Agricultural production functions.

673 Pages·1972·69.796 MB·English

by  E. O. Heady;

AGRICULTURAL
PRODUCTION FUNCTIONS
Earl O. Heady
ProfessorofEconomics
andC. F. CurtissDistinguishedProfessor
ofAgriculture,
IowaStateUniversity
John L. Dillon
Research Officer,
Commonwealth Scientific and
Industrial ResearchOrganization,
Melbourne, Australia
Iowa State University Press, ^Ames, Iowa
© 1961 by The Iowa State University Press.
All rights reserved.
Library of Congress Catalog Card Number: 60-11128.
LITHOPRINTED IN THE UNITED STATES OF AMERICA BY
CUSHING-MALLOY, INC., ANNARBOR, MICHIGAN, 1961
Preface
The application of formal productionfunction concepts in agricul-
tural research is a relatively recent development* The area of analysis
was initiated by W. J. Spillman and other pioneer economists and physi-
cal scientists in agriculture. However, economists andphysical scien-
tists fairly well “went their own way* and several decades went by with
little co-ordinated research in the prediction of physical production and
in economic application of the results. However, with increased com-
mercialization of agriculture and greater economic literacy of farm
operators there is needfor design of physical and biological research
so that the results can have greater economic interpretation and appli-
cation.
This text, considered as one in agricultural science rather than
purely in economics, summarizes certain concepts and methods relat-
ingto the prediction and use of agricultural production functions. It
also reports, in summary form, the results from selectedproduction
function studies. Emphasis is on concepts, principles, and methodolog-
ical results. Practical applicaj£.cjn is considered to be a second step in
communicatingprinciples and predictionfor farmer use. However, a
few illustrative examples are includedto indicate how complex data and
concepts can be interpreted and presentedfor practical use.
The studies reported are largely those resulting from co-operative
research efforts at Iowa State University over the past decade. These
studies include an important group of products and are drawn together
in this monographfor use of other scientists in economic and biological
phases of agriculture. Numerous studies represent pioneering efforts
in predicting production surfaces and in adapting them for economic in-
terpretations. The designs explained are not suggested as optimum for
the purposes, but are simply those which appeared to be appropriate at
the time a particular experiment was initiated or which were consistent
with the time and researchfunds available. Predictions for some of
these experiments, if designs such as those summarized in Chapter 5
might have been used, couldhave been improved. Subsequent research
has employedthese designs or modifications of them. Functionalforms
are not presented as those most appropriate under all environmental
conditions. Rather, they are usedto illustrate the types of relation-
ships and recommendations which result when particular forms of
y
vi PREFACE
functions are employed, or serve most efficiently under a given set of
conditions.
The studies of empirical production functions relating to crops,
livestock, andpoultry were possible only because of the scientific in-
terest, knowledge, and professional abilities of Damon V. Catron, John
T. Pesek, Stanley Balloun, and Norman L. Jacobson. Along with Gordon
C. Ashton, Roger Woodworth, Solomon Bloom, Vaughn C. Speer, John
A. Schnittker, William G. Brown, Robert McAlexander, Dean E. McKee,
Joseph Stritzel, John P. Doll, Gerald W. Dean, Harold O. Carter, C. C.
Culbertson, Owen W. McCarthy and R. P. Nicholson, these persons
should be considered as co-authors of this monograph. We have only
drawn together the numerous studies conducted by these persons, add-
ing a few chapters of interest to those conducting similar studies and
listing a collection of reading pertinent to agricultural production func-
tions. Accordingly, authorship of the persons named above is recog-
nized in the appropriate chapters and we should more properly be con-
sidered as editors of this monograph. Too, relative to the array of
farm-firm production function estimates presented in the final chapter,
we are grateful to Takashi Takayama, K. S. Suryanarayana, W.
Darcovich, T. Godsell, G. D. Agrawal, Y. Wang, George Mason, and
especially, Lennart Hjelm, Eje Sandqvist, and Yair Mundlak, for sup-
plementary information willingly given.
The authors hope that this text will serve to stimulate more and
improved research in agricultural production functions. Too, we hope
that it serves as foundation for further co-operative effort among per-
sonnel of biological, physical, and economic sciences. The concepts,
principles, and quantities presented are those relevant bothfor greater
scientific knowledge and more efficient and practical use of certain ag-
ricultural research.
In drawing together the set of studies conducted at Iowa State Uni-
versity, we do not depreciate or overlookthose which have been com-
pleted or are underway at other research organizations and institu-
tions. Time, space, and publication costs posed restraints which could
not be eliminated at the time of preparingthis monograph.
