LAGGED RESPONSE EN SELECTED PORK PRiCES'

'E’hesis $03 the Gear» at? M. S.
MNHIGM STATE UNIVERSITY

James G. 5m“
1962

  
 

LIBRARY

Michigan State
University

 

 

ABSTRACT
LAGGED RESPONSE IN SELECTED PORK PRICES

by James G. Snell

Various pieces of literature have advanced the idea
that pork prices at the retail level lag behind those at
farm or wholesale level. They indicate that the length of
this lag depends upon (1) the pricing policies of the
retailers and (2) the direction in which prices are moving.

Since the main short run price determining point
is at the packer or wholesale level, it was assumed that
if a lag existed it was partially due to imperfect knowledge
on the part of retailers. Therefore. no lag was expected
between farm and wholesale levels but that there would be
a lag between farm and retail and wholesale and retail
levels.

The data used were average weekly data. consisting
of prices of selected cuts at retail and wholesale levels,
farm price and quantity of U.S. l, 2 and 3 barrows and
gilts, and farm quantity of U.S. Choice beef. All of these
prices and quantities were taken at Chicago with the

exception of the retail prices which were taken from the

James G. Snell

M.S.U. Consumer Purchase Panel.

The various prices and quantities were fitted by

regression equations of the following form for determination

of the proper
(Y1)
Set j
(Yi)

lag:

=(a+b.z. +b.Q. +u)
1 1 1 1 t

= ( a + b.Z. + b.Q. + u)
1 1 1 1

£_.L_.L_.£_.
0
wNi—IO

t-3

where Yi = a given price of a specific

cut one level above that price used as an
independent variable; Z. = either farm or
wholesale price of a specific cut.
depending on the lag being determined:

Q. = farm quantities of pork and beef;

jl= a specific set of equations; t =
observation period of the variables; and
the number following the j = the number of
observation periods the independent variables
are lagged behind the dependent variable.

The equation having the largest R2 in a set was

tested by the

. . *2
F ratio test to determine whether the Su

(estimated variance of the U's) of this equation was

significantly
the same set.

After

smaller than the S: of the other equations in

the preceding equations were calculated. a

dummy variable which denoted the direction of the change in

Zi from t to t+l was added to the equations to determine

whether the direction of the price change influenced the lag.

An F ratio test was made to determine whether the S: of

the equation using the dummy variable was significantly

James G. Snell

smaller than the S: of the equation not using the dummy
variable.

Margins were computed on a lagged basis and fitted
as functions of various prices and quantities of hogs.

When computed on an over-all basis, which made no
distinction between upward and downward price movements.
there appeared to be a one week lag in farm to retail
prices and in wholesale to retail prices.

When the dummy variable approach was used. the
dummy variable seemed to have no significant value. This
indicated that there is no difference in lag between a
rising and a falling market. Because of this. the
assumption of the lag being based on a knowledge situation
loses validity.

The margins proved to have no positive value when
formulated on a lagged basis.

The conclusions reached were (1) there is no
lag between farm and wholesale prices; (2) there is a one
week lag between farm and retail prices and between
wholesale and retail prices; (3) there was no difference
in lag between an upward and a downward market; and

(4) margins cannot be explained by price and quantity alone.

LAGGED RESPONSE IN SELECTED PORK PRICES

BY

James G. Snell

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER.OF SCIENCE

Department of Agricultural Economics

1962

ACKNOWLEDGEMENTS

The author wishes to express his sincere appreciation
to all those who assisted him in the preparation of this
thesis. The author is especially indebted to Dr. Carleton
Dennis who served as the major professor and guided the
research. and to Dr. L. V. Manderschied who gave freely
of his time for consultation and assistance of the mathe-
matical part of this thesis.

Thanks are also due to Karma Beal who handled a
large part of the computational work which involved difficult
and previously untried punch card manipulation.

Special thanks are due to my wife. Lucille. who
not only provided the financial support for me to continue
my studies but also typed much of the rough manuscript.

Her encouragement. tolerance and help are sincerely

appreciated.

ii

TABLE OF CONTENTS

Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . 1
Purpose 1
Previous Studies 1
Usefulness of Results 4
II. GENERAL THEORY . . . . . . . . . . . . . . . . 5
Introduction 5
Supply and Demand 5
Production 8
The Market 11
Buyers and Sellers 12

Homogeneity of Products and
Discrimination 15
Knowledge 16
Summary 21
III. DATA AND METHODOLOGY . . . . . . . . . . . . . 23
Data Source 23
Choice of Prices 25
Methodology 27
Lags 29
Margins 37
IV. OVERrALL LAG RESPONSE . . . . . . . . . . . . 39
Farm to Wholesale Value 39
Farm to Wholesale Cut 49
Farm to Retail 67
Wholesale to Retail 71

iii

Chapter Page

V. LAGS WHEN CONSIDERING THE DIRECTION

OF PRICE CHANGES . . . . . . . . . . . . . 84

Farm to Wholesale 84

Farm to Retail 86

Wholesale to Retail 89

Summary 91

VI. MARGINS . . . . . . . . . . . . . . . . . . . 92
Farm to Wholesale Value 92

Farm to Wholesale Cut 93

Farm to Retail 96

Wholesale to Retail 97

VII. SUMMARY AND CONCLUSIONS . . . . . . . . . . . 99
Summary 99

Conclusions 103
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . 104
APPENDICES . . . . . . . . . . . . . . . . . . . . . . 107

iv

5.1.

LIST OF TABLES

1.0 . . . . . . . . .

A2 .
and S from equation sets
lag periods . . . . . .

A2 .
and Su from equation sets
lag periods . . . . . .

and S2 from equation sets
u I
by lag periods . . . . .

and S2 from equation sets
u .
by lag periods . . . .

and S2 from equation sets
u .

by lag periods . . . . .

and S2 from equation sets

16 agd 17 by lag periods

and
21 and 22 . . . . . . .

2 to 5 by

6 and

8. 9.

4. 5.

6. 7.

8. 9.

Estimates of coefficients for equation

11 and 12

13.

10.

R2 deletes from equations 19. 20

and

15.

l

14

Page

47

58

68

8O

86

88

9O

95

Figure

l-a to

3-a to

4-a to

6-a to

LIST OF FIGURES

Average weekly movements of farm
price. wholesale value and farm
quantity of hogs . . . . . . . . . .

Residuals from equation 1.0 . . . . . . .

Average weekly price movements at farm
and wholesale levels . . . . . . . . .

Residuals from equations 2.0 to 4.0 . . .

Graphic illustrations of the coefficient
of determination obtained from
equation sets 6 and 7. by lag
periods . . . . . . . . . . . . . . .

Average weekly price movements at retail.
wholesale and farm levels . . . .

Graphic illustration of the coefficient
of determination obtained from
equation sets 8. 9. 10 and 11 by
lag periods . . . . . . . . . . .

vi

Page

40 to

51 to

59 to

72 to

46

50

57

61

69

78

80

CHAPTER I
INTRODUCTION

Purpose

The purpose of this thesis is to examine the lagged
response of retail pork prices to price changes at either
the farm or wholesale level. It does not attempt to predict
prices or margins at any level and. therefore. does not
use complete statistical or economic models. A secondary
purpose is to View the effect on margins of the lagged

response in a changing price situation.

Previous Studies

In 1943 Little and Meyers attempted to determine
the time lag between farm. wholesale and retail prices of
certain selected foods.l This study was concerned with the
fact that price freezes by the Office of Price Administration
could either exert ”squeezes? or ”abnormal profits" on

certain segments of the industry. In determining the lag.

 

1Herschel W. Little and Albert Meyers. Estimated
Lags Between Farm. Wholesale and Retail Prices for Selected
Foods. U. S. Department of Agriculture Monograph (Washington.
1943): p. l.

Little and Meyers used monthly data: however. they stated
"Theideal data for this purpose would have been weekly
average prices."2

The first step in the above study was to run simple
.correlation coefficients on farm-retail and wholesale-retail
price spreads at various lagged periods. Then by interpo-
lation the proper lag was computed and a lag of 2 to 3
weeks was found for pork. Checks were run using bimonthly
data which indicated that the interpolation was correct.

A large influence was exerted by changing prices. When
prices were rising. there tended to be little or no lag;

for price decreases. retail prices seemed to lag by approxi-
mately one month. The study also included a distributed

lag equation which also supported a lag period.

Little and Meyers used a composite figure for
retail price of pork. which included both fresh and cured
pork. The farm price used was the price received by
farmers multiplied by 1.9 since 1.9 pounds of live hog
produces approximately one pound of retail pork.

They found that their results were not conclusive.
but they hoped that their study would stimulate further

study in a largely neglected field. After searching through

 

2Ibid.. p. 4.

considerable literature. this writer feels that it is still
a neglected area.

Another contribution to the estimation of lagged
price relationship of pork was made by Stout and Feltner.
Their purpose was to study differences in country and
terminal market prices and farm level and wholesale value
in a lagged relationship. For this study they used data
from September 14 to 25. 1959; November 30 to December 11.
1959; and February 15 to 26. 1960. They found. using simple
regression. that there exists a higher relationship between
unlagged prices than lagged prices. They obtained an R2
of .884 on an unlagged basis and .857 on a one day lag.3

Another area which is concerned with lags is the
study of margins. Of the existing studies. Pork Marketing.

. 4 . .
Margins and Cost is an example. This study was concerned

 

with marketing margins and costs affecting them. No attempt
was made to determine the lagged relationship though the
publication pointed out that lag in price changes cause

some of the widening and narrowing of the margins associated

 

3Thomas T. Stout and Richard L. Feltner. VA the on
Spatial Pricing Accuracy and Price Relationship in the Market
for Slaughter Hogs.” Journal of Farm Economics. XLIV (February.
1962). P. 217.

4Pork Marketing. Margins and Cost. U.S. Department of
Agriculture Miscellaneous Publication No. 711 (Washington.
1956). p. 3.

with pork prices. In determining the margins. average
monthly prices were used. The farm and wholesale prices
were obtained from Chicago; the wholesale price being
computed by Livestock Market News from National Provisioner
data. Farm price was for 200 - 220 pound barrows and gilts.
These studies still leave a wide area in which a
weekly price series could be used to determine the lag in
retail pricing and the degree to which this lag influences

margins.

Usefulness of Results

The results of this thesis may be helpful in

explaining the fluctuations of margins in pork pricing.

It may also be helpful to the retail trade by showing how
a better knowledge of the pricing situation at a lower
level could decrease fluctuations at the retail level.
This thesis also serves the purpose of gathering together
weekly average prices over a seven year period which could
be used in a more detailed and sophisticated approach to

retail price prediction.

CHAPTER II
GENERAL THEORY

Introduction

This section is devoted to the presentation of the
general theoretical concepts that can be considered to under-
lie the pork market. It is these theoretical concepts that
lay the basis for the lag study to be presented in later

chapters.

Supply and Demand

In static economic theory.1 supply and demand sche-

2.3

dules or curves are maximum concepts. The demand

 

1For the assumptions that make the system static

see Appendix I.

2Notes on lectures in Price Theory given by Milton
Freidman. January to June. 1951. in Economics 301 and 302.
University of Chicago. p. 9.

3While this author prefers to consider supply and
demand to be maximum concepts. a substantial number of
economists consider them to be exact concepts. That is.
demand can be defined as the quantity or quantities of a
product or service buyers are willing and able to take at a
given price or series of prices. Similarly. supply can be
defined as the quantity of a product or service that would
be made available to buyers at any one of the specified series
of prices if such a price were offered. It will be noted
that these definitions require only ability and willingness
to buy or sell and that no actual transactions are required.

5

schedule or curve represents the maximum quantity per unit

of time that the consumer will take at various prices;

stated in another way. the demand curve shows the maximum
prices consumers will pay for different quantities per unit
of time. The supply schedule or curve represents the maximum
quantities per unit of time that the sellers will place on
the market at various prices. or the minimum prices which
will induce suppliers to place various quantities on the
market.

The resulting prices may be termed the supply and
demand prices.5 The supply price may be viewed as the price
the producer must receive before he will deliver the good.
The price the producer receives for his product must be
sufficient in the long run to cover the cost of production
plus a normal profit. Since most production is carried
on under increasing costs. the larger the quantity. the
larger the price that is needed to keep the quantity
forthcoming. i.e.. supply priceincreases as quantity
supplied increases.

The demand price concerns the utility of the product

 

4Richard H. Leftwich. The Price System and Resource
Allocation (New York. 1961). pp. 28-31.

\ 5A. Marshall. Principles of Economics. Book 5
(New York. 1922). pp. 323-503.

to the consumer. It is the maximum price the consumer is
willing to pay for a given quantity; at a higher price. the
marginal utility of the good is less than the marginal
utility of the money the product cost. The consumer may
buy a smaller quantity at the same price or a larger
quantity at a lower price; demand as a maximum concept does
not prevent this. Just as production is usually carried
on under diminishing returns. so is a product subject to
diminishing utility. As the quantity obtained increases.
the utility of each additional unit (marginal utility)
decreases. and the larger the quantity. the smaller the
demand price will be.6

The demand and supply price may be summarized in the
following manner: the demand price is the price the good
will actually bring in the market; the supply price is the
price the producer must receive for his product to continue
production of the quantity indefinitely.7

The normal or standard approach is to consider price

as the independent variable and quantity as the dependent

one. In this approach. price changes as quantity being

 

6Friedman. pp. 35-43.

7Kenneth E. Boulding. Economic Analysis (New York.
1955). p. 114.

 

demanded changes and this results in the quantity supplied
being varied according to the demand price. This is an
intermediate or long run situation.

Marshall used the quantity independent-price
dependent approach which is a short run situation where a
given quantity brings forth a given price. In this. quantity
assumes the more dominant role and is not considered to be
9controlled" by price. This approach is also substantiated
by Working. who said. "From the standpoint of the entire
market. however. meat supplies determine prices rather than
the other way around. This refers. of course. to relatively
short run situations."8 In this paper. because of the pre-
determined supply. the quantity independent-price dependent

approach of Marshall will be used.

Production

In looking at distributed lag response in hog
production. Ferris found that in the period 1925 to 1941.
the supply of hogs was almost entirely determined by the

prices of hogs in the preceding fall farrowing time.9

 

8Elmer Working. Demand for Meat. Institute of Meat
Packing (Chicago. 1954). p. 8.

9John N. Ferris. Dynamics of the Hbg_Market with
Emphasis on Distributed Lags in Supply Response (unpublished
Ph.D. thesis. Michigan State University. 1960). p. 151.

For the period 1947 to 1958. the prices received during the
fall farrowing and the prices the preceding fall were
significant in determining the supply of hogs the following
year. This indicates that the supply of hogs on the market
at any given time is not a significant function of the
prevailing price. but rather a function of factors in the
two preceding years.

