Elasticities by nikeborome

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									        Elasticity as a measure of
             responsiveness


Y = Effect variable
X = Cause variable
Y=ƒ(X)
Y=α–βX

Where α & β are the coefficients
Summing UP
Introductory
 Economic
  Lecture 6
  Elasticity



 Definitions
Computations
Recap
       Y = α – βX in Y-X space
         Y       E (elastic)

             C
                      P
                                   R
                      Q
                          B       IE (inelastic)
             A

        O                               X
β = slope = ∆Y / ∆X
                              CA / AB > PQ / QR
     Real world example
Qd
          E ( elastic )

     C
             P
                           R
             Q
                 B        IE ( inelastic )
      A

                                 P
Conventional representation
  P
          IE ( inelastic )
      R
             B
                              C
             A
                 P           E ( elastic )
      Q

                                    Qd
        Slope of a demand curve


Slope of a demand curve = β

Higher slope = Inelastic demand curve
                 (Steep)

Lower slope = Elastic demand curve
               (Flat)
    Price elasticity of other variables


                  Y=ƒ(X)

1. Y = Qd & X = Price
                     Price elasticity of demand.
2. Y = Qs & X = Price
                     Price elasticity of supply.
3. Y = Qd & X = Income
                     Income elasticity of demand.
4. Y = Qda & X = Priceb
                            Cross price elasticity of
                            demand.
         Formal definition of the four
               combinations
        1. Price elasticity of demand

                 can be defined as

 PЄd = Percentage change in Quantity Demanded
             Percentage change in Price


Where Є = Epsilon; universal notation for
           elasticity.
PЄd = Percentage change in Quantity Demanded
             Percentage change in Price



                  Example
If, for example, a 20% increase in the price of a
product causes a 10% fall in the Quantity
demanded , the price elasticity of demand will be:

    PЄd = - 10% = - 0.5
           20%
       Formal definition of the four
             combinations

         2. Price elasticity of supply

                can be defined as

PЄs = Percentage change in Quantity Supplied
            Percentage change in Price
 PЄs = Percentage change in Quantity Supplied
            Percentage change in Price



                 Example
If a 15% rise in the price of a product causes a
15% rise in the quantity supplied, the price
elasticity of supply will be:

         PЄs = 15 % = 1
               15 %
       Formal definition of the four
             combinations

    3. Income elasticity of demand

               can be defined as

YЄd = Percentage change in Quantity Demanded
           Percentage change in Income
YЄd = Percentage change in Quantity Demanded
           Percentage change in Income



                  Example
If a 2% rise in the consumer’s incomes causes an
8% rise in product’s demand, then the income
elasticity of demand for the product will be :

   YЄd = 8% = 4
         2%
        Formal definition of the four
              combinations

    4. Cross price elasticity of demand

                  can be defined as

PbЄda = Percentage change in Demand for good a
           Percentage change in Price of good b
PbЄda = Percentage change in Demand for good a
          Percentage change in Price of good b


                  Example
 If, for example, the demand for butter rose by
 2% when the price of margarine rose by 8%,
 then the cross price elasticity of demand of
 butter with respect to the price of margarine will
 be.

         PbЄda = 2% = 0.25
                  8%
  PbЄda = Percentage change in Demand for good a
            Percentage change in Price of good b



                  Example

If, on the other hand, the price of bread (a compliment)
rose, the demand for butter would fall. If a 4% rise in
the price of bread led to a 3% fall in the demand for
butter, the cross-price elasticity of demand for butter
with respect to bread would be :
     PbЄda = - 3% = - 0.75
                 4%
                      8
          0 < |Є|<     (for absolute values of elasticity)
     Є=0
 P

                P     Є<1

           Qd                  P   Є=1
                          Qd
                                            P   Є >1
                                       Qd                  P   Є=α
                                                      Qd

                Inelastic                   Elastic              Qd

Perfectly Inelastic         Unit Elastic          Perfectly Elastic
          Total revenue and elasticity

         Firm A                     Firm B




O                               O

    * Not perfect competition
                 Firm A

P                      OAFD > OBTC
10 D     F             TR as P
                          Inelastic demand Curve
6C           T


       A B
O      90 100     Qd
                  Firm B

P                       OVZU > OYUR
                        TR as P
                          Elastic demand curve
    R    U
7
    U              Z
6

             Y      V
O       40       100    Qd
     Numerical calculation of elasticity for
                   firm A
                   Є = percentage change in Qd
 P                      percentage change in P

10 D      F             = 90 – 100       10 – 6
                           100             6

 6C           T               = - 0.15

        A B
 O      90 100    Qd
        Numerical calculation of elasticity for
                      Firm B
                        Є = percentage change in Qd
                             percentage change in P
P
                              =   40 – 100    7–6
                                    100        6
    R           U
7                                   =-3.6
    U                  Z
6

              Y         V
O             40     100 Qd
   Elastic demand between 2 points

    P

    8              ЄKL = percentage change in Qd
          K
                        percentage change in P
    6          L
                         = 16– 8   ÷   6–8
                              8         8
                         = -4

    O     8   16    Qd

TR as the P
     Inelastic demand between 2 points


                       ЄGH = percentage change in Qd
      P
                               percentage change in P
                  G        = 36– 28 ÷ 1 – 3
     3                           28           3
                             =-3
                       H
     1                          7

      O          28   36      Qd

TR    as the P
Overview of previous example
    ЄKL = percentage change in Qd
           percentage change in P
         = 16– 8 ÷ 6 – 8
             8          8
         = -4
  ЄLK = percentage change in Qd
         percentage change in P
      = 8 – 16 ÷ 8 – 6
          16          6
      = -3
           2
          Concept of arc elasticity
As Є = ∆ Q      ÷ ∆P
        Q         P
 To measure arc elasticity we take average values for Q and
 P respectively.


        ЄKL = 16– 8      ÷   6–8       =-7
               12             7          3

        ЄLK = 8 – 16 ÷        8– 6     =-7
               12               7        3

average elasticity along arc KL or LK is - 7/ 3
                  Point elasticity

                Є=∆Q          ÷     ∆P
                  Q                  P

                 Є= ∆Q         x    P
                    ∆P              Q

             d = infinitely small change in price

                     Є=dQ          x     P
                       dP                Q

A straight line demand curve will have a different Є at
each point on it except Є = 0 or Є = α .
        Previous example
P
                      dP = -1
8       K             dQ   4
            L                   P at K = 8 = 1
6                               Q         8
                                Є = - 4 x 1 = -4
                 Qd
O   8       16                  P at L = 6 = -3
                                Q        16 8
                                Є=-4x3 =-3
                                        8     2
         Qd = 60 – 15P + P2

P   60      - 15 P   P2       Qd (000s)
0   60        0       0          60
1   60       -15      1          46
2   60       -30      4          34
3   60       -45      9          24
4   60       -60     16          16
5   60       -75     25          10
6   60       -90     36           6
        7             Qd (000s)
        6
        5
Price




        4
        3
        2
        1
        0
            0   20          40           60   80
                     Quantity demanded
            PЄd = d Q x P
                  dP    Q


Differentiating the demand Equation
Given Qd = 60 – 15P + P2
then dQ/dP = -15 + 2P
Thus at a price of 3 for example,
dQ/dP = -15 + ( 2 x 3 ) = -9 Thus price Elasticity of
demand at Price 3 is - 9 x P/Q
= - 9 x 3 / 24 = - 9 / 8

								
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