1. Chapter 3 Quantitative Demand Analysis
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 nation’s 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= InQ InPop
(price and population figures are expressed in millions of dollars and people, respectively):
Based on the CEO’s 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 II. Demand Functions
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 < 0, then S and G are inversely related.
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 < 0, then S and G are inversely related.
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
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 + 100TR
100 10 20 30 40 50 Q Q

12. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100 80
800 Q 10 20 30 40 50 Q 10 20 30 40 50

13. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100 80 60
1200
800 Q 10 20 30 40 50 Q 10 20 30 40 50

14. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100 80 60
1200 40
800 Q 10 20 30 40 50 Q 10 20 30 40 50

15. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50

16. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100
Elastic 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic

17. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100
Elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

18. Elasticity, Total Revenue and Linear Demand with P = -2Q + 100TR
100
Unit elastic
Elastic
Unit elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

19. Another example Q = 80 – 2P (or P = 40 - 0.5Q)

20. At point B,
At Point E,

22. When E = -1, From Q = 80 – 2P (or P = 40 - 0.5Q)
Revenue = P*Q = ( Q)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 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 consumer’s 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 < -1, MR > 0
If E > -1, MR < 0

27. How was the formula derived?
R = P*Q
MR = dR/dQ = P + Q*dP/dQ
= P[1 + (Q/P) (dP/dQ)]
= P[1 + 1/E] = P[(1+E)/E]

28. Cross Price Elasticity of Demand
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.

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 < 0, then X is a inferior good.

32. Example
Suppose that the income elasticity of nonfed ground beef is – 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, AT&T’s own price elasticity of demand for long distance services is
AT&T needs to boost revenues in order to meet it’s marketing goals.
To accomplish this goal, should AT&T raise or lower it’s 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 AT&T.

36. Example 2: Quantifying the Change
If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

37. Answer
Calls would increase by percent!

38. Example 3: Impact of a change in a competitor’s price
According to an FTC Report by Michael Ward, AT&T’s 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 AT&T services?

39. Answer
AT&T’s demand would fall by 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:
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

42. Example of Linear Demand
Qd = P.
Own-Price Elasticity: (-2)P/Q.
If P=1, Q=8 (since = 8).
Own price elasticity at P=1, Q=8:
(-2)(1)/8=

43. Log-Linear Demand
General Log-Linear Demand Function:

44. Example of Log-Linear Demand
ln(Qd) = ln(P).
Own Price Elasticity: -2.

45. Graphical Representation of Linear and Log-Linear DemandQ 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) = ln(Px).
Own price elasticity: (inelastic).
How good is our estimate?
t-statistics of 5.29 and 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 Goals of Regression
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 CEO’s 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