Production is for all practical purposes. fixed
at its upward limit once the sows are bred.10 Production
may be gauged downward by selling the sows. but they are
normally discounted if the pregnancy is visable. Marketing
time is also essentially fixed because of the nature of
the hog. Feed represents 84% of the total production cost of
hogs;ll so economies practiced in feeding represents one
of the best ways of cutting the variable cost involved in
producing hogs. This fact exerts a large influence on the

marketing time. Hogs make their most rapid gains from 200

to 225 pounds.12 This is at the top of the weight range

 

10Arthur A. Harlow. "The Hog Cycle and the Cobweb

Theorem." Journal of Farm Economics. LXII. No. 4 (November.
1960). p. 848.

11W. E. Carroll and J. L. Krider. Swine Production

12Ibid.. p. 207.

10

that packers prefer;13 it is usually considered unprofitable
to feed the hogs to a heavier weight because each additional
pound of gain is obtained at increasing quantity of feed

per pound of gain.14 Therefore. marketing time is largely
predetermined by the nature of the product. It may be put
off two or three weeks. but this is usually considered the
practical limit.

The hog market is characterized by a predetermined
supply that must be marketed in a relatively small range of
time. i.e.. an inelastic supply curve for hogs. It is this
interaction of the more elastic demand curve and the inelastic
supply curve that determine the price of pork; price is set
by the available supply.16 This can be considered a quantity

independent and price dependent market.

 

13P. Thomas Ziegler. The Meat We Eat (Danville.
Illinois. 1958). P. 47.

14Of course. there will be times in which it will
be profitable to feed hogs to either a lighter or heavier
weight. This will depend on many factors. (See "How
Heavy Should I Feed My Hogs?.94ggriculture Situation. 1949).
But other things remaining equal. 200 to 225 pounds is
normally considered the most profitable weight.

15KarlA. Fox. The Analysis of Demand for Farm
'Products. U.S.D.A. Bulletin No. 1081 (Washington. 1953).
p. 23.

 

 

16This is the convergent case of the Cobweb Theorem

‘where price is determined by the intersection of the demand
curve with the inelastic supply curve.

11

The Market

A competitive market may be defined as a large

number of buyers and sellers. all engaged in

the purchase and sale of identically similar

commodities. who are in close contact one

with another and who buy and sell freely among

themselves.17

Perfect competition requires an additional criteria

of perfect knowledge. It is generally agreed that no market
is truly perfectly competitive. It is assumed that many
markets may be classified as such for the purpose of analysis.
Whether or not the packing industry18 can be considered
competitive has been debated. Nicholls stated that there is
evidence of dominance and price leadership among the meat
packers. but they have not resorted to aggressive pricing
actions among themselver or toward the smaller firms.19
Actually they have followed market sharing with buying prices
that approach the collusive-oligopsony level. Williams.

on the other hand. says that the changes that have occurred

since Nicholls' study have brought the packing industry

 

l7Boulding. p. 45.

18The meat packing industry was defined by Williams
to include all packing (slaughtering) plants. packer branch
houses. independent wholesaling distributors and procurement
operations of retailers.

19William H. Nicholls. Imperfect Competition Within
Agriculture Industries (Ames. Iowa. 1941). pp. 114-131.

12

. . 20 . .
closer to perfect competition. He Cites improved trans—
portation. better knowledge and decentralization as some

of the causes.

Buyers and Sellers

At the farm level the number of sellers meets the
requirement for a competitive market. In 1959. there were
1.846.758 farms producing hogs.21 None of these sellers
are large enough to influence prices by their own action.
except by the quality of their hogs. The number of farms
on which hogs are produced varies with the fluctuation of
hog prices. The farmer tends to stay in a declining market.
once he is producing. for a longer time than is required
for farmers to enter the market when the price is rising.
Even with this fluctuation in number of farmers. there is
still a relatively large number of sellers at all times.

The packing industry. on the other hand. is character-
ized by dominance of a few large firms with many smaller

local firms.22 In the past. the large firms have operated

 

20Willard F. Williams. *Structural Changes in the
Meat Wholesaling Industry.? Journal of Farm Economics. XL
(May. 1958). pp. 317-338.

21U.S. Department of Commerce. Bureau of Census.
Census of Agriculture for l959-Preliminary (Jan.. 1961). P. 14.

22Williams. pp. 315-329.

13

rather large centralized slaughtering plants. In recent
years. there has been a trend toward decentralization. with
smaller more efficient plants. At the same time. the percent
of total slaughtering done by the four largest firms has
been declining; while small local plants have increased in
number by nearly one-third.23

The situation could be likened somewhat to the
example used by Stigler of two-piece men's suits with knickers
where 78% of total output was produced by four main firms.
Hewever. there were 144 firms making two-piece suits with-
out knickers.24 Had it become very profitable to make
knickers. the other firms could have begun to produce them.
In the meat industry. there are many small firms. some of
which operate plants that are relatively efficient and not
subject to the large fixed cost which faces the larger
national firms. Many of these smaller plants produce
specialty items such as luncheon meat. sausage. etc. How-
ever. if it became abnormally profitable to sell meat by the

wholesale cut to retailers because of pricing policies of

the dominant firms. the smaller firms could enter into the

 

231bid.. p. 329.

24George J. Stigler. The Theory of Price (New York.
1952)! p. 130

l4

sale of the cuts in their own locality and force the national
firms to reduce their prices to regain their business.

If this can be considered to be relatively true. then
dominance of the large firms becomes of less importance as
long as they take only normal profits and act in a relatively
competitive manner. Even though the number of buyers does
not fit the perfectly competitive model. the situation is
such that it will be assumed that a competitive model will
not be too far removed from reality for the purpose of
analysis.

At the retail level. there are enough buyers of whole—
sale meat to assume perfect competition. Although chain
stores sell approximately 38% of the meat sold.25 there are
many smaller local chains and neighborhood food markets
that sell fresh meat.

The pricing situation at the retail level is usually
quite competitive. There may be price leaders in a given
area. but if these leaders follow a policy of pricing that
is too far removed from the competitive equilibrium. other
stores will force the leaders to adjust their prices more
in line with what the competitiveness of the situation

dictates.

 

25Facts in Grocery Distribution (Progressive Grocer;
1958). p. F-3.

15

Price reductions may be accomplished for the
purpose of a "leader" or "drawing card" by certain stores,
but this is a short run condition. If price reductions
were to continue. other stores would also lower prices;
this in turn would force all into a cutthroat situation.
which would be unprofitable to all involved.

Homogeneity of Product and
Discrimination

Homogeneity of pork can generally be assumed. The
establishment of U.S.D.A. grades and federal inspection has
made product differentiation difficult. The various packers
have established their own standards and attempted to per-
suade the consumer of product difference. This is compli-
cated to a further degree by large chains (chains are
defined as eleven or more units) establishing their own
grades. Beef grades probably have a wider range of consumer
knowledge than pork grades do. Although there has been an
attempt to persuade the consumer of product difference. the
consumer has little real basis for discriminating against
pork on the basis of who processed it.

It can also be assumed that there is relatively
little discrimination in buying and selling. In certain

cases. packers may pay somewhat more for hogs from a certain

l6

producer but this is because of the quality of the hogs which
that farm produces. The packer will sell to anyone; the
larger the quantity the lower the price. This cannot be
considered discrimination. but a saving in cost from selling
in volume business. The price that faces the consumer does

not vary because of discrimination.

Knowledge

There will never be perfect knowledge or foresight.
In this knowledge aspect. the farmer has the least perfect
knowledge of the three groups: farmer. wholesaler. or
retailer. This limitation has been alleviated somewhat
through daily radio reports. newspapers. and market outlook
studies done by various institutions. At the beginning of
production. the farmer has only a vague idea as to the
quantity of hogs that will be produced by other farmers.
By the time feeding starts. he has a better knowledge of the
situation and has some basis for a decision as to the
weight and speed at which he will feed his hogs. At market
time. again he has only a general idea as to the price he
will receive if he ships to a terminal market. Once the
farmer has committed his hogs to the terminal market. he

has little choice but to sell. He has become a price taker.

17

The declining percentage of hogs being sold on the terminal
market and the increasing percentage being sold directly
or locally may be an indication of the fact that the farmer
recognizes the limitation he faces in the knowledge situation.
By selling locally. he can limit sales to those hogs that
meet the proper weight. reduce his marketing cost and pick
a day on which the price seems most agreeable or advantageous
to him. He has placed himself in a situation that entails
more bargaining. Even though the price he receives is
usually less than he would have received on the terminal
market. his costs may also be less and the local market
enables him to put off marketing for a short time without
incurring additional costs. This removes the farmer from
the position of having to sell once he places his hogs in
the terminal market.

Packers could find this somewhat advantageous also.
They are not faced with such an inelastic supply curve; by
increasing their prices. they obtain more hogs on a given
day. The market is still a quantity independent-price
dependent one. but for any given period the supply is less

inelastic. The packer still has the knowledge of his costs

 

26A. A. Dowell and K. Bjorka. Livestock Marketing.
lst Ed. (New York. 1941). pp. 148—150.

18

and how much he must receive for the product at the whole—
sale level. Because of the time in operation. the national
packers usually have a relatively good idea of the demand
curve they face. Since they know the wholesale price they
can expect to receive and their costs. they know how much
they can pay for the factor of production. hogs. to make

a profit. When viewed in this manner. the farm price be-
comes a residual and the farmer becomes a price taker. wa-
ever. this is a short run situation. In the long run. it
is still the interaction of supply and consumer demand that
decides the equilibrium price and quantity of hogs.

Because of changing supply due to the hog cycle.
the hog market is not in equilibrium. Packers would prefer
a relatively constant supply of hogs. If the packer can
obtain a stable supply throughout the production year. he
will be able to build a plant of optimum size for his
particular needs and operate at minimum cost. Actually.
the packer must have a plant that has excess capacity in
periods of slack supply and under capacity during peak
supply. This situation makes for relatively large
average total cost and is reflected to a certain degree in
the nature of margins and how they act under various supply

conditions.

19

Just as packers prefer a more constant supply. so
do retailers. Retailers believe that consumers would
rather have stable than fluctuating prices. They. there-
fore. desire stable supplies because of the stable prices
that should follow. Retailers also prefer to change price
in a downward manner rather than in an upward direction.27
But the cost of a mistake in not raising prices when they
should will normally be greater than the cost of not lowering
prices when possible. Therefore. when prices are dropping.
retailers tend to wait for a trend to be established but
respond rather rapidly to an upward price movement. This
tends to cause an alternating widening and narrowing of
the retail margin.2

The degree of knowledge possessed by the various
participants in the market affects the fluctuation of the
margins and causes the lag in retail price adjustment to
changing supply of hogs. If the retailer bases mark-up
on replacement cost. his prices will change with or lag

. 2
behind wholesale price. depending on how often he buys meat. 9

 

27Little and Meyers. p. 2.

28George Motts. Marketing Handbodk for Michigan
Livestockereats and Wool. MSU Agricultural Experiment
Station. Bulletin 426. p. 30.

29Little and Meyers. p. 3.

20

The wholesaler knows with a large degree of accuracy
what price he must receive for the pork to make a profit.
Therefore. one would expect to find very little lag in whole-
sale price adjustment to changing supply relative to the lag
in retail price adjustment. However. U.S.D.A. Miscellaneous
Publication No. 711 indicated that wholesale prices lagged
behind farm prices during sharply changing supply.30 This
is in opposition to the findings of Stout and Feltner.31
and to the hypothesis of this thesis. The difference may
be due to the fact that Miscellaneous Publication No. 711
used prices of 200 to 220 pound hogs while Stout and Feltner
used 180 to 270 pound hogs.

There may be lags in wholesale pricing for one
particular weight of hogs. but there should be no lag when
considering all weights. Packers or wholesalers may take a
negative margin on certain weights but could not do so for
all weights.

Stout and Feltner found that there was a higher
degree of association between live hog value and wholesale

value on an unlagged basis than on a lagged one. They also

 

30U.S.D.A. Miscellaneous Publication No. 711. p. 3.

31Stout and Feltner. p. 214.

21

found that while wholesale value may influence farm price in
the long run. wholesale value had little effect on farm
price on a day-to-day basis.32 This agrees with Haas and
Ezekiel in the finding that the general trend influences
farm prices more than day-to-day changes.33 Little and
Meyers said on the basis of a priori knowledge that a lag

in price changes is to be expected and that the lag would

be different in a rising market than in a lowering one.

Summary

What the consumer can be induced to pay for meat
he buys is the final fact which limits the price
which the retailer can pay at wholesale; and the
price for which the product can be sold at whole-
sale limits the price which packers can pay for
the live hog.35

Since hog supplies change more than does consumer
demand. the focal point in pricing pork and live hogs is
at the packer buying level where the change is first felt.36
As stated before. a priori knowledge indicates there will

be a lag in retail price response to supply changes. The

 

321bid.. pp. 217-218.

33G. C. Haas. and Mordecai Ezekiel. Factors Affecting
the Price of Hogs. U.S.D.A. Bulletin No. 1440 (Washington.
1926). pp. 10-11.

34Little and Meyers. p. 4.

 

 

35Haas and Ezekiel. p. 7.

36U.S.D.A. Miscellaneous Publication No. 711. p. 21.

22

interest of this thesis is centered in this lag. The fact
that margins tend to widen during times of large supply
and narrow during times of small supply seems to indicate
margins and the adjustment lag are related. Therefore.

a secondary interest is focused on margins.

CHAPTER III
DATA AND METHODOLOGY

Data Source

The M.S.U. Consumer Purchase Panel was chosen as the
source for retail prices of pork as this purchase panel
offered an unbroken seven year period with which to conduct
this study. The M.S.U. Consumer Purchase Panel was a group
of 200 to 250 Lansing. Michigan. families who kept detailed
records of their food purchases.1 The Panel was started
in February. 1951. but it was late in 1951 before as many
as 200 families were reporting. Certain inaccuracies in
their reports may be present. but this source is probably
the best presently obtainable for the type of study to be
conducted.

The farm and wholesale or packer level data was

obtained from the U.S.D.A. Market News.2 which is a weekly

 

 

1The Panel was under the direction of Dr. G. G.
Quackenbush and Dr. James D. Shaffer. For methodological
problems of organizing and operating the panel consult
James D. Shaffer. Methodological Basis for the Operation of
a Consumer Purchase Panel (unpublished Ph.D. thesis. MSC.
1952).

2U.S.D.A.. Livestock. Meat. W001; Market News;

Weekly Summary and Report. 1952 through 1958.

 

23

24

publication. The prices were those of Chicago as it was
felt that Chicago prices would most accurately reflect
prices in Lansing.3 Chicago is generally recognized

as the wholesale pricing center for the Midwest and Lake
States. much as New York is the pricing center for the East.
The U.S.D.A. publication was chosen because it gave weekly
averages. whereas many publications issue only monthly
reports. Since the lag is assumed to be relatively short.
it was thought that weekly data could more accurately
estimate the correct lag.

