Download Spring 2016

Elasticity Measures
Lecture 10
Dr. Jennifer P. Wissink
©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved.
March 1, 2017
i>clicker questions
Can I use a cell
phone or a smart
phone or graphing
calculator or
anything like that for
the prelim?
A.Yes
B.No
Can I use a help
sheet during the
prelim?
A.Yes
B.No
Should I buy a
simple function
calculator before
Prelim 1?
A.Yes
B.No
i>clicker question
The own price elasticity of demand between points A and B on the graph below (and
reported using absolute values) is 1.6. If we calculate the own price elasticity of demand
using points A and C we would expect that
A. the elasticity would be the same, that is 1.6, silly, since it’s a straight line!
B. the elasticity would now be smaller than 1.6.
C. the elasticity would now be larger than 1.6.
Linear Demand Curve
42
41
40
B
39
Price
38
A
37
36
C
35
34
33
32
31
30
10
11
12
Quantity
13
14
POINT Own Price Elasticity of Demand at A,
where P=$36 and QD=30-1/2P

Recall the (midpoint) arc formula using points A and B.

D
X , PX
Q D /[(Q D A  Q D B )/2] 100

P/[(PA  PB )/2] 100
Linear Demand Curve
42
41
40
Now let’s make B get closer and closer to A.
–
In the limit we would get the exact elasticity at point A.
 D X ,P 
X
dQ /Q A 100
dP/PA 100
D
D
38
Price

B
39
A
37
36
C
35
34
33
32
31
30
10

Rearranging, you get:
11
12
Quantity
 D X , P  [dQ D X / dPX ]( PX / Q D X ) evaluated at A
X
13
14
Slope Compared to Elasticity
 The
slope measures the rate of change
of one variable (P, for example) in
terms of another (Q, for example).
 An
elasticity measures the percentage
change of one variable (Q) in terms of
percentage change in another (P).
Point Elasticity As We Move
Down a Linear Demand Curve
ηDx,Px=[dQDx/dPx]•(Px/QDx)
Price
Own price elasticity of
demand
$P
QD = 30 – 1/2P
$60
Demand
36
A
12
30
Q
i>clicker question
At their respective market equilibriums, in which of the markets below would you expect
market demand to be the most price elastic?
A. The market for fruit.
B. The market for fresh fruit.
C. The market for fresh fruit you do not have to peel.
D. The market for fresh apples.
E. The market for fresh Gala variety apples.
Determinants of Own Price
Demand Elasticity
 What
are the major determinants of the own
price elasticity of demand?
– Availability of substitutes in consumption.
» thumb drives versus Lexar thumb drives
– The importance of the item in individual
budgets.
» baby food versus textbooks (for you guys)
– The time frame in question.
» over a day versus over a year
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
i>clicker question
At their respective market equilibriums, in which of the markets below would you expect
market demand to be the most price elastic?
A. The market for fruit.
B. The market for fresh fruit.
C. The market for fresh fruit you do not have to peel.
D. The market for fresh apples.
E. The market for fresh Gala variety apples.
Real World Example
 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
i>clicker question
What went wrong with the Barry administration’s model concerning
gas taxes in Washington D.C.?
A.People are too poor in D.C. so they can not pay taxes.
B.They should have collected the taxes directly from demanders and not
the suppliers.
C.Gas station owners in D.C. are just not very good entrepreneurs.
D.Mayor Barry’s economic advisers were pretty mediocre.
E.Someone stole all the revenue before it got to the mayor.
Own Price Elasticity
of Demand & Total Expenditures (TE)



Suppose: Current toll for the George Washington Bridge is $15/trip.
Suppose: The quantity demanded at $15/trip is 1,000 trips/hour.
TE on trips per hour = $15,000/hour
i>clicker question
If the own price elasticity of demand for bridge trips is known to be equal
to -2.0, then what is the effect on TE of a 10% toll increase?
A. TE increase
B. TE stay the same
C. TE decrease

A 10% toll increase means the price is now $16.50 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 trips, number of trips falls to 800 trips/hour.

TE are now only $13,200/hour (= 800 x $16.50), so TE decreased!
Own Price Elasticity of Demand
& Total Expenditures


What happens to total expenditures (TE)
made by buyers in a market
when market price increases?
Note: TE = PD•QD
Price
Perfectly
Inelastic
Demand
(elasticity = 0)
– PD↑ tends to increase TE.
– 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?

Quantity
On you own: reverse this argument to determine the relationship between total
expenditure and elasticity when you consider a price decrease!
Own Price Elasticity of Demand & Total
Expenditure with Linear Demand
$TE=P•Q
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.
Own Price Elasticity of Demand & Total
Expenditure with Linear Demand
$TE=P•Q
Price
Price
elastic
Demand
Price
inelastic
Quantity
Quantity
Example: Demand Function, Demand
Curve & Own Price Elasticity of Demand

Suppose you know the demand function for compact disc
players (X) is:
QDX = (T&P)(Pop) + 3I – 2PCD + 3PB – (5,145/T&P)PX

Now… to go from the demand function to the demand curve,
plug in values for everything BUT PX
– So suppose: T&P=7; Pop=1,000; I=5,000; PCD=9; PB=15
– You get:
– Now find own price elasticity of demand at PX=$7