ELASTICITY by yurtgc548

VIEWS: 34 PAGES: 37

									Price   Quantity    Total  Marginal
                   Revenue Revenue
 10        1          10
 9         2          18       8
 8         3          24       6
 7         4          28       4
 6         5          30       2
 5         6          30       0
 4         7          28      -2
 3         8          24      -4
 2         9          18      -6
 1         10         10      -8
 Total and Marginal Revenue
Price   Quantity    Total  Marginal
                   Revenue Revenue
 10        1          10
 9         2          18       8
 8         3          24       6
 7         4          28       4
 6         5          30       2
 5         6          30       0
 4         7          28      -2
 3         8          24      -4
 2         9          18      -6
 1         10         10      -8
                  35
Total Revenue
                  30

                  25                                         Total Revenue
                  20

                  15

                  10

                      5

                          0
                              0   2   4        6        8          10         12
                                                                   Quantity per period
                 15
  MR/Price




                 10



                  5
                                                                Average Revenue
                  0
                              0   2   4        6       8         10          12
                  -5                                               Quantity Demanded
                                          Marginal Revenue
                -10
      Marginal Revenue Equation
Demand Equation Q = B + ap P

                P = -B/ap + Q/ap

           TR = PQ = -B/ap*Q + Q2/ap

         MR = d(PQ)/dQ = -B/ap+ 2Q/ap

              MR = 0   , Q = B/2

   For Q < B/2 , MR = +ve Q > B/2 , MR = -ve
    Relation of Demand & Marginal
            Revenue Curve

• The curves intercept y-axis at same point
   – Intercept of MR & Demand (DD) curve = -B/ap

• Slope of (DD) curve = 1/ ap

• Slope of MR curve = 2/ ap = 2 DD curve
              ELASTICITY

• A general concept used to quantify the
  response in one variable when another
  variable changes
• elasticity of A with respect to B =
                  % A/ %B
                   Calculating Elasticities
Price per P
Pound                                            Price per P
                                                 Pound



   P1 = 3
                                                    P1 = 3

   P2 = 2                                           P2 = 2
                                         D                                                 D




        0     Q1 = 5                                     0
                              Q2= 10         Q                  Q1 = 80       Q2= 160          Q
                  Pounds of X per week                              Ounces of X per week



              Pounds of X per month                            Ounces of X per month

              Slope: Y = P2 – P1                              Slope: Y = P2 – P1

                        X = Q2 – Q1                                  X = Q2 – Q1

                       = 2 – 3 = -1                                 = 2 – 3 = -1

                       10 – 5 = 5                                    160 –80 = 80
  Point Price Elasticity of Demand
 Ratio of the percentage of change in quantity
 demanded to the percentage change in price.
                      % Q
               Ep =
                      % P

                              Q / Q Q P
Point Definition         EP          
                              P / P P Q
Point Price Elasticity of Demand

        For P approaching 0

           Q/P = dQ/dP


  Linear equation = dQ/dP = constant
             dQ/dP = ap
    Qd = B + apP = B + dQ/dP P
             Point Price Elasticity of demand
     7



     6       A

     5
                   B

     4
                             C
Px




     3
                                   F

                                              G     Dx
     2



     1
                                                        H

     0
                                                              J
         0       100   200       300        400   500       600   700
                                       Qx
•   B = -5
•   C = -2
•   F = -1
•   G = -0.5
•   H = -0.2
Arc Price Elasticity of Demand


      Ep = Q2 - Q1         P2 - P1
          (Q2 + Q1)/2    (P2 + P1)/2


             Q2  Q1 P2  P
        EP               1

             P2  P Q2  Q1
                   1
                  Example

• Calculate the arc price elasticity from point C
  to point F.


    = (300 – 200)/ (3-4) * ((3+4)/ (300+200))
                        = -1.4
 Calculate Elasticity
Price   Quantity    Total  Marginal
                   Revenue Revenue
 10        1          10
 9         2          18       8
 8         3          24       6
 7         4          28       4
 6         5          30       2
 5         6          30       0
 4         7          28      -2
 3         8          24      -4
 2         9          18      -6
 1         10         10      -8
        Total Marginal Elasticity
Price Quantity    Total  Marginal Price
                 Revenue Revenue Elasticity
 10      1          10             -10.00
 9       2          18      8       -4.50
 8       3          24      6       -2.67
 7       4          28      4       -1.75
 6       5          30      2       -1.20
 5       6          30      0       -0.83
 4       7          28      -2      -0.57
 3       8          24      -4      -0.38
 2       9          18      -6      -0.22
 1       10         10      -8      -0.10
                  35
Total Revenue
                  30

                  25                                                        Total Revenue
                  20

                  15

                  10

                      5

                          0
                              0   2             4        6             8           10        12
                                                                                   Quantity per period
                 15
                                      Elastic
                                  Ep < - 1
  MR/Price




                 10                                  Unitary elastic
                                                        Ep = - 1
                                                                            Inelastic
                  5
                                                                           -1 < Ep < 0

                  0
                              0   2             4        6             8          10        12
                  -5                                                                Quantity Demanded
                                                    Marginal Revenue
                -10
Perfectly Inelastic Demand               Perfectly Elastic Demand


