Cost of Production Microeconomics - PowerPoint by dyu18105

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                                          R. Larry Reynolds 1997
                 Production
· Production is an activity where
  resources are altered or changed and
  there is an increase in the ability of
  these resources to satisfy wants.
· change in physical characteristics
      · change in location
      · change in time
      · change in ownership
Fall „ 97         Principles of Microeconomics   Slide -- 2
            Production and Cost
·   Production is a technical relationship between a set of inputs
    or resources and a set of outputs or goods.
    QX = f( inputs [land, labour, capital], technology, . . . )
    [Legal and social/cultural institutions influence the production
    function.]
·   Cost functions are the pecuniary relationships between
    outputs and the costs of production;
    Cost = f(QX {inputs, technology} , prices of inputs, . . . )
·   Cost functions are determined by input prices and
    production relationships. It is necessary to understand
    production functions if you are to interpret cost data.



Fall „ 97                Principles of Microeconomics             Slide -- 3
                      Costs
· Costs are incurred as a result of production. The
  important concept of cost is opportunity cost
  [marginal cost]. These are the costs associated
  with an activity. When inputs or resources are
  used to produce one good, the other goods they
  could have been used to produce are sacrificed.
· Costs may be in real or monetary terms;
· implicit costs
· explicit costs


Fall „ 97        Principles of Microeconomics   Slide -- 4
             Implicit Costs
· Opportunity costs or MC should include all costs
  associated with an activity. Many of the costs are
  implicit and difficult to measure.
· A production activity may adversely affect a
  person‟s health. This is an implicit cost that is
  difficult to measure.
   · Another activity may reduce the time for other
     activities. It may be possible to make a
     monetary estimate of the value.


Fall „ 97        Principles of Microeconomics   Slide -- 5
            Explicit Costs

· Explicit costs are those costs where
  there is an actual expenditure in a
  market. The costs of labour or
  interest payments are examples.
· Some implicit costs are estimated and
  used in the decision process.
  Depreciation is an example.

Fall „ 97    Principles of Microeconomics   Slide -- 6
                    Normal Profit
· In neoclassical economics, all costs
  should be included:
      ·     wages represent the cost of labour
      ·     interest represents the cost of Kapital
      ·     rent represents the cost of land
      ·     “normal profit [ P ]” represents the cost
            of entrepreneurial activity
             · normal profit includes risk

Fall „ 97                Principles of Microeconomics   Slide -- 7
            Production Function
· A production function expresses the
  relationship between a set of inputs and
  the output of a good or service.
· The relationship is determined by the
  nature of the good and technology.
· A production function is “like” a recipe for
  cookies; it tells you the quantities of each
  ingredient, how to combine and cook, and
  how many cookies you will produce.
Fall „ 97        Principles of Microeconomics   Slide -- 8
QX = f(L, K, R, technology, . . . )
                 QX = quantity of output
                 L = labour input
                 K = Kapital input
                 R = natural resources [land]
Decisions about alternative ways to produce good X require
that we have information about how each variable influences
QX.

 One method used to identify the effects of each variable on
 output is to vary one input at a time. The use of the ceteris
 paribus convention allows this analysis.

The time period used for analysis also provides a way to
determine the effects of various changes of inputs on the
output.

Fall „ 97             Principles of Microeconomics        Slide -- 9
              Technology
· The production process [and as result, costs]
  is divided up into various time periods;
   · the “very long run” is a period
     sufficiently long enough that technology
     used in the production process changes.
   · In shorter time periods [long run, short
     run and market periods], technology is a
     constant.

