Elasticity - PowerPoint - PowerPoint

Document Sample
Elasticity - PowerPoint - PowerPoint Powered By Docstoc
					Quantitative Demand Analysis
         (Elasticity)

         Finance 514
        Baye Chapter 3
                Elasticity
• General concept that measures the
  responsiveness of two variables to one
  another
• Mechanism to characterize demand and
  supply
• Measure of how markets react to changing
  conditions
• Allows for a more detailed understanding
  and analysis of supply and demand
                   Price Elasticity
• ED = % change in Q / % change in P
• Shortcut notation: ED = %Q / %P
• A percentage change from 100 to 150 is 50%
• A percentage change from 150 to 100 is -33%
• For arc elasticities, we use the average as the base, as in
  100 to 150 is +50/125 = 40%, and 150 to 100 is -40%
• Arc Price Elasticity -- averages over the two points
             Average quantity                      arc price
                                     •
                                                   elasticity
ED = Q/ [(Q1 + Q2)/2]
    P/ [(P1 + P2)/2]                          •       D

                Average price
     Arc Price Elasticity Example
•   Q = 1000 when the price is $10
•   Q= 1200 when the price is reduced to $6
•   Find the arc price elasticity
•   Solution: ED = %Q/ %P = +200/1100
                                   -4/8
    or -0.3636.

    – A 1% increase in price reduces quantity by .36
      percent.
    Point Price Elasticity Example
•    Need a demand curve or demand function to
     find the price elasticity at a point.
      ED = %Q/ %P =(Q / P)(P/Q)

     If Q = 500 - 5•P, find the point price
     elasticity at P = 30; P = 50; and P = 80
1. ED = (Q / P)(P/Q) = - 5(30/350) = - .43
2. ED = (Q / P)(P/Q) = - 5(50/250) = - 1.0
3. ED = (Q / P)(P/Q) = - 5(80/100) = - 4.0
                 Price Elasticity
   (Both point price and arc elasticity )

• If ED = -1, unit elastic
• If ED > -1, inelastic, e.g., - 0.43
• If ED < -1, elastic, e.g., -4.0
                                          Straight line
         price                           demand curve
                     elastic region
                                            example
                          unit elastic

                                  inelastic region
                                    quantity
             Two Extreme Examples

                                                 D


      D                D’




                                                 D’


Perfectly Elastic | ED| =  and Perfectly Inelastic |ED | = 0
          Use For Elasticity
• Elasticity is related to revenues
• Suppose demand is elastic, and you raise
  price.
• TR = P•Q, so, %TR = %P + % Q
• If elastic, P increases but Q falls a lot
• Hence TR FALLS
• Suppose demand is inelastic, and we decide
  to raise price. What happens to TR? and
  profit?
Another Way to              Elastic
                       P
  Remember                     Unit Elastic

                                      Inelastic
 • Linear demand
   curve
 • TR on the other     TR
                                              Q
   curve
 • Look at arrows to                          TR
   see movement in
   TR
                                              Q
     1979 Deregulation of Airfares
•   Prices declined after deregulation
•   And passengers increased
•   Also total revenue increased
•   What does this imply about the price
    elasticity of air travel?
  Determinants of the Price Elasticity
• The availability and the closeness of substitutes
   – more substitutes, more elastic
• The more durable is the product
   – Durable goods are more elastic than non-durables
• The percentage of the budget
   – larger proportion of the budget, more elastic
• The longer the time period permitted
   – more time, generally, more elastic
   – consider examples of business travel versus vacation travel
     for all three above.
   Time and Adjustment to an Reduction in Supply
• Consider the market for gasoline of
  the late 1970s and early 1980s (and     Price                          S2
now).                                     ($ per gallon)

• The price of a gallon of gasoline in                                          S1
   1978 was $.70 (point A).
                                         1.20                    B
• When supply declined unexpectedly
                                         1.10
   in the late 1970s, prices increased
                                         1.00                C
   to $1.20 and consumption fell to 7.0
                                          .90
   million barrels per day (from 7.4) as
                                          .80
   consumers moved along their short                                 A
                                          .70
   run demand curve (to point B).
                                       .60
• Note how little quantity demanded    .50
  fell due to this shock. In the long  .40
  run, the demand for gasoline is more .30
  responsive to price changes          .20                                      DLR
                                       .10
                                                                          DSR
• By 1982, the market equilibrated at                                         Quantity
  point C, with consumption of 6.6                         6.6 7.0 7.4        (million
  million barrels a day and a market                                           barrels of
                                                                               gas per day)
  price of $1.00 a gallon).
        Elasticity of Demand
Inelastic                            Approximately Unitary Elasticity
 Salt                          0.1     Movies owner occupied (long run) 0.9
                                       Homes,
 Matches                       0.1     Shellfish (consumed at home)     1.2
 Toothpicks (short run)
 Airline travel                0.1     Oysters (consumed at home)       0.9
 Gasoline (short run)          0.1                                      1.1
 Gasoline (long run)           0.2     Private education
                                       Tires (short run                 1.1
 Natural gas, home (short run) 0.7     Tires (long run)                 0.9
 Natural gas, home (long run) 0.1      Radio and television receivers   1.2
                               0.5                                      1.2
 Coffee
 Fish (cod), at home           0.3   Elastic
 Tobacco products (short run) 0.5      Restaurant meals run)            2.3
                               0.5     Foreign travel (long
 Legal services (short run)                                             4.0
                               0.4     Airline travel (long run)
                                                                        2.4
 Physician services
 Taxi (short run)              0.6
                                       Fresh green peas run)
                                       Automobiles (short               2.8
 Automobiles (long run)        0.6
                                                                        1.4
                               0.2
                                       Chevrolet automobiles            4.0
                                       Fresh tomatoes                   4.6
  • Can you explain why the demand for some goods
    is highly inelastic while that for others is elastic.
                    Income Elasticity
  EY = %Q/ %Y = ( Q/ Y)( Y/Q)                point income


