Agrawal Institute
Economics
Production Function
Production
It is a process of transformation of inputs into
outputs.
Production Function
It is a technical relationship between input and
outputs i.e.
Q = f (𝑰𝟏 , 𝑰𝟐 , 𝑰𝟑 ,…… 𝑰𝒏 )
Q = Output and I = Input
Inputs (Factors of Production)
Fixed Variable
Input Input
Fixed Inputs are
Variable Inputs are
those, the application
those, the application
of which does not
of which changes with
change with change
change in output.
in output.
Eg. Labour
Eg. Land
Types of Production Function
Very Short Run Production Function –
A period in which producer is unable to
change any factor of production (All factors are fixed)
Short Run Production Function –
A period in which output can be
changed by changing only one variable factor.
Long Run Production Function –
A period in which output can be
changed by changing all factors of production.
(No Fixed Factor)
Concept of Product
Product (Output) refers to the volume of goods
produced by a firm during a specified period of
time.
Total Product (TP) or Total Physical Product (TPP)
Average Product (AP)
Marginal Product (MP)
Note: - MP is the slope of TP
Fixed Factor Variable Factor TP AP MP Phase
(Land) (Labour)
1 0 0 0 0 Phase I
Increasing Returns to a Factor
1 1 5 5 5
1 2 14 7 9
1 3 24 8 10
1 4 28 7 4 Phase II
1 5 30 6 2 Diminishing Return to a Factor
1 6 30 5 0
1 7 28 4 -2 Phase III
Negative Return to a Factor
Concept of Product
Total Product (TP) – It refers the total quantity of goods
produced by a firm during a given period of time.
Average Product (AP) – It refers the amount of output
produced per unit of variable input.
𝑻𝑷
𝑨𝑷 =
𝒏
Marginal Product (MP) – It refers to change in total
product resulting from change in variable input.
∆𝑻𝑷
𝑴𝑷 = 𝒐𝒓 𝑴𝑷𝒏 = 𝑻𝑷𝒏 − 𝑻𝑷𝒏−𝟏
∆𝑵
Phases of Production
Phase I – TP increases at “Increasing Rate”
Or
MP increases
Phase II – TP increases at “Diminishing Rate”
Or
MP decreases (Positive)
Phase III – TP starts falling
Or
MP become negative
Relation between TP and MP
When MP increases then TP increases at
increasing rate.
When MP decreases (but remains positive) then
TP increases at diminishing rate.
When MP = 0 then TP is maximum
When MP becomes negative then TP falls
Relation between AP and MP
When MP > AP, then AP rises
When MP = AP, then AP is maximum
When MP < AP, then AP falls
Law of Returns to Factor (Law of Variable Proportions
Assumptions:
Only one input is variable i.e. labour.
All other factors are fixed.
All the units of variable factors are equally efficient.
Technique of production does not change.
It is possible to combine more and more units of variable
factors with the given units of fixed factors.
Law of Returns to Factor (Law of Variable Proportions
In terms of TP – This law states that TP first increases at
increasing rate, then increases at diminishing rate, reaches its
maximum and finally starts falling.
In terms of TP – This law states that MP first increases, then
decreases but remains positive and finally MP becomes negative.
Law of Returns to Factor (Law of Variable Proportions
Stage 1 (Increasing Returns to Factor)–
In this stage, TP increases at increasing rate, MP also
increases and reaches its maximum.
Reason –
• Optimum combination of inputs along with the full utilization of
fixed inputs.
• Division of labour through specialization.
Law of Returns to Factor (Law of Variable Proportions
Stage 2 (Diminishing Returns to Factor)–
In this stage TP increases at diminishing rate, reaches
its maximum. Every producer tries to operate in this stage. Also, in this
stage, MP falls but remains positive.
Reason –
• Efficiency starts declining when more variable inputs are
employed beyond the optimum capacity.
• Lack of perfect substitution between fixed inputs and variable
inputs.
Law of Returns to Factor (Law of Variable Proportions
Stage 3 (Negative Returns to Factor)–
In this stage, TP starts falling and MP becomes
negative.
Reason –
• Poor coordination between fixed and variable factors.
• Decrease in efficiency of variable factor.
Formulae
• TP = n × AP = ∑𝑴𝑷
• AP = TP ÷ n
∆𝑻𝑷
• 𝑴𝑷 = 𝒐𝒓 𝑴𝑷𝒏 = 𝑻𝑷𝒏 − 𝑻𝑷𝒏−𝟏
∆𝑵
n = Units of variable factor
1. Calculate Average Product (AP) and Marginal Product (MP):
Variable Factor (Units) 1 2 3 4 5 6
TP (Units) 8 16 24 29 29 25
2. Calculate Average Product (AP) and Marginal Product (MP):
Variable Factor (Units) 0 1 2 3 4 5 6 7
TP (Units) 0 3 8 12 15 17 17 16
3. Calculate TP and AP:
Variable Factor (Units) 1 2 3 4 5 6 7
MP (Units) 20 16 12 8 4 0 -4
5. Calculate TP and AP:
Variable Factor (Units) 1 2 3 4 5 6
MP (Units) 10 12 14 12 7 5
6. Calculate TP and MP:
Variable Factor (Units) 1 2 3 4 5
AP (Units) 50 45 40 35 30
7. Calculate TP and MP:
Variable Factor (Units) 1 2 3 4 5 6
AP (Units) 50 48 45 42 39 35
8. Find out the missing values:
Variable TP AP MP
Factor (Units) (Units) (Units) (Units)
0 …………. …………. ………….
1 …………. …………. 4
2 10 …………. ………….
3 …………. 6 ………….
4 24 …………. ………….
5 …………. 5 ………….
Example 5. Find out the missing values:
Variable TP AP MP
Factor (Units) (Units) (Units) (Units)
0 …………. …………. ………….
1 …………. 5 ………….
2 …………. …………. 8
3 …………. …………. 4
4 25 …………. ………….
5 …………. …………. 5
6 …………. …………. 0
7 …………. …………. -4
