2. Elasticity measures
What are they?
– Responsiveness measures
Why introduce them?
– Demand and supply responsiveness clearly
matters for lots of market analyses.
Why not just look at slope?
– Want to compare across markets: inter market
– Want to compare within markets: intra market
– slope can be misleading
– want a unit free measure
2
3. Why Economists Use
Elasticity
An elasticity is a unit-free measure.
By comparing markets using elasticities
it does not matter how we measure the
price or the quantity in the two markets.
Elasticities allow economists to quantify
the differences among markets without
standardizing the units of
measurement.
3
4. What is an Elasticity?
Measurement of the percentage change
in one variable that results from a 1%
change in another variable.
Can come up with many elasticities.
We will introduce four.
– three from the demand function
– one from the supply function
4
5. 2 VIP Elasticities
Price elasticity of demand: how
sensitive is the quantity demanded to a
change in the price of the good.
Price elasticity of supply: how sensitive
is the quantity supplied to a change in
the price of the good.
Often referred to as “own” price
elasticities.
5
6. Examples of Own Price
Demand Elasticities
When the price of gasoline rises by 1% the
quantity demanded falls by 0.2%, so gasoline
demand is not very price sensitive.
– Price elasticity of demand is -0.2 .
When the price of gold jewelry rises by 1%
the quantity demanded falls by 2.6%, so
jewelry demand is very price sensitive.
– Price elasticity of demand is -2.6 .
6
7. Examples of Own Price
Supply Elasticities
When the price of DaVinci paintings
increases by 1% the quantity supplied doesn’t
change at all, so the quantity supplied of
DaVinci paintings is completely insensitive to
the price.
– Price elasticity of supply is 0.
When the price of beef increases by 1% the
quantity supplied increases by 5%, so beef
supply is very price sensitive.
– Price elasticity of supply is 5.
7
8. Examples of Unit-free
Comparisons
Gasoline and jewelry
– It doesn’t matter that gas is sold by the gallon
for about $1.09 and gold is sold by the ounce
for about $290.
– We compare the demand elasticities of -0.2
(gas) and -2.6 (gold jewelry).
– Gold jewelry demand is more price sensitive.
8
9. Examples of Unit-free
Comparisons
Paintings and meat
– It doesn’t matter that classical paintings
are sold by the canvas for millions of
dollars each while beef is sold by the
pound for about $1.50.
– We compare the supply elasticities of 0
(classical paintings) and 5 (beef).
– Beef supply is more price sensitive.
9
10. Inelastic Economic Relations
When an elasticity is small (between 0
and 1 in absolute value), we call the
relation that it describes inelastic.
– Inelastic demand means that the quantity
demanded is not very sensitive to the
price.
– Inelastic supply means that the quantity
supplied is not very sensitive to the price.
10
11. Elastic Economic Relations
When an elasticity is large (greater than
1 in absolute value), we call the relation
that it describes elastic.
– Elastic demand means that the quantity
demanded is sensitive to the price.
– Elastic supply means that the quantity
supplied is sensitive to the price.
11
12. Size of Price Elasticities
Unit elastic
Inelastic Elastic
0 1 2 3 4 5 6
Unit elastic: own price elasticity equal to 1
Inelastic: own price elasticity less than 1
Elastic: own price elasticity greater than 1
12
13. General Formula for own price
elasticity of demand
P = Current price of good X
XD = Quantity demanded at that price
P = Small change in the current price
XD= Resulting change in quantity demanded
Percentage Change in Quantity Demanded
Elasticity
Percentage Change in Price
13
14. Point Formula for Own Price
Elasticity of Demand
The exact formula for calculating an
elasticity at the point A on the demand
curve.
Note: we’ll take absolute value
A D
P X
elasticity A
atA
X P
14
15. Slope of the Demand Curve
P is the
Price
change in Demand
P
price. ( P<0) slope
X
X is the P
change in P+ P
P
quantity. X
slope =
P/ X
1/slope =
X X+ X Quantity
X/ P
15
16. Slope Compared to Elasticity
The slope measures the rate of change
of one variable (P, say) in terms of
another (X, say).
