Transcript pptx - Cornell

Elasticity Measures
Part 1
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Elasticity Measures

What are they?
– Responsiveness measures

Why introduce them?
– Demand and supply responsiveness clearly matters for lots
of market analyses.
» EPI of taxes on demanders and suppliers
» Division of NSS between CS and PS
» And much more….

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
What Is An Elasticity?
A
unit free measure.
 Measurement of the percentage change in one
variable that results from a 1% change in
another variable.
 Lots of them!
 Example:
– Suppose: when PX rises by 1%, quantity demanded
falls by 5%.
– The own price elasticity of demand is -5 in this
example.
2 Very Important Elasticities
 Own
Price Elasticity of Demand:
– Captures how sensitive the quantity
demanded is to a change in the own price
of the good.
 Own
Price Elasticity of Supply:
– Captures how sensitive the quantity
supplied is to a change in the own price of
the good.
Examples:
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.
– Own 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.
– Own price elasticity of
demand is -2.6 .
Examples:
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.
Beauty Of Unit-free Comparisons

Gasoline and jewelry
– It doesn’t matter that gas is sold by the gallon for about $3.50 per
gallon and gold is sold by the ounce for about $1000 per ounce.
– We compare the demand elasticities of -0.2 (gas) and -2.6 (gold
jewelry).
– Gold jewelry demand is more price sensitive.

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 $4.99.
– We compare the supply elasticities of 0 (classical paintings)
and 5 (beef).
– Beef supply is more price sensitive.
Size Of Own Price Elasticities
And Terminology

If we “report” them as positive numbers…



Not a problem with supply (owing to law of supply)
Take absolute values with demand (owing to law of demand)
Terms work the same way for demand and supply elasticities
unit elastic
price inelastic
0
price elastic
1
2
3
4
5
6
Estimation Of Elasticity
 LET’S
STICK TO DEMAND ONLY FOR
NOW!
 How does one calculate the own price
elasticity of demand?
 Depends on the accuracy you want and
information you’ve got.
– Arc Formula: an approximation using sets of
data points & discrete differences.
– Point Formula: an exact measure, used when
we have the demand function and its slope.
Definition:
Own Price Elasticity of Demand
P
= Current price of the good X.
 QD = Quantity demanded of X at that price.
 DP = Small change in the current price.
 DQD = Resulting change in quantity demanded.

D
X , PX
Percentage Change in Quantity Demanded

Percentage Change in Price
Example: Own Price Demand Elasticity Calculation
Via “Bigger Delta” Arc Method
 Goal:
Approximate
the elasticity at point
A using B and C
Linear Demand Curve
42
41
40
B
39
 Choose
point B and
get (P=38, Q=11)
Price
38
A
37
36
C
35
34
33
32
31
30
 Choose
point C and
get (P=34, Q=13).
10
11
12
Quantity
13
14
Example: Own Price Demand Elasticity Calculation
Via “Bigger Delta” Arc Method

Goal: Approximation for
elasticity at A via points B
and C
Linear Demand Curve
42
41
40
B
39
38
Percent change in Q is
(11-13)/((11+13)/2) =
-2/12 = -16.67%
Price

A
37
36
C
35
34
33
32
31

Percent change in P is
(38-34)/((38+34)/2) = 4/36
= 11.11%


Elasticity is approx.
-16.67/11.11= -1.5
30
10
11
12
13
Quantity
NOTE: Slight modification of standard
%change formula.
– Standard: %change=[(new-old)/old]*100
– Modification: %change=
[(change)/(average of the two points)] * 100
14
Alternate Example: Own Price Demand Elasticity
Calculation Via Textbook “Smaller Delta” Arc
Method

Goal: get elasticity between A
and B (ignore C)
Linear Demand Curve

Percent change in Q is
(11-12)/((11+12)/2) = -1/11.5 =
-8.69%
42
41
40
B
39
Percent change in P is
(38-36)/((38+36)/2) = 2/37 =
5.40%
38
Price

A
37
36
C
35
34

Elasticity is approx.
-8.69/5.40= -1.6
33
32
31
30
10

WHICH ONE?????
– Bigger Delta?
– Smaller Delta?
11
12
Quantity
13
14
Elasticity: The Exact Measurement
Via The Point Formula
Arc formula for 
D
X , PX
DQ D /(average of the two Qs)

x100
DP/(average of the two Ps)

Let’s make B&C get closer and closer to A. In the limit we would get the exact
elasticity at point A.

So, taking the limit as points B and C converge on A, note the following:
–
–

(average of the two Qs) = QD evaluated at point A.
(average of the two Ps) = P at point A.
Rearranging, you now get: η = (ΔQD / ΔP) (P /QD).

Note that: (ΔQD/ ΔP) is actually the slope of the demand curve equation
when you have the equation, QD = f(P), evaluated at point A.

Note: When you GRAPH demand, the slope you see is actually (ΔP/ΔQD),
since it’s rise over run and the “rise” variable is price and the “run” variable is
quantity. Books tend to call this the slope.
Slope Compared To Elasticity

The slope measures the rate of change of
one variable (P, for example) in terms of
another (Q, for example).
– Slope of demand = ΔQD/ΔP

An elasticity measures the percentage
change of one variable (Q) in terms of
percentage change in another (P).
– Own Price Elasticity of demand = %ΔQD/ %ΔP!
Example Point Elasticity
Calculation At P=$36


QD = 30 – 1/2P OR
PD = 60 – 2Q
$
60

(dQD/dP) = -1/2 OR
(dPD/dQ) = -2 = “slope”

Note: (1/“slope” ) = -1/2

At point A, P=36  QD=12

Demand
36
A
 D X , P  (dQ D X / dPX )( PX / Q D X )
X
SO...own-price elasticity of
demand = (-1/2)(3) = -1.5

Absolute value of the
elasticity = 1.5

12
Q
Point Elasticity As We Move
Down A Linear Demand Curve


QD = 30 – 1/2P OR
PD = 60 – 2Q
 D X , P  (dQ D X / dPX )( PX / Q D X )
$
60
Demand
X

GIVEN A LINEAR DEMAND
CURVE…
36

A
For prices above the
midpoint, demand will be
price elastic.

For prices below the
midpoint, demand will be
price inelastic.

At the midpoint, demand will
be unitary elastic.
Midpoint (P=30, Q=15)
12
Q
Exercise – “Large Delta” Arc
Formula With Nonlinear Demand

Compute the elasticity of demand at P=$1.25
(the point indicated in red) on the table at the
right using the large delta arc formula.
– That is, use the row before and the row after
the row in red where P=$1.25

Percentage change in Q =
(17-19)/((17+19)/2) = -1/9 = -11.11%

Percentage change in P =
(1.40-1.12)/((1.40+1.12)/2) = 22%

Elasticity = -0.50
Quantity
10
11
12
13
14
15
16
17
18
19
20
Price
4.03
3.33
2.80
2.39
2.06
1.79
1.58
1.40
1.25
1.12
1.01