THEORY OF

PRODUCTION
DR. DEEPTI SAHOO
 THE THEORY OF
2 PRODUCTION
• Production involves transformation of
inputs such as capital, equipment, labor,
and land into output - goods and services

• In this production process, the manager

is concerned with efficiency in the use of
the inputs
- technical vs. economical efficiency
 TWO CONCEPTS OF EFFICIENCY
3

• Economic efficiency:
• occurs when the cost of producing a given
output is as low as possible

• Technological efficiency:
• occurs when it is not possible to increase output
without increasing inputs
 YOU WILL SEE THAT BASIC PRODUCTION THEORY IS SIMPLY AN
APPLICATION OF CONSTRAINED OPTIMIZATION:
4

the firm attempts either to minimize the

cost of producing a given level of output
or
to maximize the output attainable with a
given level of cost.

Both optimization problems lead to same

rule for the allocation of inputs and choice
of technology
 PRODUCTION FUNCTION
5
• A production function is purely technical
relation which connects factor inputs & outputs.
It describes the transformation of factor inputs
into outputs at any particular time period.
Q = f( L,K,R,Ld,T,t)
where
Q = output R= Raw Material
L= Labour Ld = Land
K= Capital T = Technology
t = time
For our current analysis, let’s reduce the
inputs to two, capital (K) and labor (L):

Q = f(L, K)
 PRODUCTION TABLE
6

Same Q can be produced with different combinations of

inputs, e.g. inputs are substitutable in some degree
 SHORT-RUN AND LONG-RUN
7 PRODUCTION

• In the short run some inputs are fixed and some

variable
• e.g. the firm may be able to vary the amount of labor, but
cannot change the amount of capital
• in the short run we can talk about factor productivity /
law of variable proportion/law of diminishing returns
8 • In the long run all inputs become
variable
• e.g. the long run is the period in
which a firm can adjust all inputs
to changed conditions

• in the long run we can talk about

returns to scale
 SHORT-RUN CHANGES IN PRODUCTION
FACTOR PRODUCTIVITY
9

How much does the quantity of Q change,

when the quantity of L is increased?
 LONG-RUN CHANGES IN PRODUCTION
10 RETURNS TO SCALE

How much does the quantity of Q change, when

the quantity of both L and K is increased?
11 LAW OF DIMINISHING RETURNS
(DIMINISHING MARGINAL PRODUCT)

The law of diminishing returns states that when more and more units of a variable
input are applied to a given quantity of fixed inputs, the total output may initially
increase at an increasing rate and then at a constant rate but it will eventually
increases at diminishing rates.
Assumptions. The law of diminishing returns is based on the following
assumptions: (i) the state of technology is given (ii) labour is homogenous and
(iii) input prices are given.
12
 THREE STAGES OF
13
PRODUCTION IN SHORT RUN
AP,MP
Stage I Stage II Stage III

APX

•TPL Increases at MPX X

•TPL Increases at
Diminshing rate. • TPL begins to
increasing rate.
•MPL Begins to decline. decline
•MP Increases at
decreasing rate. •TP reaches maximum •MP becomes
level at the end of stage negative
•AP is increasing II, MP = 0.
and reaches its •AP continues to
•APL declines
maximum at the decline
end of stage I
14 SHORT-RUN ANALYSIS OF TOTAL,
AVERAGE, AND MARGINAL PRODUCT
• If MP > AP then
AP is rising

• If MP < AP then
AP is falling

• MP = AP when AP
is maximized

• TP maximized
when MP = 0
 RELATIONSHIP BETWEEN TOTAL,
15 AVERAGE, AND MARGINAL PRODUCT:
SHORT-RUN ANALYSIS

• Total Product (TP) = total quantity of output

• Average Product (AP) = total product per total input

• Marginal Product (MP) = change in quantity when one

additional unit of input used
 THE MARGINAL PRODUCT OF
16 LABOR

• The marginal product of labor is the increase in output obtained by adding 1 unit
of labor but holding constant the inputs of all other factors

Marginal Product of L:
MPL= Q/L (holding K constant)
= Q/L

Average Product of L:
APL= Q/L (holding K constant)
 APPLICATION OF LAW OF
17
DIMINISHING RETURNS:

• It helps in identifying the rational and irrational stages of

operations.
• It gives answers to question –
How much to produce?
What number of workers to apply to a given fixed inputs so
that the output is maximum?
 PRODUCTION IN THE LONG-RUN
18

• All inputs are now considered to be variable (both L

and K in our case)
• How to determine the optimal combination of inputs?

