# Production Function

```Production Function
1
Production Function
Production: Any activity leading to value
Transformation of inputs into output
Q= f (L,K)
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Production Function
Short term : Time when one input (say,
capital) remains constant and an addition
to output can be obtained only by using
more labour.
Long run: Both inputs become variable.
3
Production Function
Production process is subject to various
phasesLaws of production state the relationship
between output and input.
.
4
Laws of production
Short run :
Relationship between input and output are
studied by varying one input , others being
held constant.
Law of Variable Proportions brings out
relationship between varying proportions
of factor inputs and output
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Laws of production
Long run:
Production function is subject to different
phases described under the Law of
Returns to Scale
– Studied assuming that all factor inputs are
variable.
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Law of Variable Proportions
Law of Variable Proportions (Short run Law
of Production)
Assumptions:
• One factor (say, L) is variable and the
other factor (say, K) is constant
• Labour is homogeneous
• Technology remains constant
• Input prices are given
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Law of Variable Proportions
No of Workers
L
Total Product
(TPl)
Marginal
Average
Product (MPl )
Product (APl )
1
24
24
24
2
72
48
36
3
138
66
46
4
216
78
54
5
300
84
60
6
384
84
64
7
462
78
66
8
528
66
66
9
576
48
64
10
600
24
60
11
594
-6
54
12
552
-42
46
Stages of
Returns
I)
Increasing
Returns
II)
Diminishing
Returns
III) Negative
Returns
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Law of Variable Proportions
Panel A
TPl
T
o
t
a
l
P
r
o
d
u
Total Product
T
o
t
a
l
p
r
o
d
u
c
t
TP rises at an increasing rate till
the employment of the 5th
worker.
Beyond the 6th worker until 10th
worker TP increases but rate of
increase begins to fall
TP turns negative from 11th
worker onwards.
This shows Law of Diminishing
Marginal returns
Labour
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Law of Variable Proportions
Panel B
AP/MP
Panel B represents
Marginal and average
productivity curves of
labour
APL
labour
M MPL
P
L
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Law of Variable Proportions
Increasing Returns- Stage I:
TPl increases at an increasing rate.
Fixed factor (K) is abundant and variable
factor is inadequate. Hence K gets utilised
better with every additional unit of labour
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Stage II- TPl continues to increase but at a
diminishing rate.
stage III- TPl begins to decline –Capital becomes
scarce as compared to variable factor. Hence
over utilisation of capital and setting in of
diminishing returns
Causes of 3 stages: Indivisibility and inelasticity
of fixed factor and imperfect substitutability
between K and L
12
Law of Variable Proportions
Significance of Law of Diminishing Marginal
Returns:
- Empirical law, frequently observed in
various production activities
- Particularly in agriculture where natural
factors (say land), which play an important
role, are limited.
- Helps manager in identifying rational and
irrational stages of operation
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Law of Variable Proportions
- It provides answers to questions such as:
a) How much to produce?
b) What number of workers (and other
variable factors) to employ in order to
maximize output
In our example, firm should employ a
minimum of 7 workers and maximum of 10
workers (where TP is still rising)
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Law of Variable Proportions
- Stage III has very high L-K ratio- as a
result, additional workers not only prove
unproductive but also cause a decline in
TPl.
- In Stage I capital is presumably underutilised.
- So a firm operating in Stage I has to
increase L and that in Stage III has to
decrease labour.
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Law of Returns to Scale
In the long run, all factors are variable.
• Production can be increased by adding
both L and K.
• Relationship between inputs and output is
depicted in the form of isoquant curves.
• Isoquant curves represent different
combinations of K and L that lead to the
same level of output.
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ISOQUANT CURVES
Y
Units of K
IQ300
IQ200
IQ100
o
X
Units of L
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Law of Returns to Scale
Isocost line:
• Assume that labour costs Rs.10 per unit and
capital, Rs. 7 per unit.
• Suppose the company has a budget of Rs. 70.
• It can buy 7 units of labour (with no capital), or
10 units of K (with no labour), or some inbetween combination.
• By joining the two extreme points we get an
isocost line
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Law of Returns to Scale
Y
10
X
o
Units of L
7
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Law of Returns to Scale
Y
Y
Capital
Producer has a constraintnamely, budget.
Q3=300
B
O
Labour
Q2=200
Producer attains equilibrium
when he reaches highest
attainable level of output.
1Q1=100
0
X
0
1
9
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Law of Returns to Scale
• Point of tangency between isoquant and
isocost is the point of least cost
combination of inputs.
• At point B, labour and capital are
combined in a proportion that maximises
the output for a given budget.
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Law of Returns to Scale
ε = Δq/ q &divide; Δn /n
where
Δq/ q indicates proportionate change in output
Δn /n indicates proportionate change in input
If ε &gt;1, then we have increasing returns to scale
ε =1, then we have constant returns to scale
ε &lt;1, then we have decreasing returns to scale
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Law of Returns to Scale
K
Y
A
Q140
Firm is subject to
G
increasing,
Constant and
Decreasing returns
Q120
F
to scale.
