Production Function

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Production Function
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Production Function

• Production Any activity leading to value
  addition
• 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.

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Production Function

• Production process is subject to various phases-
• Laws of production state the relationship between
  output and input.
• .

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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 Product (MPl ) Average Product (APl ) Stages of Returns
1 24 24 24 I) Increasing Returns
2 72 48 36 I) Increasing Returns
3 138 66 46 I) Increasing Returns
4 216 78 54 I) Increasing Returns
5 300 84 60 I) Increasing Returns
6 384 84 64 I) Increasing Returns
7 462 78 66 II) Diminishing Returns
8 528 66 66 II) Diminishing Returns
9 576 48 64 II) Diminishing Returns
10 600 24 60 II) Diminishing Returns
11 594 -6 54 III) Negative Returns
12 552 -42 46 III) Negative Returns
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Law of Variable Proportions

• Panel A

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
Total Product
TPl
Total product
Total Product
Labour
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Law of Variable Proportions

• Panel B

Panel B represents Marginal and average
productivity curves of labour
AP/MP
APL
MPL
MPL
labour
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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

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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 under-utilised.
• 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
IQ300
Units of K
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
  in-between combination.
• By joining the two extreme points we get an
  isocost line

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Law of Returns to Scale
Y
10
Units of K
Isocost
X
o
7
Units of L
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Law of Returns to Scale
Producer has a constraint- namely,
budget. Producer attains equilibrium when he
reaches highest attainable level of output.
Y
Y
Capital
Q3300
Q2200
B
Q1100
10019
X
O
Labour
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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

• e ?q/ q ?n /n
• where
• ?q/ q indicates proportionate change in output
• ?n /n indicates proportionate change in input
• If e gt1, then we have increasing returns to
  scale
• e 1, then we have constant returns to scale
• e lt1, then we have decreasing returns to scale

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Law of Returns to Scale
Y
Expansion Path
Q140
Firm is subject to increasing, Constant and
Decreasing returns to scale. Explanation for
these phases is provided Through concepts Called
economies And diseconomies Of scale.
G
Q120
F
K
E
Q100
D
Q80
C
Q60
B
B
Q40
A
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

• INTERNAL Those advantages and 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.,
  Cant use a conveyor belt to unload a small
  truck, but need one for unloading a train or ship

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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 School of mines in
  Dhanbad),
• Reputation of a region

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External Economies of Scale

• Economies of Information
• Trade associations, journals, seminars
• 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 Masterjis Grocery Shop

• Masterjis 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 Masterjis 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 Afternoon Even
Mon-Fri 50 40 65
Sat/Sun 165 85 30
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Case study Masterjis 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 Masterjis 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 masterjis 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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