The wholesale value figure was compiled by the U.S.D.A.
from data taken from the National Provisioner. The whole—
sale value is a composite value per cwt. of the edible
portions.

By using data from the M.S.U. Consumer Purchase
Panel and the U.S.D.A. Market News. weekly averages were
directly obtainable. Not only were the weekly average
prices given. but all the time periods used by each source
were identical except in the case of farm price and quantity
of beef which were lagged two days behind the other
variables. These appeared to be the two most logical data

sources .

 

3Harold M. Riley. Some Measurement of the Consumer
Demand for Meats (unpublished Ph.D. dissertation. Michigan
State College. 1954). p. 159.

 

25
Choice of Prices

In choosing the retail cuts to be used. it was
decided that pork chops and roasts would be the retail cuts
most likely to show the minimum lag. The retail cut of
pork chop comes from the loin and roasts usually from the
loin or butt. These wholesale cuts of loin or butt are
usually sold immediately to the retail trade.4 Ham. picnics
and other cured meat cannot move directly into the retail
trade because of the curing time. Also. these cured cuts
have a longer storage life and may be carried from fall and
winter into the spring and summer more easily than fresh
pork.5

Fresh pork may be frozen and stored in this manner.
but the freezing qualities of pork are not conducive to long
periods of storage; frozen cuts usually are sold at a
discount. This is due to the nature of fresh pork fat
which contains a double bond hydrocarbon chain. These
double bond chains are subject to cleavage by oxygen.

When cleavage occurs. aldehydes and fatty acids are formed
which generally are considered to have a detrimental

effect on the palatability of pork.6

 

4Ibid.. p. 17.

51bid.

6Ziegler. p. 192.

26

The better storing qualities of cured meat may cause
the lag to be "blurred" in that supply changes at the farm
level could be absorbed in packer storage and held for sale
in low supply periods. This is especially true of canned
ham and picnics.

It was felt that the listing of the cuts by the
purchaser for the M.S.U. Consumer Purchase Panel would be
more accurate for pork chops and roasts than for many other
cuts. The ambiguousness of ham and picnic ham is very
conducive to an inaccurate list as to what was actually
purchased. This inaccuracy is eliminated to a large extent
for this study by the wide consumer knowledge as to what is
a roast or a pork chop.

At the wholesale level the total value per cwt. of
pork was used as well as the price of specific wholesale
cuts. Loins were chosen as they are the most accurate for
an investigation of pork chop price changes. Butts were
also included because both loins and butts are good sources
of pork roast.

At the farm level. the aggregate average value of
U.S. No. l. 2. and 3 barrow and gilts as compiled by the
U.S.D.A. was chosen to reflect average changes in all pork.

The quantity of U.S. choice steers at Chicago was used as

27

a measure of the quality of beef. Steers of choice grade
consistently represented over 50% of the top three grades
of steers sold. Heifer prices were highly correlated with

those of steers.

Methodology

In analyzing the data. both graphic analysis and
least squares regression techniques were employed. It is
the assumption of this thesis that the lag could be found
by calculating regression models with the predetermined or
independent variables lagged at various time periods. The
model that obtains the highest coefficient of determination
(R2) would be accepted as representing the correct lag.

At the same time. simple graphic analysis would be very
helpful in indicating what the correct lag should be.

The various statistics were collected and punched
on cards. Each card held one observation with each obser-
vation being prices and quantities for one week. Each
year contained fifty—two observations except 1954 which
had fifty-three. The manner in which the weeks were
arranged was the reason for the latter number. This
presented no particular problem as this writer was aware

of the fact at the beginning of the 53rd. observation was

28

handled as any other observation. The punched cards were
then placed in MISTIC. the M.S.U. electronic computer. to
estimate the various regression models. Since in some
regression models a variable may be independent and in others
dependent. all variables were designated as X's when
normally some would be Z's (independent or predetermined)

and others Y's (dependent or endogenous) in the standard
regression notation. This is only a form of notation.

The general notation is as follows:

P = price f = farm p = pork
Q = quantity w = wholesale b = beef
r = retail 1 = loin

s = butt
c = pork chop
r = roast

t = observation period or week

Pr — Retail price of pork chops

Prc - Retail price of pork roast

r

Pf - Farm price of pork

pr - Farm quantity of pork

PWp - Wholesale value of pork

PW: — Wholesale price of pork loin

Pw - Wholesale price of butt

29

Qf - Farm quality of beef
b
In the above notations. the first subscript designates
the level (farm. wholesale. or retail) and the second sub-
script designates the particular item. The subscript t
designates the observation period of the variable in question.

A lag of one week is designated as t-l; a lag of two weeks

is designated as t-2. etc.

Laqs
The regression equation was written in the following
manner:
= +
(Pw )t ( 3 b1 Pf )t
P P

This would not be the "best" model to use to predict prices
as such things as wage rates and the general economy all
influence prices. Hewever. it was felt that the possible
inadequacy of this equation would not be sufficiently large
to invalidate the resulting estimates of the coefficients
or the coefficient of determination for the purpose of this
thesis.

Graphic analysis was used to approximate the lags
involved. This was helpful in choosing the approximate
lag to use in the equations. The various prices and quantities

being considered were plotted against time. By visual

30

inspection of the peaks and valleys. it was possible to
determine whether a lag was to be expected or not. After

the coefficients of the lagged equations were estimated the
resulting R2 were plotted against time for a visual inspection

of the lag.

The lagged equations are of the following form:

(Pr )t = ( a + bl Pf + b2 Qf + b3 Qf )t 3-0
c p p b
. . . . . » j-l
. . . . . j-2
= + '-
(P )t ( a bl Pf + b2 Qf + b3 of )t_3 J 3
c p p b
where j = a particular number of an equation or

a set of equations and the number following j

designates the number of observation periods

the independent variables have been lagged for

that particular equation in the jth equation or

set.
This is the general format. Other prices were substituted
to obtain the lag for other cuts or price levels. The
equations were calculated for the combined seven year
period.

When the equations were calculated. the results
were checked by the F ratio to see whether the equations
were significantly different where P = .05. The lags
were tested and cross tests were made to see if different

cuts or prices indicated different lags. The F ratio test

was made using the sum of residuals squared as calculated

31

by the electronic computer with the appropriate degrees of
freedom. By dividing the sum of the residuals squared by
the degrees of freedom associated with it the estimated

variance of the residuals or U's (Si) is obtained.

2(Y-§)2 = g2
d.f. u

To test to see if there is a statistical difference between
equations the smaller S: is divided into the larger Si.
This will give an F ratio. This will test to see if the
smaller S2 is significantly smaller than the other S2 used in
u.
computing the F ratio. If :Ei is greater than the F table
S
uJ'
critical value then the hypothesis is accepted that the
~ . . . . “2
smaller Si is Significantly smaller than the larger Su.
However. if the computed F value is smaller than the critical
table value the hypothesis that there is no statistically
significant difference is accepted. By this method it was
determined whether lags were present and whether the
equations were changed significantly by lagging the
independent variables.

The residuals were also tested for serial correlation

and then plotted against time.7 This was done not

 

7See footnotes 3 and 4. Chapter IV. pp. 47. 48.

32

to eliminate the serial correlation but rather to see if one
of the variables used in this thesis could explain the

serial correlation. For this test. the von Neumann Hart

ratio was used and tested at the .05 level.8

In determining the lag during changing prices. a

dummy variable was used. The dummy variables used were

X

13' and X o

deSignated as X 14

12. In this approach to

determine the farm to retail lag. a retail price was used

as the dependent variable. farm price. farm quantity of

pork and beef were used as the independent variable along

with the dummy variable. The dummy variable was defined

as 0 or 1: 0 if the change of the independent variable
from one observation (t—l) to the next observation (t)
was positive and 1 if the change was negative or if there

X

was no change. 12

was the change in the farm level price

X.

from one observationto the next. 13

was the change in

the price of pork loin and X was the change in the price

14

of butts. The general equation was as follows:
P = + P
( rr)t ( a bl f + b2 Qf + b3 of + b4 X12)t
~th . . .p .P .b .
Set J
(Pr )t = ( a + b1 Pf + b2 Qf + b3 Qf + b4 X12)t-3
r p p b

u. u. H.

La) NI—‘O

1.:

 

8When using various statistical tests. an a or
probability level (P) is usually stated. P = .05 means that
the obtained results have a 5%.probability of occurring by
chance alone.

33

where j = a particular set of equations in a
particular series. and the number after the j =
the number of weeks the independent variable are
lagged for the equation.

For the wholesale to retail lag. the price of a
specific wholesale cut was substituted for farm price of
pork and the appropriate dummy variable used. The same
procedure was followed to determine the farm to wholesale
lag. Each lagged equation was calculated for the combined
seven years period. These computations were made by electronic
computer. As in the over-all lag. the various lagged
equations were tested for significance by the F ratio test
and the R2 plotted against the lag for a graphic analysis
of the lag.

Throughout this thesis. no tests of significance
will be presented on the bi coefficients as both inter-
correlation and serial correlation exist in the equations.
This is assumed not to invalidate the findings of this
thesis. as it is not the purpose to obtain the true structural
coefficients. but rather to determine whether there exists
a time lag between price adjustments at various levels.

Inter-correlation is defined as correlation among
the independent variables. Multicollinearity is an extreme

case of inter-correlation where the correlation among

independent variables is so high that their separate effects

34

can't be measured. As the level of inter-correlation increases,
the standard errors of the net regression coefficients
increase and this leads to lower reliability for the
individual regression constants. In some cases. when the
inter-correlation between variables reaches a certain point.
the "weaker” of the partial regression coefficients may
under—go a sign change.9

Inter—correlation existed among the independent
- variables used in this thesis. The simple correlation (R)

between farm price of pork (Pf ) and farm quantity of pork
P

(Qf ) was -.523; R between Pf and farm quantity of

P P

beef (Qf ) was +.106; and R between Qf and Qf was -.290.

b p b
Because of this inter—correlation the Sb or standard errors

1

of the net regression coefficients may become large.

Serial correlation was also present in the equations.
This makes the usual test of significance for the coefficients
invalid. Therefore. no test for significance was made on
the coefficients. but the sign of each bi was checked to see

if it agreed with the expected results.

In determining what the signs of the bi should be.

 

9K. A. Fox and J. F. Cooney. Jr.. "Effects on Inter-

correlation upon Multiple Correlation and Regression Measures."
USDA. AMS (washington. 1954). (Mimeographed.)

35

one must consider how price changes of the factors of pro-
duction will effect the final product price and the nature
of product substitution.

Since hogs are the main factor of production in pro—
ducing pork for consumption. when the price of hogs rises.
the price of the final product must also rise as no other
factor of production can be substituted for hogs. In this
way. pr is the price of the factor of production in pro-
ducing wholesale cuts of pork. and one could consider price
of the wholesale cuts the price of the factor of production
in producing a final product of retail cuts. In this way.
the bi coefficient of a price independent variable should be
positive.

In considering the supply of a factor. as the
quantity of hogs increases. the price of pork should fall.
i.e.. quantity has an inverse effect on price. Also. as
the quantity of beef increases. price of beef should decrease.
Because pork and beef are good substitutes for each other.
the price of pork should follow that of beef. One reason
pork prices tend to follow beef prices is that pork is to
some extent an inferior good to beef. Therefore. the price
of beef has more effect on pork than the price of pork has

on beef.10

 

10Riley. p. 31.

36

From the above. one would expect the signs for the

bi coefficients for of and Qf to be negative. Hewever.
p b

there was a simple correlation between Q and Qf of -.290.

fp b

This indicates that the two variables move in opposite

directions and when Qf is relatively high. Qf is relatively
b P

lower. Since all the dependent variables are pork prices

at some level. one could expect bi of Qf to take on the
b

opposite sign from that of Of . The assumption behind this
P

f has an inverse relationship
P

with Q . Q will be measuring the effect of Q rather
fb fb fp

than itself. Q

reasoning is that since Q

and Qf do not necessarily have direct

fp b

relationship to cause the difference in the two. They move
in opposite directions because of the nature of production
of the two species and their seasonal market patterns.11

No attempt will be made to ascertain why the signs
of the bi are as they are. as this is outside the main area
of concern; however. if the signs differ from what is

expected. a priori. they will be mentioned as areas for

possible further study.

 

llH. Breimyer and C. A. Kause. Charting the Seasonal

Marketing for Meat Animals. USDA Agricultural Handbook No. 83
(Washington. 1955).

37

Margins

In investigating the various margins between
prices. the lower level price at a one week lag (t-l) was
subtracted from the higher level price at t. This defined
the margin as the difference between the two prices at their
assumed lagged relationship. The margins computed were farm
to wholesale value. farm to specific wholesale cut price.
farm to Specific retail cut price and specific wholesale
cut to specific retail cut price.

The various margins were fitted by regression
equations first as a function of the lower level price used
in computing that margin and second as a function of the
upper level price of that margin. In both cases farm
quantity of pork was included as an independent variable
because the quantity of pork moving through the marketing
channels influences margins.12 The quantity of pork is to
some extent measured by the price of pork but it was thought
that as the independent price variable moves away from the

farm level the relationship between price and the farm

quantity of pork might become less apparent. therefore.

 

12As the quantity of pork increases the margins
increase. This is also reflected in farm price so that as
quantity of pork increases. price decreases which gives an
inverse relationship to farm price and margins.

38

making farm quantity a significant independent variable.

The above procedure was followed for the over-all
lag. which used no dummy variable. Had the dummy variable
approach proved to have significant value over the over—
all lag approach a further investigation into margins

would have been made.

CHAPTER IV

OVER-ALL LAG RESPONSEl

Farm to Wholesale Value

The first step in estimating the relationship
between farm price and wholesale value was to plot them. along
with the quantity of hogs. against time. From the graphic
analysis it appeared that there was no lag between farm
price and wholesale value. When considering the quantity
of hogs on the market. there is the expected inverse relation-
ship. price being high when quantity is low and vice versa.
The relationship between farm price. wholesale value and
farm quantity of hogs is shown in Figures l-a to l-g.

The non-lagged relationship between farm price and
wholesale value was to be expected on a weekly average
since wholesalers and packers have relatively good knowledge
as to what prices can be paid and what must be received.
Because of this. prices may be adjusted when the need arises.
As previously stated in Chapter I. Stout and Feltner found

no lagged relationship between farm price and wholesale

 

lOver-all lag being defined as when there is no
distinction made between rising and falling prices. It is
the average lag.

39

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value on a day to day basis.2 This thesis tends to support
their findings.

Since there appeared to be no lag in wholesale value
response, only non-lagged equations were calculated. The
first equation was

Eq. 1. (PW )t =(a + bl pr)t. 1.0

This equation was calculated for the combined period 1952
to 1958. The estimates of the coefficients are given in

Table 4.1.

Table 4.1 Estimates of coefficients for equation 1.0.