Fall „ 97       Principles of Microeconomics   Slide -- 10
                      Long Run
· The long run is a period that:
      · is short enough that technology is unchanged.
      · all other inputs [labour, kapital, land, . . . ] are
        variable, i.e. can be altered.
      · these inputs may be altered in fixed or variable
        proportions. This may be important in some
        production processes.
      · If inputs are altered, the output changes.
      · QX = f(L, K, R, . . . ) technology is constant

Fall „ 97             Principles of Microeconomics    Slide -- 11
               Short Run
· The short run is a period in which at least
  one of the inputs has become a constant
  and at least one of the inputs is a variable.
· If kapital [K] and land [R] are fixed or
  constant in the short run, labour [L] is the
  variable input. Output is changed by
  altering the labour input. QX = f(L)
  Technology, K and R are fixed or constant.


Fall „ 97       Principles of Microeconomics   Slide -- 12
            Market Period
· When Alfred Marshall included time
  into the analysis of production and
  cost, he included a “market period” in
  which inputs, technology and
  consequently outputs could not be
  varied.
· The supply function would be
  perfectly inelastic in this case.
Fall „ 97     Principles of Microeconomics   Slide -- 13
Production in the Short Run
Consider a production process where K, R and technology are
fixed: As L is changed, the output
changes, QX= f(L)                          Production of Good X

 L = labour input                                       L   TPL   APL       MPL
 TPL = QX = output of good X
 APL = average product [TP/L]
                                                        0    0    0          --
                                         DL = 1              DTPL=4
 MPL = Marginal product [DTP/ DL]                       1    4    4           4
                                                        2    10    5          6
        TPLL
 AP L =
 APLL==                                                 3   20 6.67         10
        L
         DTPL                                           4   25 6.25           5
 MPL =
          DL                                            5   29    5.8         4
         TPL    output                                                        3
  APL =      =           = Efficiency                   6   32    5.3
         L      input
                                                        7   34 4.87           2
 Maximum of APL is at the 3 input of
                                                        8   35 4.37            1
 labour.
                                                        9   35 3.89           0
  Fall „ 97              Principles of Microeconomics                   Slide -- 14
Production in the Short Run

               TPL   output                                  Production of Good X
  APL =
               L   =            = Efficiency of
                     input              labour               L    TPL   APL     MPL
Notice that the APL increases as the first
                                                             0      0    0       --
three units of labour are added to the
fixed inputs of K and R. The maximum                         1      4    4        4
efficiency of Labour or maximum APL , given                  2     10    5        6
our technology, plant and natural
                                                             3    20    6.67     10
resources is with the third worker.
                                                             4    25    6.25      5
As additional units of labour are added                      5    29    5.8       4
beyond the third worker the                                  6    32    5.3       3
output per worker [APL ] declines.
                                                             7    34 4.87         2
                                                             8    35 4.37          1
                                                             9    35 3.89         0

   Fall „ 97                  Principles of Microeconomics                Slide -- 15
  Graphically TPL can be shown:
   TPL initially increases at an increasing



             ...
                                                           L   TPL
   rate; it is convex from below.


            .
                                                           0    0



           .
                                                     TPL
   Output, QX                                              1    4


          .
   35
      Maximum
                                                           2    10


         .
   30 output
                                                           3   20
   25
                        After some point it                4   25



        .
   20
                        then increases at a
                                                           5   29
                        decreasing rate and



       .
    15
                        reaches a maximum                  6   32



      .
    10
                        level of output,                   7   34
     5                  and declines
                                                           8   35
            1   2   3   4      5    6    7     8    9      9   35
                                              Labour
Fall „ 97                   Principles of Microeconomics             Slide -- 16
        Given the TP , the APL can calculated:                  TPL   L     APL
                 TPL                                             0    0       0
      APL =          = output = Efficiency of
                 L     input      labour                         4    1       4
                                                                 10   2       5
                                                                20    3     6.67
APL                                                             25    4     6.25


                   ... . .
 10
                                                                29    5     5.8


                 .
 8


         .                                  ..
                                                                32    6     5.3
 6
                                                                34    7 4.87
 4


  .
                                                                35    8 4.37
 2                                                 APL          35    9 3.89

           1     2   3   4   5    6    7     8    9
                                             Labour
     Fall „ 97                   Principles of Microeconomics         Slide -- 17
  Output, QX

                           .




