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Demand and Price Elasticity (PowerPoint)

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					Demand and Price Elasticity
Example from the Firm
                               Isoquants
          16       1, 16
                                                     If this firm wants to produce 4
          14                                         units of output, it should use 4
          12           Q=4                           units of labor and 4 units of
                                                     capital.
          10
Capital




           8
           6
           4                   4, 4
           2
                                                              16, 1
           0
               0   2       4          8
                                  6 Labor 10   12   14   16
• Firm Problem:
  – For a given quantity, find the least cost way of
    producing it.
  – Build your marginal cost curve.
  – Use price and marginal cost to find the profit-
    maximizing quantity.

  – “Find the lowest isocost”
• Consumer Problem:
  – For a given income, find the highest utility you
    can attain.

  – “Find the highest indifference curve”
                                        Example
                                Indifference Curve
                   16       1, 16                                                 pf = 16
                   14                                                             ph = 16
                                                                                  I = 160
                   12
Football tickets




                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                          16, 1
                    0
                        0   2       4      6   8     10    12   14   16
                                          Hockey tickets
                                      Example
                                Indifference Curve
                   16                                                 pf = 16
                   14                                                 ph = 16
                                                                      I = 160
                   12
Football tickets




                   10
                    8
                    6
                                      5, 5
                    4
                    2
                    0
                        0   2     4    6   8     10    12   14   16
                                      Hockey tickets
                            Why not (4,4)?
                                Indifference Curve
                   16       1, 16                                                 pf = 16
                   14                                                             ph = 16
                                                                                  I = 160
                   12
Football tickets




                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                          16, 1
                    0
                        0   2       4      6   8     10    12   14   16
                                          Hockey tickets
                            Why not (6,6)?
                                Indifference Curve
                   16                                                 pf = 16
                   14                                                 ph = 16
                                                                      I = 160
                   12
Football tickets




                   10
                    8
                    6
                                      5, 5
                    4
                    2
                    0
                        0   2     4    6   8     10    12   14   16
                                      Hockey tickets
                                      Demand
                                Indifference Curve
                   16                                                  pf = 16
                   14                                                  ph = 16
                                                                       I = 100
                   12
Football tickets




                   10                                            At a price of 16 (when
                    8
                                                                 income is 160 and the
                                                                 price of football tickets
                    6
                                      5, 5                       is 16), you demand 5
                    4                                            hockey tickets.
                    2
                    0
                        0   2     4    6   8     10    12   14   16
                                      Hockey tickets
                                        Demand
                                Indifference Curve
                   16       1, 16                                                 pf = 16
                   14                                                             ph = 16
                                                                                  I = 160
                   12
Football tickets




                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                          16, 1
                    0
                        0   2       4      6   8     10    12   14   16
                                          Hockey tickets
  Demand
                                Indifference Curve                           pf = 16
                                                                             ph = 16
                   16       1, 16
                   14
                                                                             I = 160
                   12




Football tickets
                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                     16, 1
                    0
                        0   2       4      6   8 10 12     14   16
                                          Hockey tickets

             P


                   16                   



                                        5
                                                                       Q
  Demand
                                Indifference Curve                           pf = 16
                                                                             ph = 10
                   16       1, 16
                   14
                                                                             I = 160
                   12




Football tickets
                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                     16, 1
                    0
                        0   2       4      6   8 10 12     14   16
                                          Hockey tickets

             P


                   16                   
                   10                        


                                        5 7
                                                                       Q
  Demand
                                Indifference Curve                           pf = 16
                                                                             ph = 40
                   16       1, 16
                   14
                                                                             I = 160
                   12




Football tickets
                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                     16, 1
                    0
                        0   2       4      6   8 10 12     14   16
                                          Hockey tickets

             P 
              40



                   16                   
                   10                        


                            2           5 7
                                                                       Q
  Demand
                                Indifference Curve
                   16       1, 16
                   14
                   12




Football tickets
                   10
                    8
                    6
                                           5, 5
                    4                   4, 4
                    2
                                                                     16, 1
                    0
                        0   2       4      6   8 10 12     14   16
                                          Hockey tickets

             P 
              40



                   16                   
                   10                        
                                                  D
                            2           5 7
                                                                       Q
Demand
              p1 = 3
              p2 = 3
              I = 54
x2




         x1
P




         Q
    Questions you have to ask
• Given these prices and income, what is
  the most I could buy of each good.

