MGM PRODUCTWITIES OF INPUTS ON
CASH CROP FARMS IN THE- THUMB AND
WNAW VALLEY AREA OF MICHIGAN, I957

Thesis for the Dogma oI M. S.
MICHIGAN STATE UNIVERSITY
M. David Brooke
I958

......

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HARGINAL PRODUCTIVITIES OF INPUTS 0N CASH
CROP FARMS IN THE THUMB AND SAGINAW

VALLEY AREA OF MICHIGAN, 1957

by
M. David Brooke

AN ABSTRACT

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

MASTER OF SCIENCE
Department of Agricultural Economics

1958

Approved by 4% V%‘~

 

M. David Brooke
ABSTRACT 1

The purpose of this study was to estimate marginal value
productivities for the various input, investment and expense cate-
gories of farm businesses. It was believed that such measures would
provide a more objective basis for estimating efficiency of and
making decisions on some of these inputs, particularly labor and
machinery investment, than farm management research methods used
in the past. It was anticipated the estimates, as a whole, would
be valuable to farm managers, agricultural extension personnel,
and representatives of lending institutions working in the area i
where the study was conducted.

The marginal value productivities were estimated by fitting
a Cobb-Douglas function to the data collected from thirty, pur-
posively sampled, cash crop farms in the Thumb and Saginaw Valley

area of Michigan for the year 1957.

b; bn

3
is linear in the logarithms. The data were fitted by the method

This function is of the form Y = qxzbzx ....xn and

of least squares to the logarithmic form of the function in order
's). The b 's are

i i
estimates of the elasticities of the input categories with respect

to determine the regression coefficients (b

to gross income. The marginal value productivities, for the

geometric mean organization of the farms surveyed, were then esti-
A.

biY A
mated from the equation MVP -= , where Y is the

X1

anti10g of the geometric mean estimated gross income and X1 is the

geometric mean of the input category Xi in the prediction equation.

 

Five regression analyses of the data were made which in-

cluded two assuming perfect complementarity among the input categories.

'M. David Brooke
2

The input categories, their geometric mean quantities, regression
coefficients and estimated marginal value productivities for the

sample were:

 

 

Geometric . Marginal

Mean Regression Value
Input Category Quantity Coefficient Product
(dollars)

X2 Land 193 T.A. .224325 24.71

X3 Labor 19 months .275044 306.87
X4 Machinery investment $14,654 .204850 .29?
X5 Drainage investment $19,135 .279131 .310

X6 Current fertilizer

and crop expenses 3 6,609 .170704 .584

 

Note: These regression coefficients have been estimated from
two different functions and thus the sum of these bi's is not the
true sum.

Geometric mean gross income was 821,252.
The estimated MVP's for land and drainage investment were

computed from the b 's obtained in the first Cobb-Douglas function

1

analysis. The other MVP's were estimated from bi's obtained in the
final Cobb-Douglas function. This latter function assumed perfect
complementarity of the inputs of land and drainage investment,
which were set up as a combined limiting factor category. The MVP
of this limiting factor was computed to be equivalent to 854.45

per drained tillable acre. (The average drainage investment per

tillable acre was 899.90.)

M. David Brooke
3

Evidence of complementarity between the inputs was found,
which might have been expected in view of the high intercorrelations
of the input categories.

Tentative conclusions were that most of these farms were
fairly well adjusted in 1957. Increasing returns to scale, indi-

cated by the sum of the b '8 being persistently greater than one,

1
suggested that prOportionate increases in all inputs would be
profitable, with some reservations. Land was a limiting factor

on the smaller farms and raw land in general was yielding lower
than expected returns, particularly in view of the high prices
being paid for land in this area. Labor had a higher return than
most other similar studies, particularly on livestock farms, have
shown. The labor organization on these farms appeared to be ef-
ficient, but with Opportunities for improvement by reducing labor
requirements at sugar beet singling and hoeing time in particular.
Large machinery investments have probably helped in the attainment-
of such high labor returns, nevertheless returns to investment in
machinery were also good, being almost equated to marginal factor
cost. Returns to drainage investment were high, emphasizing the
importance of drainage on these farms. 1957 was a favorable year
as regards this investment; even so, a further study of drainage
may be worthwhile. Less confidence could be placed in the esti-
mates of the returns to the other inputs of fertilizer and crop
expense. They were showing a very low return which may in part be

due to a less than normal response to fertilizer because of the

M. David Brooke
4

weather in 1957. More attention to these items of expenditure
could result in higher returns.

The use of these marginal value productivity estimates as
a general advisory tool on individual farms was discussed and an
example given. The conclusions were that although applications
of this particular study were limited because the farms studied
are so well adjusted, this method of analysis would be useful and

highly|desirable in areas of more poorly adjusted farms.

MARGINAL PRODUCTIVITIES 0F INPUTS ON CASH
CROP FARMS IN THE THUMB AND SAGINAW

VALLEY AREA OF MICHIGAN, 1957

by
M. David Brooke

A THESIS

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

MASTER OF SCIENCE

Department of Agricultural Economics

1958

ACKNOWLEDGMENTS

The author wishes to place on record his gratitude to the
many people who have assisted with this study and made it possible.

Sincere thanks are due to Dr. Glenn L. Johnson for his
guidance, inspiration and continuous encouragement throughout this
study and, indeed, during the whole of the author's graduate work.

The author is particularly indebted to the Kellogg Founda-
tion for providing the fellowship which enabled graduate work to be
undertaken at Michigan State University and the privilege of
visiting this wonderful country of America. Thanks are also due
to the Ministry of Agriculture, Fisheries and Fbod of England and
Isles for granting the necessary sabbatical leave and to Dr. L. L.
Boger for providing the financial resources which made the study
possible.

Assistance and constructive criticism were freely given
by many of the staff and fellow students of the Department of
Agricultural Economics, particularly Professors H. L. Brown, C. R.
Hoglund, J. M. Neilson and I. H. Vincent. Assistance given by
members of the Departments of Agricultural Engineering, Soil
Science and Fhrm Crops was also appreciated.

Thanks are given to Mrs. Sally Daly and other members of
the computing staff for carrying out a major portion of the computa-
tions, to Miss Beverly Hamilton for translating the author's il-
legible English into legible, typed American, to Mrs. Doris DeKoning

for typing the final manuscript, and to G. I. Trent for his help

in meeting the final deadline.

ii

The splendid cooperation and friendliness of the many
farmers visited, and for whom the data was collected, is gratefully
acknowledged and, also, the assistance given by members of the
staff of the Michigan Co-operative Extension Service.

Finally, the author wishes to thank his wife, Joan, for
her tolerance and encouragement during the preparation and comple-
tion of this study.

Any errors in this manuscript are, of course, the responsi-

bility of the author.

iii

TABLE OF CONTENTS

Page

3‘ CKI‘IYC'I'YIJEDGMIENTS . O O I O O O O O O C C O I O I O O C O O O O i

w.

.“ fl? ,, ‘ ' t'.‘ 5' . J
I..I~)T ( 1‘ F‘I 1"12.g.3 e e e s e s e e s e s s s s s e s e e s e- e s 5 J
1013? (I? Lfi-HIIJLR; e s e e e e e e e o e e s e s e e e e e s e e Vii

I O INTRODIJCTION O O O O O O O O O C O O O O O O P O O A.

II. PRODUCTION FUNCTION ANALYSIS . . . . . . . . . . . . 3
The Optimum A1 Iccntion of Resources . . . . . . . 7*
Grouping t‘ee Inmxts . . . . . . . . . . . . . .
Fitting the 3sta to the CobL~UonrJaz Function , , LT
Ilzrr.ossi\/e ‘Saun1fiIi;lg . . . . . . . . . . . . . . .1“

III. SAMPLING PROCEDURE AND NEASURENENT TECHNIQUES . . . . TE

The Smrir-I e . . . . . . . . . . . . . . . . . . . ‘73
'I‘IA e DU f, 6' O O O C 0 O O I D O D O O O O f O O O --‘I 5:
Correlation of Innnt Categories . . . . . . . . . 33

IV. FITTING THE PRODUCTION FUNCTIONS AND APPRAISAL
OF THE STATISTICAL RESULTS . . . . . . . . . . . . . ST

The First Function . . . . . . . . . . . . . . 38
'Ihe ASeCruvI F3uzctitn1 . . . . . . . . . . . . . . I?

TIhe 'Fhilvl Fhuxctixun, :lssxnringg ch‘fvcfi. Conq110742nt3n‘i13'
of the Inputs . . . . . . . . . . . . . . . . 47

The Fourth Function, Assuming Perfect

Conqflxunenixu‘ity (3f tin: Inrt:,s . . . . . . . . . 19
The Final Function . . . . . . . . . . . . . . . 73
Complementarity cf the Inputs . . . . . , . . . . CT
Managerial Ability . . . . . . . . . . . . . . . 33

iv

TABLE OF CONTENTS continued»

\I . EVAIJIY‘ATION s e e e e s e e e e e e e e e n e e s a
Land and Investment in Drainayw . . . . . . . .
I-aIJOI‘ e e e e e e e s e e e s s e s e e s e e

b‘flChiIIC‘r‘Y o s s e s e s e e e e e e I e e I e o

Fertil iazcx‘ Expenditure , . . . . . . . . . . .
rtImr Current Crop :XIKBDSBS; . . . . . . . . . .
Iauj-li'zir};ts O O O O O C O O O Q C O I 9 O O O I

Increasing Returns to Scale . . . . . . . . . .
The Complementarity of the Input Catogroriex; . .

Reorsv‘zmizution of n Farr: on tic Basis of the
\)

list/mates . . . . . . . . . . . . . . . . . .

IV. CONCLUSIONS AND APPLICATIONS IN THE UNITED KINGDOM
Conclusions . . . . . . . . . . . . . . . . . .
Applications in the Unite-J King-(10m . . . . . .

APPENDIX A, Estimated Marginal Value Productivity for Some

or £2.63 Fill-I313 iII tile SENT?) C s e e s e e e s
.U'PENDIX 1‘) Questionnaire Used in Personal Interviews . .
I

BIBLIOGRAPHY ....

(D
9'"

(:6
C. I

91

10?)

LIST OF FIGURES

FIGURE Page

la. Relationshi; between marginal value product, total
value product and price of the variable invut . . . . 6

1h. Product contour map showing: output dependent; on two
inputs with other innuts held constant a . . . . . . . 6

an. The COIJb-DOU’Z‘IUS production function iIIustrnting
decreasing returns to scale only . . . . . . . . . . . 1'1

2b. The Cobb-Douglas :‘wrorhxcticn surface illustrating;
symmetrical asymptotic 3:04uct Contours, with
straight line expansion paths . . . . . . . . . . . . 13

3. Relationship Between gross income n~d unifs of
limiting factor on the far s in the sarule . . . . . 55

v 1

LIST OF TABLE

TABLE PAGE

I. Summnry of ewriricul data collected ffufl the
t"..irt"—()!.c farms in the .sumnle . . . . . . . . . . 70
II. The margins} value productivities of the geometric
mean quuntities of in uts reed on tnixt; ensh
crozov ftrM-s in the Swfinnw Valley nxfl‘. 1"“me we." (‘1‘
:ICIJUSHZ, 1957 (Jerived fuvnv the first ncuuucti n
function)

4p
0 I I I I O I I O 3 I I I I I I I I I I 7"

III. Comparison of the estimntod bi's and the hi's

necessary to yield. ruinimum zzturglnol value prov; c‘s.
fir‘fit fiIUCtlon s e e s e s s e e e e e e e e e e I'L—

IV. The ”standard units” cf the limiting factors used in
the functiuns assuuin; perfect car Tcmenturitv of

the innuf catcgoxies, with their ninimnm expected

-. ,4 .
ILLIII lu‘: s w e e s s e s e s s s s e e e e e e e ~ A.

V. The verginul value productivitios of the geometric
Inean .unurtities of'iwnnits Usuc’;n1 thirt}'(gu§: crap
furvas; iii the Sarfii;z0.v \Qilleay'zxnni fiusz) . rcti (y?
H
l

IIICIIIQE‘III, 1‘9"? ()01'iX'0d frur‘ the firm] 1‘I“K);I!1Cti\ul
lhlncstjA3n, ““2ic12 11“e;itcv? I;1n(‘ :udri dl‘aixx' at Ainxwesfnneztt
(If; I'IOI‘I‘QCI C'i‘rI‘IUI‘I’IItb) a e s s e e e e e s s e e ‘34

VI. Comparison of the estirruter} hi'c and the bi’s
necessary to yield minimum morgi'ol VMTHe pruduCts,
fiI-oni f‘II‘ICI-iI'II e I s e e s s s e e s s e e s e e If:

VII. Regression coefficients and marginal value
yroductivitics of one month of Inhur, in various

far? ilu: nzwzu:;, c4)tuiJie(} ix: rwccei‘t ESIUZIIGri . . . . '14
VIII. Nunher of men and Inchinery investment her 190
tiIIéwbIO aficresz, I‘VICcifVIC, .U"eu Ii, Iicfiiiflurx . . . ()9

IX. Range in quantities of artificial fertilizers amplicu
to the three main crops of thirty Saginaw Valley
and Thumb cash crog‘ farms in 10.737 . . . . . . . . 7;;

X. Estimrted rarginal Value productivities (dollars)
for sure of the frnvns in the sample . . . . . . . SO

CHAPTER I

INTRODUCTION

The British farmer is beginning to be faced with the labor
problem which has plagued the American farmer for some time. Other
industries are becoming more and more attractive to agricultural
labor with the farmer being unable to pay comparable wage rates.

The substitution of machinery for labor which has taken
place in the United States, together with the increased farm size
is apparently part of the answer. I111 it pay to do likewise in
the United Kingdom? If so, how much does it pay? It is hoped
that this study will illustrate a method of answering these ques-
tions.

Methods of farm management analysis commonly used in the
U. K. measure labor efficiency in terms of productive work units
per man. This is a measure of output per unit of input. In some
instances, where large amounts of capital are used, a man may be
accomplishing 500 days work per annum: It would therefore be an
advantage to measure efficiency on a more objective basis. Con-
tinuous function analysis provides a method of isolating the return
to each input category; thus if the profit motive is taken as the
criterion, efficiency could be measured in terms of the income
return per unit of labor.

Machinery use is obviously difficult to assess, with much

subjective judgment involved. The possibility of measuring efficiency

in terms of returns to investment appears attractive as it would
provide some objective basis for assessing whether a farm was over
or under capitalized with machinery.

It was decided that cash crop farming in the Saginaw Valley
and Thumb area of Michigan should provide a useful and interesting
study of a method for determining the marginal value productivities
of inputs by subjecting the input-output data to a continuous
function regression analysis. The theoretical basis for this pro-
cedure is discussed in the next chapter. The farms chosen were as
purely cash crop as could be satisfactorily found. This was done
in order to simplify the problem. It would have been useful to
undertake the project on mixed farms but the accounting procedure
necessary and the complexity of the problem, as pointed out by
Beringerl and time limitations precluded the attempt.

The method of sampling and measuring the productive input
categories is discussed in Chapter III. The fitting of the pro-
duction functions and appraisal of the statistical results follow
in Chapter IV. The evaluation of these results in Chapter V in-
vestigates the usefulness of the information in the area studied.
Conclusions are drawn in Chapter V1 with a discussion on the appli-

cation of similar methods of studying farm businesses in the U. K.

 

lChristoph Beringer, "Problems in Finding a Method to
Estimate Marginal Value Productivities for Input and Investment
Categories on Multiple Enterprise Farms." (Resource Productivitya
Returns to Scale and Farm Size, Heady, Johnson and Hardin, Iowa
s€3%e Cbllege Press, 1956. pp. 106-113.)

CHAPTER II
PRODUCTION FUNCTION ANALYSIS
The Optimum Allocation of Resources

It is assumed that the maximization of profits or returns
to investments as a means to more ultimate ends is the underlying
motive of farming. Marginal analysis enables the determination
of the most profitable allocation of resources; this involves
estimating the change in the value of total product brought about
by the last unit of productive resource used. (The marginal value
product or MVP.) It is economically profitable to continue adding
units of a productive resource until the addition to total cost,

or Marginal Factor Cost (MFG) is just covered by the marginal value

product. MVP
X
(1) mx -_- wax or 1(1) = 1
1( ) 1 MFC
y x1

Where X1 is one of the inputs producing the product Y with all

other units of input (X X3, ... Xh) remaining fixed.

