Price elasticity of demand - PowerPoint by pLdevf2h

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									  Price elasticity of demand
  Often in economics we look at
  how the value of one variable
 changes when another variable
   changes. The concept called
elasticity is a summary statement
       about those changes.
                                    1
                                      Elasticity
The law of demand or the law of supply is a statement
about the direction of change of the quantity demanded,
or supplied, respectively, when there is a price change.

The concept of elasticity adds to these concepts by
indicating the magnitude of the change in quantity,
given the price change. The magnitude of the change is
reported in percentage terms.




                                                         2
  own price elasticity of demand

Ed = (% change in Q)/(% change in P)

As an example, if Ed = -2 we say for every 1 % change
in the price of the good the quantity demand changed
in the opposite direction by 2 %.




                                                        3
                                 absolute value
You may recall a function in math called the absolute value.
Basically this function makes negative values positive and
leaves positive values positive.
In the notes I will write abs( ) to mean take the absolute
value.
The own price elasticity of demand is a negative number, so
we will take the absolute value to describe some concepts
about it.



                                                               4
Elasticity can have three basic
                        values
If abs(Ed) > 1 we say demand is elastic. This means the
% change in the Qd is greater than the % change in
price.

If abs(Ed) = 1 we say demand is unit elastic. This
means the % change in the Qd is equal to the % change
in price.

If abs(Ed) < 1 we say demand is inelastic. This means
the % change in the Qd is less than the % change in
price.

                                                        5
                             Elasticity again
      P
                                   In the upper left of the
 P1                                demand curve the %
 P2                                change in the Qd is
                                   greater than the %
                                   change in the P and
                                   thus the Ed > 1 .
                               Q
         Q1 Q2
Without a real formal proof of the above statement, we
can see the % change in Qd is about 100 % and the %
change in P is less than 100 %. Demand is elastic here.

                                                          6
     Elasticity has several ranges
      P
                         of values
                                   In the lower right of
                                   the demand curve the
                                   % change in the Qd is
                                   less than the % change
 P                                 in the P and thus the
 1                                 Ed < 1.
 P
                               Q
 2               Q1 Q2
Without a real formal proof of the above statement, we
can see the % change in Qd is less than 100 % and the %
change in P is about 100 %. Demand is inelastic here.

                                                          7
     Elasticity has several ranges
      P
                         of values
                                   In the middle of the
                                   demand curve the %
 P                                 change in the Qd is
 1                                 equal to the % change
 P                                 in the P and thus the
 2                                 Ed = 1.
                               Q
             Q1 Q2
Without a real formal proof of the above statement, we
can see the % change in Qd is about equal to the % change
in P. Demand is unit elastic here.

                                                           8
        Calculation point slope method
P                If we know the slope of the demand
                 curve the elasticity at a point is found
                 by using the Q and P value of the
11               point and the slope in the following
                 way:
                 (P/Q)(1/slope).
                 Example say the slope here is -1.
                 The elasticity is (11/10)(1/-1) = -1.1
     10 Q        When we take absolute value we get
                 1.1. Elastic in this case.

                                                            9
Own price elasticity and total
    revenue changes
    Total revenue (TR) is price times
  quantity. Along the demand curve P
   and Q move in opposite directions.
  Knowledge of Ed assists in knowing
          how TR will change.

                                        10
    Elasticity and total revenue
                     relationship
When we look at the collection of consumers in the
market, at this time in our study we assume each
consumer pays the same price per unit for the product.

Also at this time in our study the total expenditure of
the consumers in the market would equal the total
revenue (TR) to the sellers.

So, here we look at the whole demand side of the
market in general.


                                                          11
       Elasticity and total revenue
       P
                        relationship
                                     TR in the market is
  P1                                 equal to the price in the
                                     market multiplied by
                                     the quantity traded in
                                     the market. In this
                                     diagram TR equals the
                                  Q area of the rectangle
         Q1
                                     made by P1, Q1 and
the horizontal and vertical axes. We know from math that
the area of a rectangle is base times height and thus here
that means P times Q.
                                                            12
     Elasticity and total revenue
                      relationship
We will want to look at the change in values of a
variable and in order to do so we want to have a
consistent measure of change. In this regard let’s say
the change in a variable is
              the later value minus the earlier value.

Thus if the price should change from P1 to P2, then the
change in price is
              P2 - P1, or similarly if the TR should
change the change in TR is
              TR2 - TR1.