Earl O. Heady
John L. Dillon
May, 1960
Contents
1. Development of Production Function Studies 1
2. Economic Applications 31
3. Forms of Production Functions 73
4. Data Analysis for Production Function Estimation • . 108
5. Data Collection for Production Function Estimation 142
6. Economic Specification of the Production Function 195
7. Miscellaneous Empirical Problems Relating to
Estimation of Production Functions 218
8. Pork Production Functions for Hogs Fed in Drylot 266
9. Pork Production Functions and Substitution Coefficients
for Hogs on Pasture 302
10. Production Functions, Least-cost Rations, and Optimum
and Optimum Marketing Weights for Broilers 330
11. Least-cost Rations and Optimum Marketing Weights
for Turkeys 374
12. Milk Production Functions and Marginal Rates
of Substitution Between Forage and Grain 404
13. Production Functions and Substitution Coefficients
for Beef 452
14. Crop Response Surfaces and Economic Optima
in Fertilizer Use 475
vii
viii CONTENTS
15. Surfaces, Isoquants, and Isoclines From Fertilization 526
16. Functions for Fixed Plants and Other Farm Situations 554
17. Comparison of Production Function Estimates
From Farm Samples Over the World 585
Bibliography 645
Index 665
CHAPTER
1
Development of Production
Function Studies
T
HIS BOOK deals with agricultural productionfunctions. Its pur-
pose is to summarize certainconcepts, empirical methods, and
quantitative researches which relate to or have been derivedfor
farm production functions. It covers both physical production functions
based on experiments with crops and livestock andfirm production
functions based on cross-sectional or time series samples. In particu-
lar, it emphasizes research completed in these areas at Iowa State
University.
USE OF PRODUCTION FUNCTION CONCEPTS
The production function is a concept in physical andbiological sci-
ence. However, it was largely developed and, until recently, used
mainly by economists. Historically, refinements in concepts relating
to production functions grew out of economics probably because ofthe
following reasons. (1) The nature of production functions is important
in economic development and in determiningthe extent to which national
products can be increased from given resource stocks. (2) The magni-
tude of production coefficients serve as the base for determining opti-
mum patterns of international or interregional trade. (3) The concept
is basic to certaintheories inthe functional distribution of income.
The conditions under which a total output can be imputedto the factors
from which it is produced with the product just exhausted depends on
the nature of the productionfunction. (4) The productionfunction pro-
vides half or one of two general categories of the data needed in deter-
mining or^specifyingthe use of resources and the pattern of outputs
which maximize firm profits. (5) The algebraic nature of supply func-
tions rests, in large part, upon the nature of the productionfunction.
Research workers in the physical andbiological sciences of land-
grant colleges andthe United States Department of Agriculture have
long conducted research providing information onthe nature of agricul-
tural production functions. However, historically, this research was
designed and conducted somewhat apart from the formal concept of
production functions represented by regression equations. More typi-
cally, research was designed onthe basis of discrete phenomena
1
2 DEVELOPMENT OF STUDIES
whereintwo or afewtreatments were usedto provide point estimates
of crop or livestock output resulting from input of factors (materials
representingtreatments) In some instances, although not designedfor
.
these purposes, the data were sufficient for deriving simple regression
equations or input-output curves. More frequently, the experimental
designs and statistical procedures used have only allowed indication of
whether mathematically significant differences exist between the yield
or output level of two or three discrete treatments or input levels.
From these differences couldbe computedthe relative profitability of
the fewtreatments or inputs. However, it was generally impossible to
apply refined economic principles in determining the most profitable
level of output and input, or the most profitable combination of inputs
for a specified output.
These designs andapproaches have proved useful inthe past and
may continue to do so under certain conditions. In many cases, re-
search workers in biological fields have been concernedonly with esti-
matingthe output from a specific quantity of new material which serves
as an innovation. Here the goal of the research oftenhas been to
answer the question: Does the material or resource, used at any level
whatsoever, give a response? Much early research onfertilizer fell
inthis framework. In some cases, the practice or treatment under
consideration represents a resource or material of discrete and limi-
tational nature. Artificial insemination is an example. Here there is
no important question of “dosage” and aformal production function ap-
proach is inappropriate. For other materials used in production, the
phenomena under consideration could have been estimated as a con-
tinuous function, but there was little needto so represent it. For ex-
ample, fertilizer rates recommendedto farmers, based on afewpoint
estimates, have not always been as high as those which would maximize
profits in the classical sense of afarm operating with unlimited capital
under static conditions. However, because farmers operate in a
decision-makingframework of uncertainty and limitedfunds, they often
have failedto use fertilizer inputs even as large as those recommended
onthe basis of trials which include only afew discrete treatment levels.
Afinal reason might be given to justify experiments designed to give
point estimates ofyield or outputfrom a few discrete input levels: the
results provide points similar to the “straight line” segments assumed
in linear programming. The optima selected withinthis framework of
assumedphysical relationships always fall “on the corners,” repre-
sented by the point estimates. However, refinements allowing optima
to fall betweenthese “corners” may not be important where price un-
certainty is so great thatex poste accuracy in decisions can never be
attained.
