Elasticity (you have to know)

ELASTICITY: The responsiveness of a dependent variable to changes in an explanatory (independent) variable.
1. Price Elasticity of Demand.
2. Income Elasticity of Demand.
3. Cross-Price Elasticity of Demand.
4. Price Elasticity of Suppy.

PRICE ELASTICITY OF DEMAND:

 The responsiveness of quantity demanded to changes in the good’s price
 Unit-free measure of elasticity (so we can compare apples and oranges).
 Coefficient of price elasticty of demand (ed): ed = % change in QD / % change in P
 Bigger the coefficient – more responsive – more elastic!
 Elastic: ed > 1 – Consumers are quite responsive to price changes in making buying decisions.
 Inelastic: ed < 1 – Consumers are NOT responsive to price changes in making buying decisions.
 Unit Elastic: ed = 1 -- % change in Quantity Demanded = % change in Price.
 Flat slope: The demand for the product is relatively elastic (quite responsive).
 Steep slope: The demand for the product is relatively inelastic.

ARC ELASTICITY OF DEMAND (Midpoint Formula):

 ed = (∆QD / Ave QD) / (∆P / Ave P)

POINT ELASTICITY OF DEMAND

 ed = (∆QD / QD) / (∆P / P) = (1/slope) * (P / QD)

Point Price (Pw) Quantity Demanded (QDw)
A $6 0
B $5 10
C $4 20
D $3 30
E $2 40
F $1 50
G $0 60




EXAMPLES:
1. ed at pt C = 10 * (P/QD) = 10 * (4/20) = 2 – Elastic
2. ed at pt D = 10 * (P/QD) = 10 * (3/30) = 1 – Unit Elastic
3. ed at pt E = 10 * (P/QD) = 10 * (2/40) = .5 – Inelastic
4. ed at pt F = 10 * (P/QD) = 10 * (1/50) = .2 – Inelastic

* At a lower price, people are less responsive to a price change than at a higher price!

FACTS ABOUT ELASTICITIES:
1. At a point above the midpoint (pt. D), demand is elastic.
2. At the midpoint (pt. D), demand is unit elastic.
3. At a point below the midpoint (pt. D), demand is inelastic.

3 CASES WHERE ed IS CONSTANT:
1. Perfectly Inelastic Demand Curve (Vertical Deamand Curve):
 Consumers will always buy the same amount regardless of changes in price. There would have to be absolutely no substitutes for this to happen (i.e. insulin).
2. Infinitely Elastic Demand Curve (Horizontal Demand Curve):
 Consumers will be responsive to any change in price!
3. Unit Elastic Demand Curve (ed =1)

PRICE ELASTICITY OF DEMAND AND TOTAL REVENUE:

 TR = P * Q

1. If Demand is Elastic (ed > 1):
a) As price increases (decreases), total revenue decreases (increases).
2. If Demand is Inelastic (ed < 1):
a) As price increases (decreases), total revenue increases (decreases).
3. If Demand is Unit Elastic (ed =1):
a) As price increases (decreases), total revenue does not change!

Point Price (Pw) Quantity Demanded (QDw) Total Revenue (TR)
A $6 0 0
B $5 10 50
C $4 20 80
D $3 30 90
E $2 40 80
F $1 50 50
G $0 60 0

 For the elastic portion of the Demand Curve (pt. A thru pt. D), as Price decreases, Total Revenue increases.
 For the inelastic portion of the Demand Curve (pt. E thru pt. G), as Price decreases, Total Revenue decreases.

* Maximize Total Revenue – at the Point of Unit Elasticity (midpoint / ed =1).

Source: Ms.Deeter- AP Economics