Question

Calculate the price elasticity of demand for each price change. Note, you will begin with the change in price from $2.25 to $3.25.

Price	Demand	Supply
$2.25	20	2
$3.25	17	5
$4.25	14	8
$5.25	11	11
$6.25	8	14
$7.25	5	17
$8.25	2	20

Assume a merchant was thinking of decreasing the price from $4.25 to $3.25. Based on your calculations, is the price decrease a good idea for the merchant? Please explain why.

How much would consumers respond to a price increase from $2.25 to $3.25. What is the effect on the merchant?

Answer 1

Let price elasticity be denoted by E_d .

From $2.25 to $3.25

E_d  =- [ (2.25-3.25 ) * 20 / (2.25) * (20-17)]

= - [- 1* 20 / 2.25 * 3 ]

= 20 / 6.75

= 2.96

From $3.25 to $4.25

E_d  =- [ (3.25-4.25 ) * 17 / (3.25) * (17-14)]

= - [- 1* 17/ 3.25 * 3 ]

= 17 / 9.75

= 1.74

From $4.25 to $5.25

E_d  =- [ (4.25-5.25 ) * 14 / (4.25) * (14-11)]

= - [- 1* 14/ 4.25 * 3 ]

= 14 / 12.75

= 1.09

From $5.25 to $6.25

E_d  =- [ (5.25-6.25 ) * 11 / (5.25) * (11-8)]

= - [- 1* 11/ 5.25 * 3 ]

= 11 / 15.75

= 0.698

From $6.25 to $7.25

E_d  =- [ (6.25-7.25 ) * 8 / (6.25) * (8-5)]

= - [- 1* 8/ 6.25 * 3 ]

= 8/ 18.75

= 0.426

From $7.25 to $8.25

E_d  =- [ (7.25-8.25 ) * 5/ (7.25) * (5-2)]

= - [- 1* 5/ 7.25 * 3 ]

= 5/ 21.75

= 0.229

Between the prices $4.25 and $3.25 , the demand is elastic, i.e E_d > 1. The percentage  decrease in price will be less than the percentage increase in quantity demanded. This will lead to a increase in total revenue for the seller. So the price decrease is a good idea for the merchant.

A price increase from $2.25 to $3.25 will lead to a fall in demand from 20 units to 17 units. The percentage increase in price will be less than the percentage decrease in quantity demanded. For the merchant, this price increase will decrease his total revenue.