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					ELASTICITY
  Chapter 9 – Mohr and Fourie
            Week 4
Today’s session


   Definition of Elasticity
   Different types of elasticity
     1. Price elasticity of demand
     Calculating the price elasticity of
      demand (at a point =>
                   point elasticity)
Elasticity
   Elasticity is a measure of responsiveness or
    sensitivity.
      How sensitive or responsive the
       dependent variable is to changes in the
       independent variable.

         Example – maize crop dependent of
          rainfall and …..
         MAIZE CROP = DEPENDENT
          VARIABLE (BEING EXPLAINED)
         RAINFALL = INDEPENDENT
          (EXPLANATORY) VARIABLE
         How sensitive to is maize crop to
          changes in rainfall
Elasticity

   Other examples –
     How responsive is investment
      spending to changes in the
      interest rate
     How responsive is governments
      tax revenue to changes in
      taxpayers’ income
     How responsive is the quantity of
      labour supplied to changes in the
      wage rate
    Elasticity

   The measure of such
    responsiveness is called elasticity.

   ELASTICITY is THE
    PERCENTAGE CHANGE IN THE
    DEPENDENT VARIABLE IF THE
    RELEVANT INDEPENDENT
    VARIABLE CHANGES BY ONE
    PER CENT.
    Elasticity


   Elasticity = % change in dep. var.
                 % change in indep. var.

E.g.’s
DV= Maize crop,       IV= Rainfall
DV=Investment,        IV= Interest Rate
DV=Qd of Rice,        IV= Price of Rice
Elasticity

We will look at different types of
  elasticity: -
1.   Price elasticity of demand
2.   Income elasticity of demand
3.   Cross elasticity of demand
4.   Price elasticity of supply
    1. Price elasticity of demand

   % change in quantity demanded if
    the price of the product changes by
    one per cent, ceteris paribus.

   If quantity demanded = dependant variable
    &              price = independent variable,
    -- how responsive is quantity
    demanded to changes in price.
continued…
       1. Price elasticity of demand

     Price elasticity of demand =
   % change in quantity demanded of a product
       % change in the price of the product
continued…
          1. Price elasticity of demand
   Example:-
   If the price of the product changes by 5%, and it
    results in a 10% change in the quantity demanded,
    ceteris paribus, the price elasticity of demand is 2.

   Product >> calculators
   Initial price = R100
   Price increases by 5% => to R105
   Quantity of calculators demanded per month was 1000
    (at initial price of R100)
   After price increase => quantity of calculators
    demanded is 900 >>> a reduction of 10%.

   So price elasticity of demand for calculators is 2
   % change in quantity demanded/ % change in price
        = -10/5
        = -2
    Elasticity

   Important – it uses percentage changes
    and not units, i.e. relative changes, not
    absolute.
   Absolute => price expressed in monetary
    terms (rands, pounds, euros), quantity
    expressed in term of physical units (kilos,
    boxes, bags).
   Price elasticity of demand is the ratio and
    this ratio is called the
        ELASTICITY COEFFICIENT
Elasticity

   ELASTICITY COEFFICIENT shows
    how people react to changes in
    prices of different goods and
    services.
   Because it is in %, we can compare
    them to each other.
    Elasticity

   E.g. because we use % changes, we
    can compare how people react to price
    changes of meat, bread, petrol, cars,
    pens….etc.
   Would not be possible if used ‘absolute
    numbers’ e.g. a R1 change in price of
    these products would have very different
    effects on the quantity demanded.
   Can compare a 1% change in the
    price of the product.
    Elasticity
   E.g. look at two products
   Cars and bread
   If the price of cars and bread ↑ by R1,
    the effect on quantity demanded would
    be very different.
   Because the price of a car of
    approximately R100,000 is far greater
    compared to the price of a bread that is
    under R10.
   % change in car price would be <1%,
    % change in price of bread (R10 each)
    would be 10%.
Today’s session


   Definition of Elasticity
   Different types of elasticity
     1. Price elasticity of demand
     Calculating the price elasticity of
      demand
      (at a point => point elasticity)
Calculating the price elasticity
of demand
   Price elasticity of demand (ep) =
    % change in quantity demanded of a product
        % change in the price of the product

   ∆Q/Q x100     (can cancel out the 100s)
    ∆P/P x 100
    = ∆Q/Q
      ∆P/P

= ∆Q/ Q x P/∆P
ep = ∆Q/∆P x P/Q
   (elasticity at a POINT)
    Calculating the price elasticity
    of demand
   Price elasticity of demand (ep) =
    % change in quantity demanded of a product
          % change in the price of the product

   ∆Q/Q x100    (can cancel out the 100s)
    ∆P/P x 100

Calculator example
Initial price R100, after increase of 5% increase, R105
Initial Qd 1000 per week, after P increase, 900 per week

Working out % change in Qd
= ∆Q/Q = 100/1000 = 0.1 (0.1x100 = 10%)
Calculating the price elasticity
of demand
   Price elasticity of demand (ep) =
    % change in quantity demanded of a product
          % change in the price of the product

   ∆Q/Q x100    (can cancel out the 100s)
    ∆P/P x 100

Working out change in price
Initial price R100, after increase of 5% increase, R105
∆P/P
=5/100 = 0.05 (0.05x100 = 5%)
Calculating the price elasticity
of demand
   Price elasticity of demand (ep) =
     % change in quantity demanded of a product
          % change in the price of the product

   ∆Q/Q x100      (can cancel out the 100s)
    ∆P/P x 100

    = ∆Q/Q
      ∆P/P

= ∆Q/ Q x P/∆P

ep = ∆Q/∆P x P/Q

(Derive this for yourself to check if you fully
  understand how we got to this final equation!)
    Continued…

    Calculating the price elasticity
    of demand
   The slope of the linear demand curve
    = ∆P/ ∆Q
   So the one part of the equation is ∆Q/
    ∆P which is the inverse of the slope of
    the linear demand curve.
   Second part of the equation is P/Q which
    is the ratio of price to quantity at any
    point on the line (therefore the know
    as POINT ELASTICITY… ELASTICITY
    AT A POINT.
    Continued…

    Calculating the price elasticity
    of demand
   Since the ratio is different at any point on
    the demand curve, the price elasticity of
    demand will be different at any point on
    the curve, since the slope (or inverse of the
    slope) is constant.
Today’s session


   Definition of Elasticity
   Different types of elasticity
     1. Price elasticity of demand
     Calculating the price elasticity of
      demand (at a point =>
                   point elasticity)

				
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posted:8/21/2011
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