29
As no one farm is generally capable of influencing either

the price of the product or factor costs to his competitors perfect

competition can be assumed. So that if Py is the price per unit

of output Y and PJ: is the price per unit of input X , then

1 l
for maximum profit

NPP

x

l
P . (z) 1
y p 3

x

l

The law of diminishing returns is assumed to apply to all
inputs used singly and in various combinations on the farm. This
assumption assures the existence of a high profit point. The law
states that as inputs of a variable factor of production are
added, in combination with fixed factors, the total product will
first increase at an increasing rate, followed by a stage of in-
creasing at a decreasing rate and finally the total product will
decrease. This is illustrated in Figure Is by the total value
product curve (TVP).

The MVP curve is the slope of the TVP curve (or g% ).
1

It pays to add X1 as long as the output achieved covers the cost
of the input; or until, at the point B , equation (1) holds. In
this case, this is the optimum combination of X1 with fixed
inputs X2, X3..... X3 .

when two inputs are variable (X1 and X2) in combination
with other fixed inputs the principle is better illustrated by a
three dimensional diagram (Figure lb), or a production surface.
The iso value contours are the loci of combinations of the two
variable inputs, with fixed inputs (X3, X4, ..., X“), capable of
producing a given amount of output, i.e., an equal elevation on
the production surface. The inputs of X1 and X2 are shown
measured along each axis. Output of Y is shown by the contours
in the third dimension.

The iso cost lines are the loci of all positive quantities
that can be purchased with a given outlay. The iso value product

contour tangent to an iso cost line represents the greatest value

of Y produced for that given cost of using inputs X1 and X2 .
This is the point of least cost combination for that output. The
expansion path, or line of least cost combination (0A), is a line
joining all these points of tangency at a given cost structure.
Figure 1b is intended to illustrate the law of diminishing
returns so that a vertical section of the production surface along
the line 0A , or line of least cost combination, may look something
like the TVP curve of Figure la. The X axis, in such a case,
would then be designated by 1&1, le x3, xv”... xn .
Though diagrammatic illustration is impossible with more
than two variable inputs, the concept still holds for any number.
Assuming that all factors are not variable in the period under
consideration, the law of diminishing returns will operate in

respect of all the variable inputs combined in proportions dic-

tated by the line of least cost combination. So that for maximum

profit:
MVP MVP - MVP

‘2’ xl( ) x2< ) ' x“( )
————L—' 8 ‘-_C—L C eeee = '__—-L
MFCx1 MV x2 MFCxn

If the MVPs of these variable inputs increase as all
variable inputs are increased, the firm is experiencing increasing
returns to scale, as a whole and with respect to each input. If
the MVPs decrease as the variable inputs continue to increase the
firm is experiencing decreasing returns to scale.

It continues to pay adding units of production as long as

the resultant increment to total value product covers the increased

(In
dollars)

1

 

Figure 1a.

 

’PVP

 

 

XII X2, X3, ..., Xn (In dollars)

Relationship between marginal value product, total
value product and price of the variable input.

 

\ \
\ \ \ ‘
W \ \ \ s
\ \ \ \
x ‘\ \\ \\ iso value
X T \ \ \ contours
1 \ \ \
\ x
\ x
J \ \ \
\ \ ' \
\ \
I? \\ \ \ \
\ \
\ \ ‘\ \ . t
\ \fi _, iso cos
" \ \\ \ \ lines
\ \
\\ \\ \
\ ‘\ \ \
\ \
x “\ \\ ‘\
. \ \ ‘ \ \
\ \\ ‘ \\
d \ \ \ \
\
\ \ \
¥ - \i \ \ \ _
v v v 1 7 I l l I ‘
x2
Figure lb. Product contour map showing output dependent on two

inputs with other inputs held constant.

cost of production, i.e., until equation (2) holds. If the
marginal value product of one input exceeds that of another it

pays to increase the use of that input before the other. For
example, it may be found that the return to drainage investment
(measured in dollars) is 20 percent, while the return to the in-
vestment in land (measured in acres) is 830 per acre. The cost

of undrained land is, say, 3400 per acre and assuming that a 5
percent return on land or drainage investment is necessary to cover
interest on borrowed capital, maintenance, tax charges, etc., it
would leave a net return on capital of 2%:percent for land and 15
percent for drainage investment. If this farmer had the choice of
either buying more land, assuming normal capital restrictions, or
completing the drainage of his existing land, it would pay him to
do the latter until the conditions in equation (2) hold true. In
practice, such decisions must necessarily be made more subjectively.
The prestige value of a larger acreage may outweigh the difference
in return to be expected from increasing the drainage rather than
the land investment. This depends on the utility function of the
individual manager. Also, such decisions must consider the future
outlook of prices of land and farm products. Other risks and
uncertainties involving weather and government policy may also be
subjectively considered. The same is true of labor supplied by

the farmer and his family which may have no established market price.
Though such considerations are not currently ignored, it is sug-
gested that a somewhat more objective basis would be of great

assistance.

Grouping the Inputs

The principles outlined are applied to data from the farms
surveyed in this research project. The inputs have been carefully
grouped into independent categories (Chapter III) in terms of
substitutability and complementarity. Classification is necessary
in order to simplify reality. N variables, while theoretically
solvable in a production function, make the task of determining
the point of maximum profit extremely difficult.

Johnson suggests:1

(l) The inputs within a category should be as near perfect
substitutes or complements as possible.

(2) Substitutes should be combined, as perfect substitutes
are really one input which can be measured in terms of the least
common denominator causing them to be good substitutes and priced
in dollar value of the least common denominator. For example, the
least common denominator of 5-10-10 and 6-12-12 fertiliser inputs
would be units made up of equal amounts of N, P, and K, measured
in terms of their dollar value.

(3) Complements should be combined, as perfect complements are
really one input made up of the complements combined in constant
proportions. They should be measured by counting the "sets” of
such good complements in their proper proportions and priced on an

index basis with constant weights assigned to each complement.

 

1Lawrence A. Bradford and Glenn L. Johnson, Farm Management
Analysis (New York: John Wiley and Sons,Inc., 1953), p. 144.

Complementary examples are sets of machinery. Tractors, with their
complements of cultivation and harvesting equipment can be counted
assets or measured in dollar value. As the data collected apply
to one year only, it is unnecessary to construct price indices.

These conditions, (1), (2) and (3), are desirable to
ensure that inputs within each category are combined in~propor-
tions dictated by the scale line for a subproduction function
treating the inputs in category as variable:

Y a If (x1, x2....., X“)

(4) These input categories should be neither perfect complements
or near substitutes relative to each other. This leaves the im-
portant economic questions involving input combinations to be
answered by the analysis rather than covering them up within
categories.

(5) Expenses and investments should be kept in separate cate-
gories, as the level of returns expected from these two types of
inputs are quite different. Cash expenses, as annual inputs, are
expected to yield at least a dollar per dollar spent. Investments
cover a longer production period than a year; hence, annual return
may be lower. Maintenance expenditures and depreciation should be
eliminated from all input categories because of the difficulty in
preventing duplication. Hence, expected returns to input cate-
gories of an investment nature should be high enough to cover in-
terest, maintenance, taxes and depreciation.

All factors affecting the gross income cannot be adequately

covered in a study such as this. Weather is uncontrollable and

10

managerial ability, as an input, at the present state of knowledge,
is immeasurable. Frank Knight2 pointed out that our ability to
make inferences depends on the existence of constant modes of be-
havior (with a known standard deviation from the mean). As the
relevant variables are often too numerous for our limited finite
human minds, it is necessary to classify them into a number of
groups which exhibit similar behavior in certain respects. Even
this simplification of the problem is insufficient as we cannot
make an exhaustive classification and we have to fall back on con-
sistency of behavior or theory of probability so that thinking can
be ordered intelligently.' Every effort was therefore made to
classify the studied variables into homogeneous groups. The un-
studied variables such as weather and managerial ability are as-
sumed to have a normal and random distribution with respect to

their effect on the dependent variable.
Fitting the Data to the Cobb-Douglas Function

The fitting of farm input-output data, in the categories
developed, enables estimates of marginal value products to be de-
termined. The function developed by Cobb and Douglas,3 later re-

vised by Douglas4 is the type used in this study.

 

2Frank E. Knight, Risk Uncertainty and Profit (Boston and
New York: Houghton Mifflin Co., 1921), Chap. VII, pp. 197-232.

3Charles W. Cobb and Paul H. Douglas, "A Theory of Produc-
tion," The American Economic Review, Supplement, XVIII (March
1928), pp. 136-163.

4Paul H. Douglas, "Are There Laws of Production?" The
American Economic Review, XXXVIII, No. 1 (March 1948), pp. 1-41.

ll

bl b2 bn

(3) Y 8 8X1 x2 eeeexn

This is a cross product equation enabling the interdepend-
encies of the variable inputs to be demonstrated. The function
is mainly used to fit gross categories of inputs, as is required
by this study. It is often found to be less useful in analyzing
single inputs such as required in a soil and fertilizer or a feed
and hog output study.

The function is linear in the logarithms and becomes:

(4) log Y = log a + b1 log X1 + b2 log X2 + ....bn log Xn

It is simple to fit to the data by least squares regression. In
this study this was accomplished with an electronic computer.

Once a fit has been obtained it is easy to manipulate and determine
the marginal productivities.

The exponents (b1 '8) in the equation are the elasticities
of the independent variables (X1 's) with respect to the dependent
variable (Y), in this case gross income. The value of these ex—
ponents indicates the percentage change in gross income associated
with a one percent change in the respective input category, all
other inputs held constant. The constant 'a' is the intercept
with the Y axis. The marginal productivities of the input
categories (Xi) may be calculated directly from the exponents by
the formula:

b9

i

1 xi

(5) MVP

 

A
where Y , the estimated gross income, is the antilor of low Y
in equation (4) and X1 is the quantity of the innut under con-
Sidelnatinn (i = 1, 000‘ n).
5 I I I O I
Cobb and Douglas originally imposed the restriction of
forcinw the sum of the exponents to equal one. This was equivalent
to assuming constant returns to scale. Later this was relaxed and
the sum of the exponents was not forced to equal one, permitting
increasing, decreasing or constant returns to scale to be
6
reflected. If
n
b. 1
I: 1‘< '
i = 1

decreasing returns to scale are exhibited, if

increasins returns to scale are exhibited, and if

n
z b,=1
1
i = 1

constant returns to scale are exhibited.

The estimated re"ression coefficients (bi's) are constant
over the entire function. This assumntion means that the unmodified
Cobb-Douglas function can only be used in certain cases where con-

stant elasticity of the function can be presumed to exist. It also

imnoses the limitation of the inability to handle more than

 

5Char1es W. Cobb and Paul H. Douglas, 22. cit.

6Paul H. Douglas, 22. ci .

13

one stage of production for any given variable at a time (see
Figure 2a). It was suggested that this may not be serious for
the data under consideration, as it was believed that these farms
were operating in stage II for all single input categories, i.e.,
where diminishing marginal returns are experienced. The optimum
combination of resources can be achieved only in stage II for all
variable inputs as a group. Though, strictly speaking, it is
irrational to operate within the range of increasing or negative
marginal returns, it was later found that the farms were operating
in stage II for each input, but in stage I for total inputs.

The function is symmetrical (see Figure 2b), with iso
Product contour lines becoming asymptotic to the vertical and hori-
zontal axes. This implies an unlimited range in which the propor-
tions of two inputs can be varied to produce a given output. Fbr
example, in the labor machinery dimension, the form of the function
indicates that a fixed amount of labor is capable of handling an
unlimited quantity of machinery if one were willing to extrapolate
beyond the range of any set of observable data. Such extrapola-
tions, obviously, would be both impracticable and professionally
dangerous. It is feasible that some production would be forth-
coming with no investment in machinery, all the work being accom-
plished by hand. H. 0. Carter7 has suggested modifications to

destroy the constant elasticity and symmetry aspects of the Cobb-

 

711. 0. Carter, "Modifications of the Cobb-Douglas Function
to destroy constant elasticity and symmetry," Resource Productivity,
Returns to Scale and Farm Size (Heady, Johnson and Hardin, Iowa
State College Press, 1956). pp. 168-174.

14

 

 

0 V I I 1 W ' 1 I - ' r‘

x1 X2 X3, '°" X

Figure 2a. The Cobb-Douglas production function illustrating
decreasing returns to scale only.

n

 

 

 

 

o ‘ V 1 m w v V V T

Figure 2b. The Cobb-Douglas production surface illustrating
symmetrical asymptotic product contours, with straight

line expansion paths.

15

Douglas function. The constant symmetry limitation dictates that
any expansion path is a straight line cutting all iso product
contour lines in the input dimension at the same angle, and passing
through the origin. (See Figure 2b, with expansion paths 0A and
OB.) Again in the case of labor and machinery this may not be
true. As machinery is added, the rate of substitution of machinery
for labor would be expected to be quite high at first and then de-
crease, hence a curved expansion path could result.

However, the advantages of the Cobb-Douglas function with
its ease of computation and simplicity outweigh its disadvantages
for the purpose of this study. The assumption of constant elas-
ticity of the regression coefficients and all that that implies
must be kept in mind. The unexplained residuals must be assumed
to be normally and randomly distributed with respect to the inde-
pendent variables as the logarithmic transformation of the variable
inputs presumes a substantial degree of normality of the distribu-
tion of the errors in the logarithmic data.

As already noted in the introduction, the continuous func-
tion analysis of a group of farms having widely different enter-

prises requires more time than available for this study.8
Purposive Sampling

The reliability of the estimates of the bi's can be deter-

mined from the equation:9

 

8Christoph Beringer, 22. cit.

9Mordecai Ezekiel, Methods of Correlation Anal sis, ’
(Second Edition, New York: John Wiley and Sons Inc., 1939,, p. 502.

16

 

2'02
{bx ‘ nd’x2(1-R§

i i

 

1(X1....Xh, Xj....Xn))

There:

202 is the sum of the squared unexplained residuals. (Try
to minimize to reduce drbx )

1

N is the sample number. (Try to maximize to reduce {bx )

1
(X1 is the variance of Xi. (Try to maximize to reduce ‘Bx )
i

R: is the percentage of variance in X,

i(Xl....Xh, X3....Xn) explained by the other studied
variables. (Try to minimize to re-
duce {b
"1

Hence, it is necessary to obtain observations of the studied
variables over as great an area as reasonable of the production

surface; otherwise the estimations of the b '5, and therefore the

i
marginal value products, are liable to have a large error, unless
a very large number of observations are made. Purposive sampling
is designed to try to overcome this difficulty of reducing the
number of observations necessary and to bring studies of this
nature within the realm of economic possibility.10 Farms are se-

lected having wide quantity variations of the studied input cate-

gories with as little correlation as possible among these categories.

This means that imperfectly adjusted farms with respect to the input

categories should be included in the sample.

 

10This is a question of weighing up the marginal utility or

accuracy of the study with the marginal cost.

17

The unstudied variables, such as weather and managerial
ability should be minimized as to number and variance with random
and normal distribution with respect to the studied variables to

prevent any bias in the estimation of the b 's. Minimizing the

i
unexplained residuals was accomplished by choosing a group of
relatively homogeneous farms having the same inherent productive
capacity, i.e., the same soil type with similar climatic conditions,
this means limited geographic range. Variations are assumed to be
randomly and normally distributed. In this study only purely cash
crop farms, or as nearly pure as possible, were observed; live-
stock enterprises were carefully excluded from the data by avoiding
such farms or by eliminating the livestock enterprise through ac-
counting techniques.

All farms should be using the same range of technology
and the same technology for a given combination of inputs. The
quality of the inputs in each input category should be the same
and they should be combined in the best possible proportions.