                               .
                              Z




                                            .
  35                                                  TPL




                               .
                         .
         The APL is the




                              .
  30     slope of a                              Graphically the relationship


                     .
         ray from                                between APL and TPL can be shown:
  25                          M
         the origin
         to the                   1 unit of L produces 4Q, APL is 4/1 = 4 or the
  20
                                                           slope of line 0H.


                 .
         TPL .                    H
   15                                    2 units of L produces 10Q,



       .
   10                                   APL is 10/2 = 5 or the slope of line 0M.


     .
                                         3 units of L produces 20Q,
    5
    4                                  APL is 20/3 = 6.67 or the slope of line 0Z.
    0



              . ... .
APL 10      1    2   3    4   5    6    7   8     9     4 units of L produces 25Q,
                                            Labour


            .
                                                            APL is 25/4 = 6.25 or



                     ..
    8


          .
                                                            the slope of line 0W.
    6                                            As additional units of L are added,
                                                 the AP falls.
    4


     .
                                                       The maximum AP is where
    2                                              APL the ray with the greatest
                                                       slope is tangent to the TP.
   Fall „ 97 1   2   3    4   5Principles7 Microeconomics
                                   6     of 8     9                       Slide -- 18
                                            Labour
     Output, QX

                              .




                                              .
                                              .
     35                                                  TPL

                            .


                                .
                                              Given TPL , the APL was
     30
                                              calculated and graphed.
     25
     20                 .               MPL was calculated as
                                        the change in TPL given a
                                        change in L.
                                                                        L
                                                                        0
                                                                             MPL
                                                                             APL
                                                                              --
                                                                              0        0
                                                                                        TPL



           .
                                                                                    4-0
      15                         The first unit of labour added         1      4
                                                                               4       4
                                 4 units of output.


         .
      10                                                                2      5
                                                                               6         10
                                “Between” the 1st and 2cd units

       . .
       5
       4
       0
                                of labour, Q increases by 6.            3
                                                                        4
                                                                              10
                                                                             6.67
                                                                              5
                                                                             6.25
                                                                                        20
                                                                                        25



             ..... .
  APL 10       1    2   3   4    5    6   7     8   9
                                           Labour                       5      4
                                                                              5.8       29


          ..
                            Note: Where MPL = APL, APL


        .. . . . .
       8                                                                6      3
                                                                              5.3       32
MPL = APL                       is a maximum.
       6                                                                7      2
                                                                             4.87       34


                  . ..
       4                                                                8       1
                                                                             4.37       35


       .
       2                                             APL                 0
                                                                  9 3.89 35
                                                    MPL Remember: MP is graphed
      Fall „ 97 1   2   3   4    5Principles7 Microeconomicsat “between” units of--L.
                                      6     of 8     9                      Slide 19
                                                Labour
  Output, QX

                           .




                                          .
                             Z




                                          .
  35                                                TPL

                         .


                             .
  30                                          Useful things to notice:


                     .
                                           1. MPL is the slope of TPL.
  25
                                           2. When TPL increases at an increasing
  20                                       rate, MPL increases. At the inflection


         .
                                           point in the TPL , MPL is a maximum.
   15                                      When TPL increases at a decreasing rate,
                                           MPL is decreasing.

       .
   10


     . .
                                           3. The APL is a maximum when:
    5
    4                                             a. MPL = APL ,
    0                                             b. the slope of the



           ..... .
APL 10      1    2   3   4   5    6   7    8 9 ray from origin is tangent to
                                           Labour TPL .

        ..
      .. . . . .
    8
                                          4. When MPL > APL the APL is increasing.
    6                                         When MPL < APL the APL is decreasing.