There are many biological and physical areas, however, where con-
tinuous relationships are involved andthe data lendthemselves to for-
mal productionfunction analysis. Also, in many of these areas, recom-
mendations to farmers could be made with greater economic meaning
if
the experimental design and statistical analysis were of a form to allow
DEVELOPMENT OF STUDIES 3
prediction of the production functions involved. Inthe past, these pro-
cedures were not often used for several reasons. (1) The scientists
conductingthe research often have used criteria other than economics
in interpretingtheir findings and in making recommendations to
farmers. Inthe past, for example, the criteria used oftenhave been
rations which gave (a) the largest gain per pound of feed, (b) the great-
est output per cow or hen, or (c) the fastest daily gain. The most prof-
itable output or resource input is seldom identical with these maxima
or minima. However, even where the objective is prediction of a phys-
ical maximum or minimum, the exact quantity can be estimated more
accurately where the data, if of appropriate nature, are usedto esti-
mate the regression equations representing the productionfunctions in-
volved. Derivatives then can be computed and equated to zero, with the
appropriate magnitude of input then derived. (2) The statistical
methods serving as a guide for research were based on early biological
procedures which supposedthe datato be discrete phenomena most ap-
propriate for point estimates. Early texts on experimental design and
statistical analysis emphasizedthese methods as appropriate for ex-
periments in biological sciences. (Early emphasis on continuous rela-
tionships and regression analysis, as characteristic of physical data
representative of production functions, was made especially by econo-
metricians.) (3) Many physical scientists have not been acquainted
with productionfunction concepts andthe economic principles which
define profit maximization or cost minimization. Since they were par-
ticularly concerned with conditions of profit maximization and compet-
ing economic alternatives within the farm or firm, economists have
been concernedwith marginal products, marginal rates of substitution,
isoquants, and isoclines; quantities which are derivedfrom continuous
productionfunctions.
Inthe past decade, however, an increasing number of physical and
biological scientists in agriculture have become acquaintedwith pro-
duction function concepts. They have'become interested in interpreting
basic relationships of nature accordingly and in using them to make
recommendations to farmers. This increased interest and activity
partly grows out of scientific advance and is parallel to that inthe field
of agricultural economics. Generally, newfields of research start with
a less formal and precise set of concepts and models. Over the dec-
ades, continuous scientific investigation and thought provide refine-
ment to the theories, concepts, and models which serve as the basis of
designs in experiments and of principles in decision making. Pioneer
agricultural economists, like other agricultural scientists, also were
concerned with physical relationships which relate to productionfunc-
tions. Without a well-defined set of concepts, they derived principles
termed “factors affectingfarm profits.” The “factors affectingfarm
profits” principles implicitly supposed certain conditions in respect to
physical production functions. Generally, these early findings in agri-
cultural economics served sufficiently in leading farmers to improve
their farming operations. But these less formal principles also have,
4 DEVELOPMENT OF STUDIES
withthe advent of time and improvedknowledge by bothfarmers and
research workers, been replaced by more exact principles of profit
maximization; principles which directly require knowledge of the rele-
vant production and price quantities. Given recognition ofthese princi-
ples, both physical scientists and economists will have greater future
interest in quantities derivedfrom production functions. While the re-
lationships represented by production functions are physical phenom-
ena, economic principle is involved when recommendations to farmers,
or decisions by them, relate to the quantity or mix of resources and
products to be used and produced respectively. Accordingly, more co-
operative research and educational activities can be expected among
economists, agronomists, engineers, and animal scientists.
NEED FOR PRODUCTION FUNCTION RESEARCH
This text emphasizes production function estimates of the two fol-
lowingtypes: (a) biological functions derivedfrom experiments where
the plant is fixed at the magnitude of an animal or acre and (b) farm pro-
duction functions derived from samples where plant size, as measured
by “fixity” of a particular resource, is either fixed or variable. Per-
haps the most appropriate use of biologicalfunctions is that of guiding
farmers intheir individual decisions. However, these same data can be
of extreme use for certain purposes of policy and economic develop-
ment. For example, a nation such as India may have limitedfacilities
for producing or purchasing fertilizer materials. With a given amount
of fertilizer for annual allocationto agriculture, how much shouldbe
distributedto various soil, geographic, and climatic areas? If the goal
is to maximize the food product available from limitedfertilizer re-
sources, productionfunctions derivedfor major regions and crops, with
an indication of marginal coefficients, can provide a basis or guide for
attainingthe goal. Similarly, the same type of information can be used
during wartime or during any other emergency period when material
shortages exist. On the other hand, farm production functions of the
type discussed in this text probably best serve for the diagnostic pur-
poses pointedout later. Inthis vein, they can provide general guidance
for farmers’ decisions, credit policy formulation, readjustment of agri-
cultural regions, etc. However, aside from studies based on highly re-
fined samples, such as some mentioned in later chapters, they seldom
can be usedto indicate “exact equilibrium use” of resources by an in-
dividual farmer.
With the passage of time, a greater knowledge level of farmers, and
an increased commercialization of agriculture, there is increased need
for experimental designs and research in biological fields which lend
themselves to estimation of productionfunctions. Data can then be
better adaptedfor economic interpretations and recommendations. An
increasing number of farmers has knowledge of principles of profit
maximization and wishto use fertilizer, feed, and similar resources in