Download Econ 201 - Notes - Michigan State University

Elasticities and
Regression Analysis
Chapter 3
1
Suppose the price of a good increased
by 50%. How would that change the
amount you buy?
Almost the Same
amount of:
Aspirin
Shoes
Inelastic
A lot less of
Diet Coke
Espresso
Royale Coffee
A little less of
Gasoline
MSU Basketball
tickets
Elastic
2
Own Price Elasticity of Demand
Defined
How sensitive quantity demanded is to
price
 More formally:

D
% DQ XD

% DPX
Where D means “change”
3
Example
What is the own price elasticity of demand
for cigarettes?
 -0.4
 Interpret this number:
 A 1% increase in the price of cigarettes
will lower the quantity demanded by 0.4 %

4
Example

If the government wanted to decrease smoking
by 10 percent, by how much would the
government have to increase the price of
tobacco?
% DQ

% DP
D
 .10
 0.4 
%DP
 .10 = .25 = 25%
%DP 
 0.4
5
What determines relative price
elasticity?









Number of substitutes
The more substitutes or the closer the substitutes, the…
Ex. Diet Coke
more elastic
Time interval
The longer time interval the…
Ex. Gasoline
more elastic
Share of budget
The larger share of the budget the …
more elastic
Ex. Salt
6
Own Price Elasticity of Demand

1.
2.
Why do we care?
Tells us what affect a D in P will have on
revenue
Tells us what affect a D in P will have on
Q (ex: taxes)
7
Own Price Elasticity of Demand
D
% DQ XD

% DPX
What sign does it have?
 Negative, Why?
 Law of Demand

8
Calculating Own Price Elasticity of Demand
At a single point, small changes in P and Q
DQ
%DQ
D 
%DPX
D
X

DP
P

Q
P
Q  DQ * P DQ

*
Q DP
DP
DP Q
D
D
D
P
D
DQ
D
D
P ($/Q)
P

D
D
Q
P
1

*
slope
Q slope
D
D
12 A
11
10
9
8
7
6
5
4
3
2
1
0
0
B
C
D
E
F
G
1
2
3
Q
4
5
6
9


The equation for
the demand curve
below is P = 12-2Q
The slope of the
demand curve is -2
P ($/Q)
Own Price Elasticity and demand
along a linear demand curve
12
11
10
9
8
7
6
5
4
3
2
1
0
A
B
C
D
E
F
G
0 1 2 3 4 5 6
Q
10
Calculating Own Price Elasticity of
P
Demand @ B
 
Q
0
1
2
3
4
5
6
P
d
12 -∞
10 -5
-2
8
-1
6
4 -1/2
2 -1/5
0
0
P ($/Q)
Point
A
B
C
D
E
F
G
D
P 1  10 1 =-5
 D (point B) 
Q slope 1  2
1
Q slope
12 A
11
B
10
9
C
8
7
D
6
5
E
4
F
3
2
G
1
0
0 1 2 3 4 5 6
Q
11
Own Price Elasticity of Demand
%DQ

 d <-1 (further from 0) is Elastic
%DP
D
% change in QD > % change in P

d>-1 (closer to 0) is Inelastic
% change in QD < % change in P
12
Calculating Own Price Elasticity of
P 1
 
Demand
Q slope
D
Q
0
1
2
3
4
5
6
P
12
10
8
6
4
2
0
d

-
-5
-2
-1
-½
-1/5
0
P ($/Q)
Point
A
B
C
D
E
F
G
d<-1: Elastic
12 A
11
B
10
9
C
d>-1:
8
7
D Inelastic
6
5
E
4
F
3
2
G
1
0
0 1 2 3 4 5 6
Q
13
Extremes
Perfectly Inelastic
 completely unresponsive to changes in
price

D
P
Ex. Insulin
5
4
5
Q
14
Extremes
Perfectly Elastic
 completely responsive to changes in
price

Ex. Farmer Joe’s Corn
P
5
D
4
Q
5
15
Elasticity and Total Revenue
 Total
revenue is
 the amount received by sellers of a good.
 Computed as:
TR = P X Q
16
Intuition Check

If an item goes on sale (lower price), what
will happen to the total revenue on that
item?
17
Elasticity and Total Revenue
 Marginal
Revenue is
 the additional revenue from selling one
more of a good.
 Computed as:
MR = DTR/DQ
18
B
C
D
E
F
3
4
5
6
6
2
5
1
4
G
2
3
Q
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
-17
-18
-19
-20
-21
-22
1
P d TR
12 -∞
10 -5
8
-2
6
-1
4 -1/2
2 -1/5
0
0
0
Q
0
1
2
3
4
5
6
P ($/Q)
Pt
A
B
C
D
E
F
G
Elasticity
Own Price Elasticity of
Demand
12 A
11
10
9
8
7
6
5
4
3
2
1
0
0
Q
19
4
4
-1/2
F
5
2
-1/5
10
G
6
0
0
0
10
2
-2
-6
-10
TR
G
1
2
3
4
5
6
6
E
18
16
1
F
5
-1
B
E
4
6
12
D
Q
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
3
3
0
C
2
D
A
B
1
8
P
0
2
Q
P ($/Q)
C
d TR MR
0
-∞
10
10
-5
6
16
-2
Pt
TR=TE
Own Price Elasticity of
Demand
12 A
11
10
9
8
7
6
5
4
3
2
1
0
0
Q
20
Income Elasticity of Demand
Defined
How sensitive quantity demanded is to
income
 More formally:
D
%DQX
M 
%DM

