Elasticity and Its Applications
Economics 230
J.F. O’Connor
Questions
• Are consumers spending more on gasoline
now ($1.40/gal.) than three months ago
($1.10/gal) ? (Yes!)
• Price of airline tickets has increased in the
past 3 months. Are consumers spending
more on airline travel? (No!)
• Why the difference? Answer lies in
responsiveness to price.
Measuring Responsiveness of
One Variable to Another
• Two Methods:
– Rate of change
– Elasticity
• Rate of Change in y with respect to x is the
change in y divided by the change in x,
ceteris paribus
• Elasticity of y w.r.t. to x is the percentage
change in y divided by the percentage
change in x, ceteris paribus
Comments
• Rate of change is measured geometrically
by slope.
• Advantage of elasticity is that, in contrast to
rate, it does not depend on the units of
measurement.
• Elasticity can be measured geometrically,
from a table, or from an equation.
Factors Affecting Quantity
Demanded
•
•
•
•
•
•
Own price
Price of substitutes
Price of complements
Income of consumers
Preferences of consumers
Advertising
Demand Curve
• Relationship between quantity demanded of
the good and its price when other factors
affecting demand are held constant.
• Then the demand curve is Q = 14 - 2P
• The convention in graphing demand curves
is to put price on the vertical axis
Demand Curve (contd.)
• The equation is then P = 7 - .5Q
• Law of Demand (empirical generalization)
– A change in price, ceteris paribus, will
result in a change in quantity demanded
in the opposite direction
– Demand curve has negative slope
Equation:
P= 7 - .5Q
ALinear Demand Curve
7
6
5
Price
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Quantity
9
10
11
12
13
14
15
Responsiveness of Quantity
Demanded to Price
• Two Measures
• Rate of change in quantity wrt to price
or (change in quantity)/ (change in
price) = inverse of the slope
• Elasticity = Percentage change in
quantity divided by percentage change
in price
What is wrong with rate of
change?
• It is an adequate measure of responsiveness
but its value depends on the units of
measurement. Hard to compare the
sensitivity of demand for airline tickets with
that of the demand for food.
• Elasticity is independent of units of
measurements. Thus, comparisons across
goods are possible
Measuring Elasticity I
Graphically
•
•
•
•
• By definition elasticity is
(1/slope)(price/quantity)
Measure elasticity at Price = 3.5$ in prior
example
(1/Slope) = - 14/7
Quantity = 7
Elasticity = - (14/7)3.5/7 = -1
•
•
•
•
•
•
•
Measure price elasticity of demand at P=5.5
(1/Slope) = - 14/7
Quantity = 3
Elasticity = - (14/7)5.5/3 = -11/ 3 = -3.7
Price elasticity of demand at P=1.5
Quantity = 11
Elasticity = -(14/7)1.5/11 = - 3/11
Observations
• Elasticity varies along the linear demand
curves while slope is constant
• Simple way to measure price elasticity take the price on the vertical axis and divide
it by the distance from price to the intercept
or maximum price. Put a negative sign in
front. Let’s try it!
ALinear Demand Curve
7
At p=5.5
6
eta = -5.5/(7-5.5)
5
= -11/3
At P= 3.5,
= -1
Price
eta = -3.5/(7-3.5)
4
3
At P = 1.5,
eta = -1.5/(71.5)
2
1
= -11/3
0
0
1
2
3
4
5
6
7
8
Quantity
9
10
11
12
13
14
15
Classifying Direct Price
Elasticity of Demand
•
•
•
•
Perfectly inelastic ( eta = 0 )
Inelastic ( eta between 0 and -1)
Unitary elastic ( eta = -1 )
Elastic ( eta less than negative one or
numerically greater than 1 )
• Perfectly elastic ( eta negative infinity )
• Note Mankiw drops negative sign
What Happens to the Amount
Spent on a Good when its Price
Increases?
• It all depends on the direct price
elasticity of demand !
• Key relationship:
• %Change in expenditure =
%change in price + % change in
quantity
The Effect of an Increase in Price
on Expenditure
• Demand
–
–
–
–
–
Perfectly inelastic
inelastic
unitary elasticity
elastic
perfectly elastic
• Repeat for a decrease
in price
• Expenditure
–
–
–
–
–
increase
increase
no change
decrease
decrease to zero
What Determines the Elasticity
of Demand?
• Availability of Substitutes
– demand for apples more elastic than demand
for fruit
• Importance in the Consumer’s Budget
• demand for housing more elastic than
demand for salt
• Time
– response increases with time
Measuring Elasticity for a Nonlinear Demand Curve
• Can still use the graphical technique
• Draw tangent at price at which elasticity is
to be evaluated
• Compute negative of price divided by the
difference between the intercept of the
tangent and the price
DemandforPlones
14
12
10
8
Price
Compute elasticity of
demand at price of
5.75 and quantity of 3.
6
Eta =- 5.75/(10-5.75)
=- 1.35
4
2
0
0
1
2
3
4
5
Quantity
6
7
8
9
10
Responsiveness to Other
Determinants of Demand
• Income elasticity
• Cross-price elasticity
• Elasticity with respect to advertising
expenditures.