1. Learning Objectives Define and measure elasticity
Apply concepts of price elasticity, cross-elasticity, and income elasticity
Understand determinants of elasticity
Show how elasticity affects revenue

2. Price Elasticity of Demand (E)
Measures responsiveness or sensitivity of consumers to changes in the price of a good •
P & Q are inversely related by the law of demand so E is always negative
The larger the absolute value of E, the more sensitive buyers are to a change in price

3. Calculating Price Elasticity of Demand
Price elasticity can be measured at an interval (or arc) along demand, or at a specific point on the demand curve
If the price change is relatively small, a point calculation is suitable
If the price change spans a sizable arc along the demand curve, the interval calculation provides a better measure

4. Computation of Elasticity Over an Interval
When calculating price elasticity of demand over an interval of demand, use the interval or arc elasticity formula

5. So, arc price elasticity of demand =
Ep = Coefficient of arc price elasticity
Q1 = Original quantity demanded
Q2 = New quantity demanded
P1 = Original price
P2 = New price

6. Computation of Elasticity at a Point
When calculating price elasticity at a point on demand, multiply the slope of demand (Q/P), computed at the point of measure, times the ratio P/Q, using the values of P and Q at the point of measure
Method of measuring point elasticity depends on whether demand is linear or curvilinear

7. The Price Elasticity of Demand
Point elasticity: measured at a given point of a demand (or a supply) curve.

8. The Price Elasticity of Demand
The point elasticity of a linear demand function can be expressed as:

9. The Price Elasticity of Demand
Some demand curves have constant elasticity over the relevant range
Such a curve would look like:
Q = aP-b
where –b is the elasticity coefficient
This equation can be converted to linear by expressing it in logarithms:
log Q = log a – b(log P)

10. The Price Elasticity of Demand
Elasticity differs along a linear demand curve.

11. Price Elasticity of Demand (E)
Responsiveness
E
Elastic
Unitary Elastic
Inelastic
Perfect elasticity: E = ∞
Perfect inelasticity: E = 0

12. Factors Affecting Price Elasticity of Demand
Availability of substitutes
The better & more numerous the substitutes for a good, the more elastic is demand
Percentage of consumer’s budget
The greater the percentage of the consumer’s budget spent on the good, the more elastic is demand
Time period of adjustment
The longer the time period consumers have to adjust to price changes, the more elastic is demand

13. The Price Elasticity of Demand
A long-run demand curve will generally be more elastic than a short-run curve.
As the time period lengthens consumers find way to adjust to the price change, via substitution or shifting consumption

14. The Price Elasticity of Demand
There is a relationship between the price elasticity of demand and revenue received.
Because a demand curve is downward sloping, a decrease in price will increase the quantity demanded
If elasticity is greater than 1, the quantity effect is stronger than the price effect, and total revenue will increase

15. Price Elasticity & Total Revenue
Quantity-effect dominates
Unitary elastic
No dominant effect
Inelastic
Price-effect dominates
Price rises
Price falls
TR falls
No change in TR
TR rises
TR rises
No change in TR
TR falls

16. As price decreases Revenue rises when demand is elastic.
Revenue falls when it is inelastic.
Revenue reaches its peak when elasticity of demand equals 1.

17. Marginal Revenue: The change in total revenue resulting from changing quantity by one unit.

18. Since MR measures the rate of change in total revenue as quantity changes, MR is the slope of the total revenue (TR) curve

19. Demand & Marginal Revenue
Unit sales (Q)
Price
TR = P  Q
MR = TR/Q
$4.50 1
4.00 2
3.50 3
3.10 4
2.80 5
2.40 6
2.00 7
1.50 -- $
$4.00
$4.00
$7.00
$3.00
$9.30
$2.30
$11.20
$1.90
$12.00
$0.80
$12.00 $0
$10.50
$-1.50

20. Demand, MR, & TR
Panel A
Panel B

21. For a straight-line demand curve the marginal revenue curve is twice as steep as the demand.

22. At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum.

23. Linear Demand, MR, & Elasticity

24. Some sample elasticities
Coffee: short run -0.2, long run -0.33
Kitchen and household appliances: -0.63
Meals at restaurants: -2.27
Airline travel in U.S.: -1.98
Beer: -0.84, Wine: -0.55

25. MR, TR, & Price Elasticity
Marginal revenue
Total revenue
Price elasticity of demand
MR > 0
Elastic (E> 1)
MR = 0
Unit elastic (E= 1)
MR < 0
Inelastic (E< 1)
TR increases as Q increases (P decreases)
Elastic (E> 1)
Unit elastic (E= 1)
TR is maximized
TR decreases as Q increases (P decreases)
Inelastic (E< 1)

26. Marginal Revenue & Price Elasticity
For all demand & marginal revenue curves, the relation between marginal revenue, price, & elasticity can be expressed as

27. The Cross-Elasticity of Demand
Cross-elasticity of demand: The percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product.

28. The Cross-Elasticity of Demand
Arc Elasticity

29. The Cross-Elasticity of Demand
Point Elasticity

30. The Cross-Elasticity of Demand
The sign of cross-elasticity for substitutes is positive.
The sign of cross-elasticity for complements is negative.
Two products are considered good substitutes or complements when the coefficient is larger than 0.5.

31. Predicting Revenue Changes from Two Products
Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by:

32. Income Elasticity
Income Elasticity of Demand: The percentage change in quantity demanded caused by a 1 percent change in income.

33. Income Elasticity
Arc Elasticity

34. Income Elasticity Categories of income elasticity
Superior goods: EY > 1
Normal goods: 0 >EY >1
Inferior goods – demand decreases as income increases: EY < 0

35. Other Elasticity Measures
Elasticity is encountered every time a change in some variable affects quantities.
Advertising expenditure
Interest rates
Population size

36. 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!

37. 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?

38. 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.

39. 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?

40. Answer
Calls would increase by percent!

41. 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?

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

43. Elasticity of Supply
Price Elasticity of Supply: The percentage change in quantity supplied as a result of a 1 percent change in price.
If the supply curve slopes upward and to the right, the coefficient of supply elasticity is a positive number.

44. Elasticity of Supply
Arc elasticity

45. Elasticity of Supply
When the supply curve is more elastic, the effect of a change in demand will be greater on quantity than on the price of the product.
With a supply curve of low elasticity, a change in demand will have a greater effect on price than on quantity.

46. 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).

47. Linear Demand Functions
General Linear Demand Function:
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

48. 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=

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

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

51. Graphical Representation of Linear and Log-Linear DemandQ P D D Q
Linear
Log Linear