# Demand and Price Elasticity (PowerPoint) by ert554898

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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
• 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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