Elasticities and Regression Analysis

1
Elasticities and Regression Analysis

• Chapter 3

2
Suppose the price of a good increased by 50. How
would that change the amount you buy?
Diet Coke
Aspirin
Gasoline
Espresso Royale Coffee
MSU Basketball tickets
Shoes
Inelastic
Elastic
3
Own Price Elasticity of Demand Defined

• How sensitive quantity demanded is to price
• More formally

Where D means change
4
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

5
Example

• If the government wanted to decrease smoking by
  10 percent, by how much would the government have
  to increase the price of tobacco?

.25 25
6
What determines relative price elasticity?

• Number of substitutes
• The more substitutes or the closer the
  substitutes, the
• more elastic
• Time interval
• The longer time interval the
• more elastic
• Share of budget
• The larger share of the budget the
• more elastic

Ex. Diet Coke
Ex. Gasoline
Ex. Salt
7
Own Price Elasticity of Demand

• 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)

8
Own Price Elasticity of Demand

• What sign does it have?
• Negative, Why?
• Law of Demand

9
Calculating Own Price Elasticity of DemandAt a
single point, small changes in P and Q
10
Own Price Elasticity and demand along a linear
demand curve

• The equation for the demand curve below is P
  12-2Q
• The slope of the demand curve is -2

11
Calculating Own Price Elasticity of Demand _at_ B
Point Q P hd
A 0 12
B 1 10
C 2 8
D 3 6
E 4 4
F 5 2
G 6 0
-8
-5
-2
-1
-1/2
-1/5
0
-5
12
Own Price Elasticity of Demand

• hd lt-1 (further from 0) is Elastic
• change in QD gt change in P
• hdgt-1 (closer to 0) is Inelastic
• change in QD lt change in P

13
Calculating Own Price Elasticity of Demand
Point Q P hd
A 0 12
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -½
F 5 2 -1/5
G 6 0 0
hdlt-1 Elastic
-
hdgt-1 Inelastic
14
Extremes

• Perfectly Inelastic
• completely unresponsive to changes in price

D
P
Ex. Insulin
5
4
Q
5
15
Extremes

• Perfectly Elastic
• completely responsive to changes in price

P
Ex. Farmer Joes Corn
5
D
4
Q
5
16
Elasticity and Total Revenue

• Total revenue is
• the amount received by sellers of a good.
• Computed as
• TR P X Q

17
Intuition Check

• If an item goes on sale (lower price), what will
  happen to the total revenue on that item?

18
Elasticity and Total Revenue

• Marginal Revenue is
• the additional revenue from selling one more of a
  good.
• Computed as
• MR DTR/DQ

19
Own Price Elasticity of Demand
Pt Q P hd TR
A 0 12 -8
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0
20
Own Price Elasticity of Demand
MR
Pt Q P hd TR
A 0 12 -8
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0
0
10
10
6
16
2
18
-2
16
TR
-6
10
-10
0
21
Income Elasticity of Demand Defined

• How sensitive quantity demanded is to income
• More formally

Where M means income
22
Interpreting Income Elasticity

• Suppose Income elasticity is 2
• A 1 percent increase in income leads to a...
• 2 percent increase in quantity demanded

23
Sign of Income Elasticity
Ex. Great Harvest Bread

• Positive
• Normal Good
• Negative
• Inferior Good

Ex. Spam
24
Cross-price Elasticity of Demand Defined

• How sensitive quantity demanded of X is to a
  change in the price of Y
• More formally

Where PY means price of Y
25
Sign of Cross Price Elasticity

• Positive
• substitutes
• Negative
• complements

Ex. Accord and Taurus , Diet Coke and Diet Pepsi
Ex. Pizza and Beer, gasoline and SUVs, software
and hardware
26
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.

27
Estimating Elasticities from Data

• Assume linear demand,
• QDx a0 axPx aYPY aMM aH1 H1
• Or assume log linear demand,
• log(QDx) ß0 ß xlog(Px) ß Ylog(PY)
• ß Mlog(M) ß H1log(H1)

28
Estimating Own Price Elasticity

• When the change is very, very small,

29
Estimating Own Price Elasticity

• If assume,
• QDx a0 axPx aYPY aMM aH1 H1
• Then,
• ax
• so,
  ax

30
Estimating Own Price Elasticity

• If assume,
• log(QDx) ß 0 ß xlog(Px) ß Ylog(PY)
• Then,
• ß x
• so,
  ß x

31
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,
• If assume log linear specification,

32
If you are a manager, why would you pay an
economist big to estimate these elasticities?

1. Quantify how a change in (own) price affects
   quantity demanded.
2. Forecast future demand.
3. 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.

33
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?

34
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.

35
Estimating Elasticities of Ethanol Gasoline
(Soren Anderson, 2010)

• Uses gas station level data from Minnesota
• Regression Specification,
• log(QDe) ß 0 ß elog(Pe) ßglog(Pg)ßFlog
  (FFV)
• ßSlog (Stations)e
• 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.

36
Estimating Elasticities of Ethanol Gasoline
(Soren Anderson, 2007)

• Regression Results,
• log(QDe) ß 0-1.65log(Pe) 2.62log(Pg)
  0.07log (FFV)-0.14log (Stations)

37
Collinearity Between Gas and Ethanol Prices