Explanation for these
E
Q100
D
phases is provided
Q80
Through concepts
C
Q60
Called economies
B
B
And diseconomies
Q40
Of scale.
Q 20
o
X
L
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ECONOMIES OF SCALE
• ECONOMIES OF SCALE are advantages
enjoyed by a firm from large scale
production.
Causes of increasing returns to scale
• Internal and external
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INTERNAL ECONOMIES
disadvantages that accrue to the firm as a
result of its scale of operation
Indivisibilities- if some of the factors are
indivisible, then it would be technically and
economically undesirable to use the
indivisible factor for a smaller scale of
production e.g., Can’t use a conveyor belt
to unload a small truck, but need one for
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INTERNAL ECONOMIES
Dimensional economies
• A mere change in the size of capital can
lead to a change in output which is
proportionately more than the cost of
enlarged input. e.g., Doubling the
diameter of a pipeline more than doubles
the water flow without doubling the cost;
doubling the dimensions of a ship more
than doubles its capacity without doubling
costs
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INTERNAL ECONOMIES
• Specialisation- In large scale production,
a process can be broken into sub
processes - specialised labour and
specialised machines lead to increase in
productivity and decrease in average cost
of production.
• Managerial economies
• Commercial economies-bulk purchases
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INTERNAL ECONOMIES
• Financial economies -Lower rate of
interest, liberal terms and conditions
because of reputation individual investors
also like to invest money.
• Risk bearing economies:
• Diversification of output, markets and
sources of supply
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INTERNAL DISECONOMIES
Internal Diseconomies
• Effective supervision no longer possible
• Unwieldy administration and ego clashes
• Industrial unrest
• Problems of re-conversion, storage and
standing costs in case of stoppage of
work or lack of demand
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External Economies of Scale
External Economies of Scale
Arise out of sharing and cooperation
received from other firms in a given
industry.
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External Economies of Scale
Economies of concentration
• Supply of skilled labour in a region
• Common services
• Specialised institutions like training
schools and research centres (Indian
• Reputation of a region
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External Economies of Scale
Economies of Information
• Economies of disintegration
• An ancillary firm may specialise in the
production of only one part
• Waste and byproducts of all firms in the
industry may be dealt with by a specialised
firm.
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External Diseconomies of Scale
• As firms expand along with expansion of the
industry, after a point economies turn into
diseconomies
• Excessive concentration leads to bottlenecks
and diseconomies
• Most firms experience these phases but some
continue to defy these laws due to innovations
and technological progress.
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Economies of Scope
• Lowering of costs that a firm experiences when it
produces more than one product together rather
than each alone
• A smaller airline can profitably extend into cargo
services, thereby lowering the cost of each
service
• Using bye products to make something instead
of throwing it away.
• Management should be alert to such
possibilities.
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Learning Curve
• As a firm gains experience in the production of a
commodity or service, AC often declines.
• Learning Curve shows the decline in the
average input cost of production with the rising
cumulative total output over time.
• Eg, 1000 hours to assemble 100th aircraft, but
only 700 hours to assemble the 200th .as
managers and workers become more efficient
as they gain production experience.
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Case study: Masterji’s Grocery
Shop
Masterji’s shop is very popular and stocks all
kinds of goods- from rice and wheat to
processed food, imported chocolates and
cheese. There is a small section which
has a photocopying machine and a STD
booth. Masterji runs the shop with the help
of his children.
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Case study: Masterji’s Grocery
Shop
• The family noticed
that the number of
shoppers varied
between times and
days (See table)
• During weekdays,
masterji could
manage with his
children, but not in
week ends.
Morn After Even
noon
Mon- 50
Fri
40
65
Sat/
Sun
85
30
165
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Case study: Masterji’s Grocery
Shop
• Sunday morning buyers were ‘ value
crowd’- bulk buyers, spent extra on
something new and attractive but wanted
a pleasant experience and were upset at
the overcrowded shop
• At certain times there were not many
shoppers
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Case study: Masterji’s Grocery
Shop
• Masterji employed 3 assistants during
week ends, but that did not solve the
problem as the shop had a small floor area
and only one billing machine
1.Can you explain masterji’s problem in
terms of law of variable proportions?
2. Pl. suggest in detail how masterji can
improve the functioning of the shop.
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Measuring Productivity
• US Bureau of Labor Statistics has been
conducting studies of output per hour in
individual industries as well as overall economy
since 1800s- earlier because of apprehensions
of human labor being displaced- this fear of
unemployment was replaced by concern for
making the most efficient use of labour in 1920s
and 30s- In recent years interest in productivity
measurement and enhancement has grown
because it is recognised as an important
indicator of economic growth.
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• Labor productivity: Ratio of output per
worker hour. Improvements in worker
productivity
• Multifactor productivity: Output is related to
combined inputs of labor, capital and
intermediate purchases.
• Advances in productivity reflect the ability
to produce more output per input
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