### Elasticity

```Elasticity
Elasticity of Demand
• Elasticity: measures the responsiveness of
demand or supply to one of its determinants
– Own price
– Income
– Price of related goods
Price Elasticity
• Own Price Elasticity of Demand : measures
how responsive the quantity demanded is to
its price
• Defined as the percentage change in quantity
demanded divided by the percentage change
in price
• Tells us how willing consumers are to buy
more if the price goes down, or buy less if the
price goes up
• Elastic Demand
– Quantity demanded relatively responsive to price
changes
• Inelastic Demand
– Quantity demanded relatively unresponsive to
price changes
Determinants of Elasticity
• Availability of Close Substitutes
– If there are many close substitutes then will tend
to be very elastic
• Necessity vs Luxury
– If it is a necessary good it will be inelastic
– If it is a luxury good it will be elastic
• Definition of Market
– Narrow definition of good would be more elastic
• Time Horizon
– Longer time horizon makes it more elastic
Calculating Elasticity
• Elasticity is not constant over the demand
curve – changes at every point
• %change in Q/%change in P (absolute value)
• %Q  Q / Q  Q  P = 1/slope x (P/Q)
%P P / P P Q (slope = P )
Q
Or: Midpoint method (why)
– Two points (Q1,P1) and (Q2,P2)
– Own price elasticity = (Q1  Q2 ) /[(Q1  Q2 ) / 2]
( P1  P2 ) /[(P1  P2 ) / 2]
•
•
•
•
•
•
Elasticity > 1 : elastic
Elasticity < 1 : inelastic
Elasticity = 1 : unit elasticity
Elasticity = 0 : perfectly inelastic (vertical DC)
Elasticity = ∞ : perfectly elastic (horizontal DC)
Linear Demand curves (except perfectly elastic
or inelastic) will be half elastic, half inelastic
and midpoint where it is unit elastic
• At any given point (Q,P) the flatter the curve
the more elastic
Perfectly Inelastic Demand
Perfectly Elastic Demand
P
P
Demand
Curve
Demand is
zero above 7
8
Demand Curve
7
6
Demand is
infinite below 7
quantity at 7
Change in price has
no effect on
quantity demanded
50
Q
Q
Slope of Demand is 1 (remember all in absolute values)
12
Elastic : 1/Slope*(p/q) = 1*(p/q >1) >1
10
Unit Elastic : 1/Slope*(p/q) = 1*(p/q =1) =1
Price
8
Inelastic
: 1/Slope*(p/q) = 1*(p/q <1) <1
6
4
2
0
1
2
3
4
5
6
Quantity
7
8
9
10
|Slope of Demand Curve| = 3
30
Elastic : 1/Slope*(p/q) = 1/3*(p/q >3) >1
25
Unit Elastic : 1/Slope*(p/q) = 1/3*(p/q =3) =1
Price
20
15
Inelastic
: 1/Slope*(p/q) = 1/3*(p/q <3) <1
10
5
0
1
2
3
4
5
6
Quantity
7
8
9
10
Midpoint Method
P
To get elasticity at this (any) point
would have to take derivative
(calculus required)
(Q1,P1) = (3,11) ; (Q2,P2) = (9,5)
11
(Q1  Q2 ) /[(Q1  Q2 ) / 2]
(3  9) /[(3  9) / 2]
4 100%

 
( P1  P2 ) /[(P1  P2 ) / 2]
(11 5) /[(11 5) / 2] 3 75%
Remember absolute value
5
3
9
Q
Revenue of Seller and Elasticity
• Total Revenue
– Total Amount Given by buyers
– Total Amount received by sellers
– TR = P x Q (market price, and market quantity)
P
Demand
TR = P x Q = 10 x 8 = \$80
10
TR
8
Q
• If at market price/quantity demand is elastic
– Raising price reduces revenue
– Lowering price raises revenue
– Why
• If at market price/quantity demand is inelastic
– Raising price raises revenue
– Lowering price lowers revenue
– Why
Inelastic Demand
Slope = 1/10 ; At original pt
Elasticity = 10 * 4/100 = 2/5 < 1
P
P
Raising Price
Raises Revenue
Lowering Price
Lowers Revenue
TR = 480
6
TR = 330
4
3
TR = 400
100
Q
80
110
Q
Elastic Demand
Slope = 1/50 ; At original pt
Elasticity = 50 * 4/100 = 2> 1
P
P
Raising Price
Lowers Revenue
Lowering Price
Raises Revenue
TR = 250
5
TR = 450
4
3
TR = 400
100
Q
50
150
Q
Income Elasticity of Demand
• Measures how responsive quantity demanded
is to changes in ones income
• % change in Q/% change in Income
– No absolute value here, because two types of
goods distinguished by sign of elasticity (+/-)
– Normal Good : positive elasticity
• Necessary Good : small elasticity
• Luxury Good : large elasticity
– Inferior Good : negative elasticity
Cross Price Elasticity of Demand
• Measures how responsive quantity demanded
is to changes in the price of a related good
• % change in Q(of good one)/% change in P (of
good two)
– Again here no absolute value because we
distinguish two types of related goods
– Substitute: positive cross price elasticity
• Price of sub goes up, then demand goes up
– Compliment: negative cross price elasticity
• Price of comp goes up, then demand goes down
• For both income elasticity of demand, and
cross price elasticity of demand
– Use midpoint method
– Cross Price:
– Income:
(Q  Q ) /[(Q  Q ) / 2]
( P  P ) /[(P  P ) / 2]
1
1
2
1
1
2
2
2
1
1
2
1
1
2
2
2
(Q1  Q2 ) /[(Q1  Q2 ) / 2]
( I1  I 2 ) /[(I1  I 2 ) / 2]
Elasticity of Supply
• Measures how responsive the quantity
supplied is to changes in that goods price
• % change in Q/% change in price
• Again if linear we can use 1/slope * P/Q
• If not use midpoint method
• Main determinant is technology/time
– How quick can they respond and does the
technology they use allow more/less production
All the Same as Elasticity of Demand
•
•
•
•
Elastic: very responsive to price >1
Inelastic: not responsive <1
Unit elastic = 1
Perfectly elastic : infinite elasticity
– Horizontal supply curve
• Perfectly inelastic: zero elasticity
– Vertical supply curve
Application
• Say new crop technology comes out which
increases corn yields per acre (GM foods)
• This shifts the supply curve out (to the right)
• But demand is fairly inelastic
• So we get a lower price, and slightly higher
quantity
• But farm revenues fall
P
3
Technology Shifts supply curve
2
Original Revenue = 3*200 = 600
New Revenue = 2*220 = 440
200
220
Q
Public Policy Implications
Application to Illegal Drugs
• Focus on reducing supply (raids etc) or focus
on reducing demand (education, rehab etc)?
• Note: demand for drug inelastic