1. Managerial Economics & Business Strategy
Chapter 3
Quantitative Demand Analysis

2. Overview I. Elasticities of Demand II. Demand Functions
Own Price Elasticity
Elasticity and Total Revenue
Cross-Price Elasticity
Income Elasticity
II. Demand Functions
Linear
Log-Linear
III. Regression Analysis

3. Elasticities of Demand
How responsive is variable “G” to a change in variable “S”
% means “percent change
If eG,S > 0 then S and G are directly related
If eG,S < 0 then S and G are inversely related

4. Own Price Elasticity of Demand
Calculation method depends on available data
Basic formula if you have %
Mid-point formula: if you have 2 price:quantity observations
Calculus method if you have a general expression

5. Own Price Elasticity of Demand - Mid-point
Be careful to be consistent in subtraction
Always negative

6. Own Price Elasticity of Demand - Mid-point
Consider 2 sales points
P = 5, Qd = 6 and
P = 4, Qd = 7.5 P 5 4 6
7.5 Q

7. Own Price Elasticity of Demand - Mid-point

8. Own Price Elasticity of Demand - Continuous or Point Estimate
If changes in Q and P are small then the average approaches the observation
The ratio of changes is simply the inverse of the slope

9. Own Price Elasticity of Demand - Continuous or Point Estimate
Consider the same 2 sales points
Develop a more general estimate of elasticity
Steps:
Find demand function
Find elasticity

10. Own Price Elasticity of Demand - Continuous or Point Estimate
Consider 2 sales points
P = 5, Qd = 6 and P = 4, Qd = 7.5
General equation is:
P = 9 - 2/3 Q or
Q = 27/2 - 3/2 P

11. Own Price Elasticity of Demand - Continuous or Point Estimate
Q/ P is the slope so Q/ P = -3/2
d = -3/2 (P/Q)
Substituting in:
d = -3/2 (P/Q) = -3P/(27-3P) or
d = -3/2 (P/Q) = 1 - (27/2Q)
Picking one of the points:
P = 5, Qd = 6 gives d = -5/4
P = 4, Qd = 7.5 gives d = -4/5
Average of the two = -1 (compare to other method)

12. Own Price Elasticity of Demand
Negative according to the “law of demand”
Elastic:
Inelastic:
Unitary:

13. Perfectly Elastic & Inelastic Demand
Price
Price D D
Quantity
Quantity
Perfectly Elastic
Perfectly Inelastic

14. 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.

15. Elasticity, TR, and Linear Demand
Price
Quantity D 10 8 6 4 2
Elastic
Inelastic

16. 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.
Need vs. Luxury
Demand tends to be less elastic the more we “need” the good.
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.

17. Own Price Elasticity Implications
If demand is inelastic:
Raise price -
revenue up
volume down  total costs down
profits up
Lower price
revenue down
volume up  total costs up
profits down

18. Own Price Elasticity Implications
If demand is elastic:
Raise price
revenue down
volume down  total costs down
profits ???
Lower price
revenue up
volume up  total costs up

19. Cross Price Elasticity of Demand
+ Substitutes
- Complements

20. Income Elasticity
+ Normal Good
- Inferior Good

21. Uses of Elasticities Pricing Impact of changes in competitors’ prices
Impact of economic booms and recessions
Impact of advertising campaigns

22. Uses of Elasticities - Calculating Revenue Changes
For own price changes:
For related product price changes (Y):

23. Uses of Elasticities - Calculating Revenue Changes
Two products drinks and chips
TRdrinks = $600
TRchips = $400
edrinks = -1.5
echips,drinks = 0.5
What happens to TR if you raise the price of drinks by 2%?
Is it profitable?

24. 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?

25. 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.

26. 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?

27. Answer
Calls would increase by percent!

28. 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 MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

29. Answer
AT&T’s demand would fall by percent!

30. Specific Demand Functions
Linear Demand
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

31. Log-Linear Demand

32. Example of Log-Linear Demand
log Qd = log P
Own Price Elasticity: -2

33. P P Q D D Q
Linear
Log Linear

34. Regression Analysis Used to estimate demand functions
Important terminology
Least Squares Regression: Y = a + bX + e
Confidence Intervals
t-statistic
R-square or Coefficient of Determination
F-statistic

35. An Example Use a spreadsheet to estimate demand
Use a spreadsheet to estimate elasticity

36. An Example - Data

37. An Example Using the data to find a general demand curve:
Q = a0 + a1*PX
There will be errors but we want to minimize them
Find elasticity estimate:
ed = Q/ P * P/Q
ed = a1 * P/Q (use average)
Or with logs:
ed = a1

38. An Example - Regression Results

39. An Example - Regression Results

40. An Example - Regression Results

41. An Example Equation is: Average elasticity of demand:
Qd = *P
Average P = 455
Average Q =
Average elasticity of demand:
-2.6 * 455/450.5 = -2.63

42. Interpreting the Output
Estimated demand function:
Qx = *Px
Own price elasticity: (elastic)
How good is our estimate?
t-statistics of indicates that the estimated coefficient is statistically different from zero
R-square of .75 indicates we explained 75 percent of the variation in quantity

43. An Example - Log-linear Data

44. An Example - Log-linear Data

45. An Example - Log-linear Data

46. An Example - Log-linear Data

47. An Example - Log-linear Data
Equation is:
ln(Qd) = *ln(P)
Average ln(P) = 6.11
Average ln(Qd) =
Elasticity of demand:
compared to -2.63

48. Interpreting the Log Output
Estimated demand function:
ln(Qx) = *ln(Px)
Own price elasticity: (elastic)
How good is our estimate?
t-statistics of indicates that the estimated coefficient is statistically different from zero
R-square of .70 indicates we explained 70 percent of the variation

49. Summary
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.