                . ..
    4                                                      5. When MPL is 0, the


     .
                                                           slope of TPL is 0, and TP
    2                                             APL
                                                           is a maximum.
                                                 MPL
   Fall „ 97 1   2   3   4   5Principles7 Microeconomics
                                  6     of 8     9                      Slide -- 20
                                           Labour
Summary: TPL , MPL and APL

In many production processes                                        Z
Q initially increases at an                                                  TPL
                                          TPL
increasing rate. This is due to                   At the
division of labour and a “better”                 inflection
mix of the variable input with the                point
fixed inputs.                                                            Diminishing
                                                                         marginal
                                                                         product
As Q [TPL ]increases at an increasing
rate, MP increases.
                                           0                                       L
As Q [TPL ]increases at a
                                          MPL      MPL is
decreasing rate, MPL decreases.                                          {MP< AP,
                                          APL      a max                  AP falls}
Where 0Z is tangent to TPL , APL is a
maximum; APL = MPL .
When TPL is a maximum, MPL is zero.                                            APL
When TPL is decreasing, MPL is                                           MPL
negative.
                      {MP> AP, AP rises}                    L1 L2       L3            L
 Fall „ 97               Principles of Microeconomics                   Slide -- 21
                                                        To calculate AP:
                     PRODUCTION                                              TPL
                                                                  APL =
                                                                             L
LABOUR      KAPITAL OUTPUT   MP       AP

  0           5       0                       0 0 = ?       AP is a maximum
            DL= 1               DTPL = 8
                              8 DTP8.015      8 1 = 8       when L = 4.
                                   L=
  1            5      8
            DL= 1
  2           5       23          11.5
                             15DTP = 19       23 2 = 11.5    Note that MP is
            DL= 1                  L
  3           5       42     19 14.0          42 3 = 14      15 between 3rd & 4th
            DL= 1               DTPL = 15
  4           5       57     15DTP = 10
                                  14.25       574 = 14.25     units of L, it is 10
            DL= 1                  L
                             10 DTP = 7       67 5 = 13.4    between 4th & 5th,
  5           5       67          13.4
            DL= 1                  L                           so it equals
  6           5       74      7 12.33                          AP = 14.25 at L=4.
  7           5       79      5 11.28
  8           5       82      3 10.25
                                                        To calculate MP:
                               1   9.22
  9           5       83
                                                                     DTPL
  10          5       82      -1   8.2                      MPL =
                                                                      DL
MP is a maximum between 2cd and 3rd unit of L.
Fall „ 97                     Principles of Microeconomics                Slide -- 22
                                                      As L is added to production
                  PRODUCTION                          process, output per worker [AP]
                                                      increases. to a maximum
LABOUR   KAPITAL OUTPUT   MP         AP               “efficiency” [output/input which
                                                      occurs at L = 4.
  0           5    0               0
  1           5    8       8        8.0                MP increases to a max between
  2           5    23     15       11.5                the 2cd & 3rd units of L.
  3           5    42     19       14.0               When MP > AP the output per
  4           5    57     15       14.25              worker is increasing.
  5           5    67     10       13.4
                                                       Division of Labour and a more
  6           5    74      7       12.33               efficient mix of L, K & R causes
  7           5    79      5       11.28               AP to increase.
  8           5    82      3       10.25               Output per worker decreases
  9           5    83       1       9.22               after the 4th worker. “Too
  10          5    82      -1       8.2                many” workers for K, R & tech,
Diminishing Marginal Productivity begins               MP< AP.
with the 4rth unit of L.

  Fall „ 97                    Principles of Microeconomics               Slide -- 23
The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6
per unit. Calculate the cost functions for this production process.
   TFC = PK x K = $6K = 6 x5 = $30, This cost does not change in the short run.
   TVC = PL x L = $4L, as L changes TVC and Output change.
                                          PRODUCTION AND COST        TC = TVC+TFC
     LABOUR       KAPITAL   OUTPUT   AP      MP    TFC     TVC       TC   AFC   AVC        ATC

               =
        0 x $4 5              0       0
                                                  $30 + $ 0
                                             --

