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1. DEPARTMENT OF AGRONOMY
AN ASSIGNMENT ON Crop Response Production Functions
SUBMITTED TO: - DR. M.L.
Kewat sir
(DEPARTMENT OF AGRONOMY)
SUBMITTED BY:- MAHENDRA
ANJNA
ENROLLMENT NO: 170111010
CLASS: - M.SC. (Ag.) PREVIOUS
YEAR
DEPARTMENT OF AGRONOMY

2. Crop response production
functions
1. The work of agronomists and other production
oriented scientists is frequently directed at the goal
of establishing the level of input necessary to
achieve maximum yield per ha. This particular
goal is implicit in all efforts intended to ensure that
resource (input) does not become limiting.
2. Another measure of desirability frequently
encountered in the literature is that of maximum
input use efficiency. Maximum input use efficiency
is said to exist when the crop yield per unit of
input is maximized.

3. A production function or total physical product curve in which yield (Y)
is a function of the amount of input (I), with all other variables held
constant, can be defined as follow:
Y= f(i) …………………………………………… 1
Two related concepts can be introduced. The average physical product
(APP) which is simply output divided by input, can be written as
APP = Y/I …………………………………………….2
The marginal physical product (MPP) is defined as the change in yield
or output associated with the addition of one or more units of input. It
can be written as
MPP = dY /dI ………………………………………..3
Economic analysis, on other hand, defines the most efficient level of resource
use in terms of value. The efficient use of land, water and other resources
depends upon their value in a given activity relative to their value in achieving
other purposes. Economically, efficient input use requires that the farmer
apply input so long as the additional revenue generated exceeds the additional
cost of that input.

4. The scientific literature on production functions fits more or less into three
classifications: (1) early related studies,
(2) physiological approaches ,
(3) semi empirical approaches.
We are restricting to crop water production functions.
Early related studies:-
Since the beginning of the twentieth century, researchers have been studying
the relationship between crop yield and water use.
De Wit (1958) analyzed the findings of the early investigations in an effort to
further identify the factors that determine transpiration and yield under field
conditions. He concluded that the relationship between dry matter yield (Y)
and transpiration (T) for arid and semiarid regions of the world was linear
with the following form:
Y = m (T/E0) ……………………………………………………..(5)
A review of Agronomic and Physiological
Production Functions:-

5. Where, m is a coefficient accounting for such factors as crop (and variety of
crop), availability of water and weather conditions not accounted for by E0.
He also concluded that this relationship was equally valid for container and
field grown crops. For humid regions, he suggested that Y = nT.
Physiological approaches:-
Plant responses are the result of the complex interaction of many physiological
processes, each of which may be affected differently by water deficits. Hsiao et
al (1976) pointed out that what is known of water stress relationships in crops
was learned almost exclusively from empirical work from thousands of
irrigation trials conducted over many decades. They presented a simplified
diagram of the general effects of water stress on yield that makes evident the
multiplicity of interactions among water stress, growth, development, ontogenic
stages and yields. Begg and Turner (1976) classified the effects of water deficit
on crop growth and development into three main categories: morphological,
physiological and ontogenic effects on the sensitivity of crops at different
stages of development.

6. Semi empirical approaches:-
The semi empirical approaches are usually characterized by efforts to
relate crop yield to either (1) soil moisture content or moisture
tension, (2) transpiration or evapo- transpiration, or (3)
applied irrigation water.
1. Crop yield as a function of evapo-transpiration:-
Stewart et al (1977) reported generalized production function based on
findings from three experiments in which corn, sorghum, beans and
alfalfa were grown over a number of years.
2. Crop yield as a function of applied water:-
Stewart and Hagan (1973) suggested that although ET is the field
level water parameter associated most directly with yield, the depth
of irrigation water applied (IRR) represents water purchased and is
most concern to planners and irrigators.

7. There exists evidence that the form of the yield v/s IRR function is
convex in contrast with the straight line form of the yield v/s ET
function. For example, Howe and Rhoades (1955) examined 13
irrigation treatments on corn in a very fine sandy loam soil and found
a sigmoidal relationship between dry matter production and applied
water. Stewart and Hagen (1973) showed that the functional relation
between yield and the seasonal irrigation depth of the field water
supply (which includes rainfall and available soil moisture at
planting) is convex (a second degree polynomial).
3. Growth stage effects:-
Jensen (1968) developed a production function which divided the
growing season into stages, with ET in each stage having a unique
effect on yield. The function expresses relative yield (actual yield
divided by potential yield, (Ya/Ymax) as a function of relative ET
(actual ET divided by ET when soil moisture is non limiting)

8. References:-
Gardner BL & Rausser GC.2001.Handbook of Agriculture Economics.Vol.1.
Agricultural Production. Elsevier.
Beattie BR & Taylor CR, 1985.The Economics of Production. John Wiley & Sons.
http://agropedia.iitk.ac.in/content/
http://www.fao.org/docrep/016/i2800e/
http://www.ccsenet.org/journal/index.php/jas/article/viewFile/22777/15487
http://www.ccsenet.org/journal/index.php/jas/article/viewFile/56697/31040