 

 

 

 

b-_
Coefficient Value S t = l 0 R2
b. S
1 b.
1
a 3.960 .158 25.02
.971
b .902 .008 111.7

 

The von Neumann Hart ratio test was used to determine
if serial correlation was present.3 In this test the

Durbin Watson d' statistic was used as follows:

 

2Stout and Feltner. p. 217.

3Serial correlation is defined as the correlation of
a series of observations and the same series lagged by one
or more units of time.

48

Z LResiduals - Previous Residuals)2

Z (Residuals)2 = d

d' was then multiplied by' —§L' to obtain the von Neumann

 

N—l
2 4
Hart ratio '—§§—.
2
N . . 6 . .
'——— d = = K where K is the observed ratio.
N—l S2

This test indicated that serial correlation was
present. The observed K ratio was .6471. ‘The critical
value for the .05 level for K or K' is greater than unity
therefore serial correlation is assumed to be present.
Because of this. the usual statistical tests of the
coefficients were not applicable. Hewever. the coefficients

are both statistically unbiased and consistent and the

 

4Dr. L V. Manderscheid, Agr. Econ. 831, class notes,

Spring. 1962. Michigan State University.
N N

 

2 (Uk — U'k_l)2 Where 2 (Uk - U'k_l)2 is S(Res. -
d. = k=2 k=2
N 2 2 N 2 2
2 Uk Prev. Res) and where 2 UR is S(Res) .
k=l k=l

5Mordecai Ezekiel and Karl Fox. Methods of Corre-
lation and Regression Analysis (New York: John Wiley and
Sons, Inc., 1961), p. 341. If the calculated value falls
below the critical value of the table K value there is
positive serial correlation and if above the table K' value,
negative serial correlation is present.

49

estimate of the dependent variable is unbiased. It was
assumed that serial correlation would not be of sufficient
importance to invalidate the findings of the graphic and
regression analysis indicating that there was no lag
between farm price and wholesale value. Figure 2 presents

the graphic illustration of the residuals from equation 1.0.

Farm to Wholesale Cut

The next step was to determine the lag between farm
price and specific wholesale cut price. Again the various
prices were plotted for a graphic analysis. This is shown
in Figures 3-a to 3—g. By visual inspection of the peaks
and valleys, it seems apparent that no lag exists between
wholesale value and price of loin or butt. Since there
was no lag between farm price and wholesale value, it would
appear that there is no lag between farm price and price of
a specific wholesale cut.

Because of the non-lagged relationship of farm price
and wholesale price. it was decided that only one price
(farm) would be used for the equations. The regression
equations used were as follows:

Eq. 2. (Pw ) = ( a + bl Pf ) (2.0)

l 19

Eq. 3. (Pw ) ( a + bl Pf ) (3.0)

S P

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These equations were calculated for the combined period
1952 to 1958. The results from these equations are presented

in Table 4.2

Table 4.2 R2 and 83* from equation sets 2 to 5 by lag

 

 

 

 

 

 

period.
Set 0 1 2 3
R2 .720
*1:
2 ‘2
S 13.49
u . .
R2 .888
3**
S2 4.41
u
2
R .776 .754 .715 .675
4 2
Su 10.85 11.94 13.86 15.82
R2 .892 .884 .843 .790
5 “2
Su 4.31 4.61 6.28 8.44

 

*gz _ 2 (Y — YLZ
u d.f.
U's (residuals).

or the estimated variance of the

**These equations were not lagged and therefore have
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serially correlated. The residuals were also plotted
against time (see Figures 4-a to 4—c). Even though serial

correlation is assumed not to invalidate the findings for

59

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62

this thesis, it was thought that a more complete model could
possibly return more significant results. The equations
were then recalculated with the additional variables of farm

quantities of pork and beef being added. The equations then

became
(Pw )t = ( a + bl Pf + b2 of + b3 Qf )t (4.0)
1 p p b
. . . . . (4.1)
Set 4
. . . . . (4.2)
(P t = ( a + bl Pf + b2 Qf + b3 Qf )t-3 (4.3)
1 p p b
(Pw )t = ( a + bl Pf + b2 Qf + b3 Qf )t (5.0)
s p p b
. . . . . (5.1)
set 5 . . . . . (5.2)
(Pw )t = ( a + bl Pf + b2 Qf + b3 Qf )t—3 (5.3)
s p. p b

These equations were calculated in the same manner
as equations 2.0 and 3.0. The resulting R2 (coefficient
of determination)and 8: (estimated variance of the residuals)
are presented in Table 4.2.

The equations 2.0. 3.0, 4.0 and 5.0 were tested
for serial correlations and the residuals plotted against
time (see Figures 4—a to 4-c) to determine the effects of

the two additional variables. Q and Qf . upon the serial

fp b

correlation. In both cases, R? was increased but the

serial correlation decreased by such a relatively small

63

amount that the two additional variables proved to have no
significant effect upon the serial correlation. Since
there appeared to be no lag. only equations 2.0, 3.0, 4.0
and 5.0 were considered when determining the serial
correlation.

The F ratio test was applied to the different sets
of equations having the same dependent variables; the
comparison being between equations 2.0 and 4.0. and 3.0
and 5.0. Since the test was to see if the S: was reduced

by a significant amount by adding the variables Qf and Qf .
p b

u from equations 4.0 and 5.0 were used as the denominator

in computing the F ratio, as these equations had the smallest

The F ratio test was made in the following manner:

 

giz-O - F 6
g2 _ 2.0—4.0 > critical value
u4°0 (1.24) > 1.20
333.0 _ F

‘é;__—' _ 3.0—5.0 < critical value
u5.0 1.02 < 1.20

where the subscript number to the S: designates
the equation associated with that particular 8%

 

6George W. Snedecor, Statistical Methods (4th Ed.;
Iowa State Press. 1946). P. 224, Table 10.7. The critical
value was determined by linear interpolation using 350 degrees
of freedom in both the numerator and the denominator.

64

and the subscript to the F ratio designates the
equations used in computing the F ratio with the
equation used as the denominator coming last in
the subscript.

Since the observed F ratio. exceeded the

F200—400'

critical valueenuiF ratio F3 0_5 0 did not, it was concluded

that the two variables Qf and Qf added a significant amount
b b

to equation 4.0 but not to equation 5.0.

Cross checks could have been made to determine which
dependent variable was more fully explained by the independent
variables but by inspection one could see that the equations

with Pw (wholesale price of butt) had a much smaller 8: than
s

the equations with PW. (wholesale price of loin) as the
1

dependent variable.

This difference may be due to the fact that loin
prices tend to be more stable than butt prices. Butt prices
follow more closely to the fluctuations of farm price. This

is substantiated by the simple correlation of Pf and the

P

two wholesale prices. R for Pf and Pw = + .849 and R

p 1

for P and P = + .924.
f w

p 5
While graphic analysis might have been sufficient

for determining the lags, lagged equations were calculated for

a mathematical proof. It was expected. a riori, that there

would be no lag between farm and wholesale level.

65

Table

4.2 shows that R2 was reduced as the independent variables

were lagged further back in time.

F ratio tests were made on the equations in each

set and since the equation having no lag had the smallest

A

Su it was used as the demonimator in computing the F ratio.

The F ratio tests for set 4

manner :

following manner:

 

 

 

—F

were made in the following

— F4.l-4.0 < critical value
(1.10) (1.20)
* . .
— F4»2__4“0 > critical value
(1.27) (1.20)
'k . .
4.3_4.0 > critical value
(1.46) (1.20)

*Significant at the .05 level.

The F ratio tests for set 5 were made in the

 

' F5.1—5.0
(1.06)

< critical value

(1.20)

66

 

 

5‘»:

5.2 = F *
g2 5.2-5.0 > critical value
u5.0 (1.45) (1.20)
g2
u5 3

. = "k ' '

§2 F5.3_5.0 > critical value
u5-0 (1.95) (1.20)

*Significant at the .05 level.

In testing both sets of equations F4 1-4 0 and

F5 1-5 0 did not prove to be significant. From these tests

it can be assumed that there is no lag of as much as one
week but a lag in the terms of days could be possible. In
respect to lags in the terms of weekly data. it can be
assumed that there is no lag between farm and wholesale
level.

In checking the signs of the b coefficients, the

expected signs were found for set 4; Pf or bl was positive,

P

Q or b was negative and Q or b was positive. For
fp 2 fb 3

set 5 the b1 coefficient had the expected sign but b2 and

b3 had reverse signs with b2 being positive and b3 being
negative. Under the relationship assumed in Chapter IV,

the sign change of the b3 coefficient was due to the inter-

correlation of Qf and Qf . Because of this the b

p b 3

67

coefficient of Q is not measuring Qf but rather the effect

fb b

of Qf . No attempt was made to determine the reason for the

P

sign change on the b coefficient of Qf .

P

By graphic analysis alone it was possible to determine

2

that there was no apparent lagged relationship between farm
price and the price of the selected wholesale cuts on an
over-all basis. The mathematical calculations were included
for the purpose of significance testing. These tests

tended to support the graphic analysis. However. this is
not to say that no lagged relationship exists when con-
sidered on the basis of a changing price structure. This

particular aspect will be taken up in a later chapter.

Farm to Retail

In determining the farm to retail lag, the first
step was to plot the various prices by weeks (see Figures
6-a to 6—g). The next step was to formulate a series of
equations. each being lagged one observation period behind

the previous one. The equation series using Pr (retail
c

price of pork chops) as a dependent variable is as follows:

(Pr )t = ( a + bl Pf + b2 Qf + b3 Qf )t (6.0)
c p p b
. . . (6.1)
Set 6. . . . . (6.2)

P)= a+bP
( rc t ( 1 fp + b2 pr + b3 be)t-3° (6.3)

68

A similar series was formulated using Pr (retail
r

price of pork roast) as the dependent variable. It is as

follows:
(Pr )t = ( a + bl Pf + b2 Qf + b3 Qf )t (7.0)
r p p b
. . (7.1)
Set 7.
. . . . . (7.2)
= + + + .
(Pr )t ( a bi Pf b2 Qf b3 Qf )t—3. (7 3)

p p b
The above equations were calculated for the combined

period 1952 to 1958 and the R2 and 8: appear in Table 4.3.

Table 4.3. R2 and 82 from equation sets 6 and 7 by lag

 

 

 

 

periods.
Set 0 l 2 3
2
R .729 .753 .737 .721
6 -2
Su .106 .096 .099 .108
2
R .683 .699 .673 .643
7 “2
Su .153 .146 .159 .174

 

The R2 from the combined data were plotted by lag
period (see Figure 5) and from this there appears to be a

lag of one week in retail prices.

69

Figure 5. Graphic illustrations of the coefficientsof
determination obtained from equation sets 6
and 7, by lag periods.

.70 ,

.65 .
Set 7
.60 (

 

A A A. A

O l 2 3
(t) (t-l) (t-2) (t-3)

Lag Period

The next step was to determine if the differences
in the various lags were statistically significant. Since
a lag of one week (eq. 1 or t-l) appeared to be the correct
lag in that it had the highest R2, the other lag periods
were compared to the equation that was lagged one week.

The E ratiosused to compare the various equations were made

in the following manner:

 

«2 = F6.0-6.1 < critical value
6.1 (1.10) (1.20)

7O

 

 

 

 

 

 

SE.
6.2 _ . .
§2 — F6.2-6.l < critical value
u6.1 (1.03) (1.20)
Set 6.
*2
u
6.3 — I I
g2 — F6.3-6.l < critical value
u6.1 (1.12) (1.20)
g:
7.0 . .
§2 — F7.0-7.l < critical value
u7.1 (1.04) (1.20)
Set 7
Si
702 _ 0 a
g2 — F7.2-7.l < critical value
u7.1 (1.08) (1.20)
«2
u
7.3 _ . .
§2 — F7.2-7.1 < critical value
u7.1 (1.19) (1.20)

None of the observed F ratios were significant at

the .05 level; however, very closely approached

F7.3-7.1
significance. In both equation sets R2 was largest when the
independent variables were lagged one week. The differences
did not prove statistically Significant. but in View of the

peaks and valleys of the price movements when the prices

were plotted against time (see Figures 6-a to 6-g) it is

71

assumed that a lag of one week exists between farm and
retail price.
In checking the signs of the bi coefficients, the
expected signs were present for the bi values for set 6.
In set 7 the signs associated with the b_ values for equations

1
7.2 and 7.3 were as expected. This was not true for the bi

values for Qf and Qf in equations 7.0 and 7.1 as both
p b

signs were positive. This is in opposition to the assumption

that the sign of the bi for Qf would be opposite to the

b
sign for the bi for Qf . It was noted that the two bi
P
values for Qf and Qf had unexpected signs when Pw was
p b s

the dependent variable in the farm-wholesale lag. In this
series, pork roast has unexpected signs on the bi values of
the two quantity variables for no lag and one of one week.
As before, the reason for this situation was not determined.

It is an area that should receive further consideration.

Wholesale to Retail

The prices of the specific cuts at the various levels
were plotted against time; by visual inspection of the peaks
and valleys, there appeared to be a lag of one week from

wholesale to retail level. (See Figures 6-a to 6—g.)

72

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The equations for the mathematical calculations of the lags

were formulated as follows:

(Pr )t = ( a + bl Pw + b2 Qf + b3 Qf )t (8.0)
c l p b
. . . . . (8.1)
Set 8.
. . . . (8.2)
(P )t = ( a + bl PW + b2 of + b3 Qf )t-3 (8.3)
c 1 p b
(pr )t = ( a + bl Pw + b2 Qf + b3 Qf )t (9.0)
r s p b
. . . . .. (9.1)
Set 9.
. . . . . (9.2)
(Pr )t = ( a + bl Pw + b2 of + b3 Qf )t-3. (9.3)
r s p b
(Pr )t = ( a + bl PW + b2 Qf + b3 Qf )t (10.0)
r 1 p b
. . . . . (10.1)
Set 10.
. . . . . (10.2)
(Pr )t = ( a + bl PW + b2 Qf + b3 Qf )t-3. (10.3)
r 1 p b

The wholesale cuts of butts and loins were used as
independent variables for roast of either of these cuts may
be sold as a roast, while only loin yields pork chops. The
combined period results are presented in Table 4.4, and the

R2 graphically illustrated in Figure 7.

80

Table 4.4 R2 and SE from sets 8, 9. and 10 by lag period.

 

 

 

 

 

Set 0 l 2 3
2
R .676 .725 .684 .630
8° 2
8n .127 .107 .123 .144
2
R .713 .716 .664 .622
9 2
8n .139 .138 .164 .185
2
R .612 .663 .574 .523
10 -2
su .188 .163 .207 .233

 

Figure 7. Graphic illustration of the coefficients of
determination obtained from equation sets 8,
9, 10 and 11, by lag periods.

