Table Of ContentPROBLEMS AND RESULTS IN THE USE
OF FARM ACCOUNT RECORDS TO DERIVE
COBB-DOUGLAS VALUE PRODUCTIVITY FUNCTIONS
By
LOUIS SCHNEIDER DRAKE
A THESIS
Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Agricultural Economics
1952
PBOBLXMS AMD R0ULTS IM THX USB
OF PAW ACCOUNT BBCORDS TO DBIXY1
OGBB-DOUOIUB TALUB PBOXXJCTIPZTT PUMCTXOM
br
Louie Schneider Drain
An Abairaot
of a thaaii praaaaiad to M u .School of Qreduate Stodlee
oP 1H nhtgan St*to College
In partial ftilftU— it of the roqulroaoato
Tor the degree of
DOCTOft OP PHILOSOPHY
Department of Agricultural Xeenoad.ee
Approved
ISOlS M M i i M r
WWlI lit AMD IBDU IiniOII
or rum aooouot w o o m to n m
COIB-DOOOLAS TALUB PhOOSCTIYITI rUSCTIO»
(41 ABSTKAOT)
A t purpose or thia «tod|r is to tort tot i— fwlwm «f tot CrtW
Dooglas toLtt pvotort&flto fwrtiw ftr trtltrtlip tot gross insoae
of t fora by considering tot Input# or fatton nsrt. This fowtiat ptr>
alts — t1 noting or olsstisitiss of gross lnooao with roopoot to rostors
and tta# norginal ▼olao prodnotlwltiss of rostors* Tho hypothesis lo sot
up that sop orison tot low nith tho fhaot&on will shoo thot tho lsttor os*
tiaotoo will bo nsoTnl to faraan. Tho hppothools is adronood that dif-
foronooo botnoon rooorded grooo Inn on a and gross iaooaao ootinotod ftoo
Cobb-Doagloo equations eon bo osooontod for by Torlotloas botnoon fans
in prlsos resolved, yields and prodostion rataa, ohoiso of enterprises,
and also of business* Spoolol ottowtlon is givon to prooodaroo whioh
will noko o totlotlool ly dotomlnod value productivity equations of pros*
tleal value to fanara.
ran
Iho dots a n lpU osooont rooords for tjrpo of-famlng oroos
5 and 6t Michigan, 1990. Tho rorns oro cl aoolflod Into too groups,
daliy and othor than dairy. This lo dona in order that tho statistical
techniques nagr bo triad on a group of honogonooos fans (dairy), as
wall aa on tho noro heterogeneous group of all fams. Tho statistical
aothod consists oT oonwortlng tho fan aooount data into logorithno and
solving for aquations ootlnatlng gross 1 noons by least oquareo*
M s tilw iU if Droho
On of tt« Cobb HwflM fuwtiN to « U m N |to m Imom « A mmr-
glaal rvtarnt to laputa n t N on ttw> prlauy m b u H — >. H m n ««
Ihti tlto gtltltoNldp Oitw m giM« iMNt and anjr parti— lor input lo
Unit la tho logarlthno # that grooo lnoono lo o ftwrtioi of laputa* and
that dlfforont fan aro ooaonttally trialo «lth ?ai U | oomblnatlono of
00 7
faotoro* all f«no bolag oa nubotaattally the mono valao produntivitar
funotlon. Thaoo aooumptloaa aro ooaoldarod*
It lo oheoa that tho Cohb-Oooglae funotlon glvoo a good oatlaato
of grooo lnooao* Tho ootlaatoo of marginal valao prodnotlTitioo of
faotoro tarn oat to bo about ao ahoald bo orpootod a priori* For dlf«*
foroat oquatlono ootlaatlag grooo lnooao tho marginal valao prodaotlvlty
of iavootaoat la load vorloo botaoon 0.03b and 0*096 la Ito ootlmatod
▼aluo* Iho ootlaato of tho marginal roturn to larootaoat la naoMiiarjr»
Inoladlng oboolooooaro and doproolatloa ao amll aa Intoroot* mngoa firsa
0.23 to 0*35* Thaoo ootlaatoo and alallar onoo rofor to tho rotara to a
aarglaal dollar of larootaoat or ohargo*
Tho roonlta of tho work ouggoot that fara hunt nooo amaljrola roporto
max profitably laelndo tho following Information •
1* latinotoa of grooo laoomo, that a foraor would homo a aotloh
00
of what ho ahould rooolro^ eoaoldorlag hlo lapato la rolatloa
to tho laputo of othor f armora.
2* Satlaatoa of arorago aarglaal valao prwdaotlrltloo of footoro
for all famo that thoro ahould bo an additional boolo fbr
00
ronnnaonriotlono for futuro oxpondlturoa on tho avorago farm.
3* Kotiaatoo of marginal Td.no produotlTltloa on individual farao
to holp dnraoro plan for tho futuro*
[)W«< m Sohnaldar DpaIh
k» fcylaniU o M of la grota Iimmm a d ast laaat
ftnoa thatr ootlastod valooo aardlng to tho affooto of jrlalda,
prloM, ohoioo of «WrpriMit a d olso of batiain.
In this ttadjr tho ootlaatoo of grooo lnooao aad aarglaal valao
prodaotlvltlaa of 1x9 a to aro baaod oa all far ao, ao aro tho ootlaatoo
of tho offoeto of dlfforoaooo In jlolda and prlooo. Tho standard of
ooaparlooa nood not noooooarllr bo tho •anrorago" fan bat mmj bo a group
of high profit far oa •
ACKNOWLEDGE ME NTS
The author wishes to express his sincere apprecia
tion to the members of his graduate committee and to his
teachers Tor their encouragement, high standards, and gen
erous assistance and criticism.