If the conditions in these last two paragraphs are success-
fully met, we can assume all these farms are operating on the same
production surface and that the interfirm, intrafirm problem

pointed out by Bronfenbrenner11 does not apply.

 

11Martin Bronfenbrenner, "Production Functions: Cobb-Douglas,
Interfirm, Intrafirm," Econometrics XII, No. 1 (January 1944),
pp. 35-44.

CHAPTER III

SAMPLING PROCEDURE AND MEASUREMENT TECHNIQUES

The Sample

Strong effort was made to select farms which were homo-
geneous with respect to the non-studied variables such as weather,
type of production, technology and managerial ability, and which
were non-homogeneous with respect to the proportions and quantities
of the studied variables. This was in accordance with the reason-
ing in the previous chapter.

Table I gives detailed data for the individual farms in
the sample.

(1) Type of farming was restricted to cash crop with the
absence, or absolute minimum, of livestock. All these farms grew
white pea beans, wheat and sugar beets, with some growing smaller
acreages of oats, corn, barley, soybeans and alfalfa. Restricting
the sample to farms growing sugar beets eliminated a large propor-
tion of those growing cash crops. Otherwise the cropping is fairly
representative for cash crop farming in the thumb area of Michigan.

The percentages of tillable crop land, by crops, in the

sample was:
White pea beans 44.1%
Wheat 21 .096
Sugar beets 20.0%
Oats 5.2%
Corn 4.9%
Barley 2.7%
Soybeans 1.2%
Alfalfa 0.5%
Other 0.4%

19

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saoo a cause haesuaosx nose fiasco aouunueaeh owesqssn hhosusoel nonla onnsnnue nacho lash

 

 

 

 

 

 

 

 

fldmxdm HEB 2H mzmsh HZOIHBMH=H HEB xbmk GNBOQAAGU 19¢: AdOHmHmzfl BO hm<xXDm
H Ham<s

20

The percentage of land under a cover or green manure crop during
the winter was 23.3 (sweet clover, alfalfa and clover or rye).
This was usually plowed down for beans in late spring.

Livestock enterprises were absent from the majority of the
farms. Some had a small flock of poultry. However, three or four
farms fattened steers, for which most of the feed was bought. The
income and expenses associated with these enterprises were fairly
easily excluded from the data.

(2) All the farms were selected from the same soil type;
the dark colored (Humic Gley) Lake Plain soils of the Saginaw
Valley and Thumb area of Michigan. These are level, poorly
drained soils formed from loams, silt loams and clay loams.1 The
principal soil types in the Saginaw Valley included Wiener and
Essexville loans; these have a high pH which may result in minor
element deficiencies, particularily manganese. The Prairie Farms,
in the region south of Saginaw, are mainly on a Clyde clay loam
which includes a mucky phase. 0n the farms selected no muck soil
occurred. In the rest of the Thumb, the main soil types included
Brookston, Kawkawlin and Conover loams. All these soils are rela-
tively high in organic matter, nitrogen and line. They are moisture
retentive (all the farms selected required full tile drainage) and
have good natural fertility. Differences in natural fertility were

assumed to be randomly and normally distributed.

 

1E. P. Whiteside, I. F. Schneider and R. L. Cook, Soils
of Michigan, Special Bulletin 402, Soil Science Department, Agri-
cultural Experiment Station, Michigan State University (January
1956).

21

One of the farms observed (No. 12) was on the fringe of
this area and little drainage was required. The data from this
farm were subsequently omitted from the analysis.

(3) The region from which the farms were selected (the
"Bean Pot" of the United States) is fairly limited geographically.
Differences in the weather had occurred throughout the region in P
1957 and this had caused some differences in crop yields, parti-
cularly with the pea beans which are notoriously susceptible to
excess moisture. It was believed that the differences that did
occur were randomly and normally distributed.

(4) All the farms, as near as could be judged, were using
technologies selected from a common bundle of available technologies;
further, it appeared that farmers shifted technologies consistently
as they substituted one input category for another. This is re-
quired in the assumptions of static production economics.

(5) The farms were using the same inputs, as defined
later, in the input categories. These categories were designed
to be as near perfect substitutes or complements of each other as
possible, with the inputs within these categories combined in least
cost prOportions.

(6) It was assumed that all the farms were operating in
the stage of decreasing returns to scale for individual inputs.

The sum of the b 's was later found to be slightly greater than

i
one indicating increasing returns to scale when all inputs are

considered; a situation which makes it impossible to estimate the

most profitable size of farm to organize from the analysis presented

herein.

22

The Data

"Purposive" sampling, as described in the previous chapter,
was undertaken in an attempt to prevent high intercorrelations
among the input categories. Farms were selected for visiting,
after discussion with county agents and farmers, to insure they
would be of the same type and that the sample contained as wide a
range as possible of the quantities and proportions of inputs used
in relation to other inputs.

Data were eventually obtained from thirty-one farms for
the operating year 1957. The data from one farm was subsequently
omitted, leaving thirty farms from which the continuous function
analysis was run. The questionnaire used in personal interviews
(see Appendix B) provided for the measurements of:

The dependent variable Y, or gross income.
The independent variables:

X2 land, in tillable acres

X3 labor, in months

X4 machinery investment, in dollars

X5 drainage investment, in dollars

X6 current fertilizer expenses, in dollars

X7 other current crop expenses, in dollars

X8 machinery storage and workshop investment, in dollars
X9 crop storage investment, in dollars

Gross Income (Y) was a measure of the actual production,

from the tillable acres (X2) for the year 1957. Income from

23

livestock was carefully excluded. However, any crop production in
1957 utilized by livestock (except grazing) was credited as gross
income. Custom work and machinery rent were also included in gross
income as it would have been almost impossible to separate the
costs and investments involved from that of normal crop production;
in any case, this represented a return to labor, machinery invest-
ment and machinery expenses.

There was no produce consumed in the house or other income
from crop sources to be credited to gross income.

Six of the farms were growing a proportion of their crops
for certified seed. In these cases the actual quantity produced
was multiplied by the unit price which would have been obtained
in the normal market. The excess costs and investments of pro-
ducing seed instead of an ordinary cash crop were then carefully
excluded from the input data. This method was a little unfair to
those farms which grew barley and oats for seed; this acreage would
otherwise have been in a higher value crop such as beans or sugar
beets.

It was found unnecessary to make estimates of beginning
valuations of crops on hand. Actual sales of the 1957 crop were
taken and additions made for that part of the cr0p still unsold.
The value of the crop still in storage was estimated on the basis
of the reasonably expected price per unit, less storage charges,
etc. The sugar beet crOp is paid for in three separate install-
ments, the final payment for the 1957 crop being in September or

October 1958. Hence, the tonnage of sugar beets produced on the

24

farm in 1957 was multiplied by 313.50 to obtain the gross income.
This was estimated as being the most probable final total price.

In the case of share-renting, total production (including
the landlord's share) was credited to gross income. If the land-
lord provided any input, such as a proportion of the seed and
fertilizer, this was noted and included in the appropriate input
category. No charge to expenses was made in the case of cash
rent, instead the land rented was included in tillable acres.

Income from government payments in respect of land in the
soil bank was excluded and such acreages and connected expenses
were excluded from the corresponding input categories.

E222 (X2) was measured in actual tillable acres whether
owned or rented with no allowances for roadways, ditches, farm
buildings, etc. Any acreage leased out was excluded.

£9225 (X3) was measured in average man month equivalents
spent working on the farm in respect of cash cr0p production in-
cluding machinery maintenance, crop storage, crop handling and
custom work. Labor used in connection with livestock was excluded.
Time spent living on the farm by the operator and his family during
the winter months when no productive cash cr0p work was being under-~
taken was excluded. In some cases operators were in the habit of
taking off-farm jobs during the winter in, for example, the
automobile industry. However, the recession during the winter of
1957 prevented many from obtaining such work. Others, who were

more fortunate, took a long vacation (perhaps in Florida).

25

The few farms employing labor full time were charged with
twelve months of work per man employed full time.

Seasonal work was usually in the nature of extra help at
harvest time. Frequently extra trucks were hired for hauling the
sugar beets. In such cases, $1.00 per hired truck driver per hour
worked was deducted from the bill for haulage. This labor was
then converted to man-month equivalents and credited as labor
input. On many farms outside help and machinery hire for harvest
were reciprocated in kind. The balance was credited or debited
to the farm gross income or variable input categories. Mexican
labor was generally employed for sugar beet thinning and hoeing
and also for bean hoeing. In one case, sugar beet harvesting was
undertaken with Mexican labor rather than hiring a mechanical
harvester. Mexican Nationals were paid by the hour (85¢), in
these cases it was relatively easy to determine the number of
eight hour days worked. This was then converted to man months on
the basis of twenty-five work days per month. The Texas Mexicans
were usually paid on a flat acreage basis of 818 - 820 per acre for
complete beet hoeing. In this case the number of actual man months
worked was computed in discussion with the farmer.2 Other farmers

employed families of Mexicans.

 

2The charge for sugar beet hoeing by Mexican labor was de-
ducted from the sugar beet check by the Sugar Beet Company. A
further deduction was made for rent in respect of housing for the
Mexicans. The Sugar Beet Company usually owned these houses;
however, in some cases the farmer was able to house the Mexicans
in which case he was paid the rent. (This was not included as
gross income.)

26

If family labor, e. g. children, was not capable of an
average output of work they were credited with a reasonable pro-

portion; similarly in the case of Mexican "family" labor.

 

Machinery and equipment investment (X4) was a measure of
the replacement value, in dollars, of the machinery and tools
used in the workshop at the beginning of the 1957 season.

The major items of machinery -- tractors, crawlers, trucks,
pickups, combines, bean harvesters, corn pickers and sugar beet
harvesters -- accounted for 70-80 percent of the investment in
machinery. Details were taken of these items as regards make,
model, age and condition. Reference was then made to a guide to
the value of used machinery3 and local machinery agents. An ob-
jective replacement value was then placed on these items of equip-
ment at early 1957 values, with a subjective account taken of
their condition. Automobiles were similarly valued4 but only that
portion of the investment corresponding to the automobile opera-
tion charge (usually 50 percent) was credited as farm machinery
expense.

The other items of machinery were valued at what the par-
ticular farmer thought they were worth in early 1957, i.e., what
he could have sold them for, or what he could have bought them for

in similar conditions.

 

3Official Tractor and Farm Equipment Guide (January-June
1957). Compiled by the National Retail Farm Equipment Association.
Published by Farm Equipment Retailing Incorporated, 2340 Hampton,
St. Louis 10, Missouri.

4Official Used Car Guide (January 1957). Published monthly
by the National Automobile DeaIers Used Car Guide Co., 200 S. 7th
St., St. Louis 2, Missouri.

27

Items of machinery dealing specifically with livestock
enterprises were excluded.

In the few cases where machinery was purchased and sold
during the operating season, proportionate investment charges were
made according to the operating time for the 1957 season.

Drainage investment (X5) was also measured in terms of
January 1957 replacement cost. Only those drainage systems which
were working efficiently were included; if any cases of the old
2" tile systems had been met they would have been ignored.

All the land on the farms in this study required tile
drainage with the one exception, already noted. The land seemed
best drained when the tiles were at intervals of 4 rods or less.

Records were made of the length of run, in rods,of each
size of tile and the type of tile (clay or concrete). Similarly
those ditches representing a farm investment were recorded in
length of run in rods with average depth and bottom measurements.
County ditches were not included. Rented or share cropped land
was treated similarly.

The replacement value was calculated as follows:5

(1) Tile:

Trench digging and tile placement for 4"-8" tile
was charged at $1.00 per rod plus 12¢ per rod for

back filling, a total of 81.12 per rod. In the case

 

5Based on figures provided by Willard A. Cutler, Assistant
Professor, Ext. Agricultural Engineering, Michigan State University.

28

of lO"-12" tile similar costs were 31.20 and 12¢
per rod respectively, a total of 81.32 per rod.
Replacement costs were then computed from the fol-

lowing table:

 

 

 

3 Cost per 8 Cost per 3 Total Replace-
Tile 100 Ft. Rod of ment Cost per

Measurement Type of Tile Tile Rod
4" clay 84 1.38 2.50
4" concrete 77 1.28 2.40
5" clay 132 2.18 3.50
5" concrete 110 1.82 2.94
6" clay 170 2.83 3.95
6" concrete 150 2.50 3.62
8" clay 260 4.33 5.45
8" concrete 210 3.56 4.62
10" clay 412 6.80 8.10
10" concrete 380 6.27 7.60
‘12" clay 540 8.91 10.25

 

(2) Ditches:
The estimated cost of spoil removal was 12¢ per
cubic yard. A further l¢ per cubic yard was required

for spreading and leveling the soil giving a total

of 13¢ per cubic yard.

29

 

Ditch Depth in Feet 5 Cost per Rod

 

3.18
4.57

(Demons
(D
O
B

 

The ditches were assumed to have a four-foot
bottom and a 1% : l slope.

Some farms had a much greater length of ditch
than others, but as this was assumed to be in lieu
of tile mains it seemed fair to include all these
ditches as an investment charge.

Other items of drainage investment included costs of land
leveling, culverts and special outlets. The investment in pumping
and associated equipment was not included; so that the return to
drainage investment, when calculated, will assume that if pumps
are necessary they are already installed, otherwise they will be
an "extra" item of drainage investment. In any case few farms in
the Saginaw Valley and Thumb area have any large investment in
pumps and high level carriers. The returns to drainage investment
must also cover the maintenance charge for ditches, this was
(generally not very great (32.00 - 84.00 per acre every fifteen or
twenty years).

Annual or current fertilizer expense (X6) included all

feartilizer purchases which were applied to the land in the 1957

30

season. No lime was used on these farms as they rarely require it.
If any difference in quantity of fertilizer used occurred between
1956 and 1957, it was noted. This was then used to compute the
difference in residual fertilizers between the two years. If
this balance was carried forward to 1958 the "excess“ residual
value was subtracted from the 1957 expense; or, if brought forward
from 1956, the difference was added to the 1957 expense.

In computing the value of residual fertilizer it was as-
sumed that 20 percent of all the nutrients (N, P and K) would be
available the following year in the form they had been applied.6

Residual P O was valued at 9¢ 1b., K O at 5¢ 1b. and N at 15¢

25
lb. (1957 prices).

2

The fertilizer equivalent of animal residues applied to
the land for the 1957 crop was also computed and credited as a
current fertilizer expense. After discussion with members of the
Department of Soils Science, Michigan State University and refer-

ence to pertinent literature,7 the following table was adopted:

 

These estimates were made on the recommendations of L. S.
Robertson, Assistant Professor of Soils Science, Department of
Agriculture, Michigan State University. They take into account
the soil type, crops grown on these farms, type of fertilizer used
and the weather.

7L. M. Turk and A. G. Weidemann, Farm Manure, Extension

Bulletin 300, Cooperative Extension Service, Michigan State College
(ifune 1945). Table 1 (page 7) compiled from "Fertilizer and Crap
Paroduction," Van Slyke, Orange Judd Publishing Company.

31

 

1957 Fertilizer Values of Animal Residues,

 

 

. E:::::t:d under Typical Conditions of Preservation
Animal W 1 h: Average conditions; Better than average
e g approx. 50 percent conditions; approx.
loss of plant 33.3 percentloss
nutrients of plant nutrients
Steers 900 lbs. $14.90 $20.00
Cows and calves 800 lbs. 13.25 18.00
Hogs 170 lbs. 2.75 3.75
Sheep (ewes
and lambs) 150 lbs. 2.50 3.10
Poultry (per
100 birds) 400 lbs. 5.15 6.00

 

Similar values per pound of plant nutrient were taken as
with the artificial fertilizers. The above figures thus apply to
1957 prices. The contribution of animal residues to soil fertil-
ity was generally small, but nevertheless not inconsiderable. In
one case where a farmer fattened 160 steers annually, on a 140
acre farm, it was computed that this contributed the equivalent of
83,200 of artificial fertilizer.

The residual values of both artificial fertilizers and
animal residues was only computed for the years of application;
further residual values were ignored. Also, note, no direct account

(was made of the soil conditioning effect and other benefits con-
tributed by animal residues.