 

 

R2 .75 ,
.70 s
.65 . set 8
sz9
.60 .
.55 . Set 10
.50 . . L .
0 l 2 3
(t) (t-l) (t-Z) (t-3)

Lag Period

81

From Figure 7 there appears to be a one week lag in
retail prices. To determine if this difference is significant
the lagged equations in each set were compared by the F
ratio test. As in the farm to retail sets, the equations
in each set that were lagged one week had a smaller Si
and a larger R2. In computing the F ratio the S: of the
equation lagged one week was used as the denominator. In
this way each equation was compared with the equation
containing the largest R2. The F ratio tests were made in

the following manner:

 

 

15':
8.0 ** . .
§2 - F8.0-8.1 < critical value
u8.1 (1.19) (1.20)
Set 8.
g:
8.2 . _
§2 - F8.2-8.1 < critical Value
’ u8-1 (1.15) (1.20)
$3.
8.3 = F *
§2 8.3-8.1 > critical value
uB-l (1.34) (1.20)

*Significant at the .05 level.
**Approaches very closely to the significant level.

82

 

 

 

 

5.2.
9.0 . .
§2 — F9.0-9.1 < critical value
u9.1 (1.01) (1.20)
Set 9 . g:
9.2 ** . .
£2 = F9.2-9.l < critical value
u9.1 (1.19) (1.20)
g:
9.3 _ * . .
§2 — F9.3-9.1 > critical value
u9.1 (1.34) (1.20)
g:
10.0 _ . .
§2 — FlO.O-10.1 < critical value
u10.1 (1.15) (1.20)
Set 10. g:
10.2 _ * . .
§2 — FlO.2-lO.1 > critical value
u10.1 (1.26) (1.20)
g:
10.3 _ * . .
§2 - F10.3-10.l > critical value
u10.1 (1.43) (1.20)

*Significant at the .05 level.
**Approaches very closely to the significant level.
Even though the results were not significant in all
cases, it was still assumed that there was a lag of one

week from wholesale to retail level. In all cases, a lag

83

of three weeks had significantly larger S: than a lag of
one week; therefore, it is safe to assume that the lag is
not three weeks. The smallest F ratios were computed using
Su of a one week lag and the 8: of the equations not lagged.
This suggests the possibility of a lag in terms of days
rather than weeks. Also the difference in the various sets
brings forth the possibility of different cuts having
different lags. However, on an over-all basis, the assumption
that there is a one week lag in wholesale to retail level
appears to be a reasonable one.

In inspecting the signs of the bi values, the
expected signs were present in sets 8 and 9. Set 10,

however, had erratic signs. Equation 10.0 had positive

signs on both the bi of Qf and Q ; equations 10.1 and

p fb
10.2 had a positive sign for the bi value for Qf and
P
a negative sign for the bi for Qf ; and equation 10.3 had
b

both negative signs. The signs were ”correct? under the
assumed lagged relationship of one week. Again this is

noted as a possible area for further investigation.

CHAPTER V
LAGS WHEN CONSIDERING DIRECTION OF PRICE CHANGE

Farm to Wholesale

To determine the effect of price change on lags, a
dummy variable was designed to denote the direction of the
price change and used as an independent variable. It was
felt that if a significantly smaller S: was found in the
equations using the dummy variable than in those equations
not using the dummy variable this would indicate that the
lag would be different for price changes of different
directions. It was expected, a priori, that a rising market
would have less lag than a lowering one. This approach would
not indicate the correct lag for different price changes,
but would indicate whether the possibility of a difference
in lag exists.

The two wholesale cuts were set as functions of the

farm price 0f pork (Pf ), farm quantity of pork and beef
P

(Q and Qf ) and a dummy variable, X

12. The equations were
p b

f

of the following form:

84

= + P
(Pw )t ( a bl f + b2 Qf + b3 Qf + b4 X12)t (11.0)
1 p p b
. . . . (11.1)
Set
11 . . . . . . (11.2)
(Pw )t = ( a + bl Pf + b2 Qf + b3 Qf + b4 x12)t_3 (11.3)
1 p p b
(PW )t = ( a + bl Pf + b2 Qf + b3 Qf + b4 X12)t (12.0)
s p p b
Set . . . . . (12.1)
12 . . . . . . (12.2)
= + ' + + 0
(Pw )t ( a bi Pf b2 Qf b3 Qf + b4 x12)t-3 (12 3)
s p p b
where X12 = 0 if the change in Pf is positive from

observation period t-l to t and lpif there is no change
or the change is a negative one.

The equations were calculated and the resulting R
and 8: presented in TabLa 5.1. Since comparisons will be
made between equations using the dummy variable and those
equations that have the same variables except the dummy one,
R2 and S: from equation sets 4 and 5 are also presented in
Table 5.1.

Statistical tests of significance could have been
made between the equations with the dummy variables and those
without the dummy variables. H0wever, by inspection of the
R2 and 8: of the various sets it was obvious that the
difference in the equations that used the dummy variables

and those not using them was not statistically significant.

86

From this it was concluded that the dummy variable added

nothing to the explanation of the dependent variables.

A2 .
R and S from equation sets 4,

 

 

 

 

 

 

 

Table 5.1 5, 11, and 12,
by laggeg period.
Set 0 1 2 3
2
R .778 .756 .726 .678
ll .2
Su 10.81 11.87 13.35 15.72
2
R .776 .754 .715 .675
4 2
Su 10.85 11.94 13.86 15.82
2
R .897 .885 .847 .796
12 ‘2
Su 4.10 4.60 6.13 8.20
2
R .892 884 .843 .790
5 2
su 4.31 4.61 6.28 8.44
Farm to Retail
In determining the farm to retail lag, the dummy

variable, X12.

following form:

was used.

The equations used were of the

= +
(Pr )t ( a bl Pf + b2 Qf + b3 Qf + b4 X12)t (13.0)
c p p b
Set . . . (13.1)
13
. . . . . . (13.2)
= +
(Pr )t ( a . bl Pf + b2 Qf + b3 of + b4 X12)t—3 (13.3)
c p p b
= -+ .
(Pr )t ( a bl Pf + b2 Qf + b3 Qf + b4 X12)t (14 0)
r - p p b
Set . . . . . . (14.1)
14 . . . . . . (14.2)
(Prr)t = ( a + bl pr + b2 pr + b3 be + b4 X12)t-3 (14.3)

The variables used in these equations were the same
as those used in sets 6 and 7 with the addition of the dummy
variable. Set 13 corresponds to set 6 and set 14 corresponds
to set 7. Therefore, comparisons will be made between sets
6 and 13 and sets 7 and 14. Sets 13 and 14 were calculated
and the resulting R2 and 8: appear in Table 5.3 along with
the R2 and 8: from sets 6 and 7.

F ratio tests could have been computed using the
8: to determine whether the dummy variable had reduced
the 8: by a significant amount. This was not done because
inspection of the 8: in Table 5.2 indicates that the ratios
obtained would be very close to unity if not at unity. In
no case would the F ratio approach the critical value of 1.20.

From this it was concluded that the dummy variable added

88

no significant information over the variables previously

used.

Table 5.2. R2 and 8: from equation sets 6, 7, 13, and 14 by
lag period.

 

 

 

 

 

 

Set 0 l 2 3
2
R .747 .755 .745 .721
13 2
§u .099 .096 .099 .108
2
R .729 .753 .745 .721
6 2
su .106 .096 .099 .108
R2 .701 .700 .673 .644
14 ‘2
su .145 .146 .159 .174
2
R .683 .699 .673 .643
7 -2
su .153 .146 .159 .174

 

The bi coefficients were consistent between the sets
being compared. This tends to add support to the conclusion
that the dummy variable is of no significant value in the
explanation of the dependent variable. That is, there does
not appear to be a difference in the farm to retail lag

between increasing and decreasing prices.

89
Wholesale to Retail

In determining the wholesale to retail lag, two

new dummy variables were formulated. They were used in the

following regression equations:

(P )t = ( a + bl Pw + b2 Qf + b3 Qf + b4 X13)t (15.0)
1 p b
Set . . . . (15.1)
15
. . . . . (15.2)
(P )t = ( a + b1 PW + b2 Qf = b3 Qf + b4 X13)t—3 (15.3)
1 p b
where X13 = 0 if the change in Pw from observation

period t-l to t is positive and 1 if there was no
change from t-l to t or if the change was negative.

Set
16

r )t = ( a + bl PW + b2 of + b3 Qf + b4 x14)t (16.0)
s p b

. . . . . (16.1)

. . . . . (16.2)

r )t = ( a + b1 PwS + b2 pr + b3 be + b4 x14)t-3 (16°3)

where X14 = 0 if the change in Pw is positive from
observation period t—l to t and 1 if there was no change
or if the change was negative.

Set
17

= + + + .
r )t ( a bl Pw b2 Qf + b3 Qf b4 x13)t (l7 0)
1 p b
. . . . . (17.1)
. . . . . (17.2)
r )t = ( a + bl Pwl + b2 pr + b3 be + b4 X13)t_3 (17.3)

As in the previous sets of equations in this chapter,

the above sets have corresponding sets differing only in the

90

addition of the dummy variable. When comparing sets of
equations, sets 15 and 8, 16 and 9, and 17 and 10 will be

2 -2 .
compared. The R and Su from the various sets are presented

in Table 5.3.

 

 

 

 

 

 

 

 

Table 5.3. R2 and 82 from equation sets 8, 9, 10, 15, 16,
u .
and 17 by lag periods.
Set 0 l 2 3
2
R .699 .728 .687 .631
15 -2
Su .118 .106 .122 .144
2
R .676 .725 .684 .630
8 2
“u .127 .107 .123 .144
2
R .729 .716 .681 .624
16 2
Su .136 .138 .156 .184
2
R .713 .716 .664 .622
9 -2
Su .139 .138 .164 .185
2
R .650 .667 .576 .537
17 -2
u .170 .162 .207 .230
2
R .612 .663 .574 .523
10 2
S .188 .163 .207 .233

 

91

As in the previous sections of this chapter, F ratio
tests were not computed as it was obvious that all such
ratioswould be very close to unity when testing comparable
equations. There was very little absolute difference in
either R2 or the 83 between similar sets.

The signs of the b coefficients were consistent
between comparable sets of equations.

As in the previous sections of this chapter, it was
concluded that the dummy variable is of no significant value

in explaining the dependent variable.

Summary

The dummy variable proved to be of no significant
value in that R? wasn't increased or 8: decreased by
significant amounts. This seems to indicate that the direction
of price change does not influence the lag in price response.
Further study, however, would need to be made before

definite conclusions could be drawn.

CHAPTER VI
MARGINS

Farm to Wholesale Value

The farm to wholesale margin was defined as

(Pw - Pf )t° The time was not lagged as there was no

P P

apparent lag between P (farm price of pork) and Pw

P P

(wholesale value of pork). To estimate the coefficients,

f

a regression equation of the following form was used:

Eq. 18 (PW - pf )t = ( a + bl Pf + b2 of )t 18.0
p p p p

2
The R resulting from equation 18.0 was .361 which
is relatively small. The bl coefficient was -.064 and the

b2 coefficient was .0001. This seems to indicate the
effect that farm price is normally thought to have: that

as Pf increases, the margin decreases. By looking at
P

Figure l—d and l-e it can be noticed that during the latter
part of 1955 and the early part of 1956, the margins between
farm price and wholesale value became quite large. These
figures show that as the quantity of hogs increased the

margin increased. This reflects the accepted idea that the

92

93

quantity of hogs moving through the marketing channels

influences pork margins in the short run and that the

I

larger the quantity the larger the margin. Equation 18.0
substantiated what is normally accepted in that the simple

correlations were +.519 for of (farm quantity of pork) and
P

-.529 for Pf (farm price of pork).

P

Farm to Wholesale Cut

The first step was to formulate the regression

equations to be used. They were of the following form:

Eq. 19 Y1 = a + bl pf + b2 0f
P P
where Y1 = (Pw - Pf ). (19.0)
1 P
Eq. 20 Y2 = a + bl Pf + Qf (20.0)
P P
where Y2 = (P — Pf )
S P
Eq. 21 Y1 = a + bl PW + b2 Qf (21.0)
1 p
. = 2.0
Eq 22 Y2 a + 101 PwS + b2 pr (2 )

 

lHarold F. Breimyer, ”Price Determination and
Aggregate Price Theory,” Journal of Farm Economics, Vol. XXIX
(1958), p. 691.

2One could say that the farm quantity of pork influences
the farm price which in turn influences the margins. Farm
‘quantity of pork has an inverse relationship with farm price
of pork; therefore, as farm price goes up, margins go down.
In this way, farm price influences pork margins.

94

This set of margins as functions of either the
‘farm level price or of the wholesale level price used in
computing the margin. The variable, farm quantity of hogs

(Qf ), was used because the quantity of hogs moving through
P

the marketing channels was believed to influence the margins.
The R? from the above equations are presented in Table 6.1.

The specific wholesale cut price seems to be a
relatively good indicator even when used without the variable,
farm quantity of hogs. This isShown in the R2 deletes given
in Table 6.1. Perhaps by adding a variable outside of the
inf0rmation being considered in this thesis, such as
industrial wage rates, R2 could be increased.

The equations having the same dependent variables
were tested by the F ratio for significance. As was

expected, the equations using P as an independent

f
P
variable differed significantly from the equations using a
specific wholesale cut price as an independent variable.
This difference was shown in the larger 8: of the

equation using P as an independent variable.

f
p
93.
19.0 = F
§2 19.0-21.0 > critical value

u21.0 (2.90) (1.20)

95

9?.

20.0 . .
§2 - F20.0-21.0 > critical value
u22.0 (3.25) (1.20)

2 2
Table 6.1. R and R deletes* from equations 19, 20, 21
and 22 by lag periods.

 

 

 

 

 

 

Equation Variable R2 R2 delete
Pf .324
19.0 P .397
of .279
P
P .324
w1
21.0 .793
Qf .739
P
Pf .087
20.0 p .560
Qf .549
P
p .087
ws
22.0 .865
Qf .848
P

 

*R2 delete is the R2 associated with the equation
had that variable been dropped.

It was expected that the specific wholesale cut
would be a Vbetter? independent variable to explain its own

margin than would be the farm price of pork.

96
Farm to Retail

The first step was to define the margin as the
difference of the retail price of a specific cut at a given

week (t) and the farm price of pork at the assumed lagged

relationship of one week (t-l). The margin for pork chops
was (Pr )t - (Pf )t-l which was deSignated as Y3. The

C P
margin for pork roast was (Prr)t — (pr)t-l which was

designated as Y

4. These margins were set as functions of

P and Qf in the following form:

f
p p
Eq. 23 Y3 = ( a + bl Pf + b2 Qf )t-l (23.1)
p p
Eq. 24 Y4 = ( a + 161 pr + b2 pr)t-1 (24.1)

When these equations were calculated, the resulting
2
R2 were much smaller than was expected. R was .235 for

equation 23.1 and .245 for equation 24.1. The R? delete

for equation 23.1 showed that had of been dropped, the R?

