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Transcript
Elasticity Measures
Part 2
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Recall:
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.
– Own 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.
– Own price elasticity of supply is 5.
Supply Elasticity
 Extremely
similar formulas are used to
calculate the own price elasticity of supply
– Arc midpoint formula
» Large delta style or small delta style
– Point formula

Just need to substitute in
– Quantity supplied and change in quantity
supplied where appropriate
Supply Elasticity
 Definition:
 S X ,P 
X
 Arc
Percentage Change in Quantity Supplied
Percentage Change in Price
Formula:
Arc formula for 
 Point

S
S
X , PX
QS /(average of the two Qs)

x100
P/(average of the two Ps)
formula:
X , PX
 (dQ
S
X
/ dPX )( PX / Q
S
X
)
Example: Arc Calculation of
Own Price Elasticity of Supply




Want supply elasticity at A
Use B: QS=9 and P=5
Use C: QS=16 and P=7
Nonlinear Supply Curve
12
10
QS
% change in
=
(16-9)/((16+9)/2)*100 =
56%
% change in P =
(7-5)/((7+5)/2)*100 =
33.33%
C
8
Price

6
B
A
4
2
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Supply elasticity at A =
56/33.33 = 1.68
Quantity
Example: Point Calculation of
Own Price Elasticity of Supply


S
X , PX
 (dQ
S
X
/ dPX )( PX / Q
S
X
)
Suppose you are given: QS = -10 + 4P
– Note, that’s the same as: PS = 2.50 +.25Q



Suppose you want the exact own price elasticity of
supply at P = $12
At P = $12, QS = -10 + 48 = 38
Note: (dQS/dP) = 4
– (Slope of drawn supply curve = .25, so.... 1/slope = 4)

So supply elasticity at P=$12 is...
(4)•(12/38) = 48/38 = 1.26
Some Technical Definitions
For Extreme Elasticity Values
 Perfectly
elastic means the quantity
demanded or supplied is as price sensitive as
possible.
– a.k.a. completely elastic
– a.k.a. infinitely elastic

Perfectly inelastic means that the quantity
demanded or supplied has no price
sensitivity at all.
– a.k.a. completely inelastic
Perfectly Elastic Demand


Demand is perfectly
elastic when a 1%
change in the price
would result in an
infinite change in
quantity demanded.
Example:
Price
Perfectly Elastic Demand (elasticity = -)
Quantity
Perfectly Inelastic Demand


Demand is perfectly
inelastic when a 1%
change in the price
would result in no
change in quantity
demanded.
Example:
Price
Perfectly
Inelastic
Demand
(elasticity = 0)
Quantity
Perfectly Inelastic Supply


Supply is
perfectly inelastic
when a 1%
change in the
price would result
in no change in
quantity supplied.
Example: wheat?
– At harvest?
Price
Perfectly
Inelastic
Supply
(elasticity = 0)
» Yes.
– Across planting
seasons?
» No.
Quantity
Perfectly Elastic Supply


Supply is
perfectly elastic
when a 1%
change in the
price would result
in an infinite
change in
quantity supplied.
Example: wheat?
Price
Perfectly Elastic Supply (elasticity = )
– Across planting
seasons?
» Yes.
Quantity
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.
Real World Example – Getting It Wrong
 Gas taxes in Washington DC, 1980
– Extra 6% tax imposed Aug 16, 1980 to raise much
needed revenue for D.C.
– Increased price at pump by 8¢ (a nearly 6% increase).
– By end of first month, QD down by 27.5%.
–  elasticity = 27.5÷6 = 4.5  pretty darn elastic!
– Way off on expected revenue, too.
– By October, sales had dropped by 40% and 242 gas
station workers were laid off.
– Tax lifted by Mayor Marion Barry on November 24,
1980.
– What went wrong? What didn’t they account for?
Real World Example – Getting It Wrong
Own Price Elasticity of Demand
& Total Expenditures






Question: What happens to total expenditures made by buyers (TE) in
a market when market price increases?
Note: TE = P•QD
P↑ tends to increase TE, but it also decreases QD.
QD↓ tends to decreases TE.
So what happens to TE?
Knowing own price elasticity will help!
– If demand is price ELASTIC, then TE ↓
» Why?
– If demand is price INELASTIC, then TE ↑
» Why?

On you own: reverse this argument to determine the
relationship between total expenditure and elasticity when
you consider a price decrease!
Bridge Toll Example




Suppose: Current toll for the George Washington Bridge is $6.00/trip.
Suppose: The quantity demanded at $6.00/trip is 100,000 trips/hour.
So: TE on trips per hour = $600,000
If the own price elasticity of demand for bridge trips is known to be 2.0, then what is the effect of a 10% toll increase?
– Note: since demand is price ELASTIC  TE↓





A 10% toll increase means the price is now $6.60 per trip.
If η=-2, a toll increase of 10% implies a 20% decline in the quantity
demanded.
If there is a 20% decline in trip, number of trips falls to 80,000/hour.
Total expenditure falls to $528,000/hour (= 80,000 x $6.60).
$528,000 < $600,000
Own Price Elasticity of Demand & Total
Expenditure with Linear Demand
$TE
Price
Price
elastic
Demand
Price
inelastic
Quantity



Quantity
Starting at the “top” of the demand curve, where demand is price elastic, as price falls,
and quantity demanded rises, total expenditures rise, but increase at a decreasing rate.
At the midpoint, where demand is unit elastic, total expenditures will be at their maximum
value.
As you continue down the demand curve, where demand is now price inelastic, as price
falls, and quantity demanded rises, total expenditures fall.
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: software is complementary with computers. When the
price of software rises the quantity demanded of computers falls.

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: hockey is substitute for basketball. When the price of
hockey tickets rises the quantity demanded of basketball tickets
rises.

Cross-price elasticities quantify effects like these.
Cross-Price Elasticity of Demand



Definition:
Arc Formula:
Point Formula:

D
X , PY
Percentage Change in Quantity Demanded of X

Percentage Change in Price of Y
 D X ,P  ( Q D X / Q D ) /( PY / PY )
Y
 D X , P Y  (dQ D X / dPY )( PY / Q D X )
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, food).
» 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, haute
cuisine).
» When the income elasticity of demand is positive but less than
1 (a necessity), consumers increase their purchases of the good
less than proportionate to the income increase (e.g. socks, bread).
– When the income elasticity of demand is negative (inferior
good), consumers reduce their purchases of the good as their
incomes rise (e.g. spam, potatoes).
Income Elasticity of Demand



Definition:
Arc Formula:
Point Formula:
 D X ,I 
Percentage Change in Quantity Demanded
Percentage Change in Income
 D X ,I  (Q D X / Q D ) /( I / I )

D
X ,I
 (dQ
D
X
/ dI )( I / Q
D
X
)
All Four Elasticities You Need to Know
 Own
Price Elasticity of Demand
 D X ,P  (Q D X / Q D ) /( PX / PX )
X
 Cross

D
X , PY
 ( Q
 D X ,P  (dQ D X / dPX )( PX / Q D X )
X
Price Elasticity of Demand
D
X
/ Q ) /( PY / PY )
D
 D X ,PY  (dQ D X / dPY )( PY / Q D X )
 Income
Elasticity of Demand
D
D
D
D
D


(
dQ
/
dI
)(
I
/
Q
X
,
I
X
X)
 ( Q X / Q ) /( I / I )
 D X ,I
 Own
 S X ,P
X
Price Elasticity of Supply
S
S
S
S
S


(
dQ
/
dP
)(
P
/
Q
X ,P
X
X)
 ( Q X / Q ) /( PX / PX )
X
X
X