1. Chapter 6: Elasticity and Demand
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

2. Elasticity

3. 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

4. Sign of Price Elasticity of Demand
The coefficient of the price elasticity of demand is always negative
It is intuitively more appealing to talk about price elasticity in terms of its absolute value.

5. Price Elasticity of Demand (E)
Table 6.1
Elasticity
Responsiveness
E
Elastic
Unitary Elastic
Inelastic
%∆Q> %∆P
E> 1
%∆Q= %∆P
E= 1
%∆Q< %∆P
E< 1

6. Elastic Demand

7. Inelastic Demand
Demand becomes less elastic as price declines along a linear demand curve.

8. Price Elasticity of Demand (E)
Percentage change in quantity demanded can be predicted for a given percentage change in price as:
%Qd = %P x E
Percentage change in price required for a given change in quantity demanded can be predicted as:
%P = %Qd ÷ E

9. Price Elasticity & Total Revenue
Table 6.2
Elastic
Quantity-effect dominates
Unitary elastic
No dominant effect
Inelastic
Price-effect dominates
Price rises
Price falls
%∆Q> %∆P
%∆Q= %∆P
%∆Q< %∆P
TR falls
No change in TR
TR rises
TR rises
No change in TR
TR falls

10. 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

11. Factors Affecting Price Elasticity of Demand
Necessities versus Luxuries
Luxuries have a more elastic demand
Definition of the market
The more finely defined the market the more elastic the demand. The more aggregate the definition of the market the more inelastic the demand
hamburger < beef <all meat products

12. Calculating Price Elasticity of Demand
Price elasticity can be calculated by multiplying the slope of demand (Q/P) times the ratio of price to quantity (P/Q)

13. 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

14. Calculating Price Elasticity of Demand
Regression analysis provides a point estimate
Arc elasticity is typically only used for teaching purposes

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

16. 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

17. Price Elasticity for Linear Demand

18. Point Elasticity When Demand is Linear
Given Q = a + bP + cM + dPR, let income
& price of the related good take specific
values M and PR , respectively
Then express demand as Q = a′ + bP ,
where a′ = a + cM + dPR and the slope
parameter is b = ∆Q ∕ ∆P

19. Point Elasticity When Demand is Linear
Compute elasticity using either of the two formulas below which give the same value for E
Where P and Q are values of price and quantity demanded at the point of measure along demand, and A ( = –a′ ∕ b) is the price-intercept of demand

20. Point Elasticity When Demand is Curvilinear
Compute elasticity using either of two equivalent formulas below
Where ∆Q ∕ ∆P is the slope of the curved demand at the point of measure, P and Q are values of price and quantity demanded at the point of measure, and A is the price-intercept of the tangent line extended to cross the price axis

21. Elasticity (Generally) Varies Along a Demand Curve
For linear demand, price and Evary directly
The higher the price, the more elastic is demand
The lower the price, the less elastic is demand
For curvilinear demand, no general rule about the relation between price and quantity
Special case of Q = aPb which has a constant price elasticity (equal to b) for all prices

22. Constant elasticity demand function

23. Constant Elasticity of Demand (Figure 6.3)

24. Constant elasticity demand function

25. Marginal Revenue
Marginal revenue (MR) is the change in total revenue per unit change in output
Since MR measures the rate of change in total revenue as quantity changes, MR is the slope of the total revenue (TR) curve

26. Demand & Marginal Revenue (Table 6.3)
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

27. Demand, MR, & TR (Figure 6.4)
Panel A
Panel B

28. Demand & Marginal Revenue
When inverse demand is linear,
P = A + BQ (A > 0, B < 0)
Marginal revenue is also linear, intersects the vertical (price) axis at the same point as demand, & is twice as steep as demand
MR = A + 2BQ

29. Proof

30. Marginal Revenue

31. Total Revenue

32. Linear Demand, MR, & Elasticity (Figure 6.5)

33. MR, TR, & Price Elasticity (Table 6.4)
Marginal revenue
Total revenue
Price elasticity of demand
MR > 0
MR = 0
MR < 0
TR increases as Q increases (P decreases)
Elastic (│E│> 1)
TR is maximized
Unit Elastic (│E│= 1)
TR decreases as Q increases (P decreases)
Inelastic (│E│< 1)

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

35. Proof

36. Marginal Revenue & Price Elasticity
Note that as E -
that MRP

37. Income Elasticity
Income elasticity (EM) measures the responsiveness of quantity demanded to changes in income, holding the price of the good & all other demand determinants constant
Positive for a normal good
Negative for an inferior good

38. Normal Good

39. Inferior Good

40. Cross-Price Elasticity
Cross-price elasticity (EXR) measures the responsiveness of quantity demanded of good X to changes in the price of related good R, holding the price of good X & all other demand determinants for good X constant
Positive when the two goods are substitutes
Negative when the two goods are complements

41. Substitute Good

42. Interval Elasticity Measures
To calculate interval measures of income & cross-price elasticities, the following formulas can be employed

43. Point Elasticity Measures
For the linear demand function Q = a + bP + cM + dPR, point measures of income & cross-price elasticities can be calculated as