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Presented By:
      Nidhi Panday
 Definition and example of Production Function.
 Types of Production Function.
 Law Of Production Function.
 Law of Variable Proportions.
 Production Function with one Variable Input.
 Production Function with two Variable Inputs.
 Assumption.
 Summary.
 FURTHER READINGS
 Production  refers to the transformation of
 inputs or resources into outputs of goods and
 services. In other words, production refers to
 all of the activities involved in the
 production of goods and services, from
 borrowing to set up or expand production
 facilities, to hiring workers, purchasing row
 materials, running quality control, cost
 accounting, and so on, rather than referring
 merely to the physical transformation of
 inputs into outputs of goods and services.
A   computer company hires workers to use
  machinery, parts, and raw materials in
  factories to produce personal computers.
 The output of a firm can either be a final
  commodity or an intermediate product such
  as computer and semiconductor respectively.
 The output can also be a service rather than
  a good such as education, medicine, banking
  etc.
 Mathematical   representation of the relationship:
 Q = f (K, L, La)
 Output (Q) is dependent upon the amount of capital
  (K), Land(L) and Labour (La) used
 There are two distinct types of production
 function that show possible range of
 substitution inputs in the production process.

 1. Fixed proportion Production function
 2. Variable proportions 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.
Production process is
 subject to various
 phases-
Laws of production state the relationship
  between output and input.
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
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.
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
No of Workers   Total Product   Marginal       Average           Stages of
       L            (TPl)                                        Returns
                                Product (MPl ) Product (APl )
      1              24              24              24          I)
      2              72              48              36          Increasing
                                                                 Returns
      3             138              66              46
      4             216              78              54
      5             300              84              60
      6             384              84              64
      7             462              78              66          II)
      8             528              66              66          Diminishing
                                                                 Returns
      9             576              48              64
     10             600              24              60
     11             594               -6             54          III) Negative
     12             552              -42             46          Returns

                                                            10
Panel A
                               TP rises at an increasing rate till
                               the employment of the 5th
                               worker.
      T                  TPl
                               Beyond the 6th worker until 10th
      o                        worker TP increases but rate of
      t
Total Product




                               increase begins to fall
      a
      l                        TP turns negative from 11th
                               worker onwards.
d
o
r
P

                l
                a
                t
                o
                T




      p                        This shows Law of Diminishing
      r                        Marginal returns
      o
      d
                Labour
      u
      c
      t
                                                    11
Panel B
                          Panel B represents
                          Marginal and average
                          productivity curves of
                          labour
AP/MP




                    APL




                  M MPL
         labour
                  P
                  L                     12
Increasing Returns- Stage I:
TPl increases at an increasing rate.
Fixed factor (K) is abundant and variable factor is
  inadequate. Hence K gets utilized better with
  every additional unit of labour
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
  utilization 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
                                         13
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




                                         14
- 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)




                                      15
-   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.




                                             16
 There are two Variable Proportions
 Production
   Function_
 1- Production Function With One Variable
 Input.
 2- Production With Two Variable Inputs
 When discussing production in the short
  run, three definitions are important:
 Total product
 Marginal product
 Average product




                               18
Total Product     TP = Q = f(L)

Marginal Product              TP
                     MPL =
                               L

Average Product           TP
                    APL =
                           L
 Production or            MPL
Output Elasticity    EL = AP
                            L


                             19
Total Product


   Total product (TP) is another name for output
    in the short run.



        TP = Q = f (L)




                                     20
 The marginal product (MP) of a variable
  input is the change in output (or TP)
  resulting from a one unit change in the
  input.
 MP tells us how output changes as we
  change the level of the input by one unit.
 Consider the two input production function
  Q=f (L,K) in which input L is variable and
  input K is fixed at some level.
 The marginal product of input L is defined
  as holding input K constant.
                                           TP
                              MPL =
                                            L
                                      21
 The average product (AP) of an input is the
  total product divided by the level of the
  input.
 AP tells us, on average, how many units of
  output are produced per unit of input used.
 The average product of input L is defined
  as holding input K constant.


                 TP
           APL =
                  L
                                   22
Total, Marginal, and Average Product of Labor, and Output Elasticity


            L          Q         MPL         APL           EL
            0         0            -           -             -
            1         3            3          3             1
            2         8            5          4           1 .2 5
            3         12           4          4             1
            4         14           2         3 .5         0 .5 7
            5         14           0         2 .8           0
            6         12          -2          2             -1




                                                     23
24
-In the long run, all inputs are variable.
Isoquants show combinations of two inputs that can
produce the same level of output.
-In other words, Production isoquant shows the various
combination of two inputs that the firm can use to produce
a specific level of output.
-Firms will only use combinations of two inputs that are in
the economic region of production, which is defined by the
portion of each isoquant that is negatively sloped.
-A higher isoquant refers to a larger output, while a lower
isoquant refers to a smaller output.
                                             25
Isoquants   K                                  Q
            6   10   24   31    36   40   39
            5   12   28   36    40   42   40
            4   12   28   36    40   40   36
            3   10   23   33    36   36   33
            2    7   18   28    30   30   28
            1    3    8   12    14   14   12
                 1    2    3     4    5   6    L




                           26
   THE PRODUCTION FUNCTIONS ARE BASED ON
      CERTAIN ASSUMPTIONS.

   1 Perfect divisibility of both inputs and outputs

   2 Limited substitution of one factor for another

   3 Constant technology

   4 Inelastic supply of fixed factors in
    the short run
A  production function specifies the maximum
  output that can be produced with
 a given set of inputs. In order to achieve
  maximum profits the production
 manager has to use optimum input-output
  combination for a given cost. In this
 unit, we have shown how a production
  manager minimizes the cost for a given
 output in order to maximize the profit. Also,
  we have shown how to maximize
 the output at a given level of cost.
 Adhikary,M (1987), Managerial Economics
  (Chapter V), Khosla,Publishing House, Delhi.
 Google.
Production Function Guide: Types, Laws, and Graphs