Other current crop expenses (X7) included power and

 

Illachinery costs, seed costs and other items. (See Questionnaire
ism Appendix B.) These costs excluded machinery depreciation and

aJLso machinery maintenance charges, e.g. major overhauls and tire

32

purchases, otherwise double accounting would have taken place in
respect to the machinery investment category (X4). The refund of
State and Federal gas tax was deducted from the fuel and oil ex-
pense. Vehicle taxes and insurance were not included as these
were not deemed productive expenses.

All seed used during the 1957 season was credited as an
expense; this, therefore, included seed purchases and a charge for
home grown seed.‘

Maintenance expenses to buildings were excluded and also
all charges of an investment nature to land, e.g. land leveling,
ditch filling and wood clearing. All interest, taxes and insurance
charges were excluded.

If a difference in winter wheat acreage occurred between
1957 and 1958, the acreage difference was credited or debited to
crop expense. The valuation of winter wheat was computed from
quantity of fertilizer applied to the crop, seed cost of 35.00/acre
(2 bushels of seed at an average cost of $2.50/bu.) and sowing
costs of $2.60/acre. (Drilling at $1.40/acre plus discing and
other cultivations at 31.20/acre.)8

Differences in beginning and ending acreages of green
manure crops were also credited or debited as crop costs. These

green manure creps were valued as follows:9

 

8These figures were arrived at after discussion with
farmers and M. H. Erdmann, Associate Professor, Ext. Farm Crops,
Dept. of Agriculture, Michigan State University.

9These figures were arrived at after discussion with
members of the Department of Soil Science, Michigan State Univer-
sity and reference to:

33

 

Type of Seeding Quality of Stand

 

Poor Average Good
Catch crop:‘ Sweet clover 84.00 8 7.50 8 9.00
Catch crop: Alfalfa ’ 4.00 8.50 10.00
Catch crop: Rye 4.00
1-2 year alfalfa 16.00

 

The machinery storage and workshop investment (X8) was
arrived at by making notes of the types of buildings with their
respective floor space measured in square feet. The workshop
represented building investment only. The replacement value was
then computed from:10

Frame building without concrete floor 31.50/sq. ft.
Frame building with concrete floor 1.75/sq. ft.
Pole barn building without concrete floor 1.15/sq. ft.

Pole barn building with concrete floor 1.35/sq. ft.

 

(1) J. R. Guttay, R. L. Cook and A. E. Erickson, "The Effect
of Green and Stable Manure on the Yield of Crops and on the Physical
Condition of Tappan-Parkhill Loam Soil," Soil Science Society of
America Proceedings, Vol. 20, No. 4, Oct. 1956, pp. 526-528.

—(2) L. S. Robertson, R. L. Cook, P. J. Rood and L. M. Turk,
"Ten Years Results from the Ferden Rotation and Crap Sequence
Experiments," Michigan Agricultural Experimental Station Journal,
Article No. 1331.

The values of the green manure crops are in terms of
response of pea beans (priced at $6.40/cwt.), as this was the usual
crop to follow.

10These replacement costs were estimated in discussion with
R. L. Maddex, Assistant Professor, Ext. Agricultural Engineering,
Michigan State University, and reference to:

(1) Current Costs of New Farm Buildin 5, James S. Boyd, Professor,
Dept. of AgriculturalEngineering,Michigan State University. Paper
presented at the Rural Appraisers Conference, Grand Rapids, Michigan,
Sept. 12, 1957.

34

The pole barn type of construction was presumed to be the
nearest approach to the replacement value of the old traditional
wooden barn that was being used for machinery storage.

Crop storage investment (X9) was estimated in a similar
method to machinery storage. Notes were taken of the type of
storage with capacity measured in bushels. The buildings were
then valued on the basis of:11

(1) Grain or bean storage:
a) Round metal bins 35e/bu.

b) Outside concrete bins 50¢ "

c) 01d wooden bins in existing
buildings 20¢ "

d) Wooden frame bins in existing
buildings . 35¢ "

e) Concrete bins + building +
grain handling equipment 75¢ "

f) Wooden frame bins + building +
grain handling equipment 85¢ "

(2) Corn storage (shelled corn equivalent):
a) Round wire, or cheap pole crib 30¢ "
b) Cheap "home made" crib 15¢ "
It is realized that this method of estimating the value of buildings

in terms of replacement values may tend to overestimate the "real"

 

(2) Arthur H. Schultz, Building and Equipment Costs, Dept. of
Agricultural Engineering, North Dakota Agricultural College.
11These replacement costs were obtained from similar sources
as for the machinery storage and workshop investment (X8).

35

value and thus under estimate the marginal value productivity or

returns to building investment.

determined by the inCome it earns.

12

The value of a fixed asset is

There is no market price for

existing farm buildings which reflect their value as an earning

asset.

Correlation of Input Categories

Although much effort was made to reduce the intercorrela-

tions among the input categories, they remained high.

Land, in

particular, was very highly correlated with other inputs.

The simple correlations, with the exception

(X8 and X9), were found to be:

H 2‘.

.9268
.8505
.8449
.8641
.8117

.8533

.8901
.7578

.7653

r
X3X4

x6x7

.8670
.7504
.7465
.6423

.7973

.7888

.7383

of buildings

.8649

~.8061

.7625

.7646

.8501

12Bradford and Johnson, 22. cit., p. 133. Economically an

asset is fixed in a production process if:

(1) There is a difference between the cost of acquiring more of
it and what can be realized by that quantity in hand by utilizing
it in another process or selling it.

(2) The earning power of an asset makes it worth less in its
present use than the cost of acquiring more of it, and more than

36

Where:
Y is gross income in dollars; X2 is tillable acres of land;
X3 is labor months; X4 is machinery investment in dollars; X5 is

drainage investment in dollars; X6 is current fertilizer expenditure
in dollars; X7 is other current crap expenses in dollars.

The intercorrelations of the two remaining input categories
of building investment (X8 and X9) were not high.

This would suggest that the farms in this sample were

uniformly adjusted as regards proportions of inputs used. In fact,

 

it may be suspected that some of these inputs were almost perfect \

complements, e.g., land and drainage investment.

 

its Opportunity cost or salvage value.
i.e., an asset is fixed as long as it is not worth varying.

CHAPTER IV

FITTING THE PRODUCTION FUNCTIONS AND APPRAISAL

OF THE STATISTICAL RESULTS

The data obtained from the farms were used as the basis
for five regression analyses.

The first function was run with all the variable input
categories described in the previous chapter. The figures were
converted to logarithms and fitted to the Cobb-Douglas function
by the method of least squares.

The second function simply omitted the two input categories
of drainage and machinery storage investment in an attempt to ob-
tain a better fit with greater confidence in the estimates of the
regression coefficients.

The complementary nature of the input categories suggested
the third simple function with one input category in terms of the
limiting factor, expressed in natural numbers. This function, which
also presumed linearity was found to be inappropriate as curvi-
linearity was exhibited. The fit was improved in the next function
by expressing the data in logarithms.

The fifth, and final, Cobb-Douglas function made use of the
knowledge gained from the previous functions. Land and drainage were
expressed in terms of the limiting factor of either. The machinery
investment and labors input categories remained while the fertil-

izers and crop expense categories were combined. The other input

37

38

categories were omitted. The fit was considerably improved over
the second function and greater confidence could be placed in the

estimates of the regression coefficient.

The First Function

The data obtained from the farms in the categories of
gross income and all the variable inputs described previously,
expressed in logarithms, were fitted to a Cobb-Douglas production
function. The resultant coefficients and associated standard
errors were as follows:

Land - .224325 _+_.184355

b2 -

Labor b3 = .268144 :.136333
Machinery investment b4 : .131911 i .149213
Drainage investment h5 = .279131 1.130859
Current fertilizer expense h6 = .034962 _+- .114102
Other current crop expenses b7 = .108955 ;:.l40355
Machinery storage

investment b8 = .027582 1.121716
Crop storage investment b9 2 .007784 3 .019189

The sum of the regression coefficients (bi.8) was 1.082794
which indicated increasing returns to scale.

The multiple correlation coefficient (R) was computed to
be .9608, which with a sample size of thirty, eight independent
variables and one dependent variable would be expected to be this
high in 5 percent of the cases in a similarly drawn sample from a

universe with a true (R) of .90.1 As extreme values were selected

 

1Mordecai Ezekiel, 22. cit.

39

in the sample, (R) is higher than would be expected from a random
sample of farms in the universe studied, but not necessarily dif-
ferent than for a similarly drawn sample from the same universe.

The coefficient of determination (R2) was .923, which
means that 92.3 percent of the variation in the logarithm of the
estimated gross income (Y) was associated with the independent
variables included in the analysis. The remaining 7.7 percent
of the variance was likely associated with such factors as weather 7
and managerial ability (see page 10).

Log 0‘ was computed to be 1.095816. The estimate of gross
income (Y) was then computed as log Y by inserting log 4‘ , the
estimated bi's and the logs of the geometric means of the input
categories in the prediction equation (equation 4, Chapter II).
It was found that log Y = 4.327391 or that the geometric mean of
the estimated gross income = $21,252.

The standard errors of estimate (5) of the dependent vari-
able (1og Y) was .08387, i.e., under the conditions prevailing in
1957 for the sample and assuming random distribution, log Y would
be eXpected to fall between 4.327391 ;:.08387, for the geometric
mean organization of the farms in 68.27 percent (one standard de-
viation) of the sample, or in natural numbers between $17,520 and
325,779. The standard errors of estimate widens as the quantities
of the inputs are increased.

The marginal value products of geometric mean quantities
of the inputs were then computed (Table II) from the equation:

MVP =bY
1
i x
1

40

TABLE II

THE MARGINAL VALUE PRODUCTIVITIES or THE GEOMETRIC MEAN

QUANTITIES or INPUTS USED ON THIRTY CASH CROP FARMS IN

THE SAGINAW VALLEY AND THUMB AREA or MICHIGAN, 1957
(DERIVED FROM THE FIRST PRODUCTION FUNCTION)

 

 

 

Geometric Mean MVP
Input Category Quantity of Input (Dollars)
X2 Land 193 tillable acres 24.71
X3 Labor ' 19 months 299.47
X4 Machinery investment 813,44l .209
X5 Drainage investment $19,135 .310
X6 Fertilizer expense $2,647 .281
X7 Other crop expense $3,827 .605
X8 Machinery storage
investment $5,917 .099
X9 Crop storage investment 3668 .248

 

The reliability of these estimates of marginal value
productivity is related to the level of significance of the re-
gression coefficient. Examination of the standard errors of the
bi's and their respective t scores indicated they were significantly
different from zero at the 5 percent level for drainage investment
(b5), 7 percent level for labor (b3) and 24 percent level for land
(ha). The estimates of the bi's for the other input categories
were less reliable.

A better method of testing the regression coefficients for

significance, than against the null hypothesis, is to compare them

41

with the regression coefficients necessary to yield marginal value
products equal to a set of minimum expected returns. On the basis
of observation and discussion with farmers and farm management
specialists2 the following were drawn up as reasonable minimum

expected returns or reservation prices:

Land: A) Undrained $35.00 per tillable acre

B) Adequately drained 355.00 per tillable acre
Labor ' $225.00 per month
Machinery investment 30 percent
Drainage investment 10 percent
Current fertilizer expenditure $1.06 per $1.00 of expense
Other current crop expenditure 61.06 per 31.00 of expense
Machinery storage investment 13 percent
Crop storage investment 13 percent

The minimum expected return to land was based on a 4-5
percent interest charge, one percent for taxes and maintenance and
3-4 percent to cover the risk factor--a total of 10 percent--with
land valued at 8350 per acre when undrained and $550 per acre when
drained. The minimum expected return to labor was based on a wage
rate of 3170-3200 a month obtained by the Mexican National and the
higher wage rate obtained by local casual labor at the rush periods
of harvesting and sowing. It was suggested that the marginal unit
of labor was a cross between the last unit added (i.e., at harvest
time) and the next unit to be subtracted (i.e., at singling and
hoeing). The return to machinery investment must cover depreciation,
interest on investment, taxes, maintenance and insurance. Similarly
the return to drainage investment must cover the interest charge on

investment, all maintenance charges for tiles and ditches,

 

2Professors L. H. Brown, C. R. Hoglund and J. M. Neilson,
Dept. of Agricultural Economics, Michigan State University.

42

depreciation and the risk factor. If necessary, it must also
cover pumping charges, interest on investment in pumping equipment
and high level carriers, plus a charge for their maintenance.

A return of a dollar plus interest per dollar spent on
fertilizers and other current crop expenses was expected. The
returns to buildings had to cover interest on investment (6 percent),
depreciation (4 percent) and maintenance and insurance (3 percent).

The estimated minimum expected returns were substituted as
marginal value productivities in the equation

A
MVP = biY .

These were then solved for the bi's. Table III compares these

bi's with the estimated bi's.

TABLE III

COMPARISON OF THE ESTIMATED bi's AND THE bi's NECESSARY

TO YIELD MINIMUM MARGINAL VALUE PRODUCTS, FIRST FUNCTION

 

 

b1 Estimated b1 Estithed b1 Mi: ”3: Riiigns Difference
b2 .224325 .184355 .326255 -.09193

b3 .268144 .136333 .206819 .051325
b4 .131911 .149213 .194790 -.065879
b5 .279131 .130859 .094234 .186697
be .034962 .114102 .140664 -.105702
b7 .108955 | .140355 .203378 -.094423
be .027582 .127157 .037159 -.009577
b .007784 .019189 .004194 .003590

CD

 

43

The regression coefficients were compared by the means of

a "t test."3 These showed that the estimated b 's were not sig-

i
nificantly different from the bi.5 necessary to yield minimum re-
turns, except in the case of drainage investment which was differ-
ent at the 20 percent level of significance.

The reliability of the estimated bi's for fertilizer and
crop expenses was low. This is the reason for the difference be-
tween these estimated bi's and the bi's necessary to yield minimum
expected returns not being significant. The resultant estimated
MVP's nevertheless appeared to be the most widely different from
the expected, of the input categories under consideration. As
some of this may be due to the high intercorrelations among the
input categories, a system of errors may exist. This could mean
that some of the MVP's of fertilizer and crop expenses were being
picked up by other inputs. Thus the MVP's of land, machinery
investment and drainage investment were possibly overestimated and
those of fertilizer and crop expenses underestimated.

The bean crop suffered from the weather in 1957 so that a
full response to fertilizer applied may not have been achieved,
thus lowering the return to that input.

Little faith can be placed in the reliabilities of the mar-

ginal value productivities of building investment (X and X9), because

8

 

.A
3 b. - sb. ‘5 .
t = 1 1 where b1 13 the estimated regression
a
(b.
I

coefficient and sbi is the regression coefficient to yield minimum

expected returns. Dixon and Massey, Introduction to Statistical
Analysis (McGraw-Hill Book Company, Inc., Second Edition 1957),
p. 115.

44

of the high standard errors of their bi's and also the difficulty
of actually measuring the value of buildings. Wagley4 attempted

to measure building investment, or value, in terms of animal units.
The resultant regression coefficient was negative and no MVP

was computed as it was felt unlikely that increasing the quantity
of buildings would actually decrease gross income. Most attempts
to measure the investment in farm buildings in physical or monetary
units have proved unproductive. No method (including the Cobb-
Douglas method) of estimating returns to buildings investment is
able to differentiate between the marginal value productivities of
highly correlated independent variables unless the sample size is
very large.

The unexplained residuals5 were computed for each farm and
plotted against estimated gross income to enable any larger than
normal discrepancies to be discovered. The distribution appeared
to be normal and random. Most of these can be attributed to in-
fluences outside the scope of this study such as weather and

managerial ability.
The Second FUnction

Knowledge gained from the first function suggested that the

lower than expected returns to land may have been due tooverestimation

 

4R. V. Wagley, "Marginal Productivities of Investments and
Expenditures, Selected Ingham County Farms, 1952," (unpublished
M. S. dissertation, Dept. of Agricultural Economics, Michigan State
College, 1953), pp. 45-50.

5Actual gross income minus estimated gross income.