               =
        1 x $4 5              8       8       8
                                                  $30 =$30
                                                      + $4
               =
        2 x $4 5              23     11.5    15   $30 =$34
                                                      + $8
               =
        3 x $4 5              42     14      19   $30 =$38
                                                      + $12
               =
        4 x $4 5              57     14.25 15
                                                  $30 =$42
                                                      + $16
               =
        5 x $4 5              67     13.4    10
                                                  $30 =$46
                                                      + $20
        6            5        74     12.33    7   $30 + $24 =$54
                                                      =$50
        7            5        79     11.28    5
                                                  $30 + $28
        8            5        82     10.25    3
                                                  $30 =$58
                                                      + $32
        9            5        83     9.22     1   $30 =$62
                                                      + $36
        10           5        82     8.2     -1
                                                      + $40
                                                  $30 =$66
                                                         =$70
      Fall „ 97                       Principles of Microeconomics                  Slide -- 24
The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6
per unit. Calculate the cost functions for this production process.
      AFC = TFCQ = $30Q                                  ATC = AVC + AFC = TCQ
      AVC = TVC Q
                                          PRODUCTION AND COST

     LABOUR       KAPITAL   OUTPUT   AP      MP     TFC     TVC       TC     AFC     AVC     ATC

        0            5        0       0      --
                                                             $0       $30
                                                   $30
        1            5        8       8      8               $4       $34 $3.75 $ .50 $4.25
                                                   $30
        2            5        23     11.5    15    $30       $8       $38 $1.30 $ .35 $1.65
        3            5        42      14     19    $30       $12      $42 $ .71 $ .29 $1.00
        4            5        57     14.25   15    $30       $16      $46 $ .53 $ .28 $.81
        5            5        67     13.4    10    $30      $20       $50 $ .45 $ .30 $.75
        6            5        74     12.33   7     $30      $24       $54 $ .41 $ .32 $.729
        7            5        79     11.28    5    $30      $28       $58   $ .38   $ .35 $.734
        8            5        82     10.25    3    $30      $32       $62   $ .37   $ .39 $.76
        9            5        83     9.22    1     $30      $36       $66   $ .36   $ .43 $.79
        10           5        82     8.2     -1    $30      $40       $70   $ .37   $ .49 $.86


      Fall „ 97                        Principles of Microeconomics                   Slide -- 25
Things to note . . .
  As AP increases, AVC decreases.                        Since AFC declines, it will “pull”
  When AP is a maximum, AVC is a minimum.                the ATC down as Q increases
  AFC declines so long as Q or output increases.         beyond the minimum of the AVC.
  {Up to the point where TP becomes negative.}
                                      PRODUCTION AND COST

  LABOUR      KAPITAL   OUTPUT   AP      MP     TFC     TVC       TC     AFC     AVC     ATC

     0           5        0       0                               $30
                                         --
                                               $30       $0
     1           5        8       8       8              $4       $34 $3.75 $ .50 $4.25
                                               $30
     2           5        23     11.5    15
                                               $30       $8       $38 $1.30 $ .35 $1.65
     3           5        42      14     19
                                               $30       $12      $42 $ .71 $ .29 $1.00
     4           5        57     14.25   15
                                               $30       $16      $46 $ .53 $ .28 $.81
     5           5        67     13.4    10
                                               $30      $20       $50 $ .45 $ .30 $.75
     6           5        74     12.33    7
                                               $30      $24       $54 $ .41 $ .32 $.729
     7           5        79     11.28    5
                                               $30      $28       $58   $ .38   $ .35 $.734
     8           5        82     10.25    3
                                               $30      $32       $62   $ .37   $ .39 $.76
    9            5        83     9.22     1    $30      $36       $66   $ .36   $ .43 $.79
    10           5        82     8.2     -1
                                               $30      $40       $70   $ .37   $ .49 $.86


  Fall „ 97                        Principles of Microeconomics                   Slide -- 26
 TPL is Q
                         Z                                               TVC = L x PL

