Demand and Price Elasticity

1
Demand and Price Elasticity
2
Example from the Firm
If this firm wants to produce 4 units of output,
it should use 4 units of labor and 4 units of
capital.
Q 4
3

• 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

4

• Consumer Problem
• For a given income, find the highest utility you
  can attain.
• Find the highest indifference curve

5
Example
pf 16 ph 16 I 160
6
Example
pf 16 ph 16 I 160
7
Why not (4,4)?
pf 16 ph 16 I 160
8
Why not (6,6)?
pf 16 ph 16 I 160
9
Demand
pf 16 ph 16 I 100
At a price of 16 (when income is 160 and the
price of football tickets is 16), you demand 5
hockey tickets.
10
Demand
pf 16 ph 16 I 160
11
Demand
pf 16 ph 16 I 160
P
?
16
5
Q
12
Demand
pf 16 ph 10 I 160
P
?
16
?
10
5
Q
7
13
Demand
pf 16 ph 40 I 160
P
?
40
?
16
?
10
5
Q
7
2
14
Demand
P
?
40
?
16
?
10
D
5
Q
7
2
15
Demand
p1 3 p2 3 I 54
x2
x1
P
Q
16
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)

17
Demand
p1 3 p2 3 I 54
x2
18
x1
18
P
?
3
9
Q
18
Demand
p1 4 p2 3 I 54
x2
x1
P
?
3
9
Q
19
Demand
p1 4 p2 3 I 54
x2
18
x1
13.5
P
?
4
?
D
9
Q
3
20
Demand
p1 2 p2 3 I 54
x2
x1
P
?
?
?
2
9
Q
3
20
21
Demand
p1 2 p2 3 I 54
x2
18
27
x1
P
?
?
?
2
9
Q
3
20
22
Demand
p2 3 I 54
x2
x1
P
?
4
?
3
?
2
D
9
Q
3
20
23
Demand
x2
PERSON 1
x1
24
Demand
x2
PERSON 1
x1
x2
PERSON 2
x1
25
Demand (Person 2)
p1 3 p2 3 I 54
x2
18
x1
18
P
?
4
Q
9
26
Demand
p1 4 p2 3 I 54
x2
18
x1
13.5
P
?
4
?
Q
7
27
Demand
p1 2 p2 3 I 54
x2
18
x1
27
P
?
?
?
2
Q
12
28
Demand
p2 3 I 54
x2
x1
P
?
4
?
3
?
2
D
9
Q
7
12
29
Demand
p2 3 I 54
x2
x2
x1
x1
P
P
?
?
4
4
?
?
3
3
?
?
2
2
D
D
9
Q
7
12
9
Q
3
20
30
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 TVs with peaches?
• Better method is to use the elasticity
• When P changes by 1, how much (by what percent)
  does Q change?
• Doesnt depend on scale
• Ties directly to revenue/expenditure.

31
Calculating Elasticity

• Own-price elasticity

32
Calculating Elasticity

• Own-price elasticity
• In this class, you will calculate the arc
  elasticity

33
Own price elasticity

• Another way to calculate the elasticity is using
  the point elasticity
• Although we wont use it in this class, it is
  handy to show some properties of elasticity.

34
Own price elasticity

• Own price demand elasticity is (almost) always
  negative.
• Why?

35
Own price elasticity

• Own price demand elasticity is (almost) always
  negative.
• Why?
• For this reason, we drop the negative sign.

36
Own price elasticity

• Elasticity changes as P and Q change.
• Why?

37
Own price elasticity

• If h gt 1, say good is elastic at that price
• Why?

38
Own price elasticity

• If h lt 1, say good is inelastic at that price
• Why?

39
Own price elasticity

• At P0, elasticity equals 0
• Why?

40
Own price elasticity

• At Q0, elasticity equals infinity.
• Why?

41
Own price elasticity

• One demand curve may be steeper, but not more
  inelastic.
• Why?
• Example Demand A p10, q10, slope-1
• Demand B p10, q20, slope-.5

42
Own price elasticity
At a price of 10, these demand curves have the
same elasticity
P10
20
10
43
P
P
?
?
4
4
?
?
3
3
?
?
2
2
D
D
9
Q
7
12
9
Q
3
20

44
Review

• Own price demand elasticity is (almost) always
  negative (so we ignore the negative).
• Elasticity changes as P and Q change!
• If h gt 1, say good is elastic at that price
• If h lt 1, say good is inelastic at that price
• At P0, elasticity equals 0
• At Q0, 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).