45

of the returns to drainage investment. This was particularly
suspected in view of the high intercorrelation (.86) of these two
inputs. Similarly the estimated returns to machinery investment
were lower than expected. This input was highly correlated (.80)
with machinery storage investment so that some of the estimated
returns may have been reflected in overestimation of the returns

to this latter category. Also, the b for machinery storage and

i
workshop investment was extremely unreliable.

The input categories of drainage investment and machinery
storage investment (Xé) were therefore omitted and a further Cobb-
Douglas regression analysis run. It was suggested that land and
drainage were good complements so that as land was now virtually
combined with drainage investment the input category of land re-
ferred to tillable acres having an average drainage investment of
899.90 associated with them. The returns to the machinery invest-
ment category would now be expected to reflect some of the MVP of
machinery storage. Thus the new machinery investment category is
interpreted as having a normal complement of storage facilities.
This amounted to about $440 in storage investment per 81000 of

machinery storage.

The resultant b 's and associated standard errors were:

i
Land 132 . 37202 1'. . 17857
Labor b:5 . 27342 3 . 14346
Machinery investment b4 .21117 1; .12513
Current fertilizer expenses b5 .06743 :1 .11907

46

Other current crop expenses b6 .10987 3 .14018
Crop storage investment b7 .00752 1; .02001
The sum of the bi's = 1.04143.

The log of the estimated geometric mean gross income
(log Y) was 4.32739, equivalent to $21,252.

The multiple correlation coefficient (R) = .9518.

The coefficient of determination (R2) = .9059.

The standard error of estimate = .088624, i.e., the log
Y would be expected to fall between 4.3279 2’. .088624 in 68.27
percent of the sample, or between 317,329 and $26,053.

The marginal value products were computed to be:

MVPXZ, land 3 40.97 per drained T. A.
MVan, labor $305.38 per month
MVPX4, machinery investment 6 .3339 per invested dollar
MVPx , current fertilizer

5 expense 3 .543 per dollar spent

MVP , other current crop
6 expense 3 .6101 per dollar spent

MVP , crop storage investment 8 .2393 per invested dollar

The reliability of most of the b '8 had been slightly im-

1
proved, but not sufficiently to increase greatly the confidence in
the estimates of the MVP's, except in the case of land. The es—

timated b for this new input category (X2) of average drained

1
land was now significant at the 5 percent level. The b1 for
machinery investment, including its complement of storage and work-

shOp facilities, was now significant at the 12 percent level.

47

The Third FUnction1,AssumiggflPerfect
Complementarity:of the Inputs

The possibility that the wrong function was being fitted
now suggested itself. Perhaps it was, in fact, a case of comple-
mentary inputs. The very high intercorrelations of the input
categories (except building investment) supported this idea. If
the inputs were perfect complements, and as such exhibited constant
returns to scale, the assumptions of linear programming6 should
apply, whereby production is increased until the constraints of
limiting resources are exhausted.

The arithmetic means of the input categories used in the
first function were taken to be "standard units" of inputs and the
optimum combination of these inputs was taken to be the propor-
tions among the arithmetic mean quantities of the input categories
of the sample. The actual quantity of each input used on each farm
(except the building categories X8 and X9, which were assumed to be
non-limiting factors) was divided by its respective "standard unit"

to determine which was the limiting factor of production7 and the

 

6The assumptions of linear programming are:

i, The processes of production are independent, with no
complementarity between products;

ii, Linear relationships exist, i.e., constant returns to scale;

iii, The units of input are continuous;

iv, A finite number of production processes and resources are
available;

v, The quantity of an input required to produce the unit
product and the net return per unit of output are fixed and known.
Also the productivity of a resource is limited to the total quantity
available. '

7The limiting factors in the sample of thirty appeared to
be randomly distributed among the input categories. They were:

48

quantity. A simple regression was then run between units of
limiting factor, irrespective of which category, against gross
income.

The regression coefficient was computed to be $43,045.90 with
a standard error of $2677.60. The reliability was, therefore, high.

4" was -83,919.

The correlation coefficient (r) was computed to be .949866,
which would be expected to be this high in 5 percent of a similarly
drawn sample if the true coefficient were as low as .91. The co-
efficient of determination (r2) was .902. These support the hypo-
thesis of complementarity among the inputs.

The standard error of estimate (S) of the dependent variable
(Y) was 85794.4, i.e., the arithmetic mean of estimated gross
income would be expected to fall between $19,919 and $31,508 in
68.27 percent of the sample.

Examination of the unexplained residuals when plotted
against the quantity of limiting factor showed the unsuitability
of a linear production function. A definite curve about the zero
residual line resulted which again, indicates increasing returns
to scale. This showed up still more clearly when units of limiting
factor were plotted against gross income (Figure 3). This evidence
of increasing returns to scale supplements that of the Cobb-Douglas
analyses, for which the sum of the bi's was persistently greater

than one.

 

Land 5 Drainage investment
Labor 4 Fertilizer expense
Machinery investment 4 Other crop expenses

Olmvb

49

The Fburth Functionj Assuming Perfect
Complementarity of the Inputs
The evidence of increasing returns to scale, and lack of
fit in the last linear regression fitted to gross income and units
of limiting factors, suggested a better fit may be obtained by ex-
pressing the data in logarithms, i.e., as a one variable input

Cobb-Douglas function. The results were:

b = 1.049541 6' b = .079394
r = .928383 fr = .070231
r2 = .861895
1034 = 4.56179
A

logY = 4.3273 _+_ .097322
A much better fit was obtained.8 The ability of this
function to predict gross income for this sample was not signifi-
cantly different from that of the next and final function. (Refer
forward for a comparison of these two functions on pages 56 and 58.)
Fbr this function, it is necessary to resort to a residual
method for estimating average returns which approximate marginal
returns for the "average organization" to the individual limiting
factors from the results of this analysis. Thus the AV? or the MVP of
the limiting factor for the average organization in ordinary units is:
Estimated gross income

from a standard unit of -
limiting factor

The number of ordinary units in a
standard unit of the limiting factor

Charges for non-
limiting factors

 

8One farm (no. 19) a peared to have an extremely low limit-
ing;factor (fertilizer input) in relation to gross income achieved,
and this was still affecting the fit. When the data from this farm
*were>omitted the fit was improved still further. (r2 = .8912)

Actual Gross Income
(Thousands of Dollars)

 

50

 

80,,
I
I.
I
70- I
/
/
I
. I
604 ,’
I
I.
.I
’I
0
50a 1’ .
0/
I
I
‘I
I
40‘ ,’
/
x
I
I
I
30 4 ’I
I
/ e
I
I
e v’
20' 0”,
g - )‘.. .
vfic’._
”/. .
10‘ ’. ’.
O I T I I I l w t ' ' r f T *1 F V T *3
.l .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.31.4 1.5 1.61.? 1.8
Units of Limiting Factor
Figure 3. Relationship between gross income and units of

limiting factor on the farms in the sample.

51

The standard units of the limiting factors, used in this
analysis, with their respective expected returns, or minimum

charges, are presented in Table IV.

TABLE IV

THE "STANDARD UNITS" OF THE LIMITING FACTORS USED IN THE
FUNCTIONS ASSUMING PERFECT COMPLEMENTARITY OF THE INPUT
CATEGORIES, 'ITH THEIR.MINIMUM EXPECTED RETURNS

 

 

 

 

Input "Standard Unit" Expected Expected Returns

Category of Input Returns9 girufigtz::a531;5§:'

of Limiting Factors
Land 233.3 T.A. 835/14. 38,165.5
Labor 22.275 months 3225/honth 55,011.9
Machinery investment $17,084 30 percent $5,125.2
Drainage investment $23,007 10 percent 32,300.?
Fertilizer expenses 33,210 106 percent $3,402.6
Other crop expenses $4,458 106 percent $4,725.5

The estimating equation is leg Y = log x + b log (units

of limiting factor).

If the limiting factor is one, then log

A
log Y = 4.561792 + 1.049541 x O
or log 9 -.- 4.561792
and log 9 a $36,457.

The productivity coefficients were then calculated to be:

Land $68.11 per tillable acre
Labor $571.83 per month
Machinery investment .7522 per dollar

 

9Refer to p. 41.

52

Fertilizer expenses 3.4667 per dollar
Other crop expenses 2.7930 per dollar
Drainage investment .4358 per dollar

These estimates are considerably higher than those deter-
mined from the normal Cobb-Douglas analyses due to the same excess
return being credited to each estimated AVP or MVP in turn, i.e.,
if a mistake is made in estimating one, the same error will be
reflected in each of the other estimates. Consistent under- or
overestimation of the AVP's or MVP's by this residual method of
computation can thus occur with all the estimates being biased
in the same direction. This is a general characteristic of
residual computation of AVP's and MVP's which can occur in farm
accounting, linear programming and budgeting unless care is taken.

The unreliability of those estimated MVP's was one reason
for fitting the next function even though the ability of the two

functions to predict gross income was not significantly different.
The Final FUnction

It was now becoming apparent that land and drainage invest-
ment, in the area from which this sample was taken, were almost
jperfect complements. Hence, as with the regression analysis as-
suming perfect complementarity, the number of units of limiting
factor of either land or drainage, measured in terms of the geometric
mean quantities of either, was set up as one variable input (X2).
Labor (X3) and machinery investment (X4) were left as they were,
as the MVP of these input categories are of particular interest to

both farm management men and policy makers and it appeared that

53

reliable estimates of their MVP‘s were obtainable. Current fer—
tilizer and crop expenses were lumped together as one input (X5),
as it appeared that no headway was being made in obtaining a reli-
able regression coefficient for either alone. Crap storage in-
vestment-was omitted because of the unreliability of the regression
coefficient; hence, the return to the other inputs may, but do not
necessarily, as the constant turned out to be slightly larger,
reflect some of the returns to crop storage.

The estimated bi's and their standard errors were found
to be:

Units of limiting factor

(either land or drainage investment) b .435713 I .145849
b

Labor .275044 .t .113725
Hachinery investment b .204850 1 .123718
Current fertilizer and crop expenses b3 .170704 1 .136325
More reliance could now be placed on the estimates of the
regression coefficients and hence also the resulting marginal value
productivities. The estimated bi's were now different from zero
at levels of significance of one percent for the limiting factor
(b2), 3 percent for labor (b3). 12 percent for machinery invest-
ment (b4) and 23 percent for current fertilizer and crap expenses
(b5).
The sum of the bi.. was 1.08631, again indicating increas-
ing returns to scale.

The marginal value products were then computed as in

Table v e

54

TABLE V

THE MARGINAL VALUE PRODUCTIVITIES OF THE GEOMETRIC MEAN QUANTITIES
or INPUTS USED ON THIRTY CASH CROP FARMS IN THE SAGINAw VALLEY
AND THUMB AREA OF MICHIGAN, 1957. (DERIVED FROM THE FINAL
PRODUCTION FUNCTION, IHICH TREATED LAND AND DRAINAGE

INVEs'nsNT As PERFECT COWLEMENTS)

 

 

 

Geometric Mean MVP

Input Category Quantity of Input (dollars)

X2 Limiting factor .88038 10,507.05

X2 in terms of drained land 193 T.A. 54.45

X3 Labor 19 months 306.87
x4 Machinery investment $14,654 .2968

X5 Current fertilizer and

crop expenses $6,609 .5484

 

As it was assumed that land and drainage were perfect com-
plements, the MVP of limiting factor (X2) now represents the
marginal return to adequately drained land. This was recomputed to
be $54.45 per drained tillable acre. It is of interest to note
that the MVP for undrained land, from the first function fitted,
was computed to be $24.71 per tillable acre. The returns to
average drainage investment per tillable acre was computed to be
$31.00, using an MVP for drainage investment of 31 percent. The
sum of these two, representing total MVP of a drained tillable
acre, is $55.71, which is almost the same as the $54.45 per
drained tillable acre computed from this final function.

The log of the geometric mean gross income (log Q) was

4.327391 with a standard error of estimate §.of .078368, i.e., the

55

geometric mean estimated gross income would be expected to fall
between $17,743 and $25,454 in 68.27 percent of the sample.
Log ‘ was 2.494105.

The multiple correlation coefficient (R) was .95919 which
would be expected to be as high as this in 5 percent of the cases
in a similarly drawn sample if the true (R) was .93.

The coefficient of determination (R2) was .92.

The estimated marginal value productivity of current ferti-
lizer and crop expenses still appeared low. As these inputs were
highly correlated with other inputs some of the returns may still
be reflected in overestimated MVP's of these other inputs. Fbr
instance it pays to apply more fertilizer to adequately drained
land than undrained land as responses are less risky. Hence an
overestimate in the MVP to drainage investment may result. In
1957 it is doubtful whether a normal response to fertilizer was in
fact obtained. The bean crap in particular was adversely affected
by the weather. As beans occupy 44 percent of the acreage of the
sample this would mean a large reduction in response to fertilizer
applications. Trials conducted by Michigan Agricultural Experi-
ment Station on similar soils in 195710 showed economic responses
in the cases of wheat and corn at low levels of fertilizer appli-
cation only. Many of the farmers in the sample were using the

accepted full fertilizing rates and hence it may be suspected that

 

1OJ. F. Davis, L. S. Robertson and I. B. Sundquist, unpub-

lished results from "Fertilizer Input-Output Studies, 1957," con-
ducted cooperatively by the Departments of Soil Science and
Agricultural Economics, Michigan State University.

56

they were in fact not obtaining an economic response of at least
a dollar per dollar expense at the margin.

The input categories of land, labor, machinery investment
and drainage investment were quite highly correlated with the crop
expenses category. Hence judgment must be used in interpreting
the results. The MVP of machinery investment possibly also re-
flects some of the returns to fuel costs, which was a large item
in the crop expense category. This could cause overestimation of
the MVP of machinery investment with corresponding underestimation
of the MVP of current crop and fertilizer expenses.

The estimated regression coefficients were compared with
the regression coefficients necessary to yield minimum expected

returns.11 These are presented in the following table.

TABLE VI

COMPARISON OF THE ESTIMATED bi's AND THE bi's NECESSARY TO

YIELD MINIMUM MARGINAL VALUE PRODUCTS, FINAL FUNCTION

 

 

 

' hi to Yield
b1 Estimated b1 Estimated bi. Minimum Difference
df’ Returns
b2 .435713 .145849 .457321 -.021608
b3 .275044 .113725 .201666 .073378
b4 .204850 .123718 .241579 -.036729

 

 

11See p. 41.

57

The regression coefficients were almost identical in the
case of drained land. Those for labor and machinery investment
were not significantly different. However, the regression coeffi-
cient for current fertilizer and crop expense (b5) was significantly
different, probably due to the inclusion of the fertilizer expense
in this input category.

The unexplained residuals were plotted against estimated

gross income. The distribution appeared to be normal and random.
Complementarity of the Inputs

To test the hypothesis that the input categories, used in
the limiting factor production functions, are better complements
than can be fitted with a Cobb-Douglas function, a test was set
up to compare the unexplained residuals of these functions with
those of the first and final Cobb-Douglas functions.

The percentage of (the variance in Y minus the variance
explained by the restrictions of the production function) explained
by the analysis is given by:

2 1: u2

R s _2
Z(Y—Y) 3:5
I!

 

where: I u2 is the sum of the squared unexplained residuals (Y-Y),
Y is the actual gross income, I is the mean, n is the number in the
sample (30) and m is the number of restrictions (2 in the cases of
the limiting factor functions, 9 for the first and 5 for the last

Cobb-Douglas functions).

58

(a) First Cobb-Douglas function, R2 - .799614

(b) Final Cobb-Douglas function, R2 - .948745

(c) Limiting factor function in natural numbers, R2 2 .748333

(d) Limiting factor function in logarithms, R2 = .8848.

It was then hypothesized that there was no difference be-
tween the Rz's. These percentages were tested by means of a chi
square test.12

R2 :z'z = l 737 a difference significant at be-

(c) and (d) ' ’
tween the 10 percent and 25 percent levels.
2 2 .

R (c) and (b) ‘X = 3.4607, a difference significant at be-
tween the 5 percent and 10 percent levels.

2 2 .

