Agricultural production function

1. Lecture 2
Meaning of agricultural production function
Types of production function
Implicit and explicit production function
Continuous and discontinuous production function

2. Agricultural Production Function
 An agricultural production function can be written as
Y=f (x1,x2,x3…xn; xn+1…xm;xm+1,xm+2…….xl)
Here y is the quantity of output and xi are the quantities of input
This only indicates the existence of some mathematical function
or relation between output and input. This concept of
production function is perfectly general. A specific production
function may be represented by only a single point, a single
Continuous or discontinuous or by system of equations

3. Classification
 Decision variables
 Predetermined variables
 Uncertain variables

4. Decision variable
 The decision variables are X1,X2,X3…..xn inputs whose
respective levels or quantities x2,x2,x3,x4….xn are under the
control of decision maker, the bulk of research involves only
this subset of variables. Some inputs may be variable while
others may be fixed during planning period under
consideration.

5. Predetermined variable
 The quantities of input variables xn+1, Xn+2…xm constitute a
subset of such variables the levels xn+1…xm of these inputs
are known to the decision maker at the time of decision
making .thus the decision maker can only make use of the
information about their levels without his ability to control
their levels.

6. Uncertain variables
 The third set of variables is of uncertain variables. these
represented by Xm+1,Xm+2……Xl and their corresponding
quantities by xm+1,xm+2…..xl. their levels of these variables
are uncertain and thus unknown to the decision maker who is
thus unable to exercise any control on their use.

7.  Types of Production Functions:
1. Continuous Production Function: This is obtained for those
inputs which can be split up in to smaller units. All those
inputs which are measurable give raise to continuous
production function.
Example: Fertilizers, Seeds, Plant protection chemicals,
Manures, Feeds etc
2. Discontinuous or discrete Production Function: Such a
function is obtained for resources or work units which are
used or done in whole numbers. In other words, production
function is discrete, where inputs cannot be broken in to
smaller units. Alternately stated, discrete production is
obtained for those inputs which are counted.
Example: Ploughing, Weeding, Irrigation etc.,

8. 3.Short Run Production Function (SRPF): Production
Function in which some inputs or resources are fixed.
Y= f ( X1 / X2, X3,…………..,Xn)
Eg: Law of Diminishing returns or Law of variable proportions
4. Long Run Production Function (LRPF): Production
function which permits variation in all factors of production.
Y = f( (X1, X2 , X3, ……………., Xn)
Eg: Returns to scale.

9. The production function can be expressed in three ways:
1. Tabular form: Production function can be expressed in the
form of a table, where one column represents input, while
another indicates the corresponding total output of the
product. The two columns constitute production function.
Input
(x)
Output
(y)
0 2
10 5
20 11
30 18
40 25

10.  Graphical Form : The production function can also be
illustrated in the form of a graph; where horizontal axis (X
axis) represents input and the vertical axis (Y axis) represents
the output.

11.  3. Algebraic Form: Algebraically production function can be
expressed as Y= f(X)
 Where , Y represents dependent variable, output (yield of
crop, livestock enterprise) and X represents independent
variable, input (seeds, fertilizers, manure etc),
 f = denotes function of
 When more number of inputs is involved in the production of
a product, the equation is represented as Y=f(X1, X2, X3, X4
……… Xn)
 In case of single variable production function, only one
variable is allowed to vary, keeping others constant, can be
expressed as Y=f(X1 | X2, X3 ………. Xn)

12.  The vertical bar is used for separating the variable input from
the fixed input. The equation denotes that the output Y
depends upon the variable input X1, with all other inputs held
constant.
 If more than one variable input is varied and few others are
held constant, the relationship can be expressed as Y=f(X1, X2
| X3, X4 …….. Xn)
Production function can also be expressed as
Y=a+bx _____________ Linear production function.
 Where Y is dependent variable,
 a is constant, b is coefficient, X is independent variable

13.  The constant a represents the amount of product obtained
from the fixed factor if none of the variable input is applied,
while b is the amount of output produced for each unit of X
(input) applied.
 Y = aXb
Is an exponential equation and is known as Cobb-Douglas
production function.
 Y = a+bx±cx2 is quadratic equation

14. Production function depends on the following factors:
1.Quantities of inputs used
2. Technical knowledge of the producer.
3. Possible processes in production
4. Size of the firm
5. Nature of firm’s organization
6. Relative prices of factors of production.

15. Assumptions of production function
 The production function is defined only for non negative
values of inputs and outputs.(y≥0,xi≥0)
 Every possible combination of inputs is assumed to result in
maximum level of output .this means that the production
function presupposes technical efficiency
 The input output relationship or the production function is
single valued and continuous for which there exist first and
second order partial derivatives of output ,Y w.r.t each input
variables.
 The returns to scale are assumed to be decreasing.

16. Assumptions of production function
 The exact nature of the firm production is assumed to be
determined by a set of technical decisions taken by producer
 All parameters and determining the firms production function
do not change over the time period considered. besides these
parameters are not permitted to be random variables
 All the products and factors of production are perfectly
divisible