The document discusses production analysis and key concepts including: 1. Production refers to the transformation of inputs into outputs using a given technology. A production function shows the relationship between inputs like labor, capital, and technology and the maximum output. 2. The law of diminishing returns explains that as one variable input is increased while others stay fixed, marginal and then average product will eventually diminish. 3. Returns to scale refer to how output changes proportionally with a proportional change in all inputs and can be increasing, constant, or decreasing.

1. Production Analysis
Meaning of Production:
The term“Production”means transformation of physical “inputs” into physical “outputs”.
The term “inputs” refers to all those things which are required by the firm to produce
a particular product.
The term “output” refers to finished products.
In the words of Prof J. R. Hicks, “Production means any activity whether physical or mental
which satisfy the wants of other people through exchange”.
Production Function
Meaning of Production Function:
A production function refers to the functional relationship, under the given
technology, between physical rates of input and output of a firm, per unit of time.
In other words, it shows for a given technology (technique) of production the output
that can be obtained from various levels of factor inputs, during a given period of time.
Since it relates inputs to outputs it is also called as, “Input-Output Relation”.
In algebraic terms the production function may be written as,
Q = f (a, b, c, d, ……….n, T)
Where Q=physical quantity of output per unit of time.
f =functional relationship.
a, b, c, d, n = quantities of various inputs per unit of time.
T = prevailing state of technology or know how
Types of Factor Inputs:
• Fixed factors
• Variable factors
This distinction holds good in the short run. In the long run all factors will become
variable in nature.

2. Types of Production Functions:
• Short run Production Function
• Long run Production function
Short run Production function
• In this case producers will keep all fixed factors as constant and change only a few variable
factor inputs. In short run we have two production functions:
A. Quantities of all the inputs both fixed and variable will be kept constant and only one
variable input will be varied.
Ex: The Law of Diminishing Returns.
B. In this case keeping all the inputs constant, only two variable factor inputs are varied.
Ex: Iso - Quants and Iso - Cost curves.
Long run Production Function
In this case producer will vary the quantities of all factor inputs in the same
proportion.
Ex: The Law of Returns to Scale.
The Law of Variable Proportions
(or)
The Law of Diminishing Returns
The Law of Variable Proportion explains how variation in one factor input leads to
variations in output, keeping the quantities of other factors fixed.
According to Prof. Benham, “As the proportion of one factor in a combination of
factors is increased, after a point, first the marginal and then the average product of that factor will
diminish”.
Assumptions of the Law
1) Only one factor unit is to be varied, while all other factors should be kept constant.

3. 2) Different units of variable factors are homogenous.
3) Techniques of production remain constant.
4) The law will hold good only for short and given period.
5) It is possible to vary the proportion in which the various inputs are considered.
Trends in Output
From the above table we can observe the we can observe the following tendencies in
TP, AP and MP:
1. Total output goes on increasing as long as MP is positive. It is the highest when MP is zero and
TP declines when MP becomes negative.
2. MP increases in the beginning, reaches highest point and then diminishes at the end.
3. AP will have the same tendencies as the MP. In the beginning MP will be higher than AP but at
the end AP will be higher than MP.

4. Explanation of diagrammatic representation
From the diagram it is clear that there are three stages:
I. First stage : The Law of Increasing Returns
II. Second stage : The Law of Diminishing Returns
III. Third stage : Negative Returns
Uses in Decision Making / Practical Importance
i. It helps to work out the more ideal combination of factor inputs or the least cost combination
of factor inputs.
ii. It is useful to a businessman in the short run production planning at the micro level.
iii. The law gives guidance, that by making continuous improvements in technology, the producer
can postpone the occurrence of diminishing returns.
Cobb-Douglas Production Function
This is more realistic in approach, as it consider two variable factor inputs at a time.
Q = f (L, k, )
Where L = Labour