To illustrate this case we will use production isoquants.

An isoquant is a locus of all technically efficient methods
or all possible combinations of inputs for producing a
given level of output.
19
PRODUCTION TABLE

Units of K
Employed Isoquant
20 ISOQUANT
 TYPES OF ISOQUANT
21

There exists some degree of substitutability between inputs.

Different degrees
Sugar
of substitution:
Natural
Cane Capital
flavoring
syrup

K 1 K 2 K3 K 4
Q

Sugar All other L 1 L2 L3 L4 Labor

ingredients
b) Input – Output/ L- c) Kinked/Acitivity
a) Linear Isoquant Shaped Isoquant
(Perfect substitution) (Perfect Analysis Isoquant –
(Limited substitutability)
complementarity)
 Marginal Rate of Technical Substitution
22 MRTS

• The degree of imperfection in substitutability is measured with

marginal rate of technical substitution (MRTS- Slope of Isoquant):

MRTS = L/K

(in this MRTS some of L is removed from the production and

substituted by K to maintain the same level of output)
23 PROPERTIES OF ISOQUANTS

• Isoquants have a negative slope.

• Isoquants are convex to the origin.

• Isoquants cannot intersect or be tangent to each other.

• Upper Isoquants represents higher level of output

 ISOQUANT MAP
24

• Isoquant map is a set of

isoquants presented on a
two dimensional plain.
Each isoquant shows
various combinations of
two inputs that can be
used to produce a given
level of output.
25 LAWS OF RETURNS TO SCALE

• It explains the behavior of output in response to a proportional

and simultaneous change in input.
• When a firm increases both the inputs, there are three technical
possibilities –
(i) TP may increase more than proportionately – Increasing RTS
(ii) TP may increase proportionately – constant RTS
(iii) TP may increase less than proportionately – diminishing RTS
 Increasing RTS
26
K
Product Line

3K

3X
2K

2X
K
X

0 L 2L 3L
L
 Constant RTS
27
K
Product Line

3K

3X
2K

2X
K
X

0 L 2L 3L
L
 Decreasing RTS
28
K
Product Line

3K

3X
2K

2X
K
X

0 L 2L 3L
L
29 ELASTICITY OF FACTOR SUBSTITUTION

• () is formally defined as the percentage change in the capital labour ratios (K/L)
divided by the percentage change in marginal rate of technical substitution (MRTS), i.e
Percentage change in K/L
()=
Percentage change in MRTS

д(K/L) / (K/L)
()=
д(MRTS) / (MRTS)
30 COBB – DOUGLES PRODUCTION
FUNCTION: -
X= b0 Lb1 Kb2

X= Out put
L = qty of Labour
K = qty of Capital
bo , b1 , b2 Coefficient

b1 - Labour
b2 - Capital
31 CHARACTERISTICS OF COBB – DOUGLES
PRODN FUNCTION: -
1. The Marginal Product of Factor:
(a) MP L = dx/dl

X = b0Lb1Kb2
dx/dl = b0 b1 Lb1-1Kb2
= b1 (boLb1 K b2) L-1
= b1 X/L

= b1 (AP L)
APL Average Product of Labour
Similarly
(b) MP K = dx/dk
= b2 b0Lb1Kb2-1
= b2 ( b0 Lb1 Kb2) K-1
= b2 X/K

APk Average Product of Capital

32 2. THE MARGINAL RATE OF TECHNICAL SUBSTITUTION

MRTS L.K = MPL

MPK

= dx/dL = b1(X/L)

dx/dk b2(X/K)

MRTS LK = b1 K

b2 L