The document discusses production functions and the law of variable proportions. It defines production functions as relationships between inputs and outputs. Specifically, it discusses Cobb-Douglas production functions, which take the form of a power equation relating capital and labor to output. Isoquants and isocosts are also introduced as showing equal levels of output and cost from different input combinations. The law of variable proportions is summarized as explaining how adding more of a variable input initially increases then decreases marginal returns in the short run when one input is fixed.

2. According to the Parkinson:
“Production is the organized activity of transformation
resources into finished products in the form of goods and
services”.
Mechanical or chemical steps used to create an object, usually
repeated to create multiple units of the same item. Generally
involves the use of raw materials, machinery and manpower to
create a product.

4. Production function expresses a functional or technical
relationship between physical inputs and physical outputs
of a firm at any particular time period.
The output is thus a function of inputs
The factors used for production are called “inputs”.
The production we get is called “output”
Definition for Production function:
“The production function is the name given to the
relationship between the rates of productive services and
the rates of output of the product.”
------ Stigler

5. Definition for Production function:
“Production function is that function which defines the
maximum amount of output that can be produced with a
given set of inputs”.
--- Michael R Baye.

6. It can be expressed in an allegorical equation:
Where
Q stands for the quantity of output
a, b, c, d…..n are the various inputs.
Production function has to be expressed in a precise
mathematical equation i.e.
It is showing the there is constant relationship
between application of input (x) and the amount of
output(Y).
 )...........,,,( ndcbaQ
bxaY 

9. Production function is invented by Jnut Wicksell and first tested
by C.W. Cobb and P.H. Douglas in 1928.
This famous statistical production function is known as Cobb-
Dougles production function.
American manufacturing industry.
Cobb-Dougles production function takes the following
mathematical form
Where,
Y= Output
K= Capital
L= Labour
A, α = Positive Constant
)( 1  
 LKAY

10. Assumptions:
It assumes that output is the function of two factors,
i.e. capital and labour
There are constant returns to scale
All inputs are homogenous
There is perfect competition
There is no change in technology
Criticism:
Cobb-Douglas production function is criticized because it shows
constant returns to scale. But constant returns to scale are not actuality.
Industry is either subject to increasing returns or diminishing returns.
No entrepreneur will like to increase the inputs in order to have
constant returns only. His aim will be to get increasing returns and not
constant returns

11. PRODUCTION FUNCTION
SHORT RUN
ONE
VARIABLE
TWO
VARIABLE
LONGRUN

12. “Iso” means equal
“Quants” means quantity.
It means the quantities throughout a given iso quant
are equal. Isoquants are also called iso product curves.
 ),( KLQ
This function has three variables
Q= output of commodity,
L= Labour and
K=Capital.

13. Q=2 Q=5 Q=9 Q=12 Q=14
K L K L K L K L K L
1 20 2 20 3 20 4 20 5 20
2 12 3 12 4 12 5 12 6 12
3 8 4 8 5 8 6 8 7 8
4 6 5 6 6 6 7 6 8 6
5 4 6 4 7 4 8 4 9 4
6 3 7 3 8 3 9 3 10 3

14. Features of Isoquants:
Downwards Slopping
Convex to Origin
Do not intersect
Do not touch axes
Types of Isoquants
Depending upon the degrees of substitutability of inputs, there
are four types of Iso-quants.
Linear Isoquants
Input-Output Isoquants
Kinked Isoquants
Smooth Isoquants

15. Linear Isoquants:
It represents perfect substitutability
of factors of production.
Input-Output Isoquants
zero substitutability
Kinked Isoquants
If the factors of production show
limited substitutability
Smooth Isoquants
continuous substitutability of
factors of production

16. Iso costs refers to that cost curve that represents the
combination of inputs that will cost the producer the same
amount of money.
In other words, each iso cost denotes a particular level of
total cost for a given level of production.
If the given level of production changes, the total cost
changes and thus the iso cost curve moves upwards. And
vice versa.

17. The marginal rate of technical substitution refers to the
rate at which one input factor is substituted with other
to attain a given level of output
Combina
tions
Inputs Units
MRTS
K L
A 1 20 -
B 2 15 5:1
C 3 11 4:1
D 4 8 3:1
E 5 6 2:1
F 6 5 1:1

18. The iso costs curve indicates the alternative combinations
of various factors of production which can produce a given
output. Of these, an entrepreneur would like to choose the
combination of input factors, which costs him the least
Combi
nations
Inputs Units Cost
Rs.K(Rs.9) L (Rs.9)
1 3 20 3*9 + 20*6=147
2 4 13 4*9 + 13*6=105
3 5 10 5*9 + 10*6=105
4 6 8 6*9 + 8*6=102
5 7 6 7*9 + 6 * 6=99
6 8 5 8*9 + 5* 6=102

19. PRODUCTION FUNCTION
SHORT RUN
ONE
VARIABLE
TWO
VARIABLE
LONGRUN

20. Law of variable proportion/ Law of diminishing
returns/ law of returns
The law of variable proportion explains the input- output relation,
the change in output due to addition of one variable input.
This is a short run phenomenon.
The short run is a period in which at least one input is fixed.
Thus in the short-run, the increase in production is possible only
by increasing the variable inputs
The law also brings diminishing tendency in production is also
known as the law of diminishing returns

21. Law of variable proportion/ Law of diminishing
returns/ law of returns
Labour TP AP MP Stages
0 0 0 0 Stage
I1 10 10 10
2 22 11 12
3 33 11 11 Stage
II4 40 10 7
5 45 9 5
6 48 8 3
7 48 6.85 0 Stage
III8 45 5.62 –3

22. Law of variable proportion/ Law of diminishing
returns/ law of returns
Labour TP AP MP Stages
0 0 0 0 Stage
I1 10 10 10
2 22 11 12
3 33 11 11 Stage
II4 40 10 7
5 45 9 5
6 48 8 3
7 48 6.85 0 Stage
III8 45 5.62 –3

23. Assumptions:
The production technology remains unchanged
Homogeneous Variable Factors
At least One Input is Fixed
The fixed Factor is indivisible
Cause For Operation of the Law of Diminishing Returns
Wrong Combinations of inputs will give Diminishing returns
Scarcity of Certain factors like land and capital in the short
run will give diminishing marginal productivity of the variable
factor
Imperfect substitutes also give diminishing returns