The elasticity measures the percentage
change of one variable (X, say) in terms
of another (P, say).
16
17. Example: Elasticity
Calculation at “A”
Slope =
(40-32)/(10-14)=-2 Linear Demand Curve
1/slope = -1/2 42
P/X = 36/12 = 3 at 41
40
point A 39
38
P/X x 1/slope Price 37
A
36
= -1.5 35
34
Elasticity of 33
demand = -1.5 32
31
Absolute value of 30
10 11 12 13 14
the elasticity = 1.5 Quantity
17
18. Exercise -- Linear Demand
Compute the
elasticity at the point Quantity Price
10 40
indicated in red on 11 38
the table 12 36
(X=18,P=24). 13 34
14 32
Slope = -2 15 30
16 28
1/Slope = -1/2 17 26
18 24
P/X = 24/18 = 4/3 19 22
20 20
Elasticity = -2/3
18
19. Elasticities and Linear
Demand
Linear Demand
Exact
Quantity Price Slope 1/Slope Elasticity
10 40
11 38 -2 -0.5 -1.7273
12 36 -2 -0.5 -1.5000
13 34 -2 -0.5 -1.3077
14 32 -2 -0.5 -1.1429
15 30 -2 -0.5 -1.0000
16 28 -2 -0.5 -0.8750
17 26 -2 -0.5 -0.7647
18 24 -2 -0.5 -0.6667
19 22 -2 -0.5 -0.5789
20 20
The elasticity varies along a linear demand (or supply) curve.
This is illustrated in the linear demand curve table above.
Note: Usually we would report last column as absolute value
19
20. Supply Elasticities
The price elasticity of supply is always
positive.
Economists refer to the price elasticity of
supply by its actual value.
Exactly the same type of point and arc
formulas are used to compute and estimate
supply elasticities as for demand elasticities.
20
21. Some Technical Definitions
For Extreme Elasticity Values
Economists use the terms “perfectly elastic”
and “perfectly inelastic” to describe extreme
values of price elasticities.
Perfectly elastic means the quantity
(demanded or supplied) is as price sensitive
as possible.
Perfectly inelastic means that the quantity
(demanded or supplied) has no price
sensitivity at all.
21
22. Perfectly Elastic Demand
We say that
Price
demand is
perfectly elastic
when a 1%
Perfectly Elastic Demand (elasticity = )
change in the
price would result
in an infinite
change in
quantity
demanded.
Quantity
22
23. Perfectly Inelastic Demand
We say that
Price
demand is
perfectly inelastic
when a 1%
change in the
Perfectly
price would result Inelastic
Demand
in no change in (elasticity = 0)
quantity
demanded.
Quantity
23
24. Perfectly Elastic Supply
We say that
Price
supply is
perfectly elastic
when a 1%
Perfectly Elastic Supply (elasticity = )
change in the
price would result
in an infinite
change in
quantity supplied.
Quantity
24
25. Perfectly Inelastic Supply
We say that
Price
supply is perfectly
inelastic when a
1% change in the
price would result
Perfectly
in no change in Inelastic
Supply
quantity supplied. (elasticity = 0)
Quantity
25
26. Determinants of elasticity
What is a major determinant of the own
price elasticity of demand?
– Availability of substitutes in consumption.
What is a major determinant of the own
price elasticity of supply?
– Availability of alternatives in production.
26
27. Using Demand Elasticity:
Total Expenditures
Do the total expenditures on a product go up
or down when the price increases?
The price increase means more spent for
each unit.
But, quantity demanded declines as price
rises.
So, we must measure the measure the price
elasticity of demand to answer the question.
27
28. Bridge Toll Example
Current toll for the George Washington
Bridge is $2.00/trip.
