EC 500

1
EC 500

• Chapter 3
• Quantitative Demand Analysis

2
Headline

• Winners of Wireless Auction to Pay 7 Billion
• The CEO of a regional telephone company
  picked up the March 14 New York Times and began
  reading on page D1
• The Federal Government completed the biggest
  auction in history today, selling off part of the
  nations airways for 7 billion to a handful of
  giant companies that plan to blanket the nation
  with new wireless communications networks for
  telephones and computers
• The CEO read the article with interest
  because his firm is scrambling to secure loans to
  purchase of the licenses the FCC plans to auction
  off in his region next year.

3

• The region serviced by the firm has a
  population that is 7 percent greater than the
  average where licenses have been sold before, yet
  the FCC plans to auction the same number of
  licenses. This troubled the CEO, since in the
  most recent auction 99 bidders caught up to a
  total of 7 billion-an average of 70.7 million
  for a single license.
• Fortunately for the CEO, the New York Times
  article contained a table summarizing the price
  paid per license in 10 different regions, as well
  as the number of licenses sold and the population
  of each region. The CEO quickly entered this
  data into his spreadsheet, clicked the regression
  tool button, and found the following relation
  between the price of a license, the quantity of
  licenses available, and regional population size .

4

• InP 2.23 - 1.2 InQ 1.25 InPop
• (price and population figures are expressed in
  millions of dollars and people, respectively)
• Based on the CEOs analysis, how much money
  does he expect his company will need to buy a
  license? How much confidence do you place in this
  estimate?

5
Overview

• I. The Elasticity Concept
• Own Price Elasticity
• Elasticity and Total Revenue
• Cross-Price Elasticity
• Income Elasticity
• II. Demand Functions
• Linear
• Log-Linear
• III. Regression Analysis

6
1. The Elasticity Concept

• How responsive is variable G to a change in
  variable S

If EG,S 0, then S and G are directly related.
If EG,S
If EG,S 0, then S and G are unrelated.
7
The Elasticity Concept Using Calculus

• An alternative way to measure the elasticity of a
  function G f(S) is

If EG,S 0, then S and G are directly related.
If EG,S
If EG,S 0, then S and G are unrelated.
8
Own Price Elasticity of Demand

• Negative according to the law of demand.

Elastic
Inelastic
Unitary
9
Perfectly Elastic Inelastic Demand
Price
Price
D
D
Quantity
Quantity
10
Own-Price Elasticity and Total Revenue

• Elastic
• Increase (a decrease) in price leads to a
  decrease (an increase) in total revenue.
• Inelastic
• Increase (a decrease) in price leads to an
  increase (a decrease) in total revenue.
• Unitary
• Total revenue is maximized at the point where
  demand is unitary elastic.

11
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
30
40
50
Q
Q
0
0
10
20
12
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
80
800
30
40
50
Q
Q
0
10
20
10
30
40
50
0
20
13
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
80
1200
60
800
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
14
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
80
1200
60
40
800
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
15
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
80
1200
60
40
800
20
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
16
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
Elastic
80
1200
60
40
800
20
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
Elastic
17
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
Elastic
80
1200
60
Inelastic
40
800
20
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
Elastic
Inelastic
18
Elasticity, Total Revenue and Linear Demand with
P -2Q 100
P
TR
100
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
30
40
50
Q
Q
0
10
20
30
40
50
0
10
20
Elastic
Inelastic
19
Another example Q 80 2P (or P 40 - 0.5Q)
20

• At point B,
• At Point E,

21
(No Transcript)
22
When E -1,

• From Q 80 2P (or P 40 - 0.5Q)
• Revenue PQ (40 - 0.5Q)Q
• 40Q 0.5Q2
• MR dR/dQ 40 Q
• MR 0 implies Q 40.
• Point Revenue is maximized when E -1 (implying
  MR 0).

23
Decision of Singapore Airlines

• Should it increase fares to boost cash flow, or
  adopt a cut price and make it up in volume?
• Price elasticity is -1.7. What is your
  suggestion? Why?
• If it cuts fares by 5, how much sales will
  increase?
• -1.7 change in Q / 5
• thus, change in Q 8.5

24
Factors Affecting Own Price Elasticity

• Available Substitutes
• The more substitutes available for the good, the
  more elastic the demand.
• Time
• Demand tends to be more inelastic in the short
  term than in the long term.
• Time allows consumers to seek out available
  substitutes.
• Expenditure Share
• Goods that comprise a small share of consumers
  budgets tend to be more inelastic than goods for
  which consumers spend a large portion of their
  incomes.
• Are foods more elastic than transportation?

25
Price and MR
26

• Point When E -1, MR 0
  Revenue is maximized.
• Formula
• If E -1, MR 0
• If E 0
• If E -1, MR

27

• How was the formula derived?
• R PQ
• MR dR/dQ P QdP/dQ
• P1 (Q/P) (dP/dQ)
• P1 1/E P(1E)/E

28
Cross Price Elasticity of Demand
If EQX,PY 0, then X and Y are substitutes.
If EQX,PY 29
(No Transcript)
30
Example

• You are the manager of Publix. Suppose that the
  price of recreation increases by 15. Then, how
  it will affect the sales of foods?
• Cross elasticity of food and recreation 0.15
• 0.15 change in Qfood / 15
• Thus, change in Qfood 2.25
• Is it a substitute?

