# Production Theory by dhawanapoorv

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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 utilised
 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
Efficient Resource Utilisation
 Firm maximises production for a given
rupee outlay on labor and capital
 Minimise rupee outlay on labor and capital
inputs necessary to produce a specified
rate of output
 Produce the output rate that maximises
profit

   To solve these problems, production
isoquants and isocosts are used
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
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
maximises 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
Specialisation 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 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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