                                                          13
       Elasticity and total revenue
       P
                        relationship
                                      Now in this graph
 P1                                   when the price is P1
         a
 P2                                   the TR = a + b(adding
                                      areas) and if the price
         b c
                                      is P2 the TR = b + c.

                                    Q The change in TR if
          Q1 Q2                          the price should fall
from P1 to P2 is (b + c) - (a + b) = c - a.
Similarly, if the price should rise from P2 to P1 the change
in TR is a - c. I will focus on price declines next.

                                                             14
       Elasticity and total revenue
       P
                        relationship
                                     Since the change in TR
                                     is c - a, the value of the
 P1                                  change will depend on
         a
 P2                                  whether c is bigger or
         b c                         smaller, or even equal
                                     to, a. In this diagram
                                     we see c > a and thus
                                   Q the change in TR > 0.
          Q1 Q2
This means that as the price falls, TR rises. I think you
will recall that in the upper left of the demand the
demand is price elastic. Thus if the price falls in the elastic
range of demand TR rises.
                                                                  15
                       Elasticity and TR
You will note on the previous screen that I had c - a. In
the graph c is indicating the change in TR because we
are selling more units. The area a is indicating the
change in TR when there is a price change. We have to
bring the two together to get the change in TR.

Thus a lower price has a good and a bad.
Good - sell more units.
Bad - sell at lower price.




                                                        16
      Elasticity and total revenue
      P
                       relationship
                                        Now in this graph
                                        when the price is P1
                                        the TR = a + b(adding
                                        areas) and if the price
  P                                     is P2 the TR = b + c.
  1        a
           b           c                In this diagram we see
  P
                                    Q c < a and thus the
  2                 Q1 Q2               change in TR < 0.
I think you will recall that in the lower right of the
demand the demand is price inelastic. Thus if the price
falls in the inelastic range of demand TR falls.

                                                             17
       Elasticity and total revenue
       P
                        relationship
                                      Now in this graph
                                      when the price is P1
  P                                   the TR = a + b(adding
           a                          areas) and if the price
  1
  P                                   is P2 the TR = b + c.
           b       c                  In this diagram we see
  2
                                  Q c = a and thus the
               Q1 Q2                  change in TR = 0.
I think you will recall that in the middle of the demand
the demand is unit elastic. Thus if the price falls in the unit
elastic range of demand TR does not change.

                                                             18
             Elasticity and TR
P
             When the price falls the quantity
             demanded always rises. As the
             quantity demanded rises
     D
         Q   (because of the price change)
             the TR is first rising in the
TR           elastic range, levels off when
             demand is unit elastic and TR
             falls in the inelastic range.
         Q




                                                 19
                          Marginal revenue
Marginal revenue is defined as the change in total revenue as
the number of units cold changes. In the demand graph we
have seen that in order to sell more the price has to be
lowered. So, there is a relationship between elasticity and
marginal revenue.
If price falls and demand is elastic we know TR rises so MR
is positive.
If Price falls and demand is inelastic we know TR falls and so
MR is negative.
If price fall and demand is unit elastic we know TR does not
change.

                                                                 20
Other demand elasticities

There are other elasticities besides
    the own price elasticity of
  demand. Let’s see a few here.


                                       21
                              demand shifters
We saw that things like taste and preference, price of other
goods, income and the number of buyers shift the demand
curve if they change. How much do they shift the demand
curve?
We use other elasticity concepts as an indication of how much
the curve will shift given a change in one of these factors.




                                                                22
                cross price elasticity of
                               demand
Edxy = % change in Qdx / % change in Py.
The bigger the value the more the demand shifts.
If the value is negative we have complements and if positive
we have substitutes.
If the absolute value is between 0 and 1 the cross elasticity is
inelastic, if = 1 unit elastic and if greater than 1 elastic.




                                                                   23
     income elasticity of demand
Edxm = % change in Qdx / % change in M.
The bigger the value the more the demand shifts.
If the value is negative we have an inferior good and if
positive we have a normal good.
If the absolute value is between 0 and 1 the income elasticity
is inelastic, if = 1, unit elastic, and if greater than 1, elastic.




                                                                      24
                          Elasticity of supply
The elasticity of supply is used to indicate the percentage
change in the quantity supplied given a percentage change in
price.
The elasticity of supply is calculated in a manner similar to the
other elasticities we have seen and has a similar interpretation
in terms of the range of values the elasticity might take, i.e.
elastic, inelastic and unit elastic.




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