 TPL    When TP or Q
                                              L2 x PL
        increases                                                               TVC
                                                        TVC increases at a decreasing rate.
        at an
        increasing                  TPL
                                              L2 x PL
        rate,                                 L1 x PL                         Q* is the output
                                                                              with the lowest
                                                                              AVC! [Max AP]


   0             L1 L2       L3           L                              Q*             Q
 At L1 [inflection point] the MP is a maximum; the point of Diminishing Marginal
 productivity begins, each additional worker increases output, but at a smaller and
 smaller amount.
At L2 the AP is a maximum; output per worker is a maximum, “maximum efficiency;”
additional units of labour are less “productive.”
At L3 the TP is a maximum; this is the maximum amout of output [Q] that can
be produced given the size of the plant [fixed input K]. Additional [marginal] L is
negative.


  Fall „ 97                       Principles of Microeconomics                   Slide -- 27
       The average variable cost [AVC] and marginal cost [MC] are “mirror” images
MPL    of the AP and MP functions.
APL
APL
                                  APL                                    APL

                            MPL                                    MPL
                 L1 L2    L3         L    The maximum of the AP is consistent with
                                          the minimum of the AVC.
           1                         $
 MC =        x PL                                                  MC
                                                                   MPL
          MP
                                                                         APL
                                                                         AVC
        1
 AVC =    x PL
       AP                        AVC

                                                                               Q
                                                        APL x L2
  Fall „ 97                    Principles of Microeconomics                Slide -- 28
                                              MC will intersect the AVC at the
  $                                           minimum of the AVC [always].


                                          ATC
                                                  AVC
ATC*                               R                MC will intersect the ATC
                                                    at the minimum of the ATC.
AVC*      TC = ATC* x Q**         J              The vertical distance between
        TVC = AVC* x Q*                          ATC and AVC at any output is
                                                 the AFC. At Q** AFC is RJ.

                      Q* Q**            Q
 At Q* output, the AVC is at a minimum AVC* [also max of APL].
       At Q** the ATC is at a MINIMUM.




  Fall „ 97               Principles of Microeconomics              Slide -- 29
                    The Long Run

· The long run is a period of time where:
      · technology is constant
      · All inputs are variable
· The long run period is a series of short run
  periods. [For each short run period there is a set of TP,
    AP, MP, MC, AFC, AVC, ATC, TC, TVC & TFC for each
    possible scale of plant]




Fall „ 97            Principles of Microeconomics   Slide -- 30
 LONG RUN COSTS

                     MC1              Plant ATC* is the          LRMC
  $                         ATC!       optimal size!
                           MC2                                                ATC6
                                    ATC2
                                            ATC3                      ATC5
                                                          ATC*
                                                          ATC*
                                                                      LRAC
                                                          There is a long run
Cmin                                                      marginal cost function.
                                                   At Q* the cost per unit are
                                                   minimized [the least inputs
                                                   used].
                                           Q*                     Q
For Plant size 1, the costs are ATC1 and MC1 :
For a bigger Plant 2, the unit costs move out and down. It is more cost
effective.    As bigger plants are built the ATC moves out and down.
 Eventually, the plant size is “too large,” the ATC moves out but also up!
An “envelope curve” is constructed to represent the long run AC [LRAC].



 Fall „ 97                 Principles of Microeconomics                 Slide -- 31
                    The LRAC
· LRAC is “U-Shaped”
· The LRAC initially decreases due to “economies of
  scale”
   · economies of scale are due to division of labour.
· Eventually, “diseconomies of scale” begin
      · usually lack of adequate information to manage
        the production process




Fall „ 97           Principles of Microeconomics   Slide -- 32
            Calculation of LRAC
· With a little mathematics, the long
  run cost functions can be calculated.
· It is easier to use equations rather
  than tables and graphs.
· If consumer behavior, production and
  cost is understood, you can then think
  about how to achieve your objectives.

Fall „ 97        Principles of Microeconomics   Slide -- 33

								
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