P
would have been reduced by approximately one-half; the delete
was .124 with an R2 of .235. In equation 24.1, Q added

f
P

nothing as the R2 delete for Qf was .245 and R2 was .245.
P

The margins could have been redefined on a non-lagged

basis where Y. = (Pr )

— P where ' = a s ecific
J t (f)t( J p

P P

97

retail cut) but since the actual difference in the variation
of the margin would have been relatively slight, the R?
from the equation could not be expected to be increased
greatly.

In this approach, more information was needed to
explain the action of the margins by regression. However,
it was felt before the calculations were made that R2
would not be large as the price difference between farm
level and retail level was relatively large. However,

2 .
larger R were expected than were obtained.

and Y were not set as functions of

The margins Y3 4

Pr or Pr as the results for the wholesale to retail margins
c r
. 2 .
indicated that extremely small R would be obtained; there-

fore, these calculations were not made.

Wholesale to Retail

As in the farm to retail margin approach, the first
step was to formulate the proper margin on a lagged basis.
Since a lag of one week was indicated in Chapter IV, the
assumed correct margin was defined as the difference
between a specific retail cut at a given time (t) and a
specific wholesale cut at a one week lag (t—l). The

margins were (Pr )t - (Pw ) which was designated as

C 1 t-l

98

which was designated as Y . These

P
Y and ( r ) 6

5 - (Pw )
r

t t-l
s

margins were set as functions of Pw , Pw , Pr and Pr in

l s c r
the following manner:
. . = + + .
Eq 25 Y5 ( a bl PW b2 Qf )t_l (25 1)
l p
. . = + + .
Eq 26 Y6 ( a bl Pws b2 of )t_l (26 1)
Eq. 27. Y5 = ( a + bl Pr + b2 of )t (27.0)
C P
Eq. 28. Y6 = ( a + bl Prr + b2 Qf )t (28.0)

These equations were then calculated and the R2

obtained were extremely small. The R2 was .223 for equation
25.1, .028 for equation 26.1 and .007 for equation 27.0

and 28.0. The 8i for these equations were very large.

From the R2 and the 8: it could be easily seen that this
approach has no value in explaining the margins as formulated
in this thesis. Because of the extremely small R2 and the

*2 . .
extremely large Su' further statistical tests were not

made on these equations.

CHAPTER VII

SUMMARY AND CONCLUSIONS

Summary

This study was to determine the lag reaction of
retail pork prices to changes in prices at farm and whole—
sale levels. It was assumed that if a lag existed it was
partially due to imperfect knowledge on the part of those
concerned at the higher level. It was assumed that there
was imperfect knowledge on the part of retailers. It was
also assumed that this imperfect knowledge was due to
prices being determined by the fluctuations of an inelastic
and predetermined supply and that changes in supply are
first felt at the packer or wholesaler level. Based on
the above assumptions of imperfect knowledge on the part
of retailers and packer level price determination, it
was thought that there would be no lag from farm to
wholesale, but that there would be a lag from farm to
retail and wholesale to retail. A.hypothesis was made that
if a lag was present it would differ when prices were rising
than when prices were falling. A second hypothesis was

made that margins could best be determined when computed

99

100

on a lagged basis if the assumption that there is a lag
was correct.

The data used were average weekly data, consisting
of prices of selected cuts at retail and wholesale levels,
farm price of U.S. l, 2, and 3 barrows and gilts, farm
quantity of U.S. 1, 2, and 3 barrows‘and gilts, and the
farm quantity of choice beef. All of these prices were
Chicago prices with the exception of retail prices which
were taken from the M.S.U. Consumer Purchase Panel.

The various prices were fitted by regression equations
of the following form for determining the proper lag:

Y = a + bi Zi + bi Qi + u

l
where Yi = a given price one level above
that price used as an independent variable;
Zi = either farm or wholesale price, depending
on the lag being determined; and Qi = farm
qualities of pork and beef.
The independent variables were lagged from observation
t to observation t-3. This was done to determine the correct
lagged relationship between the dependent and the independent

variables.

An additional variable, called a dummy variable, was

used to determine whether by differentiating between an
upward and downward movement of the independent price
variable a better explanation of the dependent variable could

be obtained. This dummy variable was used in the regression

101

equations along with the independent variable P Q and

fl

. p f
0f. . . p
b

Margins were computed on a lagged basis and fitted
as functions of various prices and quantities of hogs.

All calculations were made by an electronic computer.
Whenever statistical tests were made the probability level
was P = .05.

‘ When computed on an over-all basis which made no
distinction between upward or downward price movements,
there appeared to be a one week lag in farm to retail prices
and in wholesale to retail prices, although this lag was not
statistically significant in all cases. There appeared to
be no lag between farm and wholesale prices.

The above statements were based on the findings of
the regression equations and by graphic analysis. They also
fulfilled an assumption made for this study and possibly
indicated that the retailer has less perfect knowledge than
does the packer or wholesaler. Also the pricing focal point
seems to be at the packer or wholesale level.

When the quantities of pork and beef were used along

with a specific level of price, Q (farm quantity of beef)

fb

took on a different sign than was expected. This was due to

the intercorrelation between Qf and Qf which caused the
p b

102

b value associated with Qf to actually measure the effect
b

of Q (farm quantity of pork) rather than itself. Since

f
P

the correlation between Q and Qf was negative, the assumption

fp b

was made that the b value associated with Qf would take on
b

the opposite sign of the b value associated with Qf . This
P
assumption held true in most cases.

When the dummy variable approach was used, the dummy
variable seemed to have no significant value in that it
added little to R2 and did not reduce Si by any significant
amount. This could indicate that there is no difference
in lag between a rising and falling market. If there is
no difference in lag when the market is rising from when
the market is lowering, the possibility of the lag being
based on a knowledge situation loses validity. If the lag
is the same in either market, this would seem to indicate
that the lag is of a technological nature. On a knowledge
basis, one can assume that retailers would prefer to make a
mistake in over pricing than one of under pricing. On
upward price movements, retailers would respond relatively
quick to keep from taking a loss; while on a downward
market, one could assume that retailers would prefer to wait

for a trend to be established before changing prices. If

103

there is no difference in lag, then the possibility of the
pricing policies and habits of retailers determining the
lag is substantiated. A lag of this nature would be a
technological one rather than one based on uncertainty.

The margins proved to have no positive value when
formulated on a lagged basis. The only conclusion that
could be drawn was that the approach used in this thesis
cannot explain the movements of margins by the movements of
the various prices and quantities of hogs. More information
that is outside the approach used for this thesis would

be needed to provide an adequate explanation of margins.

Conclusions

There are four main conclusions of this thesis.
These are: (1) there is no lag between farm and wholesale
price; (2) there is a one week lag between farm and retail
prices and between wholesale and retail prices; (3) a dummy
variable that denotes the direction of the price change for
the independent variable was of no significant value in

explaining the movements of the dependent variable and there

is no difference in lag between an upward and downward
market; and (4) margins cannot be explained by price and

quantity alone.

BIBLIOGRAPHY

6

Boulding, Kenneth E. Economic Analysis. Third edition;
New YOrk: Harper and Brothers, 1955.

 

Breimyer, Harold M. FPrice Determination and Aggregate

Price Theory,” Journal of Farm Economics, Vol. XXXIX

 

(1957). . '

Breimyer, H. M., and C. A. Kause. Charting the Seasonal
Marketing for Meat Animals, U.S. Department of
Agriculture Handbook No. 83 (Washington, 1955).

Carroll, W. E. and J. L. Krider. Swine Production.
Second edition; New York: McGraw—Hill Bock Company,
1956.

 

Dowell, A. A. and K. Bjorka. Livestock Marketing. First
edition; New Ybrk: McGraw—Hill Book Co., Inc., 1941.

 

Ezekiel, Mordicai. VThe Cobweb Theorem,? Quarterly Journal
of Economics, Vol. XII (February, 1938).

 

Ezekiel, Mordicai. and Karl Fox. Methods of Correlation
and Regression Analysis. New York: John Wiley and
Sons, Inc., 1961.

 

 

Ferris, John N. Dynamics of the H69 Market with Emphasis
on Distributed Lags in Supply Resppnse. Unpublished
Ph.D. dissertation, Michigan State University, 1960.

 

Fox, Karl A. The Analysis of Demand for Farm Products.
U.S. Department of Agriculture Technical Bulletin
No. 1081 (1953).

Fox, K. A. and S. F. Cooney, Jr. Effects of Intercorrelation
upon Multiple Correlation and Regression Measures.
U.S. Department of Agriculture. Washington, D.C.:
Agricultural Marketing Service, 1954. (Mimeographed.)

 

104

105

Freidman, Milton. Notes on Lectures in Price Theory,
Given in Economics 301 and 302 at University of
Chicago, January and June, 1951.

Haas, G. C. and Mordicai Ezekiel. Factors Affecting the
Price of Hggs. U.S. Department of Agriculture
Bulletin No. 1440. Washington, D.C.: U.S.
Government Printing Office, 1937.

Harlow, Arthur A. 9The Hog Cycle and the Cobweb Theorem,"
Journal of Farm Economics, Vol. XLII (Nevember, 1960).

Johnson, Glenn L. Course Outline for Agriculture Economics
854, Michigan State University, Winter, 1961.

Leftwich, Richard H. The Price System and Resource
Allocation. Rev. Edition; New York: Rinehard and
Winston, 1961.

Little, Herschel W. and Albert L. Meyers.. Estimated Lags
Between Farm, Wholesale and Retail Prices for
Selected Foods. U.S. Department of Agriculture
June, 1943. (Mimeographed.)

Manderscheid, Lester V. Class notes taken in Agriculture
Economics 831, Spring 1962, Michigan State University.

Marshall, Alfred. Principles of Economics. Eighth edition;
London: Macmillan, 1922.

Motts, George. Marketinngandbook for Michigan Livestock
Meats and Wool. Michigan State University Agriculture
Experiment Station Special Bulletin 426, Aug., 1959.

Nicholls, William H. Imperfect Competition Within Agri-
culture Industries. Ames: The Iowa State College
Press, 1941. '

 

Progressive Grocer. Facts in Grocery Distribution, 1958.

Riley, Harold M. Some Measurements of Consumers Demand for
Meats. Unpublished Ph.D. dissertation, Michigan
State College, 1954.

106

Shaffer, James D. Methodological Bash; for the Operation of
a Consumer Purchase Panel. Unpublished Ph.D.
dissertation, Michigan State College, 1952.

Snedecor, George W. Statistical Methods. Ames: The Iowa
State College Press, 1956.

Stigler, George J. The Theory of Price. Rev. Edition:
New York: The Macmillan Co., 1952.

Stout, Thomas T. and Richard L. Feltner. "A Note on Spatial
Pricing Accuracy and Price Relationship in the Market
for Slaughter Hogs," Journal of Farm Economics,

Vol. XLIV (Feb., 1962).

United States Department of Agriculture:

Livestock, Meat, Wool; Market News; Weekly Summary
and Report, 1952 through 1958.

Pork Marketinngargins and Costs, Misc. Publication

United States Department of Commerce, Bureau of Census,
Census of Agriculture for l959--Pre1iminary (Jan., 1961).

Williams, Willard F. FStructural Changes in the Meat
Wholesaling Industry,? Journal of Farm Economics,
V01. XL (May, 1958).

Working, Elmer. Demand for Meat. Institute of Meat Packing.
Chicago: The University of Chicago Press, 1954.

Ziegler, Thomas. The Meat We Eat. Danville, Ill.: The
Interstate Printers and Publishers, 1958.

APPENDIX

ASSUMPTIONS OF STATIC ECONOMICSl

l. Assumptions which fix the production functions of the
economy:

a. The state of the arts is assumed constant, i.e.,
the total production of any set of production
factors remains fixed.

2. Assumptions which fix the utility functions of the
economy:

a. Tastes, habits, customs (i.e., everything affecting
utility functions) are assumed fixed.

b. The ownership pattern for resources and, hence, the
equilibrium distribution of private real incomes
is assumed fixed.

c. Population is assumed constant.

d. Utility functions are independent among people,
i.e., jealousy and 9copying9 of tastes and value
systems are absent.

3. Assumptions which specify the institutional set—up of
the economy.

a. Government is assumed fixed.

b. It is assumed that goods and services are sold in a
market where both producing and consuming individuals

and groups can make their choices free of force or
coercion but with consumers subject, however, to

limitations imposed by their real incomes.

c. Non-firm and non-household groups are assumed fixed.

 

1Dr. Glenn L. Johnson, Agr. Econ. 854, class notes,
Winter, 1962, Michigan State University.

107

The following tables contain the data used in this thesis.

XRPENDEX II

 

 

Table II a. Data for the year 1952.
Week Prc Prr pr pr Pwp Pwl Pvs be
c/lb. c/lb. $/cwt head $/cwt $/cwt $/cwt head

1 .661 .508 18.06 50,364 20.21 42.00 39.00 9,338
2 .665 .525 17.79 75,482 20.27 40.67 39.00 10,421
3 .641 .541 17.69 65,778 20.18 40.75 38.00 9,258
4 .687 .538 17.77 64,375 20.08 40.91 38.00 12,285
5 -.652 .483 17.73 55,452 19.70 39.50 37.25 10,158
6 .628 .520 17.62 55,732 19.84 39.50 37.25 9,508
7 .659 .491 17.49 57,936 19.82 39.08 37.00 8,861
8 .635 .504 17.16 44,612 19.70 39.91 38.00 10,196
9 .640 .506 16.85 44,543 19.54 40.33 38.00 9,562
10 .658 .530 16.89 39,607 19.73 43.00 38.00 8,917
11 .664 .500 16.87 44,451 19.70 43.85 38.00 9,313
12 .640 .500 16.76 47,944 19.73 43.85 38.00 7,4'.
13 .639 .548 16.64 46,152 19.28 43.84 37.00 10,657
14 .663 .508 16.57 43,070 16.66 39.17 37.00 9,003
15 .661 .469 10.66 34,585 18.85 39.17 37.00 6,:70
16 .603 .492 16.81 39,751 17.44 43.83 38.00 9,15;
17 .660 .510 17.05 38,717 19.18 41.70 37.50 7,662
18 .670 .552 17.49 38,992 19.54 45.17 37.50 11, 71
19 .690 .556 19.49 40,069 20.92 53.17 40.00 11,579
20 .722 .555 20.22 34,618 21.70 53.17 43.00 12,697
21 .762 .515 21.42 35,030 22.30 53.17 44.40 11,375
22 .765 .591 20.79 28,374 22.38 53.17 44.00 11,91.
23 .743 .639 21.69 41,811 22.26 53.17 42.50 12 323
24 .760 . 71 20.23 30,673 22.12 53.17 40.50 13,17.
25 .740 .514 29.25 28,520 21.70 51.53 38.70 11,475
26 .738 .567 20.20 28,520 21.55 49.00 37.00 10,721
27 .770 .548 21.05 19,469 21.93 49.08 37.75 9,744
28 .713 .607 21.40 28,998 22.30 50.17 40.10 17,115
29 .757 .583 21.70 24,889 22.64 52.92 42.00 12,92;
30 .698 .561 22.52 19,793 22.91 52.92 43.00 12,655
31 .767 .586 23.09 23,884 24.19 59.36 47.80 14,441
32 .758 .643 22.67 18,908 24.24 60.97 48.00 17,554
33 .769 .635 22.11 17,051 ,23.90 59.53 46.30 17,719
34 .780 .623 21.77 21,158 23.74 58.37 43.70 16,235
35 .784 .631 20.65 20,024 23.27 55.73 41.60 15,655

