Elasticity of Demand

AG BM 102

Introduction

• Key issue: how responsive is the consumption of a product to a change in its price?

• The demand curve provides a quantitative answer

• But the answer depends on units of measurement

• Elasticity does not depend on units of measurement!

Definition:The own price elasticity of demand - the percentage change in the quantity demanded in response to a one percent change in the price of the product

An Example - Beef

Price/lb. Quantity

lb./cap.

Price/lb. Quantity

lb./cap.

$5.00 50 $3.75 75

$4.75 55 $3.50 80

$4.50 60 $3.25 85

$4.25 65 $3.00 90

$4.00 70 $2.75 95

2

3

4

5

$/lb.

40 50 60 70 80 90 100lbs./capita

Beef Demand

Calculating the Equation for the Demand Curve

• Take any two points, such as $4.00 and 70 lb, and $3.00 and 90 lb.

• The equation for a straight line is Q = a + b P

• In that equation a and b are constants that together define a specific line.

• You did this with x and y in algebra

Q a bP

b Q Q P P ( ) / ( )1 2 1 2

a Q bP 1 1

Q lbs P! . , $4 . , 70 001 Q lbs and P2 290 00 . $3.

b ( ) / ( )70 90 4 3 20

a 70 20 4 150( )

Q P 150 20

b Q Q P P ( ) / ( )1 2 1 2

a Q bP 1 1

Q a bP

Check to see if points are on the line

Q = 150 – 20P

P = 4, Q = 150 - 20 (4) = 70

P = 5, Q = 150 - 20 (5) = 50

Formula for Demand Elasticity

( ) / ( ) / ( ) / ( )Q Q Q P P P2 21 1 1 1

Note: ε is the Greek letter epsilon

Elasticity at P=$4.00 and Q=70 lbs.

( ) / ( ) / ( ) / ( ) .90 70 70 3 4 4 1 14

( ) / ( ) / ( ) / ( )Q Q Q P P P2 21 1 1 1

Interpreting elasticity

• Inelastic

• Elastic

• Unitary elastic

1

1

0 1

Inelastic demand means that the quantity change is proportionately

less than the price change

Demand is not especially price responsive – an example, the

demand for milk

Elastic demand means that the quantity change is proportionately

more than the price change.

Demand is particularly price responsive – an example, the

demand for lobster

Another view of the formula

( ) / ( ) * ( ) / ( ) ( / )Q Q P P P Q b P Q2 2 1 11 1 1 1

( ) / ( ) / ( ) / ( )Q Q Q P P P2 21 1 1 1

Point elasticity

Note

• The units cancel out, so elasticity is not dependent on the units used in the data

• For straight-line demand curves, the value of the elasticity changes as you move along the line

• The closer you are to the vertical axis the more elastic is demand

• The closer to the horizontal axis the more inelastic is demand

Elasticity at P=$5.00 and Q=50 lbs.

Elasticity at P=$4.00 and Q=70 lbs.

b P Q/ ( / ) .20 5 50 2 0

b P Q/ ( / ) .20 4 70 1 14

Some demand issues• Is the demand for all food elastic or

inelastic?

• Is the demand for all meat elastic or inelastic?

• Is the demand for beef elastic or inelastic?

• Is the demand for prime rib elastic or inelastic?

Concluding comments

• Elasticity allows us to talk about demand without worrying about the units of measurement

• It makes discussion of demand curves easier

• Makes analysis of changes in demand easier