5. K = Capital
= factor (fixed) component of input.
For empirical measurement, the Cobb-Douglas production function is presented with
power terms as : Q = aLK
Where Q = total output
L = Labour units – input
K = Capital units – input
• It is widely used in empirical research on production.
• In estimating regression of a Cobb-Douglas production function, it showed the transformation
into a linear form by using double log terms.
Log Q = log a + b log L + c log K
Iso-quants and iso-costs
There are a large number of combinations of factor inputs which can produce a given output
and the producer has to select the most economical combination out of them.
Iso quant curve is a technique developed in recent years to show the equilibrium of a
producer with two variable input.
Meaning and definitions:
The term ‘Isoquant’ consists of 2 words – ‘iso’ and ‘quant’. ‘Iso’ means ‘equal’ and ‘quant’
means ‘quantity’.
Therefore Isoquant curve means Iso-product curve or equal product curve or constant
product curve.
Iso-product curve may be defined as “ A curve which shows the different
combinations of two inputs producing the same level of output”.
• According to Prof. Keinstead, “ Iso-product
Curve represents all possible combinations of two factors that will give the same TP”.
The following table shows the various hypothetical combinations of 2 factor inputs-
labour and capital, which are capable of producing the same quantity of output –100 units of a
commodity.

6. Iso-Quant Map
• A catalogue of different combinations of inputs with different levels of output shown on a
graph is called as Iso-quant map or equal-product map.
• In other words, a number of isoquants representing different quantities of output are known
as Iso-quant map.

7. Diminishing Marginal Rate of Technical Substitution (DMRTS)
• The DMRTS measures the rate of reduction in one factor for an additional unit of another
factor in the combination, without affecting any change in the quantity of output .
Properties OfIso-Quants / Equal
Product Curves
1. The Iso-quant curves slope downwards from left to right – This is so because, if one factor is
increased, another factor must be reduced in order to produce the same quantity of output.
2. Iso-quant curves cant intersect each other – This is so because the amount of factors required
to produce 100 units of a commodity
cant be equal to the amount of factors required to produce 200 units of a commodity.
3. Iso-product curve lying to the right or higher level indicates the higher level of output and vice
versa.
4. The Iso-quant curves are convex to the point of origin . The convexity of the curve is due to the
DMRTS.
5. An Iso-product curve will not touch either X or Y axis.
Iso – cost Curves or Lines:

8. An Iso-cost line is a line which shows various combinations of two inputs that the firm can buy
at given prices with a given outlay. It shows two things:
1. Prices of two inputs
2. Total outlay of the firm.
• Factor X : Rs. 50/unit
• Factor Y : Rs. 40/unit
X Y
At Rs. 2000 50 40
At Rs. 3000 75 60
At Rs. 4000 100 80
Producers Equilibrium (Least cost combination of factors)
• The producing firm needs two instruments to find out the equilibrium position. They are:
1. Its Iso-quant map
2. Its Iso-cost line

9. An iso-product curve represents different possible combinations of two factor inputs with
the help of which a given level of output can be produced. On the other hand, an Iso-cost line
shows the total outlay of the producer and the prices of factors of production.
Laws of Returns to Scale
The Laws OF Returns To Scale
• The LRS explain the behavior of output in response to a proportional and simultaneous change
in inputs.
Three technical possibilities:
 Increasing returns to scale
Total output may increase more than proportionately.
 Constant returns to scale

10. Total output may increase proportionately
 Decreasing returns to scale.
Total output may increase less than proportionately .
1. Increasing Returns to Scale
When a certain proportionate increase in both the inputs K and L leads to more than
proportionate increase in output ,it exhibits increasing returns to scale
The causes of increasing returns to scale:
• Higher degree of specialization
Certain inputs cannot be divided into parts to suit small scale production.
• Technical and managerial indivisibilities
Use of specialized labour and modern machinery increases productivity for
variety of inputs.
• Dimensional relations

11. Length and Breadth
15*10=150 sqft
30*20=600 sqft
2. Constant Returns to Scale
When an increase in inputs results in proportionate increase in output , it is called constant
returns to scale.
3.Decreasing Returns to Scale
When a certain proportionate increase in inputs K and L leads to less than proportionate increase
in output ,it exhibits decreasing returns to scale.

12. • Causes:
 Decrease in managerial efficiency
 Exhaustibility of natural resources