Where M means “income”
21
Interpreting Income Elasticity
%DQ
M 
%DM
D
X



Suppose Income
elasticity is 2
A 1 percent increase
in income leads to a...
2 percent increase in
quantity demanded
22
Sign of Income Elasticity
Ex. Great
Positive
 Normal Good Harvest Bread
 Negative
M
 Inferior Good


Ex. Spam
%DQ

%DM
D
X
23
Cross-price Elasticity of
Demand Defined
How sensitive quantity demanded of X is
to a change in the price of Y
 More formally:
%DQXD
 XY 
%DPY

Where PY means “price of Y”
24
Sign of Cross Price Elasticity
Positive
Ex. Accord and Taurus ,
 substitutes Diet Coke and Diet Pepsi
 XY
 Negative
 complements
Ex. Pizza and Beer,

%DQ

%DPY
D
X
gasoline and SUVs,
software and hardware
25
Estimating Elasticities from Data
Demand for Good X
QDx = f(Px, PY, M, H1 , H2, …)
where,
Px is the price of good X,
PY is the price of good Y,
M is income,
H1 is size of population,
H2 is consumers’ expectations.
26
Estimating Elasticities from Data
Assume linear demand,
QDx = α0+ αxPx + αYPY + αMM + αH1 H1 …


Or assume log linear demand,
log(QDx)= β0+ β xlog(Px)+ β Ylog(PY)+
β Mlog(M) + β H1log(H1)…
27
Estimating Own Price Elasticity
D
DQ
D
Q
P
 DQ
%DQ
P
Q

*


*

D
P
Q
D
P
Q
D
P
%DPX
P
D
X
D
D
D
D
D
D
When the change is “very, very” small,
%DQ
D 
%DPX
D
X
Q D x Px

*
Px Q D x
28
Estimating Own Price Elasticity
If assume,
QDx = α0+ αxPx + αYPY + αMM + αH1 H1 …
Then,
D
Q x
 αx
Px
so,
Px
%DQ
Q x Px

*
D 
= αx
D
Px Q D x
%DPX
Q x
D
X
D
29
Estimating Own Price Elasticity
If assume,
log(QDx)= β 0+ β xlog(Px)+ β Ylog(PY)+…
Then,
Q x Px
*
β x
Px Q D x
so,
D
%DQ
Q x Px = β

*
D 
x
Px Q D x
%DPX
D
X
D
30
Estimating Cross Price Elasticity
[Similar to estimating own price elasticity except consider
the affect of a change in the price of Y on the quantity
demand of X.]

If assume linear specification,
XY
%DQ DX
PY

 Y
%DPY
QD
X

If assume log linear specification,
XY
%DQ DX

 Y
%DPY
31
If you are a manager, why would
you pay an economist big $$$ to
estimate these elasticities?
1.
2.
3.
Quantify how a change in (own) price
affects quantity demanded.
Forecast future demand.
If you offer a product line, you want to
know how a change in price in one good
affects the quantity demanded of another
good you produce.
32
Elasticities and Public Policy
If you are a public official, why might you
care about elasticities for alcohol, drugs
and cigarettes?
 How do you estimate these elasticities?

33
Words of Caution

There are many complicated issues
associated with estimating elasticities. To
accurately estimate these elasticities, one
needs detailed knowledge of the
product/industry, sophisticated statistical
techniques, reasonable variation in
prices/quantities and precise data.
34
Estimating Elasticities of Ethanol
Gasoline (Soren Anderson, 2010)
Uses gas station level data from Minnesota
Regression Specification,
log(QDe)= β 0+ β elog(Pe)+ βglog(Pg)+βFlog (FFV)
+ βSlog (Stations)+ε
where,
Pe is price of ethanol, Pg is price of gasoline, FFV is the
number of flex-fuel vehicles in county and Stations is the
number of station with ethanol in county.
35
Estimating Elasticities of Ethanol
Gasoline (Soren Anderson, 2007)
Regression Results,
log(QDe)= β 0-1.65log(Pe)+ 2.62log(Pg)
+0.07log (FFV)-0.14log (Stations)
36
Collinearity Between Gas and
Ethanol Prices
37