• Use these to plot your intercepts

• Think about the slope (ratio of prices)
Demand
                   p1 = 3
                   p2 = 3
                   I = 54
x2
18




         18   x1
P


3    



     9
              Q
Demand
              p1 = 4
              p2 = 3
              I = 54
x2




         x1
P


3    



     9
         Q
Demand
                         p1 = 4
                         p2 = 3
                         I = 54
x2
18




             13.5   x1
P

4    
         

                    D

     3   9
                    Q
Demand
                       p1 = 2
                       p2 = 3
                       I = 54
x2




                  x1
P

     
         
2            

     3   9   20
                  Q
Demand
                       p1 = 2
                       p2 = 3
                       I = 54
x2
18




                  27
                  x1
P

     
         
2            

     3   9   20
                  Q
Demand
                       p2 = 3
                       I = 54
x2




                  x1
P

 4   
 3       
 2           
                  D
     3   9   20
                  Q
           Demand

           x2


PERSON 1




                    x1
           Demand

           x2


PERSON 1




                    x1
           x2


PERSON 2



                    x1
Demand (Person 2)
                        p1 = 3
                        p2 = 3
                        I = 54
    x2

     18




              18   x1
     P


     4    



          9
                   Q
Demand
                          p1 = 4
                          p2 = 3
                          I = 54
x2

 18




              13.5   x1
P

 4    
          



      7
                     Q
Demand
                          p1 = 2
                          p2 = 3
                          I = 54
x2

 18




                   x127
P

      
          
 2            

              12
                   Q
Demand
                           p2 = 3
                           I = 54
x2




                      x1
P

 4   
 3       
 2           
                  D
     7 9     12
                      Q
                  Demand
                                              p2 = 3
                                              I = 54
x2                      x2




                   x1                            x1
P                       P

 4                      4   
 3                      3       
 2                      2           
                   D                      D
     3   9   20              7 9     12
                   Q                              Q
    Measuring responsiveness
• One method is to just look at the slope
   – When P changes by 1, how much does Q change?
   – Depends on the scale.
   – How do you compare TV’s with peaches?
• Better method is to use the elasticity
   – When P changes by 1%, how much (by what percent)
     does Q change?
   – Doesn’t depend on scale
   – Ties directly to revenue/expenditure.
        Calculating Elasticity
• Own-price elasticity
                      %Qx
                 x 
                      %Px
        Calculating Elasticity
• Own-price elasticity
                        %Qx
                   x 
                        %Px
• In this class, you will calculate the arc
  elasticity:
                           Qx
                  % Qx Ave( Qx )
             x        
                  % Px     Px
                          Ave( Px )
         Own price elasticity
• Another way to calculate the elasticity is
  using the point elasticity:
                         1 Px
                  x 
                       slope Qx
• Although we won’t use it in this class, it is
  handy to show some properties of
  elasticity.
         Own price elasticity
• Own price demand elasticity is (almost)
  always negative.
                        1 Px
                 x 
                      slope Qx
• Why?
         Own price elasticity
• Own price demand elasticity is (almost)
  always negative.
                        1 Px
                 x 
                      slope Qx
• Why?

• For this reason, we drop the negative sign.
         Own price elasticity
• Elasticity changes as P and Q change.

                       1 Px
                x 
• Why?               slope Qx
         Own price elasticity
• If  > 1, say good is elastic at that price

                         1 Px
                  x 
• Why?                 slope Qx
         Own price elasticity
• If  < 1, say good is inelastic at that price

                         1 Px
                  x 
• Why?                 slope Qx
         Own price elasticity
• At P=0, elasticity equals 0

                        1 Px
                 x 
• Why?                slope Qx
         Own price elasticity
• At Q=0, elasticity equals infinity.

                         1 Px
                  x 
• Why?                 slope Qx
         Own price elasticity
• One demand curve may be steeper, but
  not more inelastic.
                      1 Px
               x 
                    slope Qx
• Why?

Example: Demand A: p=10, q=10, slope=-1
         Demand B: p=10, q=20, slope=-.5
   Own price elasticity


                 At a price of 10, these demand curves
                 have the same elasticity


P=10




       10   20
P                            P

4                            4      
3                            3          
2                            2              
                    D                             D
    3   9      20                    7 9     12
                     Q                                Q



                          Qx
                 % Qx Ave( Qx )
            x        
                 % Px     Px
                         Ave( Px )
                            Review
• Own price demand elasticity is (almost) always negative
  (so we ignore the negative).
• Elasticity changes as P and Q change!
   – If  > 1, say good is elastic at that price
   – If  < 1, say good is inelastic at that price
• At P=0, elasticity equals 0
• At Q=0, elasticity equals infinity.
• One demand curve may be steeper, but not more
  inelastic.
• A change in own price is movement along a demand
  curve (demand is the same, but quantity demand
  changes).

				
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posted:5/3/2012
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