R (b) and (d) x = .69206, indicating no significant dif-
ference between these functions at between the 50 percent and 75
percent levels.

This means that the limiting factor function, expressed in
logarithms (page 49) is not a significantly poor predictor of gross
income than the Cobb-Douglas function. The advantage of the final
Cobb-Douglas function is its ability to give reliable estimated

MVP's as Opposed to the unreliable residual method of computing

them from the previous function.
Managerial Ability

The farmers in the sample were rated from 0-10 according

to an informal assessment of their managerial ability made during

 

12C. Eisenhart, M. W. Hastay and W. A. Wallis, Techniques
of Statistical Analysis (First edition, McGraw-Hill Book Company,
Inc., 1947), pp. 255-257, especially expression (16), page 257.

59

the interview. The profit motive was taken as the basis of the
assessment but the farm records were ignored while the rating was
being made. Assessments were made of their I.Q. together with
their understanding, and use of, simple economic theory as applied
to farming and their apparent ability to rationalize and come to
decisions. This rating was then correlated with the percentage

of estimated gross income actually achieved.13

First Cobb-Douglas function r = .38318

r2 = .1468?

Final Cobb-Douglas function r = .37660
2

r = .14183

The correlations were low, but nevertheless significantly
different from zero, fourteen percent of the variation in unex-
plained residuals being associated with this measure of managerial
ability. The correlation has probably been reduced due to lowering
gross income, by the accounting procedure, for farmers growing
seed crops. These farmers generally were assessed as having above
average managerial ability. Share renting was not common but may
have been correlated with a lower managerial rating, thus affecting
the correlation of gross income and managerial ability as yields
on share rented land were generally lower than on owner occupied
land.

If this is a reasonable assessment of managerial ability

it would indicate that in this area difference in managerial ability

 

13
Actual gross income
Estimated gross income

«9M

60

is not a major factor to be considered, i.e., management on these
farms is a relatively simple matter or, of course, the level of
management was relatively uniform and did not vary so greatly from
farm to farm. The larger proportion of the unexplained residuals
must be due to other unstudied variables such as weather, sug-
gesting that these are more important factors than management.
Weather can influence gross income quite considerably, particularly

in relation to the bean crop.

CHAPTER V
EVALUATION

It must be stressed that these results apply only within
the conditions of the study, the range of data collected and with
the conditions of weather, price and state of knowledge existing

in that area in 1957.
Land and Investment in Drainage;

Land and investment in drainage are considered concurrently
as their complementary nature has been demonstrated. This was par-
ticularly so in the final Cobb-Douglas regression analysis because
of the reliability of the estimated regression coefficient from
which the estimate of the marginal value productivity of drained
land was obtained. 1

Farmers had good reason to be concerned with the high sale
Value of land, whether drained or undrained, in this area. Un-
drained land was estimated to be yielding less than expected returns
and returns to drained land almost covered expected returns. It is
pr Obable that the drainage part of the investment in drained land,
in 1957, was yielding a more than adequate return with under re-
co“Finest as regards the investment in the raw land.

Reference to Table X, in Appendix A, indicates that the
marginal value productivity of land tends to fall as farm size
in“greases. The proportion of land in the mix of the input categories

61

62

tends to increase as farm size increases and this would result in
the falling MVP for land. However, it does not fall rapidly, in
fact the graph of gross income plotted against tillable acres is
almost a straight line. The return to drainage investment appears
to be similar irrespective of farm size.1

The importance of adequate drainage on these farms is ob-
vious and this is supported by the estimated return of 30 percent
on investment in 1957. Farmers estimate that a general increase
in yield of 50 percent, or better, results from tile drainage.2
1957 was a favorable year as regards returns to drainage invest-
ment, so that a study should be extended over a number of years
to obtain a more generally acceptable figure. It would be ex-
pected that the marginal return to 100 percent adequately drained
farms would not be significantly different from minimum expected
returns. If the estimated returns are much higher in average
seasons it would indicate that it may pay farmers to tile drain
their land at even closer intervals than the present accepted
standard. As such a high return to drainage has been estimated
from farms having on the average 80 percent of their tillable
acres adequately drained, it suggests further investigation in

this direction may be worthwhile.

 

1The estimated returns to drainage investment are higher
in the case of some of the 200-300 acre farms (see Table X,
Appendix A). This is due to a lower percentage of the land being
drained on these farms.

2C. R. Hoglund, Managerial Decisions in Organizinggand
Operating a Farm, Ag. Econ. Bull. No. 625, p. 6. Department of
Agricultural Economics and the Agricultural Experiment Station,
Michigan State University, September 28, 1955.

63

Labor

The estimate of the regression coefficient for labor in the
final regression equation was highly reliable, but not signifi-
cantly different from the regression coefficient required to yield
minimum expected returns. Reference to Table VII shows that the
resultant estimate of the MVP for labor was higher than those ob-
tained in other studies, particularly those involving livestock.

The reliability of the estimate of the b for labor in this study

1
gives greater confidence to the MVP estimate for labor. It is
not surprising that farms in this area are moving out of dairying
and concentrating on cash crop production.

The total derivative to one month of labor was computed
to be 31,297; this is the MVP of one month of labor in the geometric
mean organization plus the sum of the MVP's of the increases in
the other input categories associated with one month of labor.
This result is higher than the average gross income per man month,
in a report on this area,3 of between 8598 and $1,007 for 1957.
This is largely due to (l) the method of measuring the input of
labor, (2) the fact that the farms in the area report included a
proportion of dairy farms which would have a lower gross income

per man month than cash crap farms, and (3) increasing returns to

scale.

 

3F'arming Today, Area 8 report, 1958. CoOperative Extension
Service, Department of Agricultural Economics, Michigan State Uni-
versity.

64

TABLE VII

REGRESSION COEFFICIENTS AND MARGINAL VALUE PRODUCTIVITIES OF ONE MONTH
OF LABOR, IN VARIOUS FARMING AREAS, OBTAINED IN RECENT STUDIES

 

 

Total Derivative

 

 

MVP
b 5' b to One Month of
Study i i (dollars) , Labor
(dollars)
1 Almont Township .160 .119 91.24 682.43
Michigan 1953
2 Burnside Township .186‘ .096’ 123.42‘ 816.19‘
Michigan 1953
3 N W Illinois, 1950 .006 .084 8.40 1334.00
(Hog enterprise) per hour ‘
4 N W Illinois, 1950 .222 .141 137.4 694.00
(Dairy enterprise) per hour
5 N W Illinois, 1950 .129 .166 143.6 1206.00
(Crop enterprise) per hour
6 Ogemaw-Arenac Co., .382’ .301‘ 198.25‘ 660.03'
Mich. 1953
(Beef enterprise)
7 Ogemaw-Arenac Co., .414‘ .154' 148,7’ 428.90‘
Mich. 1953
(Processed milk farms)
8 089-8.-”enac Gas, e277 e113 123e96 594.61
Mich. 1953 ~
(Fluid milk farms)
9 Soil 3. South Cen. .076 .296 40.79 705.57
Mich. 1953
(Dairy enterprise)
10 Soil P4 Southern Mich.-.034 .528 -21.43 599.91
1953 (Dairy enterprise)
11 Soil P. SO. Cen. Mich. .434 .237 262.08 798.43
1953 (Dairy enterprise) .
12 Soil 0. 30. Gem. Mich. .519 .299 304.9 797.26
1953 (Dairy enterprise) «
13 Ingham Co., Mich. 1952 .042 .130 30.19 787.01
(Dairy enterprise)
This study .275 .124 306.87 1279.00

 

.Unreliable because of high intercorrelation with machinery
investment.

65

The method of estimating labor input was a little more
rigorous than most previous studies in that no account was taken
of time spent on the farm between seasons. It was assumed that
these Operators then had the Opportunity to take off the farm em-
ployment. This is usually available during the winter when average
weekly earnings should be possible of $86-87 per week or 3350 per
month.4 All family labor was reduced to average man month equi-
valents.

Even though returns to labor are relatively high, there
is room for improvement. The most obvious being reduction in
labor requirements for hoeing and singling sugar beets. The
mechanical thinner was introduced into this area around 1950, at
that time studies showed a 10 percent reduction in crop yield
due to mechanical thinning which more than offset the 40 percent
decrease in labor costs for hoeing.5 Since then improvements in
the thinners and techniques of using them have taken place and
more recent studies6 by the sugar beet companies in that area
have not shown significant differences in yields due to mechanical

thinning; on the contrary, frequently the yield has been improved

 

‘Nichi an Labor Market, Vol. XII, No. 4 (April 1957). and
Vol. XIII, No. 4 (April 1958). Published by Michigan Employment
Security Commission, 7310 woodward Avenue, Detroit 2, Michigan.

5George N. French, A Report on Tests of Mechanical weeding
and Thinning Equipment in Michiggg and The Extent of Sprigg
Mechanization in the Eastern Beet Areaj 1951. Proceedings of the
American Society of Sugar Beet Technologists, 1952, pp. 586-592.

6Monitor Sugar Beet Company, Mechanical Thinning of Sugar
Beets,gl955. The Monitor Sugar Beet Co., Bay City, Michigan.

66

due to timeliness of the operation. These 1955 studies did not
always show great reductions in labor requirements; however, it

is generally suggested that a 50 percent reduction in labor require-
ments for thinning and hoeing the sugar beets would result.7
Mexican labor used for hoeing costs farmers 3170 to 8200 per
month, if they were obtaining a return of $306 for the marginal
month of labor it would support their perseverance with hand labor.
Other methods of reducing labor requirements during this period
are now being investigated. The new approach is to obtain a more
even stand of plants by using monogerm seed, better placement
drills and obtaining ideal seed bed conditions.

Modern machinery and new techniques have reduced sowing
time considerably. .Unfortunately, this has resulted in all the
sugar beets being ready for hoeing at the same time. In an area
where custom labor is limited it is a case of "first come, first
served." Hence, reduction of the total Mexican laborers force
employed by the sugar beet companies in the Thumb area is not
immediately likely. The shortening of the sugar beet thinning
season could mean these Mexicans being partially unemployed between
hoeings, in which case a higher wage rate for hoeing might be de-
manded. Mechanical thinning would then appear a more attractive

proposition. It should also be noted that the mechanical thinner

—__

7c. R. Hoglund and K. T. wright, Estimated Labor Require-
ggpts for Sggar Beet Productions in Michigan, 9.9 ton_yield, Four
Methods of Production. Adapted from Michigan Circular Bulletin

."—-—_

215, Uune 1949.

67

does enable a partial thinning of the stand at a critical stage
when hand labor is not immediately available.

Other opportunities for improving labor efficiency would
be at the later peak period of harvesting. Materials handling is
a relatively recent field of study which may provide answers to
this end of the problem.

The techniques of minimum tillage, which is now a recog-
nized practice on these farms, have enabled substantial reductions
in cultivation requirements so that farmers can now cope with
what were once time consuming jobs. Modern machinery with its
high work output has been of great assistance in this respect.

The MVP of labor tends to increase with increase in farm
size. This might be expected from the evidence of increasing
returns to scale, also as the number of tillable acres per man
month tends to increase with farm size. It is interesting to
note that these returns are significantly higher on the 130-150
acre, family size, holdings than the small, 70-100 acre holdings;
but returns do not increase so rapidly on the larger farms. This
might suggest that the 130-150 acre holding is a minimum size in
order to employ fully the operator's and family labor, and provide
adequate returns to that labor.

Few farmers employed full time labor. Those that did,
provided some incentive to keep the workers on the farm. They
were all provided with rent free housing and most of them had some
opportunity to augment their income by crepping a few acres of

their own accord, using their employer's machinery at a nominal

charge.

68

Machinery

This area is very highly mechanized which has assisted
in the reduction of labor requirements and led to an improvement
in the returns to labor. Reference to Table VIII indicates some
of the substitution of machinery for labor in this area during the
past twenty years. It should be pointed out that more machinery
and less labor were spread over a larger acreage, as the average
farm size in the reports on this area,8 from which Table VIII was
derived, increased from 102 acres in 1935 to 149 acres in 1956.

The b1 for machinery investment is not significantly dif-
ferent from that necessary to yield minimum returns. However, the
returns appear lower on the small farms suggesting their over-
investment in machinery, or underinvestment in respect of land.
Machinery investment per tillable acre decreases with increase in
farm size. The Opportunities on these small farms to reduce their
investment in machinery are not as great as might first be thought.
The real difficulty is that the bean crop needs immediate harvest-
ing during a critical period; hence, the bean harvester or combine
must be immediately available. As already pointed out, modern
methods of sowing have resulted in most of the crop, in this area,
being ready for harvesting at the same time, so that the neighbors'
or the custom combine may not be available and the crop consequently
lost. This position has not been improved by the persistent use

of bean varieties which mature at the same time. Grain and sugar

 

8Farmin Toda , Area 8 report, 1935-56, 93. cit.

69

TABLE VIII

mm or MEN AND MACHINERY INVESTMENT PER 100 TILLABLE
ACRES, 1935-1956, mm s, MICHIGAN9

 

 

Year Number Deflated Machinery
of Men Investment
1937-41 = 100
1935 1.96 81200
36 1.79 1212
37 1.73 1344
38 1.76 1563
39 1.65 1649
40 1.60 1716
41 1.52 1858
42 1.57 2042
43 1.36 2033
44 1.30 1936
45 1.33 2057
46 1.36 2050
47 1.34 1980
48 1.32 2053
49 1.37 2395
50 1.38 2691
51 1.33 2722
52 1.28 2914
53 1.23 2982
54 1.23 2991
55 1.11 2978
56 1.07 2930

 

beet harvest is spread over a longer period enabling outside as-
sistance to be possible. An alternative is cooperative machine
ownership. Only one real case of this was met on the farms visited.
Here, four farms, each of about 120 acres, c00peratively owned a
combine, a bean harvester and a sugar beet harvester. Generally,

more friendships have been broken than made in cooperative ownership

 

9Area 8 is cash crop and dairy farming in the Saginaw

Valley and Northern Thumb areas of Michigan.

70

of harvesting equipment. However, in this case, the success of
the venture can be judged from a five year history of almost per-
fect harmony. The basis was a properly drawn up agreement whereby
expenses were paid on a crop proportion basis and from a central
fund raised by custom work with this machinery. Fuel and oil were
provided by the farmer concerned and labor assistance was paid for
on a regular hourly basis. In the case of beans, only twenty
acres could be harvested at one time by any one farmer; each had
to take his turn.

Many farms appeared to have more tractors than necessary.
All farms had two tractors and some small farms even had three.
The reason given for this was ease of Operation. The idea was to
have a large high horsepowered tractor for the heavy work of
ploughing and preparing a seed bed, etc., and a light, more
maneuverable tractor for row-crop work. This allowed the small
tractor to be hitched up with inter-row cultivation equipment
throughout the season, leaving the larger one free for other work
and thus avoiding the time consuming job of attaching and unat-
taching equipment. The essence of farming in this area appeared
to be to have the equipment to get the job done as quickly and as
efficiently as possible because of the critical periods of crop
sowing, growth and maturity. Pride of possession also seemed to
be a factor, as many small farms had invested in overly large

combines.

71

Fertilizer Expenditure

The estimated bi for fertilizer expense had a high standard
error which made the estimate of the MVP unreliable. Reasons
have already been given for suspecting that returns to the fer-
tilizer input were, in fact, less than a dollar for a dollar in
1957. Also, the MVP may be underestimated with corresponding
overestimates in the MVP's of land and drainage investment. Nothing
more will be added here, except that fertilizer input-output
studies in this area10 have indicated that more than a dollar re-
turn per dollar invested is obtained in average years with the
generally accepted levels of fertilizer application. Table IX
indicates the variation in quantities of fertilizers applied to
the three main crops on the farms in the sample in 1957.

It appeared that wheat was most frequently over fertilized
particularly with nitrogen and this was borne out by observations
of the farmers concerned. The breeding of a short, stiff-strawed
wheat for this area is urgently required. Many farmers were using

more than optimum quantities of nitrogen on sugar beets.
Other Current Crop Expenses

The estimated b was unreliable reducing the confidence in

i

the estimate of the MVP for other crop expenses. The estimates

 

10L. S. Robertson and W. B. Sundquist, An Economic Analysis
of Some Controlled Fertilizers Input-Output Experiments in Michigan.
Data 1955 and 1956. Unpublished technical bulletin. Michigan
Agricultural Experiment Station.

