseph . 253.355 253. 355
van Baron 681.134 681.134
waahtenau 3.758 3. 758
Vexrord 112.493 112.493

”PEDIX E

121

Appendix K see 1 - ESTIMATED DENSIT! 0? MILK
Péo uc TION. PER SQUARE MILE.
MICHIGAN. NOVEMBER 1959

Production Available

 

Market and b Count Square Miles
Contributing Counties {pounds in County
Keizgazoc 28 56

x amazoo

St. Joseph §:3 IE. 22 5 go

Van Buren 1.625. 471 07

Allegan ;.;68:460 823
I O 0

Average production per square mile a 5.086 pounds.

Battle Creek
Barry , 4.355.870 549
Calhoun 6. 414. 445 709
Kalamazoo 2.855.012 567

316 Joseph EIEIBI428 508
I O 2.33,

Average production per square mile a 6.834 pounds.

Jackson 6
Jackson 9 3 O
can... 5:82:35 03
Branch 4. 653. 360 506

8‘. Joseph 11 8 8 508
15.382.156 3325

Average production per square mile a 8,106 pounds.

Lansing
Ionic 6. 257. 326 575
Clinton 6. 251. 580 571
In 7. 334. 633 . 559
Ea 6 .278.A73 567

n
Barry 4.2;6.4£g . 549
' e 0 15:83!

average production per square lile = 10.804 pounds.

Huskegon
Huskegon 2.826. 416 504
Ottawa 4.403.461 54
Newaygo 4.168.725 57

Oceans 2 602 60 836

Average production per square mile = 5.071 pounds.

122

Appendix a. page 2 - tannins swam or am
raowcucl. rm scum: nu.
«mama. momma 1959

 

Production Available

 

lartet and b Count uare lilac
Contributing Counties {Pounds n County
Grand Rapids
K031 8.323 a 711 862
Montcalm 3. .111 712

33'... 2:323:21: 33%
Ottawa '5§t§8i:;%§ 3:;g;

Average production per square nile a 7.545 pounda.

Flint
Geneeee 7.092.322 644
Saginaw 6.038.262 812
Shiawasaee 6.405.806 540
Cratiot 1.916.197 566
unntcain 3.040.111 712
lecoata 1.787.483 563

Isabella 2.0;}.343 ' ‘3'%%§
- O O 0

Average production per square nile a 6.431 pounds.

City-Saginaw
“£33111”! 6.038. 262 812
h: 4.222.889 446
m0 ’ 1. e 337 368
loeco 661.697 547
08¢" 2.178.654 574
Oiadvin 841.747 503
Isabella 2,073,343 572

Clare £44,852 z_§%%
D O I

Average production per square aile a 4.241 pounds.

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Appendix E. page 3 - ESTIMATED DENSITY OF HILK

PRODUCTION. PER SQUARE MILE.
uIcmcm. nomzm 1959

Production Available

 

Market and Count Square lilac

Contributing Countica pounds; in County

Detroit
Monroe 333.891 562
Lenavee 6.949.766 754
am edaie 6. 377.192 601
Branch 4.653.360 506
8‘. JOHN! 2.318.428 23:
Wayne 1.334.205 -
Wanhtonav 6 . 524. 595 716
Jack-on 6.295.953 703
Calhoun 6.414.445 709
Kano-b 7 . 303. 243 481
Oakland 5.336.819 877
Livingston 5.727.611 571
Ifishll 7.334.633 559
Elton 6.278.473 567
Barry 4.356.470 5‘9
st. Clair 7.788.693 745
Lapeer 10.173.234 659
Oeneaee 7.092.322 644
Shiauaaaee 6.405.806 540
Clinton 6.251.580 571
Ionia 6.2 7.326 575
Montca1n 3. .111 712
Gratict 1.916.197 566
Saginaw 6.038.262 812
Tuecola 6.178.986 816
Sanilac 13.173.134 951
Huron 020 822

. . 17397

Average production per square nile a 8.939.

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