The document discusses production functions and their key components. It defines a production function as explaining the quantitative relationship between inputs and outputs in production. There are four main components: inputs, outputs, short-run production functions where one input is variable, and long-run production functions where all inputs are variable. The document also discusses concepts like total product, marginal product, average product, the law of diminishing returns, and returns to scale.

1. Production Function
Dr. S. Ramakrishna Chary
MGIT

2. What is Production?
 Production is a crucial economic activity because it improves the utility of a
product by transforming it into the form required by the consumer. Leather, for
example, is less commonly utilized in its raw state until it is converted into
attractive products such as shoes, bags, and other accessories. To an
economist, production refers to any process that transforms one or more
commodities into another. The link between a firm’s outputs and inputs is the
production function. Production refers to the transformation of inputs into
outputs. The rate at which output changes when all inputs are adjusted
simultaneously is referred to as returns to scale. Returns to scale is a metric
that evaluates the change in productivity after increasing all production inputs
over time.

3. What is Production Function?
 Production function is a concept in economics that explains the
relationship between physical output and input. Output refers to
the number of goods or services produced in a given time period.
Input, on the other hand, is the number of resources or materials
that are used to produce output. While production is simply the
process of creating goods and services for consumption,
production function is the concept explaining the quantitative
relationship between input and output. There are four main
components of the production function.

4. Importance of Production Function
 It refers to the relationship between the quantities of output of production and the input or
factors of production.
 It explains the amount of output that can be produced according to the quantity of input.
 Four main factors of production exist: land, labour, capital, and entrepreneurship.
 There are two types of factors of production: Fixed factors and Variable factors.
 Fixed factors refer to those aspects of production that remain the same regardless of changes
in the output.
 Variable factors are those that may change as output changes.
 The formula for production function is Q= f(K, L), where Q is the output, f refers to function, K
is the capital and L stands for labour.
 There are two kinds of production functions: Long Run and Short Run Production Function.

5. Types of Production Function
Short Run Production Function and Long Run Production Function are two types of
production function.
 Short run production function is the relationship between the
specific variable input and quantity of output.
 In the short run production function, only one factor is variable,
while others remain fixed.
 Long run production function explains the relationship between
all inputs and the quantity of output.
 In the long run production function, all factors of production, or
inputs are variable.

6. Total Product, Marginal Product, Average Product
 Total Product refers to the total amount of goods and services produced in a given period of time within a given input.
 Marginal Product is the quantity of total goods and services when an additional unit of the variable factor is used.
 Average Product refers to the total product per unit of variable factors or input.
 The relationship between total product and marginal product is:
1. An increase in total product at an increasing rate results in an increase in marginal product.
2. The increase of total product at a diminishing rate causes the marginal product to decrease.
3. Finally, as the total product begins to decrease, the marginal product falls and becomes negative.
 The relationship between average product and marginal product can be explained as:
1. When the average product is greater than the marginal product, the average product increases.
2. As the marginal product becomes more than the average product, the average product decreases.
3. As both marginal and average product fall, the marginal product falls at a greater rate and eventually becomes negative, while
average product remains positive.

7. The Law of Variable Proportions or the law of diminishing returns
 The Law of Variable Proportions states that as the quantity of only one input
increases, the total product first rises at an increasing rate, then at a decreasing rate,
finally the total output ends up falling.
 Total product refers to the total amount of goods and services produced within the
given input in a specific period of time.
 The Law has some assumptions:
1. Only one input will be variable, others are fixed.
2. It operates on the short run production function.
3. The condition of technology is given and is fixed.
4. The price of input or factors of production are fixed.
5. The proportion of variable factor units can be changed.

9. There are three Stages of this law:
1. Increasing Returns: In this phase, the increase in one input leads to increase in the
quantity of output at an increasing rate until it reaches its highest point. This phase
sees an increase in both the total product and the marginal product.
2. Diminishing Returns: This stage is when the quantity of output increases but at a
decreasing or diminishing rate. In the second phase, the total product increases
but the marginal product starts decreasing but is positive.
3. Negative Returns: In this phase, the output begins to decrease at a diminishing
rate. Here, both total product and marginal product decrease. The marginal
product becomes negative.

10. There are several reasons for the law of variable
proportions, three of which are:
1. Increasing Returns: It states that a better utilisation of factors leads to an increase in the
efficiency of these factors and thus increases overall output.
2. Diminishing Returns: This happens as the combination of factors becomes less optimum
and because the variable and fixed factors become imperfect substitutes of one
another.
3. Negative Returns: This happens as the efficiency of both negative and fixed factors falls
and the quantity of fixed factors begins to decrease or fall.

11. The law of Return to Scale in Production
Functions
 Changes in output when all factors change in the same proportion are referred
to as the law of return to scale. This law applies only in the long run when no
factor is fixed, and all factors are increased in the same proportion to boost
production.
 There are three stages in all.
• Increasing the scale’s return
• Constant scale returns
• Decrease in Returns on the scale

12. Unit of
Labour
Unit of capital % increase in
labour and
capital
Total
production
% increase in
TP
Stages
1 3 – 10 – increasing
2 6 100% 30 200%
3 9 50% 60 100%
4 12 33% 80 33% constant
5 15 25% 100 25%
6 18 20% 110 10% diminishing
7 21 16.6% 120 8.3%

14. Increasing returns to scale
It describes a condition in which all of the factors of production are raised, resulting in a higher rate of
output. For example, if inputs are raised by 10%, the output will be increased by 20%.
Reasons
• Due to the economy of scale
• Specialization through better division of labor
Constant returns to scale
It describes a condition in which all of the factors of production are increased at the same time, resulting in
a steady growth in output. For example, if inputs are raised by 10%, the output is also increased by 10%.
Reasons
As the firm’s production grows, it reaches a point where all of the economy’s resources have been fully
utilized, and output equals input.
Diminishing returns to scale
When all of the production factors are increased simultaneously, output grows at a slower rate. For
example, if inputs are raised by 10%, the output will be increased by 5%.
Reasons
•The major cause of diminishing returns to scale is large-scale economies, diseconomies of scale occur
when a company has grown to such a size that it is difficult to manage
•Lack of coordination

15. Assumptions of Return to scale
The following are the returns to scale assumptions: Capital and labor are the only two variables of
production used by the company. In a fixed proportion, labor and capital are integrated. Factor
prices do not fluctuate, and the State of technology remains the same.
Difference between return to scale and return to a factor
•Return to factor has only one variable while the rest of the factors remain constant, whereas
return to scale has all of the variables changing
•In return for factor, the factor proportion changes as more and more variable factor units raise
production
•In return to scale, the factor proportion remains constant when factors are re-added in the same
proportion to increase output
•When you return to a factor, you get a negative return. Returning to scale has the effect of
decreasing returns
•Return to scale is a long-term phenomenon, whereas return to a factor is a one-time event