Suppose the quantity demanded at
$2.00/trip is 100,000 trips/hour.
If the price elasticity of demand for
bridge trips is 2.0, what is the effect of a
10% toll increase?
28
29. Bridge Toll: Elastic Demand
Price elasticity of demand = 2.0
Toll increase of 10% implies a 20%
decline in the quantity demanded.
Trips fall to 80,000/hour.
Total expenditure falls to $176,000/hour
(= 80,000 x $2.20).
$176,000 < $200,000, the revenue from
a $2.00 toll.
29
30. Bridge Toll Example, Part 2
Now suppose the elasticity of demand
for bridge trips is 0.5.
How would the number of trips and the
expenditure on tolls be affected by a
10% increase in the toll?
30
31. Bridge Toll: Inelastic Demand
Price elasticity of demand = 0.5
Toll increase of 10% implies a 5%
decline in the quantity demanded.
Trips fall to 95,000/hour.
Total expenditure rises to
$209,000/hour (= 95,000 x $2.20).
$209,000 > $200,000, the revenue from
a $2.00 toll.
31
32. Elasticity and Total
Expenditures
A price increase will increase total
expenditures if, and only if, the price elasticity
of demand is less than 1 in absolute value
(between -1 and zero)
– Inelastic demand
A price reduction will increase total
expenditures if, and only if, the price elasticity
of demand is greater than 1 in absolute value
(less than -1).
– Elastic demand
32
33. Elasticity and Total
Expenditure (Graph)
At the point M, the demand Elasticity > 1: Price reduction
curve is unit elastic. M is the Price increases total expenditure; price
midpoint of this linear increase reduces it.
Elasticity = 1: Total
demand curve expenditure is at a
Above M, demand is elastic, maximum
so total expenditure falls as Elasticity < 1:
Price reduction
the price rises
reduces total
Below M, demand is expenditure;
inelastic. so total price increase
M increases it.
expenditure falls as price
falls.
Total expenditure is
maximized at the point M,
where the elasticity = 1.
Quantity
33
34. Change in Expenditure
Components
Old (price, quantity) is
(P,Q).
Price
New (price, quantity) is
(P*,Q*).
Expenditures increase if
P
G is bigger than E. E
Since the point (P,Q) is P*
above the midpoint of the
linear demand curve, we
F G
know that total
Demand
expenditures will increase
at the lower price (P*,Q*).
So, E must be smaller
than G. Quantity
Q Q*
34
35. Two real world examples
Gas taxes in Washington DC
Vanity plates in Virginia
35
36. Other Price Elasticities: Cross-
Price Elasticity of Demand
Elasticity of demand with respect to the price of a
complementary good (cross-price elasticity)
– This elasticity is negative because as the price of
a complementary good rises, the quantity
demanded of the good itself falls.
– Example (from last week) software is
complementary with computers. When the price
of software rises the quantity demanded of
computers falls.
– Cross-price elasticity quantifies this effect.
36
37. Other Price Elasticities: Cross
Price Elasticity of Demand
Elasticity of demand with respect to the price of a
substitute good (also a cross-price elasticity)
– This elasticity is positive because as the price of a
substitute good rises, the quantity demanded of
the good itself rises.
– Example (from last week) hockey is substitute for
basketball. When the price of hockey tickets rises
the quantity demanded of basketball tickets rises.
– Cross-price elasticity quantifies this effect.
37
38. Other Elasticities: Income
Elasticity of Demand
The elasticity of demand with respect to a
consumer’s income is called the income elasticity.
– When the income elasticity of demand is positive (normal
good), consumers increase their purchases of the good as
their incomes rise (e.g. automobiles, clothing).
– When the income elasticity of demand is greater than 1
(luxury good), consumers increase their purchases of the
good more than proportionate to the income increase (e.g.
ski vacations).
– When the income elasticity of demand is negative (inferior
good), consumers reduce their purchases of the good as
their incomes rise (e.g. potatoes).
38