108

109

 

 

 

 

 

 

Table II a. Data for the year 1952, continued.
W
Week Prc Prr Pf p pr Pwp PWl PWS be
¢/lb- ¢/1b. 3/CW'0 head 35/0171. 35/th $5/cwt. heat.
36 .770 .606 20.49 18,667 22.25 52.17 41.50 13, 782
37 .784 .609 .19.86’ 24,559 21.43 2.50 40.40 16, 379
38 .790 .601 19.18 26,475 22.34 53.50 39.30 15,414
39 .780 .592 20.30 27,164 22.26 54. 54 39.40 14,456
40 .783 .552 20.54 30,498 21.86 54.67 39.50 14,363
41 .787 .615 19.77 34,105 21.31 53. 87 39.10 16,553
42 .792 .614 19.31 39,369 20.80 50.57 38.50 17,478
43 .744 .567 18.60 43,502 20.08 45.70 37.40 15,357
44 .743 .576 17.44 40.733 18.93 41.00 35.90 14.214
45 .709 .496 17.71 40,083 19.19 41.80 35.25 12,631
46 .702 .537 17.20 50.471 19.96 44.90 36. 62 13,147
47 .700 .517 16.77 70,755 19.16 38.80 34. 00 14,207
48 .739 .513 16.63 45,054 18.95 36.00 32. 25 9,233
49 .675 .509 16.57 68,003 19.11 36.27 32.00 10,650
50.694 .443 16.44 71,127 18.99 36.33 32.00 11,519
51.669 .494 16.45 64,128 19.27 36.60 33.90 12,590
52 .668 .510 18.03 38,513 20.04 38.62 36.67 4,686
Table II b. Data for the year 1953.
week Prc Prr pr pr Pup 2,,1 Pug be
¢/lb. ¢/1b. 6/cwt head $/cwt 8/cwt 3/cwt head
1 .683 .498 17.68 67,153 -20.38 39.83 37.00 10. 668
2 .673 .517 18.29 64,204 20.79 40.23 37.00 12,881
3 .718 .509 18.15 64,024 21.02 40.06 36.70 12,436
4 .703 .550 18.66 50,533 21.20 40.03 36.90 10, 990
5 .667 .503 18.65 46,524 20.75 39.45 37.30 9,970
6 .713 .459 18.73 39,974 20.70 39.95 36.80 11,383
7 .691 .515 19.87 37,179 21.70 45.60 39.70 13,736
8 .706 .571 20.29 34,371 21.91 47.90 42.00 12,870
9 .760 .573 20.14. 34,034 21.96 47.08 40.38 11,670
10 .762 .557 20.54 36, 393 22,03 46, 57 40.20 14,342
11 .722 .560 20.79 33,314 22.07 45,96 39.20 .14, 696
12 .709 .525 21.15 34,410 22.34 47.07 41.20 12,510
13 .746 .571 20.62 34,521 22.30 46.92 42.80 12,129
14 .696 .556 20.97 27,608 21.98 44.98 42.50 11,506
15 .699 .590 21.47 29,122 22.24 45,63 42.10 15,006
16 .714 .595 21.72 31,774 22.81 47.50 42.80 19,211
17 .774 .591 23.40 28.087 25.00 59.97 47.40 19,505
_18 .837 .620 23.36 31,193 24.87 58.03 40.50 17.853
19 .808 .611 23.86 25,811 24. 69 54.25 46.30 18,732
20 .781 .664 24.55 24,339 24,87 53,97 17,705

48.90

110

 

 

 

Table II b. Data for the year 1953, continued.
Week Prc Prr pr pr Pup PW]. Pug be
¢/1b. ¢/lb $/cwt head 8/8wt 8/bwt 8/6wt head
21 .827 573 24.38 25.109 25.52 55.35 89.60 ’18,388
22 .859 615 28.89 25,196 26.88 60.37 51. 50 16,591
23 .891 652 25.60 26,625 26.68 61.50 51. 90 18,266
28 .888 .652 28.17 21,085 25.70 53.30 88. 80 21,827
25 .803 618 28.98 21,709 25.70 52.87 88.15 28,808
26 .787 619 25.86 28,173 26.10 58.87 89.00 20,283
27 .836 635 25.39 16,916 26.33 53.18 89.30 18,767
2 .820 608 25.77 16,565 26.88 55.20 89.30 19,363
29 .815 635 26.90 15,785 27.81 60.67 51.35 16,365
30 .873 678 26.58 18,591 28.86 65.83 52.60 15,531
31.886 .708 25.39 15,701 27.02 52.60 51.00 18,997
32 .850 .585 22.92 16,391 25.85 89.03 88.20 19,886
33 .825 .602 28.75 13,821 26,76 56.63 88.55 18,062
38 .883 676 25.66 16,697 27.60 60. 87 50.00 17,813
35 .866 .631 28.98 20,786 27.12 58.80 88. 70 16,198
36 .830 .601 28.16 15,183. 25.26 58. 80 85. 00 11,528
37 .785 .683 28.79 21,308 26.98 55. 79 88.38 11,831
38 .808 .683 25.02 26,286 27.10 56.03 87.50 21,883
39 .817 .682 25.08 27,056 25.92 51.27 87.60 15,632
80 .817 .563 28.57 31,855 25.88 53.70 87.20 15,025
81 .788 .615 22.17 35,826 23.31 86.10 88.70 17,091
82 .779 .553 22.03 35,582 23.60 51.90 80.60 18,187
83 .807 .560 21.53 80,739 23.75 89.80 39.00 18,508
88 .735 .580 20.61 87,886' 22.62 86.20 37.70 13,908
85 .771 .536 20.62 88,578 21.93 88.90 37.80 16,937
86 .739 .531 20.85 83,935 22.87 88.12 36.00 13,688
87 .733 .633 20.93 81,770 22.38 80.30 38.30 16,182
88 .700 .538 22.28 32,266' 23.38 82.33 36.25 13,863
89 .715 .535 23.86 51,988 28.80 85.75 80.30 12.822
50 .738 .521 23.55 39,777 25,87 87.33 88.30 15,138
51 .771 .569 28.12 81,622 25.50 87.33 87.00 18,173
52 .758 .652 28.98 27,530 26.76 51.58 89.75 10,502

 

 

Table II 0.. Data for the year 1958.

111

 

 

Week Prc Prr pr pr Pwp Pwl Pug be
¢/lb. ¢/lb. s/bwt head s/bwt 8/cwt 8/8w8 head

1 .789 .593 28.86 81,705 27.88 56.27 52.25 18,855
2. .825 .657 28.27 88,735 27.17 52.63 89.50 13,557
3 .797 .589 25.28 83,537 28.18 55.20 51.00 18.223
8 .807 .606 25.38 80,657 27.62 51.20 88.20 15,372
5 .817 .591 25.92 32,382 27.85 50.53 88.00 11,055
6 .808 .588 25.70 30,088 27.17 88.93 88.00 12,808
7 .779 .590 25.66 28,939 27.27 51.03 88.60 12,398
8 .800 .550 26.03 26,587 27.88 58.60 89.60 18,810
9 .790 .591 25.61 28,939 28.10 56.25 50.00 12,082
10 .817 .608 25.60 26,980 27.81 53.10 88.60 18,979
11 .850 .617 25.38 29,960 27.28 51.33 87.80 13,016
12 .807 .596 25.70 28,983 27.58 51.00 87.00 18,297
13 .768 .619 26.57 25,725 . 28.21 53.80 87.60 13,358
18 .807 .629 26.85 25,910 28.72 56.67 89.00 18,682
~15 .801 .6063 27.05 26,721 28.76 55.87 50.00 13,028
16 .886 .639 27.58 23,388 29.07 55.06 50.00 12,881
17 .820 .600 27.85 28,682 29.78 57.67 89.80 16,500
18 .818 :659 26.90 28,926 28.78 55.67 87.95 12,038
19 .800 .609 26.30 26,228 28.21 55.13 86.80 17,078
20 .808 .638 26.32 27,733 28.87 61.77 87.00 20,253
21 .885 .663 26.38 35,831 29.07 68.03 87. 21,793
22 .868 .678 25.21 30,061 28.01 59.20 88.10 18,373
23 .832 .618 25.06 23,738 28.15 61.17 85.00 18,055
28 .879 .573 28.38 28,022 27.32 58.93 86.60 21,337
25 .802 .567 22.57 19,333 25.89 50.70 80.80 19,838
26 .793 .508 23.89 18,030 26.28 58.17 80.50 15,617
27 .768 .631 23.95 18,191 26.23 57.37 82.80 18,802
28 .789 .680 23.35 28,850 25.86 60.82 88.50 18,383
29 .797 .577 22.88 21,618 25.70 61.00 83.30 17,680
30 .750 .536 21.68 21,118 25.36 55.97 39.90 18,773
31 .818 .520 21.68 18,886 23.51 87.80 36.00 16,356
32 .785 .538 22.18 18,859 23.25 88.80 36.70 19,612
33 .770 .598 22.98 16,271 28.68 53.73 39.20 16,561
38 .797 .528 23.11 18,301 28.78 53.87 80.00 15,736
35 .778 .590 22.37 19,899 22.29 87.63 39.70 10,389
36 .790 .585 20.10 23,036 21.27 88.60 36.70 17,087
37 .788 .558 20.21 22,156 22.37 52.50 38.00 15,577
38 .821 .560 20.20 30,882 22.68 82.80 38.20 19,258
39 .801 .898 19.69 38,868 21.90 87.60 38.00 17,198
80 .751 .576 19.66 33,605 20.87 83.80 36.80 15,888
81 .761 .519 18.96 38,683 20.29 82.00 35.80 17,058
82 .751 .893 18.72 38,338 20.36 83.30 36.60 16,810
83 .736 .876 18.91 35,558 20.88 82.00 36.00 17,807
88 .780 .537 19.03 82,915 20.18 83.10 37.80 16,883
85 .731 .502 18.98 85,825 21.12 83.90 38.60 16,962

112

 

 

 

 

 

 

 

 

Table II 0. Data for the year 1958, continued.
week Prc Prr pr pr Pup 2,,1 P‘s be
¢/1b. ¢/lb. s/cwt head 8/bwt 8/8wt s/cwt head
86 .739 .893 19.31 82,756 22.35 88.00 80.00 13,232
87 .788 .510 18.79 65,581 21.28 81.80 37.50 9,787
88 .727 .515 18.20 51,885 21.11 80.29 35.25 7,378
89 .753 .860 17.89 68,669 20.86 39.60 33.80 18,688
50 .678 .830 17.51 61,216 20.53 38.67 38.00 17,019
51 .678 .888 17.01 68,171 19.65 38.33 38.00 16,683
52 .735 .897 17.23 80,090 19.82 38.83 38. 50 10,798
53 .715 .875 17.22 56,218 19.83 39.00 35.00 15,023
Table II d. Data for the year 1955.
Week Prc Prr pr pr Pup Pm PW3 be
¢/lb. ¢/1b. $/cwt head $/cwb 8/cwt 8/cwt head
1 .692 .870 16.82 57,298 19.72 38.17 38.70 11,507
2 .659 .808 16.70 58,673 19.71 39.83 38.50 12,828
3 .659 .898 16.78 53,951 19.93 82.83 38.50 18,593
8 .629 .835 16.78 85,515 19.63 39.83 38.10 12.880
5.673 .500 16.88 87,897 18.93 38.03 33.00 11,205
6 .688 .831 16.35 80,388 18.78 39.97 33. 00 11,178
7 .690 .881 16.10 83,221 18.66 81.17 30.00 11,898
8 .717 .870 15.75 39,858 18.82 82.08 38.38 9,500
9 .680 .866 15.87 82,601 . 17.98 38.57 32. 50 12,587
10 .681 .830 15.21 86,592 17.38 36.63 29.90 13,513
11 .681 .857 15.95 37,395 17.93 38.17 29.60 11,317
12 .706 .811 16.85 38,833 18.68 81.57 33.10 13,037
13 .676 .397 17.19 82,365 18.95 788.83 38.80 13,852
18 .705 .803 17.02 30,898 19.07 83.67 38.00 9,073
15 .730 .502 17.18 36,975 19.35 83.32 32.60 13,800
16 .708 .886 16.75 36,728 18.82 82.03 30.30 12,778
17 .699 .895 16.59 32,016 18.73 83.83 30.60 .21,365
18 .703 .861 16.98 36,163 19.30 88.70 28.80 13,617
19 .751 .582 16.95 36,269 19.69 89.67 32.50 18,689
20 .762 .508 17.88 33, 977 19.82 89.83 32.60 19,786
21 .750 .508 17.50 38, 297 19.88 89.53 33.00 17,285
22 .788 .880 17.92 28.321 19.98 89.25 33.75 17,551
23 .765 .503 18.80 28,912 21.21 56.00 35.90 20,888
28 .808 .592 20.31 28,032 22.10 60. 63 39.15 19,502
25 .819 .528 20.59 23,118 22.08 58.67 81.20 18,718

I

11.3

 

 

 

 

 

 

 

 

 

 