    Price P     D                      Price P




                                                                     D




        0                          Q       0                         Q
                    Qty Demanded                      Qty Demanded
         Perfectly inelastic demand
Qd does not change at all when price changes
              Inelastic demand
                    -1 < E  0
           Unitary elastic demand
                    E = -1
               Elastic demand
                      E < -1
          Perfectly elastic demand
Qd drops to zero at the slightest increase in price
                    Exercise
• For each of the following equations, determine
  whether the demand is elastic, inelastic or unitary
  elastic at the given price.
   a) Q =100 – 4P and P = $20
   b) Q =1500 – 20 P and P = $5
   c) P = 50 – 0.1Q and P = $20

   a) -4, elastic
   b) -0.07, Inelastic
   c) -0.67, Inelastic
Marginal Revenue and Price Elasticity
            of Demand

        MR = d(PQ) = dQ*P + dP*Q
              dQ     dQ      dQ

          = P + QdP = P 1 + dP.Q
                dQ          dQ P

                      1 
           MR  P 1    
                   EP 
• P * Qd = TR   Elastic Demand

• P * Qd = TR   Elastic Demand

• P * Qd = TR   Inelastic Demand

• P * Qd = TR   Inelastic Demand
      Problem
Present Loss                          :         $ 7.5 million
Present fee per student               :         $3,000
Suggested increase                    :         25%
Total number of students              :         10000
Elasticity for enrollment at state universities is -1.3 with respect to tuition changes



            1% increase in tuition = 1.3% decrease in enrollment
            Increase of 25%        decline in enrollment by 32.5%


                       3000 * 10000 = $30,000,000
                       3750 * 6750 = $25,312,500
   Determinants of Price Elasticity of
              Demand

  Demand for a commodity will be less elastic if:
• It has few substitutes
• Requires small proportion of total expenditure
• Less time is available to adjust to a price change
 Determinants of Price Elasticity of
            Demand

  Demand for a commodity will be more elastic if:
• It has many close substitutes
• Requires substantial proportion of total
  expenditure
• More time is available to adjust to a price change
        Income Elasticity of Demand


The responsiveness of demand to changes in income.
Other factors held constant, income elasticity of a
good is the percentage change in demand associated
with a 1% change in income


                              Q / Q Q I
 Point Definition        EI             
                              I / I   I Q
    Income Elasticity of Demand



                      Q2  Q1 I 2  I1
Arc Definition   EI           
                      I 2  I1 Q2  Q1
Demand of automobiles as a function of income is
              Q = 50,000 + 5(I)
         Present Income = $10,000
         Changed Income = $11,000


         I1 = $10,000,      Q = 100,000
         I2 = $11,000,      Q = 105,000


                    EI = 0.512
• Normal Goods ΔQ/ΔI = +ve, EI = +ve
  – Necessities 0 < EI  1
  – Luxuries EI > 1


• Inferior Goods ΔQ/ΔI = -ve, EI = -ve
   Cross-Price Elasticity of Demand
 Responsiveness in the demand for commodity X
 to a change in the price of commodity Y. Other
 factors held constant, cross price elasticity of a
 good is the % change in demand for commodity
 X divided by the % change in the price of
 commodity Y
                                QX / QX QX P
Point Definition       E XY                   Y
                                 P / PY
                                   Y       PY QX
 Cross-Price Elasticity of Demand


                          QX 2  QX 1 PY 2  PY 1
Arc Definition   E XY               
                           P 2  P 1 QX 2  QX 1
                            Y     Y



 Substitutes             Complements
   EXY  0                     EXY  0
  Importance of Elasticity in Decision
               making

• To determine the optimal operational policies
• To determine the most effective way to respond to
  policies of competing firms
• To plan growth strategy
 Importance of Income Elasticity

– Forecasting demand under different economic
  conditions
– To identify market for the product
– To identify most suitable promotional
  campaign
Importance of Cross price Elasticity

– Measures the effect of changing the price of a
  product on demand of other related products
  that the firm sells


– High positive cross price elasticity of demand is
  used to define an industry
                    Exercise
• A consultant estimates the price-quantity
  relationship for New World Pizza to be at
  P = 50 – 5Q.
   – At what output rate is demand unitary elastic?
   – Over what range of output is demand elastic?
   – At the current price, eight units are demanded
     each period. If the objective is to increase total
     revenue, should the price be increased or
     decreased? Explain.
P =50 -5Q
MR = 50-10Q
• For unitary elastic MR = 0 so Q =5
• MR will be +ve when Q<5, so demand will be
  elastic when 0<=Q<5.
• P for Q=8 is P=50-5*8 = 50-40 = 10
   Q / P  1 / 5
• Ep= -1/5*10/8 = -0.25. As demand is inelastic,
  when we increase price, TR increases.
Question: Demand for a firm’s product has been estimated to
  be
   Qd = 1000-200P
   If the price of the product is Rs 3 per unit, find out the
  price elasticity of demand at this price.
Solutuion: Price elasticity of demand is
  ep= dQ/dP*P/Q
  in the given demand function 200 is the coefficient of price
  which measures dQ/dP. In order to find out price elasticity
  of demand at price Rs3, we have first to find out the
  quantitydemanded at this price by using the given demand
  equation. Thus,
 Q=1000-200*3=400
 Thus, P=Rs3 and quantity demanded at the price is 400
  units. Substituting the values of dQ/dP, P and Q in the
  price elasticity formula, we have
 ep= dq/dp*P/Q=200*3/400=3/2=1.5
Q. The price elasticity of demand for colour
  TVs is estimated to be -2.5. if the price of
  colour TVs is reduced by 20 percent, how
  much percentage increase in the quantity of
  colour TVs sold do you expect?
Solu. Price elasticity of demand being equal
  to -2.5 means that one pwercent change in
  price causes 2.5 percent change in quantity
  demanded or sold. 20 percent reduction in
  price of colour will cause increase in
  quantity sold by 2.5*20=50 percent.

								
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