31
Income Elasticity
If EQX,M 0, then X is a normal good.
If EQX,M 32
Example

• Suppose that the income elasticity of nonfed
  ground beef is 1.94. If income increases by
  10, how it will affect the demand for nonfed
  ground beef?
• 1.94 change in Qg_beef / 10
• Thus, change in Qg_beef -19.4
• Is it a normal good?

33
Uses of Elasticities

• Pricing.
• Managing cash flows.
• Impact of changes in competitors prices.
• Impact of economic booms and recessions.
• Impact of advertising campaigns.
• And lots more!

34
Example 1 Pricing and Cash Flows

• According to an FTC Report by Michael Ward,
  ATTs own price elasticity of demand for long
  distance services is -8.64.
• ATT needs to boost revenues in order to meet
  its marketing goals.
• To accomplish this goal, should ATT raise or
  lower its price?

35
Answer Lower price!

• Since demand is elastic, a reduction in price
  will increase quantity demanded by a greater
  percentage than the price decline, resulting in
  more revenues for ATT.

36
Example 2 Quantifying the Change

• If ATT lowered price by 3 percent, what would
  happen to the volume of long distance telephone
  calls routed through ATT?

37
Answer

• Calls would increase by 25.92 percent!

38
Example 3 Impact of a change in a competitors
price

• According to an FTC Report by Michael Ward,
  ATTs cross price elasticity of demand for long
  distance services is 9.06.
• If competitors reduced their prices by 4 percent,
  what would happen to the demand for ATT services?

39
Answer

• ATTs demand would fall by 36.24 percent!

40
3. Interpreting Demand Functions

• Mathematical representations of demand curves.
• Example
• X and Y are substitutes (coefficient of PY is
  positive).
• X is an inferior good (coefficient of M is
  negative).

41
Linear Demand Functions

• General Linear Demand Function

Income Elasticity
Own Price Elasticity
Cross Price Elasticity
42
Example of Linear Demand

• Qd 10 - 2P.
• Own-Price Elasticity (-2)P/Q.
• If P1, Q8 (since 10 - 2 8).
• Own price elasticity at P1, Q8
• (-2)(1)/8 - 0.25.

43
Log-Linear Demand

• General Log-Linear Demand Function

44
Example of Log-Linear Demand

• ln(Qd) 10 - 2 ln(P).
• Own Price Elasticity -2.

45
Graphical Representation of Linear and Log-Linear
Demand
P
D
D
Q
Linear
Log Linear
46
3. Regression Analysis

• One use is for estimating demand functions.
• Important terminology and concepts
• Least Squares Regression Y a bX e.
• Confidence Intervals.
• t-statistic.
• R-square or Coefficient of Determination.
• F-statistic.

47
An Example

• Use a spreadsheet to estimate the following
  log-linear demand function.

48
Summary Output
49
Interpreting the Regression Output

• The estimated log-linear demand function is
• ln(Qx) 7.58 - 0.84 ln(Px).
• Own price elasticity -0.84 (inelastic).
• How good is our estimate?
• t-statistics of 5.29 and -2.80 indicate that the
  estimated coefficients are statistically
  different from zero (significant).
• R-square .17 (not much meaningful, though)

50
More on Regression

• Using Excel Example
• AUCTION_DATA.XLS
• Goals of Regression
• Prediction, marginal effects, and testing
  hypothesis
• Dummy independent variables
• Differences
• Dummy Dependent Variables Models
• Choice Models

51
Conclusion

• Elasticities are tools you can use to quantify
  the impact of changes in prices, income, and
  advertising on sales and revenues.
• Given market or survey data, regression analysis
  can be used to estimate
• Demand functions.
• Elasticities.
• A host of other things, including cost functions.
• Managers can quantify the impact of changes in
  prices, income, advertising, etc.

52
Back to Headline

• In P 2.23 1.2 In Q 1.25 In Pop
• The coefficient of InPop(1.25) tells us the
  percentage change in price resulting from each 1
  percent change in population.
• Since the population in the relevant region is 7
  percent higher than the average, this means
• 1.25 change in P / change in Pop
• 1.25 change in P / 7 -? change in P
  1.25 7 8.75
• In other words, the price the CEO expects
  to pay in his region is 8.75 percent higher than
  the average price paid in the March 14th auction.
  Since that price was 70.7 million, the expected
  price needed to win the auction in his region is,
  other things equal, 76.9 million.
• The CEOs model predicts that the demand for
  licenses will be greater in his region due to the
  greater size of the market ultimately serviced by
  the holders of the licenses

53
Exercises and Homework

• Chapter 3
• In-class
• Q. 2, Q.7, Q. 11, Q. 13
• Homework
• Q. 3, Q. 4, Q. 10 (excel regression)
• Q. 12, Q. 19