Table II d. Data for the year 1955, continued.
Week Pro Prr pr pr Pup PW1 Pws be
¢/lb. ¢/l . $/cwt head fi/cwt $/cwt 3/cwt head
26 .827 .601 19.70 21,073 20.69 88.80 39.70 16,035
27 .721 .558 18.68 20,718 20.58 87.75 39.12 13,702
28 .689 .877 18.37 21,118 20.25 88.65 39.10 13,318
29 .639 .868 17.20 19,028 19.12 83.60 33.80 13,928
30 .686 .829 16.86 19,127 18.38 81.83 31.65 18,539
31 .751 .503 15.82 15,881 18.17 39.97 31.20 12,280
32 .787 .863 16.29 19,170 18.90 81.30 31.90 16,167
33 .692 .869 16.56 28,658 19.25 85.20 32.20 12,332
38 .783 .872 16.86 28,175 18.37 86.28 31.75 11,812
35 .761 .883 16.19 25,865 18.03 83.90 31.95 15,288
36 .723 .858 16.37 22,971 18.65 88.67 33.00 13,892
37 .768 .883 16.35 32,887 18.63 88.53 38.10 17,997
38 .720 .506 16.16 31,908 18.83 82.78 38.25 16,992
39 .733 .852 15.90 33,592 17.56 81.67 33.15 16,310
80 .736 .856 15.38 83,758 17.35 82.10 33.50 17,825
81 .710 .838 18.98 81,753 16.97 39.63 32.35 19,718
82 .692 .508 18.33 88,859 16.51 38.08 29.85 16,552
83 .658 .825 13.59 58,181 15.88 35.02 26.55 18,776
88 .679 .821 13.56 65,811 16.35 38.12 28.55 16,506
85 .608 .826 13.15 59.861 16.27 35.35 28.31 16,573
86 .613 .392 12.01 78,811 15.72 33.07 28.05 18,786
87 .686 .883 11.26 53,580 15.82 32.06 26.50 13,305
88 .638 .885 10.98 82,980 15.23 31.82 28.80 16,286
89 .570 .888 10.72 73,838 18.73 31.17 28.50 18,186
50 .603 .822 10.57 77,787 18.58 30.57 28.80 15,762
51 .599 .375 10.73 89,078 18.17 27.85 28.85 15,368
52 .616 .852 11.06 57,082 18.63 31.17 28.50 13,285
Table II 6. Data for the year 1956.
Week Pro Prr pr pr Pup Pu1 PW8 be
¢/ lb. ¢/lb. $/cwt head £3/cwt 3/cwt $/cwt head
1 .589 .366 10.85 56,808 15.02 31.17 25.88 11,878
2 .598 .387 10.92 71,818 18.87 29.18 25.20 16,890
3 .578 .819 11.03 63,508 18.72 31.85 28.85 18,598
8 .600 .806 12.90 80,790 16.03 37.20 26.20 18,380
5 .667 .822 13.60 86,660 16.28 39.35 27.95 18,763

188

 

 

 

Table II e. Data for the year 1956, continued.
Week Pr Prr pr pr Pwp PHI Pws be
¢/lb. ¢/1b. 8/cwt head 8/cwt SS/cwt $/cwt head
6 .635 822 12.56 87,296 15.80 33.03 27.80 18,295
7.630 808 12.02 81, 921 15.39 38.18 27.30 16,983
8.619 .800 11.78 37, 718 15.59 33.77 27.00 16,885
9.603 .391 11.91 88, 986 15.26 31.78 26.75 16,657
10 .638 810 11.99 82, 906 15.25 31.62 25.10 13,926
11 .571 .351 12.53 38,900 15.28 32.90 28.30 16.336
12 .683 .357 13.72 32,200 16.03 37.08 26.90 17, 831
13 .688 .838 18. 55 31, 881 *16.68 38.13 29.90 12,039
18 .631 830 15 28 30, 583 17.20 39.83 29.35 15,827
15 .666 .853 15. 02 38,768 16.70 37.97 28.50 17,228
16 .619 810 18.98 35,860 16.99 80.75 28.25 16,351
17 .703 893 15.22 80,383 17.55 83.51 28.80 17,827
18.688 896 15.16 31,581 17.22 80.75 28.85 21,007
19.692 .857 15.29 27,338 17.38 80.30 28.05 15,831
20 .693 859 16.77 25,897 18.51 86.80 30.00 18,971
21 .733 .509 17.67 26,351 19.07 88.92 33.55 19,320
22 .732 515 17.36 . 25,767 19.57 52.97 37.82 15,595
23 .797 .577 17.27 28,860 19.09 88.55 38.35 28,518
28 .788 .501‘ 16.88 23,858 18.89 88.35 35.80 23,015
25 .781 -520 15.98 20,127 18.06 38.63 33.75 18,508
26 .765 .820 16.82 21,071 18.39 81.18 33.00 18,570
27 .783 .516 16.89 21,561 18.65 86.72 33.00 21,587
28 .769 .897 16.30 22,692 18.13 86.63 32.75 20,181
29 .738 882. 16.38 20,988 18.88 87.83 33.75 19,817
30 .682 .513 16.58 18,378 18.19 86.63 33.55 13,818
31 .728 890 16.82 21,088 18.86 86.28 32.80 18,087
32 .701 880 16.78 19,318 18.35 88.85 32.00 18,219
33 .758 508 16.91 18,759 18.81 83.83 32.55 16,568
38, .698 .396 17.07 18,669 18.52 86.88 35.50 18,658
35 .708 .585 16.58 28,192 18.03 88.90 36.00 19,218
36 .768 .556 16.27 . 28,309 18.82 88.60 36.50 12,306
37 .771 .588 15.92 31, 307 18.20 85.73 35.30 16,688
38 .737 890 16.21 31,268 18.62. 87.83 38.55 15,801
. 39 .735 .551 16.83 29, 758 18.96 89.03 35.80 18,179
80 .761 513 16.33 26,518 17.89 82.73 38.80 16,820
81 .782 .550 16.05 35, 310 17.68 88.15 38.85 15,296
82 .728 .887 16.08 36,118 18.19 88.08 35.15 17,829
83 .783 .508 15.60 85,358 17.25 80.95 33.30 18,332.
88 .688 .836 18.61 39, 785 16.90 37.13 30.10 18,938
85 .681 .888 18.93 83,887 17.08 38.65 30.15 12,655
86 .716 .808 18.85 87, 283. 17.12 36.25 28.50 18,038
87 .716 .885 18.93 28,086 17.62 35.50 29.06 16.660
88 .679 .828 15.88 86,818 17.87 35.50 29.15 15,038
89 .721 .860 16.11 80,187 18.25 .37.05 29.15 18,572
50 .670 .851 16.97 81,280 18.57 36.38 30.65 18,598
51 .728 .815 16.89 37,280 18.92 38.85 33.80 18, 795
52 .711 .833 17.36 30,738 19.56 83.00 38.92 19,135

 

115

 

 

 

Table II f. Data for the year 1957.
Week Prc Prr pr pr Pwp PW1 PWS Q fb
¢/lb. ¢/1b. 8/cwt head 3/cwt. $/cwt 3/cwt head

1 .676 .895 17.10 35,169 19.25 38.98 38.50 16,108
2 .669 .885 17.19 83,567 19.32 39.23 38.80 18.890

3 .750 .875 18.12 37,886 20.67 88.85 36.85 22,361
8 .722 .507 18.38 36.228 20.52 83.00 36.00 17,678

5 .753 .888 18.25 35,989 20.73 88.03 36.00 18,650
6 .758 .529 17.59 38,630 20.15 82.23 36.20 13,766

7 .702 .858 16.98 31,678 19.78 81.93 38.70 17,077
8 .709 .888 16.90 28,371 19.71 80.98 33.19 17,573

9 .737 .527 16.88 29,703 19.89 81.05 33.05 16,397
10 .728 .880 16.68 30,132. 19.88 80.20 33.20 15,788
11 .702 .887 17.29 25,593 19.68 80.85 33.06 18,986
12 .728 .508 17.86 27,002 19.88 80.69 32.88 15,386
13 .715 .839 17.78 31,628 20.08 82.35 33.22 16,809
18 .750 .867 17 .83 25,535 19.88 80.53 38.88 18,170
15 .725 .892 18.02 28,281 20.39 83.82 39.38 19,810
16 .720 .519 18.17 22,280 20.36 83.06 36.50 18,938
17 .710 .523 17.95 30,000 20.25 82.60 35.31 17,588
18 .685 .857 17.93 26,822 20.11 81.31 38.00 13,685
19 .702 .877 17.99 28,172 20.83 83.72 38.38 22,852
20 .765 .535 17.78 27,977 20.63 86.06 35.50 23,598
21 .726 .586 18.11 28,936 20.36 88.66 35.00 20,352
22 .780 .500 19.06 16,993 20.96 86.38 35.17 13,386
23 .767 .533 19.85 29,378 22.05 52.72 38.00 15,858
28 .788 .529 19.15 28,078 22.23 53.66 38.50 18,093
25 .761 .519 19.36 19,963 21.17 83.88 35.00 19,757
26 .727 .865 19.50 20,058 21.27 82.62 33.75 15,028
27 .770 .600 19.72* 11,882 21.65 88.63 33.92 18,228
28 .735 .538 20.38 20,887 22.88 50.69 38.25 19,930
29 .765 .593 21.07 19,010 23.88 51.69 80.75 19,069
30 .793 .519 21.38 15,831 , 23.09 86.38 38.12 17,928
31 .795 .501 22.18 16,503 23.27 87.28 37.50 17,560
32 .796 .593 21.90 17,596 23.68 50.56 39.12 21,897
33 .708 .585 21.29 19,703 23.03 87.69 39.69 21,060
38 .779 .583 20.52 21,330 22.67 87.30 39.88 19,936
35 .823 .555 21.20 19,992 22.82 89.50 39.25 18,977
36 .787 .555 21.09 20,088 22.69 51.63 -39.83 18,317
37 .788 550 20.21 27,088 21.76 89.06 80.62 21,267
38 .751 .538 18.89 29,078 20.78 87.03 38.00 20,918
39 .780 .508 17.91 26,861 19.35 85.88 35.12 16,071
80 .753 .558 18.37 28,179 19.72 87.53 36.38 19,892
81 .791 .508 17.60 31,016 19.55 87.19 36.50 18,288
82 .783 .530 17 .25 39,193 19.68 86.22 37 .21 15,583
83 .712 .885 17.02 39,955 18.97 83.82 36.50 19,907
88 .733 .570 16.77 35,638 18.63 82.72 38.31 22,397
85 .786 .882 16.77 81,136 19.17 83.16 33.50 17,081

116

 

 

 

 

 

 

 

Table II f. Data for the year 1957, continued.
Week Prc Prr pr pr pr Pal Pws be
¢/1b. ¢/lb. 8/bwt head 3/ewt 8/6wt s/cwt head
86 .721 .898 17.11 81,108 20.21 88.92 37.17 22,818
87 .728 .516 17.18. 39,359 19.15 39.88 36.00 18,689
88 .732 .538 17.80 30,710 20.28 83.75 37.00 18,387
89 .781 .863 17.93 82,971 19.90 81.60 35.50 17,790
50 .776 .583 18.56 38,906 21.09 85.58 36.50 19,710
51 .762 .588 18.80 80,893 21.09 88.13 37.88 19,683
52 .727 .553 19.68 27,992 21.59 85.88 38.00 18,087
Table II g. Data for the year 1958.
Week Prc Prr pr pr Pup Pwl P.“8 be
¢/lb. ¢/lb 3/ewt head S/ewt fi/cwt $/bwt head
1 .787 .551 18.28 36,108 20. 26 83.50 37.50 13,031
2 .718 .877 18.90 83,276 21.81 86.18 37.00 15,760
3 .751 .880 19.05 82,095 21.68 87.91 38.00 16,502
8 .782 .503 19.76 32,018 22.36 88.95 38.85 16,687
5 .752 .582 19.31 33,688 21.57 85. 75 37.50 18:860
6 .718 .517 19.80 30,372 21.85 86.15 38.00' 12,159
7 .781 .582 20.31 25,520 22.28 88.23 38.62 15,161
8.762 585 20.75 25,805 22.55 87.98 39.69 13,260
9 .768 .583 20.17 29,591 22.56 88.20 80.69 10,855
10 .753 .585 20.59 30,202 22.82 88.15 39.90 11,012
11 .796 .527 20.88 27,135 22.99 89.85 80. 75 10,298
12 .793 .528 21.62 28,318 23.87 89.88 88. 00 10,689
13 .809 576 22.01 26,765 23.17 89.28 88. 55 18,159
18 .792 591 21.18 28,325 22.97 89.13 81. 90 1L 123
15 .802 .531 20.95 32,656 23.51 89.86 81.00 18, 629
16 .783 577 20.78 37,579 23.22 88.33 80.81 12,938
17 .800 .531 20.28 80,108 22.97 88.81 81.00 17,385
18 .765 .668 20.88 38,006 22.72 87.81 80.88 17,378
19 .768 .565 21.86 30,863 23.20 89.83 80.50 18,655
20 .792 .600 23.21 33,071 28.37 58.69 82.81 19,832
21.813 598 22.58 32,355 28.21 52.53 88.50 16,592
22 .803 612 22.67 25,580 28.62 52.50 85.88 17,587
23.885 569 22.37 30,356 28.53 52.20 85.38 20,788
28 .833 .651 22.65 28,977 28.98 53.93 85.50 20,387
25 .829 553 23.89 22,672 .25.13 55.30 86.50

21,235

117

Table II g. Data for the year 1958, continued.

 

 

Week Prc Prr pr pr Pwp Pwl Pws be
¢/1b. ¢/Ib. 8/cwt head 3/cwt $/cwt 3/ewt head

26 .790 .689 23.88 23,710 28.98 53.37 86.38 20,803
27 .778 .639 28.32 15,582 25.83 55.16 86.81 17,706
28 .798 .683 23.78 21,366 25.01 . 53.50 87.00 19,257
29 .796 .626 22.89 20,551 28.89 50.83 87.50 23,278
30 .818 0656 23002 16,672 2h0h9 50017 h6088 19,513
31 .787 .581 22.86 20,989 25.10 51.88 86.88 22,603
32 .812 .618 22.87 22,363 28.72 89.75 86.69 22,062
33 .809 .607 22.26 21,856 28.01 87.75 88.35 21,678
38 .881 .588 20.53 23,618 22.31 85.10 80.75 23,133
35 .810 .578 19.68 22,787 21.68 88.28 38.12 28,680
36 .817 .532 20.06 21,780 21.93 51.59 38.33 19,952
37 .778 .559 20.39 28,325 22.98 58.19 39.81 21,267
38 .802 .582 20.66 29,231 22.60 51.85 81.98 28,823
39 .881 .563 20.90 32,853 22.22 52.88 82.60 22,207
80 .805 .537 19.62 33,275 21.02 88.35 39.19 20,982
81 .818 .588 19.68 33,211 21.33 50.35 38.75 23,880
82 .820 .590 19.08 38,831 21.26 50.19 39.88 28,682
83 .873 .668 18.95 81,196 20.99 89.53 ‘ 38.20 27,636
88 .810 .568 18.66 39,803 20.79 87.82 36.62 21,810
85 .789 .515 18.72 82,828 21.28 87.88 36.75 25,123
6 .781 .556 18.81 86,970 21.39 87.98 37.25 27,651
87 .798 .602 17.89 39,858 20.53 82.66 35.25 20,627
88 .769 .530 18.57 29,550 20.90 88.51 38.25 19,276
89 .727 .880 18.05 83,378 20.36 82.13 33.50 17,363
50 .696 .887 18.21 83,872 20.66 85.87 35.38 20,761
51 .758 .558 18.20 39,107 20.87 83.19 38.62 18,181
52 .715 .627 18.70 20.53 88.88 35.75 18,668

 

 

“‘J’Qil‘ ~34} ‘ Ila.

 

 

\au

 

MICHIGAN STATE UNIVERSITY LIBRARIES

31

'1

93

I

1

75 0593

I