 

72

TABLE IX
RANGE IN QUANTITIES 0F ARTIFICIAL FERTILIZERS APPLIED TO THE THREE

MAIN CROPS OF THIRTY SAGINAW VALLEY AND THUMB CASH CROP
FfiRMS IN 1957

Pounds of Fertilizer Appliedgper Acre

 

 

Cro Plant
P Nutrient Lowest Highest Suggested 11
Level Level Optimum Rates
Sugar Beets N 20 130 40
P205 72 234 80 - 160
K20 72 376 40 — 80
Beans ‘N 0 12 15
P205 0 48 30 - 60
K20 0 48 15 - 30
Wheat N 8 67 16
P205 21 200 48 - 96
K20 21 200 24 - 48

 

from this study suggest an inefficient use of this input in 1957,
with the reservation that some of the return to fuel, in particular,
may be reflected in overestimated returns to the machinery invest—

ment and labor input categories.

Buildings

Little confidence can be placed in the estimates of returns

to crop storage and machinery storage investments. Other studies

 

11Fertilizer Recommendations for Michigan Crops, Extension
Bulletin 159 (Revised), Oct. 1957. Michigan State University
Cooperative Extension Service, p. 16.

73

which have attempted to estimate the regression coefficient of in-
vestment in buildings have met with the same difficulty of ade-
quately measuring the value of buildings. No observation on the

returns to building investment will therefore be made.
Increasing:Returns to Scale

Since the sum of the bi's was consistently greater than
one, and also because of supporting evidence from examination of
the data with inputs treated as perfect complements, increasing
returns to scale are indicated. Increasing farm size and conse-
quent reduction in the number of farms in this area cannot, there-
fore, be expected necessarily to reduce overall production.

Increasing returns to scale also means that it is impossible
to compute a high profit point unless one or more of the input
categories are held constant. In any case, extrapolation beyond
the range of the data is not advisable. However, as suggested by
Kaldor,12 management may eventually prove the limiting factor;

this important input, by necessity, was not included in the empirical

production function.
The Complementarity of the Input Categories

The complementary nature of the input categories has been

demonstrated, particularly in relation to the inputs of land and

 

12N. Kaldor, "The Equilibrium of the Firm," Economic Journal,
Vol. 44 (1934), pp. 60 ff.

74

drainage investment as shown in the final function. Also, the
function assuming perfect complementarity of the inputs, when ex-
pressed in logarithms, was not significantly different in its
ability to predict gross income than the final function. How-
ever, the superiority of the final Cobb-Douglas function is in
its ability to produce less biased estimates of the MVP's of the
input categories.

The simple linear function assuming perfect complementary
of the inputs did not provide a good fit as increasing returns to
scale were exhibited. If the optimum proportions of inputs had
been known and used to discover the limiting factors a better fit
may have resulted. This suggests that a linear programming study

in this area may prove interesting and worthwhile.
Reorganization of a Farm on the Basis of the Estimates

It has already been noted that the farms in the sample ap-
peared to be fairly well adjusted to conditions existing in 1957.
An attempt was made to discover maladjusted farms as this would
have increased the reliability of the estimated regression coef-
ficients. As this attempt, unfortunately, was not too successful,
there are few farms in the sample which can profitably be investi-
gated with a view to attaining a much better adjustment. However,
one farm.(No. 16) was sufficiently out of adjustment to warrant
examinamion and can be used to illustrate the use of this type of

analysis for individual farm management advisory purposes.

75

Observations and estimations using the results obtained
from this study must be tempered with an appreciation of the limi—
tations of the results. This will be kept in mind in the following
illustration.

Farm No. 16 extends to 296 tillable acres. The cropping
in 1957 included 46 acres of wheat, 126 acres of white pea beans
and 85 acres of sugar beets. These are all high value crops.
Yields in 1957 were lower than normal, largely because of the wet
weather conditions. However, only 170 acres had been effectively
tile drained. The poor drainage existing on the remainder had
certainly contributed to the reduction in yields in 1957 and the
yield potential in more normal years. The gross income achieved
was 326,019 or 888.00 per acre, whereas the average gross income
achieved in the sample was $110.00 per acre.

The quantities of inputs used on this farm in 1957 with

their estimated marginal value products were:

 

Estimated Estimated Geometric Mean

 

MVP MVP for the Sample

Inp“t °““”t1ty (dollars) (dollars)
Land 296 TA 25.00 24.06
iLabor 51 months 177.63 306.87
Machinery

investment $17,795 .37916 .2968
Drainage

investment $21,551 .42721 .3020
Fartilizers and

cr0p expense 6 7,425 .75724 .5484

 

tr; _

76

It will be assumed that farm size cannot be increased and
will remain limited to the 296 acres.

Examination of the estimated MVP's shows that the marginal
return to labor was lower than average with a higher than average
return to machinery investment. This was not surprising in view
of the high labor requirement on this farm for hand lifting of
the sugar beets. Sixty-five acres were lifted by Mexican hand
labor; the remaining 20 acres by custom machine harvesting at $20
per acre. With such a large acreage of sugar beets an investigation
into the reduction in labor requirements and other costs by the
purchase of a sugar beet harvester seemed in order. It is esti-
mated that a reduction of 16 months of Mexican labor could be
achieved by the purchase of a mechanical sugar beet harvester
costing 83,500.

A partial budget would show:

Increased costs:

Gas, oil, repairs, etc. 3400.
Interest on investment @ 6% 210.
Depreciation @ 20% 700.

31,310.

Reduced costs:

16 months Mexican labor @

3170/month $2,720.
20 acres custom harvesting @
SZO/acre 3 400.
3,120.
Net reduction in annual costs $1,810.

This would reduce costs sufficiently to enable the cost of

the harvester to be met out of increased profits in two years.

77

If the other inputs remained fixed the effect on the esti-

mated MVP's would be:

Land 5 23.30 per tillable acre
Labor 8242.117 per month
Machinery investment .2964 dollar per dollar
Drainage investment .3982 " " "
Fertilizer and crop expenses .7083 " " "

The MVP for labor has been increased considerably with a
corresponding reduction in the MVP for machinery investment. Already
an improvement in the adjustment has been achieved. A slight re-
duction in all the MVP's is noticed, this is due to a slightly lower
estimated gross income.

The estimated MVP for drainage appeared to be very high,
which is not surprising considering the large acreage still requir-
ing tile drainage. Adequate drainage of the remainder would cost
about 8140 per acre requiring an increased investment of 817,640.

A charge of 8 percent to cover interest on investment, depreciation
and maintenance would result in increased annual costs of $1,411.

It might be expected that under similar conditions existing in

1957, an income of 5110 per acre should be achieved as fertilizer
usage was not greatly different from the average. Increased returns
would be 86,541, leaving a net increase of 55,130. This should
enable repayment of the loan necessary to finance this increased
investment within four years.

If these two major changes could be financed it would have

the following effect on the estimated MVP's of the inputs:

78

Land 8 27.53 per tillable acre
Labor $276.99 per month
Machinery investment .3391 dollar per dollar
Drainage investment .2587 " " "
Fertilizer and crop expense .8104 " " "

Estimated gross income had increased to $35,248.00.

The farm now appears to be in much better adjustment with
marginal returns more in line with minimum expected returns. (See
page‘4l.) The estimated MVP of drainage had been reduced with sub-
stantial increases to the MVP's of the other input categories. This
illustrates the reverse effect of the law of diminishing returns on
the inputs held constant.

Mention has been made of the possibility of increasing
returns by increasing the quantity of fertilizer applied to these
crops on the now drained land. The estimated MVP for fertilizer
and crop expense is less than 51.06 (the suggested minimum return)
which implies the higher input of fertilizer would be unprofitable.
However, the reliability of this estimated MVP is questionable and
outside evidence would support a decision to apply increased quan-
tities of fertilizer.

Drained land is usually easier to manage and cultivate with
fewer hold ups in work than undrained land. Hence, it is quite
possible that other current crop expenses, such as gas and machinery
repairs, would be reduced, thus tending to offset the suggested in-
crease in fertilizer expense.

This example illustrates the use of the Cobb-Douglas type
of analysis as a guide to advice on the individual farm. It thus

complements usual farm management methods in helping to delimit

79

general weaknesses in the farm business. The details required for
making the ultimate decision being achieved by such practices as
partial budgeting. This particular example also illustrates, in a
simple way, the real advantage of being able to allocate a definite
return to each of the machinery investment and labor input categories,
thus giving a more objective basis for advice than labor efficiency
measured in terms of productive work units per man.

The high profit point was then calculated for this farm with
acreage assumed fixed at 296 acres. Unless one or more of the input
categories are held constant a high profit point cannot be calculated
as the sum of the bi's is greater than one, i.e., increasing returns
to scale.

At the high profit point (using the final Cobb-Douglas
function) estimated gross income is $45,511. The land is now as-
sumed to be fully drained, the increased investment necessary has
already been computed. It was then computed that the optimum
organization would mean altering the quantities of the other inputs
to:

Labor 52 months
Machinery investment 531,076.
Fertilizer and other expenses 3 7,329.

After draining the remaining acreage the only input that
appears to need radical change from the quantities used in 1957 is
that of machinery investment. The need for a sugar beet harvester
has already been examined. The other item of equipment lacking on

this farm is a combine. A bean harvester is already owned but a

spike—tooth combine capable of threshing beans would be an asset

80

in view of the large acreage of beans which must be harvested
quickly at a critical period. A new twelve foot self-propelled
combine, of the type suggested, would cost about 37,500, which with
the addition of the sugar beet harvester would bring the investment
in machinery up to $28,795. This is nearer the suggested optimum
investment.

The increase in the labor input could hardly be justified
in practice, neither could the reduction in fertilizer and crOp
expense. At least another 3700 could be spent on fertilizer to
bring applications more in line with suggested optimum rates. It
is also likely that the other crop expenses of gas, oil and machinery
repairs would be increased due to the additional machinery.

Although caution must be taken in interpreting the results
after calculating the high profit point, it is useful in that it
gives the farm operator something to shoot for. It is also a guide
as to the inputs which could be profitably increased or which need

further examination.

CHAPTER VI

CONCLUSIONS AND APPLICATIONS IN THE UNITED KINGDOM

Cbnclusions

The cash crop farms of the Saginaw Valley and Thumb area
of Michigan, represented by the sample in this study, appeared to
be fairly well adjusted to the conditions existing in 1957. Im-
provements are likely to be obtained by new technology, such as
improved varieties of crops, particularly wheat; better techniques
of weed control, particularly in relation to sugar beets and beans;
and improved methods of planting and/or thinning sugar beets. Labor
efficiency will probably be largely improved by attention to the re-
turns to other inputs as the ideal of equation (2), Chapter II, is
approached. Some possibilities of reducing labor requirements have
been noted but much improvement in this direction, except during
the spring peaks, cannot be assumed.

A linear programming study in this area may show that a
recombination of crops, either before or after these technical ad-
vances are made, could increase the returns to inputs. However,
any improvement in this direction would be influenced by the strict
allotments at present enforced for wheat and the acreage quota
system for sugar beet growing. The build up of diseases in this
area due to overcropping, particularly in relation to sugar beets
and beans, will also dictate the pattern of crop combination in the

not so distant future.

81

82

Higher yields might not automatically cause increases in
the marginal productivities of the inputs. The demand for the
main crops in this area is relatively inelastic so that price de-
clines might result from increased production. Present conditions,
therefore, would suggest attempting to improve the productivities
of inputs within existing yields. Reduction in labor requirements
per acre by increasing farm size and technological advances would
appear to be another approach. This, of course, is in line with
present economic thought and the trend to a larger business unit;
but if this actually increases overall production, as the evidence
of increasing returns to scale suggests, the farmer may be no bet-
ter off. This observation is made with reservations because of
the danger of extrapolating beyond the range of the data in this
study. The lower return to machinery investment on the smaller
farms, because of the relatively inflexible and expensive units of
input required, also lends support to the trend to spreading this
high investment over a larger acreage.

Adequate drainage is essential in this area. The study
shows high returns were obtained to this investment in 1957 and
other evidence1 suggests that high returns are normally expected
in average years. Further detailed investigation of returns to

drainage investment over a longer period of time, may be worthwhile.

 

1c. R. Hoglund, 93. cit.

83

Applications in the United Kingdom

One of the original intentions in this research project
was to study the substitution of machinery for labor in this area.
Unfortunately, because the farms in the sample were generally well
adjusted, and this appears typical of the area, insufficient dif-
ferences occurred to pursue a detailed investigation of this
nature. This was a disappointment because of the usefulness of
such information in the U. K. However, one of the few maladjusted
farms was selected to illustrate the applications of functional
analysis at the micro level, and at the same time this illustrated
a rather obvious case of the substitution of machinery for labor.
This, in turn, illustrated the potentiality of the functional type
of analysis to assist in the examination of the substitution of
machinery for labor on less well adjusted farms. These are probably
the case in the U. K., particularly in relation to labor and
machinery.

The danger of high intercorrelations of the input cate-
gories reducing the reliability of the estimates of the regression
coefficients is demonstrated by this study. Dr. Glenn L. Johnson,
who supervised this study and has had considerable experience with
this type of study, had not previously met with such high inter-
correlations. Thus it is hoped that such an extreme example
rarely occurs. Purposive sampling is a method of attempting to
reduce the intercorrelations of the input categories, if this can-

not be undertaken, the sample size must be increased to compensate.

84

The University agricultural economists, in the U.,K., have the time
and facilities to do this. In the field, where the local farm
management advisers and District Officers of the National Agricul-
tural Advisory Service2 are left to collect data from which farm
business reports are compiled, time is an important factor. They
are not usually in the position to undertake purposive sampling.
However, the records are, or could be, made available to the Uni-
versities. This would enable larger samples covering similar

types of farms over a wide area to be compiled; the danger of in-
troducing more variables would have to be watched. Grouping of the
farms is done strictly on an enterprise and farm size basis, as op-
posed to the Area Reports of the Michigan Co-operative Extension
Service.3 Hence more reliable estimates of regression coefficients
may be obtained than has previously been achieved by using these
records.4 The recent institution of the "mail-in" system for
collecting farm records by the Michigan Co-operative Extension
Service could result in worthwhile estimates of marginal productiv-
ities to be made. The farm records collected in the U. K. would

have to be improved somewhat to ensure more precise measurement of

 

2The district Officer is almost the equivalent of the County
Agent in the Co-operative Extension Service.

3F'arm business reports issued by the Michigan Co-operative
Extension Service are to be made available on a stricter farming
type basis for 1957 onwards.

4Louis S. Drake, "Problems and Results in the Use of Farm
Account Records to Derive Cobb-Douglas Value Productivity Functions"
(unpublished Ph. D. dissertation, Department of Agricultural Econ-
omics, Michigan State College, 1952).

85

the input categories. The major difficulty would be streamlining
the accounting procedure to make the newer measures of efficiency
worthwhile, the objective use of which has been demonstrated in
this study. It would also entail an extensive education program
for the officers concerned regarding the theory behind, and the
need for, such improvements to measures of farm business effi-
ciency. Many found difficulty in grasping the principles of farm
management analysis; currently employed and older members of the
profession even ridiculed that approach as being unnecessary;
hence, any further advances may have a difficult passage. A bias
may result from the use of these farm records in that they are
frequently assumed to be obtained from the better managed farms.
Strictly speaking this would mean that any conclusions can only
be applied to this group of farms. The same would therefore
apply to conclusions reached by traditional methods from these
farms. However conclusions would probably also apply to the so-
called not-so-well managed farms, as the tendency is for them to
be more poorly adjusted. It is the author's Opinion that in the
U. K. this difficulty would not tend to apply as the records ob-
tained were fairly representative of managerial ability.

The problem of studying multiple enterprise farms has not
yet been fully resolved;5 as mixed farming is more general in the

U. K. than the U. 8. this problem is emphasized.

 

5ChristOph Beringer, 22. cit.