           EY = Q/ [(Q1 + Q2)/2] arc income
               Y/ [(Y1 + Y2)/2] elasticity


• Arc income elasticity:
   – suppose dollar quantity of food expenditures for families earning
     $20,000 is $5,200; and food expenditures rises to $6,760 for
     families earning $30,000.
   – Find the income elasticity of food
   – %Q/ %Y = (1560/5980)•(10,000/25,000) = .652
   – With a 1% increase in income, food purchases rise .652%
          Income Elasticity Definitions
•   If EY >0, then it is a normal good
    –   some goods are Luxuries: EY > 1 with a high income
        elasticity
    –   some goods are Necessities: EY < 1 with a low income
        elasticity
•   If EY is negative, then it’s an inferior good
•   Consider these examples:
    1. Expenditures on new automobiles
    2. Expenditures on new Chevrolets
    3. Expenditures on 1996 Chevy Cavaliers with 150,000 miles
    Which of the above is likely to have the largest income elasticity?
    Which of the above might have a negative income elasticity?
   Point Income Elasticity Problem
• Suppose the demand function is:
             Q = 10 - 2•P + 3•Y
• find the income and price elasticities at a price of P =
  2, and income Y = 10
• So: Q = 10 -2(2) + 3(10) = 36
• EY = (Q/Y)( Y/Q) = 3( 10/ 36) = .833
• ED = (Q/P)(P/Q) = -2(2/ 36) = -.111
• Characterize this demand curve, which means
  describe them using elasticity terms.
           Cross Price Elasticities
EAB = %QA / %PB = (QA/ PB)(PB /QA)

• Substitutes have positive cross price elasticities:
  Butter & Margarine
• Complements have negative cross price
  elasticities: DVD machines and the rental price of
  DVDs at Blockbuster
• When the cross price elasticity is zero or insignificant, the
  products are not related
                    Problem

Find the point price elasticity, the point income
elasticity, and the point cross-price elasticity at
P=10, Y=20, and PS=9, if the demand function
were estimated to be:

    QD = 90 - 8·P + 2·Y + 2·Ps

Is the demand for this product elastic or inelastic?
Is it a luxury or a necessity? Does this product
have a close substitute or complement?
                  Combined Effect of
                  Demand Elasticities
• Most managers find that prices and income change
  every year. The combined effect of several
  changes are additive.
   %Q = ED(% P) + EY(% Y) + EX(% PR)
  – where P is price, Y is income, and PR is the price of a related good.

• If you knew the price, income, and cross price
  elasticities, then you can forecast the percentage
  changes in quantity.
   Example: Combined Effects of Elasticities
• Toro has a price elasticity of -2 for snow-throwers
• Toro snow throwers have an income elasticity of 1.5
• The cross price elasticity with professional snow
  removal for residential properties is +.50
• What will happen to the quantity sold if you raise
  price 3%, income rises 2%, and professional snow
  removal companies raises its price 1%?

Q: Will Total Revenue for your product rise or fall?
           Questions for Thought
• Studies indicate that the demand for Florida
  oranges, Bayer aspirin, watermelons, and airfares
  to Europe are elastic. Why?
   – Why is the demand for salt, matches, and
       gasoline (short-run) inelastic?
• Are the following statements true or false?
   – A 10% reduction in price that leads to a 15% increase
     in amount purchased indicates a price elasticity of more
     than 1.
   – A 10% reduction in price that leads to a 2% increase in
     total expenditures indicates a price elasticity of more
     than 1.
             Demand Estimation
• Interviews
   – Surveys
   – Focus Groups
   – Simulated Markets
• Price Experimentation
   – Varying prices across different markets
• Statistical Analysis
   – Estimate demand curves
   – The problem of ceteris paribus and omitted variables
       Price Elasticity of Supply

• The price elasticity of supply is the percent
  change in quantity supplied divided by the
  percent change of the price causing the
  supply response.
  – Analogous to the price elasticity of demand.
  – However, the price elasticity of supply will be
    positive because the quantity producers are
    willing to supply is directly related to price.
    Determinants of Supply Elasticity

• Ability of sellers to change the amount of
  the good they produce.
  – Beach-front land is inelastic.
  – Books, cars, or manufactured goods are elastic.
• Time period.
  – Supply is more elastic in the long run.

				
DOCUMENT INFO