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.

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

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.

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

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

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

PRODUCTION FUNCTION

SHORT RUN

ONE VARIABLE

TWO VARIABLE

LONGRUN

“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.

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

Features of Isoquants:

Downwards Slopping

Convex to Origin

Do not intersect

Do not touch axes

Types of IsoquantsDepending upon the degrees of substitutability of inputs, there are four types of Iso-quants.

Linear IsoquantsInput-Output IsoquantsKinked IsoquantsSmooth Isoquants

Linear Isoquants:It represents perfect substitutability of factors of production.

Input-Output Isoquantszero substitutability

Kinked IsoquantsIf the factors of production show limited substitutability

Smooth Isoquantscontinuous substitutability of factors of production

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.

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 UnitsMRTS

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

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

PRODUCTION FUNCTION

SHORT RUN

ONE VARIABLE

TWO VARIABLE

LONGRUN

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 inputsThe law also brings diminishing tendency in production is also

known as the law of diminishing returns

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

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

Assumptions:The production technology remains unchangedHomogeneous Variable FactorsAt least One Input is Fixed The fixed Factor is indivisible

Cause For Operation of the Law of Diminishing ReturnsWrong Combinations of inputs will give Diminishing returnsScarcity 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