Those who helped particularly in the preparation of
this dissertation are Professor T. K. Cowden, who gave
much encouragement and confidence in the worth of study—
in;’; agricxilture at the level of the whole farm as a unit;.
Professor L. V/. Y/itt, who showed how to specify the prob
lem and how to set up the method of study; Professor L# H.
Brown, who gave invaluable suggestions for uses of the
method and the results; Professor V. E. Smith, whose know
ledge of production functions provided the author with
most necessary criticisms as the work was in progress;
Professor Leo Katz, who showed now to set up and test the
statistical work, within the limitations of the data; and
Professor Glen T. Johnson, visiting professor at Michigan
State College, who pointed out basic porblems and numer
ous potentialities in the use of the Cobb-Douglas function
and gave much valuable counsel and criticism.
Others who contributed to the work are Professor K. T.
.’/right, who gave ideas for analyzing the data in consider
ation of its intended use; Professor C. R. Koglund, who
suggested ways of finding out how data could be improved
for work with gross income functions in the future; and Pro
ii
fessors W. D. Baten and L. L. Boger, both of whom helped
generously with mathematical problems.
The author acknowledges his debt to Professor E. E.
Peterson, In whose course In agricultural production econ
omics he came on the application of the exponential gross
Income function to farming. Professor Peterson helped
him set out the Idea of the work In definite form, and to
coordinate the method with the available data.
Teachers other than those directly concerned with
the dissertation have helped the author to form a phil
osophy of an economic system and to realize the possibil
ities of service through study of the economics of agri
culture. These professors are D. C. Cline, R. W. Llnd-
holn, Leonard Ball, I.!, F. Cravens, and Raleigh 3arlowe.
Thanks are due the farm account clerks for their
willing aid with the computations, typing, and diagrams.
By his understanding cooperation In granting the au
thor an extended leave of absence, Dean Fay L. Partlo of
the Michigan College of Mining and Technology helped to
make the work possible.
It Is Impossible to give specific credit——or enough—
to the anonymous workers who, over the years, have devel
oped the Michigan farm account system, compiled the data,
and thus provided the foundation on which this work could
be built.
ill
VITA
Louis Schneider Drake was born in Leelenau County,
Michigan, on June 11, 1912* He attended, public schools
in Traverse City, Bellaire, and Mancelona, Michigan,
and graduated from the Mancelona High School in 1929*
At Michigan State College he specialized in agricultural
economics and farm management, and obtained the degree
of Bachelor of Science in 193U- from that institution,
lie obtained a graduate as si stantship in farm mangement
at Cornell University and pursued graduate studies from
193^4- to 1937* At that time he accepted a position as
Land Use Specialist for the Resettlement Administration,
and was 1 ter transferred to the Bureau of Agricultural
Economics as Acting B. A. E. Representative for New York
State. He received the degree of Master of Science from
Cornell University In 1939* He was with the federal
government as Assistant B. A. E. Representative for
Michigan and B. A. E. Representative for Connecticut un
til 191^2. He had meanwhile, from 1939 until 19U2 been
a partner In a commercial potato farm in Houghton County,
Michigan, and continued In the farming business until
l?li-8. In 19-4-6 he accepted a position with the Michigan
College of Mining and Technology in the department of
engineering administration, where he was successively
an Instructor, an assistant professor, and an associate
professor of economics, which position he now holds.
iv
INTRODUCTION
A Brief of the Purpose, Materials, Methods
and Results of the Dissertation
I# Purpose of the study and definition of terms: the
purpose of this study is to show how certain types
of formulas can aid fanners in determining
A* How their gross Incomes compare with those of
other farms when investments and expenses are
considered;(estimate of gross income);
3, What increase In gross Income farmers should
expect If they increase any single kind of out
lay by a "iven proportion (elasticities of prose
income v.'ith respect to factors of production) ;
C. What the additional returns for additional out
lays are (estimates of marginal returns to fac-
tors);
D* Why net Income usually varies from Its expected
amount (effects on net Income of yields, pro
duction rates, prices, and size of business)*
II. Materials: Two types of materials are used In this
study;
A. The analytic tools: the Cobb-Douglas gross in-
a b k
come estimating equstions--P r Cx y ...z_ •
(Chapter I)
3* The data: observations of I9I+ farms in type-of-
farming areas 5 and 6, HIchipan, 1950 (Chapter II)
v
Ill* Methods (Chapters III and IV)
A* Classificatory methods
1. Inputs: factors of the farm business are
classified into different categories with
different degrees of refinement. Thus
more insight is gained into the componental
structure of gross income;
2* Farms: the farms are divided into two
group s:
a* 86 dairy farms
b* 108 farms other than dairy.
3* Mathematical methods
1. The categories of factors end *rooc income
are taken off the farm account records;
2* These data are converted into logarithms;
3* Regression equations are calculated by the
Doolittle method;
Standard errors of estimate of single co
efficients are computed in some cases;
5* The elasticities of gross income with re
spect to categories of factors are given by
the coefficients of the terms on the rl;^it—
hand side of each logarithmic equation;
6. Marginal value productivities of categories
of factors are determined by taking the
partial derivatives of the gross income
vi
