Production function ppt in economics

Present by
Mansi Tyagi
Sadhana Tyagi

It’s an activity that
transforms
input into
output.

. Technology
. Inputs
C- capital
E- entrepreneurship
L- land
L- labour
•••••••••••••••••••••••••••••••

A production function can be an
equation,table or graph presenting the
maximum amount of a commodty that a
firm can produce from a given set of
inputs during a period of time.
Inputs Process Output
Capital
Labour
Land
Product
or
service
generated
Entrepreneurship

The production function can be mathematically
written as:
Q = f(L, K, T…..n)
Where,
Q = output
L = labour
K = capital
T = level of technology
n = other inputs employed in production
••••••••••••••••••••••••••••••Production function

• How to obtain Maximum output
• Helps the producers to determine whether
employing variable inputs /costs are
profitable
• Highly useful in longrun decisions
• Least cost combination of inputs and to
produce an output

Types
Short –Run
(Inputs kept constant
One input (Labour) is varied)
Long – Run
(Varying all inputs)
Law of variable
proportion
Law of returns to
scale

#One variable factor
#Remaining Constant
Q = f(L,C’)
Labour
capital

Two types:-
 Linear homogeneous
 Non-homogeneous
#All inputs are variable
Long run Production
Function
Q = f(L,C)
capital
Labour
200Q
100Q

Paul H.Douglas and C.W Cobb of the U.S.A have studied the production of the american manufacturing
industries and they formulated a statistical production function.
Empirical estimation is the power function of the form :
Q = ALa Kb
where,
Q = Output
L = labour input
K = capital input
A, a and b are positive constants.
Q = AL3/4 K1/4
.
Cobb-Douglas Production
Function
1/4+3/4 =1

Properties
1. Constant return to scale:
Q = ALa Kb
Q’ = A(gL)a(gK)b
= ga +b
( ALa Kb )
Q’ = ga +b
Q
2. Average product of factor in C-D function:
Avg. product of L = Q/L =
Avg. product of K = Q/K =
ALa -1Kb
ALa Kb-1

3. Marginal product of factor in C-D function:
Marginal product of L holding K constant = dQ/dL= aQ/L
Marginal product of K holding L constant = dQ/dL= bQ/K
4. The marginal rate of substituition between K&L:
MRsLk = dQ/dL = a(Q/L)/b(Q/K) = a/b* K/L
dQ/dK
5. C-D function & elasticity of substitution:
(es = 1)
d(K/L)* a/b
a/b*d(K/L)
= 1es =

WINTERTemplate
Law of Variable Proportion
 If one factor is used more & more,keeping the other factors constant.
 The total output will increase at an increasing rate in the beginning and then at
diminishing rate and eventually decreases absolutely.
It states that:
ASSUMPTIONS :
 Constant Technology
 Short run
 Homogeneous Factors
 Variable Input Ratio

Table illustrates the operation:
Units of
Labour
L
Total
Product
(Quintals)
Q
Average
Product
(Quintals)
Marginal
Product
(Quintals)
1 80 80 80
2 170 85 90
3 270 90 100
4 368 92 98
5 430 86 62
6 480 80 50
7 504 72 24
8 504 63 0
9 495 55 -9
10 480 48 -15
Negative
IR
DR

STAGE 1 : INCREASING RETURNS
As the production of one factor in the combination of factor
is increased upto a point, the MP of the factor will increase.
Reasons:  Indivisibility of factors
Quantity of fixed factor
 Division of labour
 Economies
STAGE 2 : DIMINISHING RETURNS
As the production of one factor in the combination of factor
is increased after a point the average & MP of that factor will
diminishing.
Reasons:  Scarcity of fixed factors
 Indivisibilty of fixed factor
 Lack of perfect substitution of factor of production

STAGE 3 : NEGATIVE RETURNS
MP of variable factor is negative.
Reasons:  Excessive variable factor
 Inefficiency of fixed factor

Law of Returns to Scale
 It is a Long run analysis & all factors are variable.
 It seeks to analyse the effects of scale on the level of output.
Three kinds of returns to scale:
INCREASING RETURNS TO SCALE
CONSTANT RETURNS TO SCALE
DECREASING RETURNS TO SCALE

ISOQUANTS
Isoquant is a curve representing the various combinations of
two inputs that produce the same amount of output.
Also called as equal product curve.
Slope of an isoquant indicates the rate at which factors K and L
can be substituted for each other while a constant level of
production is maintained.
ASSUMPTIONS :
 There are two inputs: Labour L & Capital C to produce a
commodity X.
 L,K & X are Perfectly divisible.
Technology of product is given. Isoquant
curveK
L

Factor
Production
Labour Capital
A 5 9
B 10 6
C 15 4
D 20 3
E 25 2
Example:

Perfect
substitutability
between factors of
production.
An output can be
produced by
either using one or
both.
Strict
complementarity's
between inputs.
If a quantity
of one input is
increased there will be
no change in output
Types of Isoquant
Linear Isoquant: Input- Output Isoquant

ISOQUANTS are negatively inclined.
ISOQUANTS are convex to the origin.
Two ISOQUANTS can’t intersect each
other.
ISOQUANTS doesn’t touch either axis.
PROPERTIES OF
ISOQUANTS

Production function ppt in economics

Production function ppt in economics

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Production function ppt in economics