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Costs of Production

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					 Production theory
  Provides framework for
economics of production of
            firm
 The Organization of Production

   Inputs
       Labor, Capital, Land
 Fixed Inputs
 Variable Inputs
 Short Run
       At least one input is fixed
   Long Run
       All inputs are variable
What is production
   Production refers to transformation of
    inputs or resources into outputs of goods
    and services

 Inputs = resources used in production of
  goods (fixed and variable)
 Output = end result
Basic production decision
1.How much of commodity to produce
2.How much inputs should be used

To answer these questions, the firm
a. Requires engineering data on production
   possibilities
b. Economic data on input and output prices
Production function
   Production is a function that transforms
    inputs into output
       Q = f (L, N, K……T)

Factors affecting production are
1.Technology
2.Inputs (land, labour etc)
3.Time period (short run vz long run)
Production function with 2 inputs

                Q = f(L, K)
       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
Production Function
With Two Inputs

     Discrete Production Surface
Production Function
With Two Inputs

    Continuous Production Surface
Production function with one variable
input


 1) Total Product:   TP = Q = f(L)
                             TP
2) Average Product:   APL =
                              L
                            TP
3) Marginal Product: MPL =
                             L
4) Production or            MPL
   Output Elasticity: EL = AP
                               L
Concepts of production

 Total Product :This is amount of total
  output produced by a given amount of
  factor, other factors held constant.
 Average Product: This is total output
  produced per unit of factor employed
  AP =TP/no. of units of factor employed
 Marginal Product: This is addition to total
  production by employment of extra unit of
  factor
Production function with one variable
input
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           1.25
   3            12            4             4            1
   4            14            2            3.5          0.57
   5            14            0            2.8           0
   6            12            -2            2            -1
Law of variable proportions or law of
diminishing returns
 As more and more of one factor input is
  employed, all other input quantities held
  constant, a point will be reached where
  additional quantities of varying input will
  yield diminishing marginal contribution to
  total product
 Short run law
 Some factors fixed, other factors variable
 State of technology fixed and unchanged
 Possibility of varying proportion of factors
Production function with one variable
input
Stages of return
Stage 1:Increasing returns. MP increasing,
  AP increasing, TP increases till G at
  increasing rate, after that at decreasing
  rate. G= point of inflexion
Stage 2:Diminishing returns. MP decreasing
  and falls till zero, AP decreasing, TP
  increases at a decreasing rate
Stage 3:Negative returns. MP negative, AP
  decreasing, TP is also falling
Contd..
 Stage of operations – stage2
 Stage 1 – fixed factor too much for
  variable factor. Fixed factor is more
  intensively utilized
 Stage 3- variable factor too much in
  relation to fixed factor

   Applications – agriculture, studying
Optimal use of variable input

 Marginal Revenue
                       MRPL = (MPL)(MR)
 Product of Labor
Marginal Resource             TC
                       MRCL =
  Cost of Labor                L

Optimal Use of Labor   MRPL = MRCL
Optimal use of variable input

  Use of Labor is Optimal When L = 3.50

   L      MPL     MR = P   MRPL     MRCL
  2.50     4       $10     $40      $20
  3.00     3        10      30       20
  3.50     2        10      20       20
  4.00     1        10      10       20
  4.50     0        10      0        20
Optimal use of variable input
Production with two variable inputs

Isoquants show combinations of two inputs
that can produce the same 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.
Isoquant
   An isoquant is a curve representing
    various combinations of 2 inputs that
    produce the same level of output

   ISO+QUANT= same + quantity
Production with two variable inputs

                         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
Production with two variable inputs

                         Economic
                         Region of
                         Production
Production with two variable inputs

  Marginal Rate of Technical Substitution


   MRTS = -K/L = MPL/MPK
Marginal rate of substitution

   The marginal rate of technical substitution
    of L for K (MRTS lk) is the amount of K a
    firm will give up for increasing the amount
    of L used by 1 unit and remain on same
    isoquant

MRTS lk = MP l = w
          MP k r
Production With Two Variable Inputs

          MRTS = (-2.5/1) = 2.5
Production with two variable inputs
Perfect Substitutes   Perfect Complements
Optimal combination of inputs

Isocost lines represent all combinations of
two inputs that a firm can purchase with
the same total cost.

 C  wL  rK      C  Total Cost
                  w  Wage Rate of Labor ( L)
   C w
 K  L           r  Cost of Capital ( K )
   r r
Isocost
   An isocost shows all different
    combinations of labor and capital that a
    firm can purchase, given the total outlay
    (TO) of firm and factor prices.

   The slope of an isocost is – Pl.
                                 Pk
Producer’s equilibrium
   An producer is in equilibrium when he
    maximizes output for total outlay.
   i. produces given output at minimum cost
   ii. Produces maximum output at given level
    of cost

   Equilibrium = isocost tangent to isoquant

   Here, MRTS lk = MPl /MPk = w/r

   i.e.At equilibrium, MPl = MPk
                         Pl   Pk
Optimal combination of inputs
             MRTS = w/r
Returns to Scale- Change in all inputs

       Production Function Q = f(L, K)

                Q = f(hL, hK)

If  = h, then f has constant returns to scale.
If  > h, then f has increasing returns to scale.
If  < h, the f has decreasing returns to scale.
Stages of return – Returns to scale
 The percentage increase in output when all inputs
  vary in same proportion is known as returns to
  scale
1.Constant returns to scale – Output increases in
  same proportion as increase in input
2.Increasing returns to scale-Output increases by
  greater proportion as increase in input
3. Decreasing returns to scale – Output increases
  by lesser proportion as increase in input
Returns to Scale
Constant     Increasing   Decreasing
Returns to   Returns to   Returns to
  Scale        Scale        Scale
Reasons
Causes  of increasing returns
Specialization in large scale production. In
some industries, small scale production is
not possible

Causes  of decreasing returns
Coordination and control maybe difficult.
Information maybe lost or distorted when
transmitted
Production data of Silicone chip firm
 L   K     % inc L, K    Q     % inc TP   Returns
 1   100        -       100       0       increase
 2   200      100       220      120      increase
 3   300       50       350       59      increase
 4   400     33.33       500    42.9      increase
 5   500      25         625     25       constant
 6   600      20         750     20       constant
 7   700     16.66       860    14.66     decrease
 8   800     14.29       940     9.3      decrease
 9   900     12.5       1000     6.4      decrease
Empirical production function
   Cobb-Douglas Production Function
               Q = AKaLb
      b + a = 1 (constant returns)

   Estimated using Natural Logarithms
       ln Q = ln A + a ln K + b ln L
Effect of technology
 What is the effect of technology on
  production?
 How do isoquants change?
Innovations, Global Competition
 Product Innovation
 Process Innovation
 Product Cycle Model
 Just-In-Time Production System
 Competitive Benchmarking
 Computer-Aided Design (CAD)
 Computer-Aided Manufacturing (CAM)
Elasticity of Substitution
    When price of a factor falls, the equilibrium
     position will be disturbed. The producer will
     substitute the cheaper factor for other factor.
     The degree of substitutability of factor L for
     factor K, resulting exclusively from change in
     relative factor prices, is called elasticity of
     technical substitution.

    E subs = Δ(K/L)/(K/L)
              Δ(MRTS)/(MRTS)

				
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posted:9/6/2011
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