86

This method of analysis should complement other methods
of farm management work. They are not substitutes. A new slant
on the farm business is obtained which gives a better basis for
estimating efficiency. This is particularly helpful in relation
to labor utilization and machinery investment. When making up
standards of efficiency of farming assuming fixed acreage, most
of the other inputs such as feed, fertilizer or livestock have
measures of efficiency derived from independent input-output
studies and more confidence can be placed in them. This is not so
with the inputs of labor and machinery investment; these have
little or no independent evidence from which measures of efficiency
can be made. Supplementary studies to determine the marginal value
productivity of labor for different crops and livestock would be
useful in planning the best combination of enterprises where labor
is the limiting factor. This is particularly so in the U. S., and
the same position is rapidly approaching in the U. K.

Interpretation of the results for individual farms depends
on how good a job is made of selecting homogeneous farms for the
sample and the efficiency of measuring the input categories. Per-
haps more important is the assumption inherent in the Cobb-Douglas
production function of constant elasticity, although modifications

can be introduced into the function to overcome this difficulty.6

 

6A. N. Halter, a. 0. Carter and J. G. Hocking, "A Note on
the Transcendental Production FUnction," Journal of Farm Economics.
Vol. XXXIV, NOVs 1957' ppe 966‘974e

87

The method can also be applied to the study of resources at a macro
level, to aid in the better all around allocation of these resources.
Fbr instance, the immigration of labor off the farms in the U. K. is
continuing; increasing machinery investment and farm size may be
Spart of the answer. Also pertinent is the recent Farm Improvements
Hill which provides assistance in the modernization of buildings

and other fixed investments to land. Many farmers, while welcoming
the assistance, question whether this may be the best allocation

of capital on their farms. Knowledge of the marginal value produc-
tivities of inputs would help give a more objective basis for con-

sideration of these problems.

APPENDIX A

Estimated Marginal Value Productivities for Some of

the Farms in the Sample

89

 

 

 

 

 

 

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APPENDIX B

Questionnaire Used in Personal Interviews

CONFIDENTIAL

Name:

Address:

92

Farm No:

Tel. No:

 

Farm.Size:

Owned

Rented .Total

 

Tillable

 

an Tillable

 

woodland and other

 

 

Total

 

 

 

 

Tillable acreage leased out:

Labor:

Operator

Family

Hired: a. Full time
b. Seasonal

c. Hexicen

Subtract labor for livestock

Net total labor for crop enterprises

Net tillable acres

 

Nos.

Average man
-month
Honths Nos. Days equivalents}

 

 

 

 

 

 

 

 

 

 

 

 

Total

Seasonal labor details (when and where used)

 

W3 e details (flat rate, piece rate, bonus, etc.)

Housing facilities

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Oats:
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Barley:

 

Corn:
Cash crop

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Silage

 

Beans:
Cash crop
Certified seed

 

 

Sugar Beet:

 

Other:

 

 

Alfalfa a clover:
Hay, silage and.pasture
Full season, unharvested green crop

 

 

 

 

 

 

Green manure crop ( )
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Total

Subtract acreage unconnected with cash
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Total Tillable crop acreage:

Livestock number;

 

 

 

 

 

     

 

     

   

 

   

 

   

 

 

 

 

 

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94
Gross Income
- 1 2 3 h 5
Physical Ending Total Beginning Annual
Crop Income Production es Valuation 1+2 Valuation Prodifition
3..

Wheat :

Cash crop bu.

Seed bu.
Oats:

Cash crop bu.

seed bu.
Barley: bu.
Corn:

Cash crop bu. '1
Beans :

Cash crop bu.

Seed bu.
Sugar Beet Tons
Other
Custom work a machine rented
Produce consumed in house

(not livestock)
Other income from crop source _
Gross income, excluding livestock 3
1 2 3 h 3 5 7
Sales Ending Total Beginning Purchase Total Annual
, Valuation 1+2 Valuation n+5 Prod.
Livestock income

 

Milk 8: other dairy produce

 

Cattle

 

Poultry & eggs

 

Sheep 8: wool

 

Other livestock income

 

 

 

 

 

 

 

 

 

fi.

Gross livestock income $
Grand total 33

 

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..u.
Fertilizer & Time
Analysis ”86 Quantity Price. Cost '
Lin;
Total 5.»
Less that used for livestock crops (ES
Net cost to cash crop production g.)

Residual Fertilizers & Lime: (cropland only)
Only if very different in beginning and ending inventory.

Difference in fertilizer and lime usage between 1957 8: 1956 or
the new. '

P205 lbs. difference 3: $5 a x 95 - g,»
K20 lbs. difference 3: 53’ = x ¢ =- a)
N2 lbs. difference 3: % - 3: ¢ - $

Difference in Residual Value $9

Substract if difference balance is carried forward to 1958, or add if brought
forward from 1956 and before.

Total Fertilizer G: lime investment 9

Alterations in cropping during last 1; zear :

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96

Other expenses

inning ture Total Ending Annua
aluation aluation Cost‘

A. Power 8: machinery:
Custom work an machinery hire
Fuel & oil for farm use (less refund)
Implement 8: machinery repairs (not
of an investment nature)
Haulage '
Electricity (farm share)
Auto operation (farm share)
Other
Total power & machinery costs

B. Fertilizer & lime investment (p. h)
0. Seed

D. Other:
Baleing wire 8: sacks
Crop sprays & pest control
Postage, telephone, etc.
Miscellaneous
Total other costs

Subtract or add value of difference in
winter wheat, clover & alfalfa stands.

(1). 6)

E. Livestock:
Feed purchases:
concentrates
others
Veterinary't medicine
Breeding fecs
Other, dairy sundries etc.

      

crop expense V

 

otal livestock expenses t

 

Total of other expenses (crop & livestock) §9____

Ehcpenses not to include maintenance & repair work of an investment nature to
buildings ,mnachinery and land, or depreciation, interest 8: insurance charges.

 

 

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97
-6-

.Establishment and Valuation Winter Wheat, Clover’& Alfalfa Stands

Only if there is a difference between beginning &.ending inventory'acreages
(1957). Costs &.va1nes at 1957 Prices.

 

1956 fer 1957 for

1957 crop 1958 crop
'Winter Wheat

Fertilizer costs per acre (excluding N2 top dressing)
Seed cost per acre
Other costs

Tota1.per acre costs
Multiplied by acreage
Total cost of establishment of winter wheat

 

 

 

 

 

 

 

 

 

 

Difference in cost or valuation t
Clover &.alfa1fa seedings
Brought forward from 1956

 

Seeding Acreage Age Condition ' Value value
. per acre ” ”

 

—r

 

 

 

 

 

 

 

 

 

 

 

Total value t '

 

Carried forward to 1958

 

 

 

 

 

 

 

 

 

 

 

 

Total value h

Difference in valuation 8

NB Add.valuations to crop expenses (p.5) if difference balance is brought
forward from 1956, or subtract if carried forward to 1958.

 

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98

Machinery'& Eguigment Investment

 

Item

   
    
 
  
 
   
      
 

 

Combine

 

Bean harvester

 

Corn picker

Sugar beet—barvester
Beet loader

 

 

or corn p

   

3

 
 

Corn 8..- arain handling:
Marato'r , Blower or Auger
Drier

 
 
   

  

Cleaning equipment
er

 
   
   

    
 

or

    
 
  
    
  
 
   
    
  
  
 
  
 
  
 
  

 

‘

lime oer
Seeder

equi

  

 

ons & trailers
Newer

Cultivation equipment:
bottom

Spring tooth harrows
or sp
Clod buster
Cul
Field cultivator
Roller
Cultivator: row
Rotary'hoe
Down the row thinner

Leveller
Grader or
Bulldozer

  

  
    
 

 

 

 

 

 

 

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Item No. Age Condition value

 

Other crop machinery

Wbrkshop egpipnent:
welder

Engines, motors
"WECEP pump
General farm.tools L I
(forks, shovels etc.) !

+~

 

 

 

 

 

 

 

 

 

 

 

Total crop machinery investment t

 

 

 

 

 

Add preportion of investment for farm automobile $
Livestock equipment
Mbwer 7 i
Rake ‘ ._
Forage harvester __.
Blower

 

Feed grinder

 

Manure spreader
Manure loader ' ' ‘__
Dairy equipment .
Other livestock equipment 1

_L__

 

 

 

 

 

 

 

 

 

 

 

Total livestock machinery investment B
Beginning inventory, total machinery investment B
Book value of machinery investment :3.

values
Sales

Use be &.valuation at 1-1-

Purchases

I

*Note:

   
      

     

 

      

        

      

   

01331 a dad.

alue

Date tem Date Item

     

 

tal Prop.

 

  

Beginning inventory:
Prop 0 added
Prop. subtracted

 

Total Machinery investment 9

Netes on.machinegy (ownership shareing?)

 

   

 

 

 

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100

Buildin s
570% to include that used for livestock & fodder or not used.

 

 

 

 

 

 

 

" ' Size farmers estimate
of invesunent value
Liachinery storage 8: workshop Sq. ft.
Crap storage:
a. Small grains or beans bu.
be com crib b“.
Total

 

 

Livestock buildings & fodder, forage etc.:

Farmers estimate of total building investment:

Drainage (cropland only)

Undrained
not requiring drainage
requiring drainage
Drained ‘
good
fair, imperfect but cropable ‘
very poor

TOTAL crop acreage

Tiles (discount old 2" tile systems)

(‘I
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acres
acres

 

acres
BOPBO
acres

acres

 

Size Type Depth Length of run in rods Replacement Investment

1,"

 

cost per rod

Total tile inveth $

 

 

 

   

 

 

   

 

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101
-10-

Ditching (farm investment only)

Depth Length of run in rods Unit' cost Investment

Total ditch.1nvestment 8

 

Other drainage investment

    
   
 
 
 
 

Items

Land leveling
Culverts

Settling tanks
PUmps
Other

  

Investment charge for farm use of county ditches $

 

Total drainage investment $

Notes on drainage:

 

 

 

 

 

 

 

 

 

 

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Assessment of farm.practices used and laborA&.machinery'organization

1. Crogging: (e.;. green manuring)

2. Cultivations: (e.g. minimal tillage)

mm

h. Preharvesting (e.g. PestA& weed control)

5. Harvesting

6. Other crqp handling procedures

If the operator could start afresh, what machinery'&.equipment mguld he
have and how would this be combined?

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BIBLIOGRAPHY

A. Books

Bradford, Lawrence A. and Johnson, Glenn L., Farm Mana ement
Analysis (New York: John Wiley and Sons, Inc., 19535.

Dixon and Massey, Introduction to Statistical Analysis (McGraw-Hill
Book Company, Inc., Second Edition, 1957).

Eisenhart, C., Hastay, M. W. and Wallis, W. A., Technigues of
Statistical Analysis (McGraw-Hill Book Company, Inc., 1947,
First Edition).

Ezekiel, Mordecai, Methods of Correlation Analysis (New York: John
Wiley and Sons, Inc., Second Edition, 1949).

Knight, Frank H., Risk, Uncertainty and Profit (Boston and New York:
Houghton Mifflin Co., 1921).

B. Articles and Periodicals

Beringer, Christoph, "Problems in Finding a Method to Estimate
Marginal Value Productivities for Input and Investment
Categories on Multiple Enterprise Farms, " Resource Pro-
ductivity, hturns to Scale and: Farm Size, Heady, Johnson

md Hardin, Iowa State College Press, 1956.

Brofenbrenner, Martin, "Production Functions: Cobb-Douglas, Inter-
firm, Intrafirn," Econometrics, XII, No. 1, Jan., 1944.

Carter, H. 0., "Modifications of the Cobb-Douglas Function to
Destroy Constant Elasticity and Symmetry," Resource
ProductivityI Returns to Scale_gnd Farm Size, Heady,
Johnson and Hardin, Iowa State College Press, 1956.

Cobb, Charles W. and Douglas, Paul H., "A Theory of Production,"
The American Economic Review, Supplement, XVIII, March, 1928.

French, George W., "A Report on Tests of Mechanical weeding and
Thinning Equipment in Michigan," Proceedings of the American
Society of Sugar Beet Technologists, 1952.

French, George W., "The Extent of Spring Mechanization in the
Eastern Beet Area, 1951," Proceedings of the American Society
of Sugar Beet Technologists, 1952.

103

104

Guttay, J. R., Cook, R. L. and Erickson, A. E., "The Effect of
Green and Stable Manure on the Yield of Crops and on the
Physical Condition of Tappan-Parkhill Loam Soil," Social
Science Societyof America Proceedings, Vol. 20, No. 4,
Oct. 1956.

Halter, A. N., Carter, H. O. and Hocking, J. G., "A Note on the
Transcendental Production Function," Journal of Farm
Economics, Vol. XXXIV, Nov., 1957.

Robertson, L. 5., Cook, R. L., Rood, P. J. and Turk, L. M., "Ten
Years Results from the Ferden Rotation and Crop Sequence
Experiments," Michigan Agricultural Experimental Station
Journal, Article No. 1331.

C. Bulletins and Reports

Farming Today, Area 8 Report, 1958, Co-operative Extension Service,
Department of Agricultural Economics, Michigan State Univer-
sity.

Fertilizer Recommendations for Michigan Crops, Extension Bulletin
159 (Revised), Oct., 1957. Michigan State University Co-
operative Extension Service.

Hoglund, C. R., "Managerial Decisions in Organizing and Operating a
Farm,"Ԥg, Econ. No. 625, Department of Agricultural
Economics and the Agricultural Experiment Station, Michigan
State University, Sept. 1955.

Michigan Labor Market, Vol. x11, No. 4 (April, 1957), and Vol. x111.
No. 4 TAprii, 1958), published by Michigan Employment Security
Commission, 7310 Wbodward, Detroit 2, Michigan.

Officia1_Tractor and Farm Equipment Guidg, (January-June 1957).
Compiled by the National Retail Farm Equipment Association,
published by Farm Equipment Retailing Inc., 2340 Hampton,
St. Louis 20, Missouri.

Official Used Car Guide (January 1957), published monthly by the
National Automobile Dealers Used Car Guide Co., 200 S. 7th
St., St. Louis 2, Missouri.

Turk, L. M. and weidemann, A. 6., Farm Manure, Extension Bulletin 300,
Co-Operative Extension Service, Michigan State College
(June 1945). Table 1, page 7, compiled from "Fertilizer and
Crap Production," Van Slyke, Orange Judd Publishing Company.

105

Whiteside, E. P., Schneider, I. F. and Cook, R. L., Soils of
Michigan. Special Bulletin 402, Soil Science Department,
Agricultural Experiment Station, Michigan State University
(January 1956).

D. Mimeoggaphs

Boyd, James 5., Current Costs of New Farm Buildingg (Professor,
Department of Agricultural Engineering, Michigan State
University). Paper presented at the Rural Appraisers
Conference, Grand Rapids, Michigan, 12th Sept., 1957.

Hoglund, C. R., and wright, K. T., Estimated Labor Requirements
for Sugar Beet Pgoduction in Michigan, 9.9 ton Yield,
Four Methods of Production. Michigan Circular Bulletin
215, June 1949.

Mechanical Thinning of Sugar Beets, 1955. The Monitor Sugar Beet
Co., Bay City, Michigan.

Schultz, Arthur B., Building and Equipment Costs, Department of
Agricultural Engineering, North Dakota Agricultural College.

E. Unpublished Material

Davis, J. F., Robertson, L. S. and Sundquist, W. B., "Fertilizer
Input-Output Studies, 1957." Conducted co-operatively by
the Departments of Soil Science and Agricultural Economics,
Michigan State University.

Drake, Louis 8., "Problems and Results in the Use of Farm Account
Records to Derive Cobb-Douglas Value Productivity Functions,"
Ph. D. dissertation, Department of Agricultural Economics,
Michigan State College, 1952.

wagley, R. V., "Marginal Productivities of Investments and Expendi-
tures," Selected Ingham County Farms, 1952," M. S. disser-
tation, Department of Agricultural Economics, Michigan
State College, 1953.

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