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Production Function Guide: Types, Laws, and Graphs

  • 1. Presented By: Nidhi Panday
  • 2.  Definition and example of Production Function.  Types of Production Function.  Law Of Production Function.  Law of Variable Proportions.  Production Function with one Variable Input.  Production Function with two Variable Inputs.  Assumption.  Summary.  FURTHER READINGS
  • 3.  Production refers to the transformation of inputs or resources into outputs of goods and services. In other words, production refers to all of the activities involved in the production of goods and services, from borrowing to set up or expand production facilities, to hiring workers, purchasing row materials, running quality control, cost accounting, and so on, rather than referring merely to the physical transformation of inputs into outputs of goods and services.
  • 4. A computer company hires workers to use machinery, parts, and raw materials in factories to produce personal computers.  The output of a firm can either be a final commodity or an intermediate product such as computer and semiconductor respectively.  The output can also be a service rather than a good such as education, medicine, banking etc.
  • 5.  Mathematical representation of the relationship:  Q = f (K, L, La)  Output (Q) is dependent upon the amount of capital (K), Land(L) and Labour (La) used
  • 6.  There are two distinct types of production function that show possible range of substitution inputs in the production process.  1. Fixed proportion Production function  2. Variable proportions production function
  • 7. 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. Production process is subject to various phases- Laws of production state the relationship between output and input.
  • 8. 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 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.
  • 9. 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
  • 10. No of Workers Total Product Marginal Average Stages of L (TPl) Returns Product (MPl ) Product (APl ) 1 24 24 24 I) 2 72 48 36 Increasing Returns 3 138 66 46 4 216 78 54 5 300 84 60 6 384 84 64 7 462 78 66 II) 8 528 66 66 Diminishing Returns 9 576 48 64 10 600 24 60 11 594 -6 54 III) Negative 12 552 -42 46 Returns 10
  • 11. Panel A TP rises at an increasing rate till the employment of the 5th worker. T TPl Beyond the 6th worker until 10th o worker TP increases but rate of t Total Product increase begins to fall a l TP turns negative from 11th worker onwards. d o r P l a t o T p This shows Law of Diminishing r Marginal returns o d Labour u c t 11
  • 12. Panel B Panel B represents Marginal and average productivity curves of labour AP/MP APL M MPL labour P L 12
  • 13. Increasing Returns- Stage I: TPl increases at an increasing rate. Fixed factor (K) is abundant and variable factor is inadequate. Hence K gets utilized better with every additional unit of labour 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 utilization 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 13
  • 14. 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 14
  • 15. - 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) 15
  • 16. - 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. 16
  • 17.  There are two Variable Proportions Production Function_ 1- Production Function With One Variable Input. 2- Production With Two Variable Inputs
  • 18.  When discussing production in the short run, three definitions are important:  Total product  Marginal product  Average product 18
  • 19. Total Product TP = Q = f(L) Marginal Product TP MPL = L Average Product TP APL = L Production or MPL Output Elasticity EL = AP L 19
  • 20. Total Product  Total product (TP) is another name for output in the short run. TP = Q = f (L) 20
  • 21.  The marginal product (MP) of a variable input is the change in output (or TP) resulting from a one unit change in the input.  MP tells us how output changes as we change the level of the input by one unit.  Consider the two input production function Q=f (L,K) in which input L is variable and input K is fixed at some level.  The marginal product of input L is defined as holding input K constant. TP MPL = L 21
  • 22.  The average product (AP) of an input is the total product divided by the level of the input.  AP tells us, on average, how many units of output are produced per unit of input used.  The average product of input L is defined as holding input K constant. TP APL = L 22
  • 23. Total, Marginal, and Average Product of Labor, and Output Elasticity L Q MPL APL EL 0 0 - - - 1 3 3 3 1 2 8 5 4 1 .2 5 3 12 4 4 1 4 14 2 3 .5 0 .5 7 5 14 0 2 .8 0 6 12 -2 2 -1 23
  • 24. 24
  • 25. -In the long run, all inputs are variable. Isoquants show combinations of two inputs that can produce the same level of output. -In other words, Production isoquant shows the various combination of two inputs that the firm can use to produce a specific level of output. -Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped. -A higher isoquant refers to a larger output, while a lower isoquant refers to a smaller output. 25
  • 26. Isoquants K Q 6 10 24 31 36 40 39 5 12 28 36 40 42 40 4 12 28 36 40 40 36 3 10 23 33 36 36 33 2 7 18 28 30 30 28 1 3 8 12 14 14 12 1 2 3 4 5 6 L 26
  • 27. THE PRODUCTION FUNCTIONS ARE BASED ON CERTAIN ASSUMPTIONS.  1 Perfect divisibility of both inputs and outputs  2 Limited substitution of one factor for another  3 Constant technology  4 Inelastic supply of fixed factors in the short run
  • 28. A production function specifies the maximum output that can be produced with  a given set of inputs. In order to achieve maximum profits the production  manager has to use optimum input-output combination for a given cost. In this  unit, we have shown how a production manager minimizes the cost for a given  output in order to maximize the profit. Also, we have shown how to maximize  the output at a given level of cost.
  • 29.  Adhikary,M (1987), Managerial Economics (Chapter V), Khosla,Publishing House, Delhi.  Google.