Production function

1. PRODUCTION
FUNCTION
By: Ibteshan Anam
Course: MBA (General)
Roll. No. : 22L9MBA33103
Subject: Managerial Economics

2. Concept
◦ 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.

3. ◦ 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.

4. Types of Production Function
Short Run
◦ 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/constant.
Long Run
◦ 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.

5. Total Product, Marginal Product, Average
Product
& Relationship Among Them
◦ Total Product (TP) refers to the total amount of goods and services produced in a
given period of time within a given input. = AP*L, Summation of MP
◦ Marginal Product (MP) is the quantity of total goods and services when an additional
unit of the variable factor is used. = change in TP/ change in labour
◦ Average Product ( AP) refers to the total product per unit of variable factors or
input. = TP/Labour
The relationship between TP and MP is explained through the Law of Variable Proportions.
As long as the the TP increases at an increasing rate, the MP also increases. This goes on till MP
reaches maximum. When TP increases at a diminishing rate, MP declines.

6. Law of Variable Proportions
◦ The Law of Variable Proportions, often known as the Law of Returns to a Factor.
◦ It states that increasing the quantity of one element of production while keeping all other variables
variables constant causes the marginal product of that factor to decrease.
◦ The Law of Variable Proportions is concerned with how the output varies when the number of units of a
units of a variable component is increased. As a result, it relates to the effect of altering the factor ratio on
factor ratio on output.
◦ The rule depicts the short-term relationship between the units of a variable element and the amount of
amount of output. This assumes that all other variables remain constant. This is also known as the return
as the return to a variable factor relationship.
◦ This rule illustrates short-run production functions in which one element fluctuates while the rest remains
rest remains constant.

7. Law of Variable Proportion: Assumptions
◦ A constant state of technology
◦ Variable Factor Proportions
◦ Homogeneous factor units
◦ Brief Run

8. Law of Variable Proportion: Stages
◦ The Law of Variable Proportions is divided into three stages, which are explained below-
Stage 1 (Stage of Increasing/Growing Returns):-
The first stage occurs when the overall product grows at an increasing pace. This occurs because the
efficiency of the fixed elements rises as the product's variable inputs grow.
◦ The TPP expands at an increasing rate, as does the MPP. The MPP grows as the variable factor’s units
increase.
2. Stage 2 (Stage of Diminishing Returns):-
The second stage occurs when the total product rises at a decreasing pace until it reaches its maximum
value.
◦ The TPP continues to grow, although at a slower pace. The growth, though, is positive. Furthermore,
as the number of units of the variable component increases, so does the MPP.
◦ The marginal and average products are both positive, but they are rapidly declining.

9. Stage 3 (Stage of Negative Returns):-
The third stage occurs when the overall product drops and
and the marginal product becomes negative.
◦ The TPP now begins to decline, and the MPP drops and
becomes negative. As a result, it is known as the "stage
of negative returns."
The point of inflection or inflection point is a point in which the concavity of
the function changes.

10. Significance of three stages
Stage I
A producer does not operate in
Stage I. In this stage, the
marginal product increases with
an increase in the variable
factor.
Stage II
This stage is the most relevant
stage of operation for a
producer
Stage III
Producers do not like to operate
in Stage III either. In this stage,
there is a decline in total product
and the
marginal product becomes
negative.

11. Law of Returns to Scale
◦ In the long run all factors of production are variable. No factor is fixed. Accordingly, the scale of
production can be changed by changing the quantity of all factors of production.
Definition:
◦ “The term returns to scale refers to the changes in output as all factors change by the same
proportion.”
◦ If there are only two inputs, labor L and capital K, we write the equation as Q = F(L,K).
Assumptions
◦ All the factors of production (such as land, labor, and capital) but organization are variable
◦ The law assumes a constant technological state. It means that there is no change in technology
during the time considered.
◦ The market is perfectly competitive.
◦ Outputs or returns are measured in physical terms.

12. Categories of Return to Scale
1. Increasing Returns to Scale:
The proportional change in the output of an organization is greater than the proportional change
in inputs, the production is said to reflect increasing returns to scale.
For example, to produce a particular product, if the quantity of inputs is doubled and the
increase in output is more than double, it is said to be an increasing returns to scale.
When there is an increase in the scale of production, the average cost per unit produced is lower.
This is because at this stage an organization enjoys high economies of scale.
→A movement from a to b indicates that the amount of
input is doubled.
Now, the combination of inputs has reached to 2K+2L
from 1K+1L. However, the output has Increased from
10 to 25 (150% increase), which is more than double,
which is greater than change in input.

13. 2. Constant Returns to Scale:
The production is said to generate constant returns to scale when the proportionate change in
input is equal to the proportionate change in output.
◦ For example, when inputs are doubled, so output should also be doubled, then it is a case of
constant returns to scale.
→When there is a movement from a to b,
it indicates that input is doubled. Now,
when the combination of inputs has
reached to 2K+2L from IK+IL, then the
output has increased from 10 to 20,
which is equal to the change in
input.

14. 3. Diminishing Returns to Scale:
Diminishing returns to scale refers to a situation when the proportionate change in output is less
than the proportionate change in input.
For example, when capital and labor is doubled but the output generated is less than doubled,
the returns to scale would be termed as diminishing returns to scale.
→when the combination of labor and capital
moves from point a to point b, it indicates that
input is doubled. At point a, the combination
of input is 1k+1L and at point b, the combination
becomes 2K+2L.
However, the output has increased from 10 to
18, which is less than change in the
amount of input.

16. Thankyou