Question

When the local grocery store puts cereal on sale, reducing its price from $4.40 per item to $3.40 per item, the quantity sold increases from 220 per week to 230 per week.
1. This illustrates the elasticity of
2. What formula is used to determine the percentage change in quantity demanded?
3. What is the percentage change in quantity demanded for the cereals described above?
4. What formula is used to determine the percentage change in price?
5. Calculate the percentage change in price for the cereal.
6. Finally, using the whole formula, calculate the value of the price elasticity of demand for cereal.
7. Explain what this result means in words.

Suppose that a store decreases the price of laundry detergent from $4.10 to $3.50. As a result, quantity demanded increases from 210 to 230.

8. Using the mid-point formula, calculate the percentage change in price.
9. Using the mid-point formula, calculate price elasticity of demand. Your answer should be expressed in absolute value terms.

Answer 1

Answer:

1. Price elasticity of demand

2 & 3. 4.55%

4 & 5. 22.73%

6. 0.2

8. 15.79%

9. 0.56  

Explanation:

Given that,

Initial quantity demanded = 220

New quantity demanded = 230

Initial price = $4.40

New price = $3.40

1. This illustrates the price elasticity of demand.  Price elasticity of demand is defined as the responsiveness of quantity demanded to any change in the price of the commodity.

2 & 3. Percentage change in quantity demanded:

= [(New quantity demanded - Initial quantity demanded) ÷ Initial quantity demanded] × 100

= [(230 - 220) ÷ 220] × 100

= 0.04545 × 100

= 4.55%

4 & 5. Percentage change in price:

= [(New price - Initial price) ÷ Initial price] × 100

= [($3.40 - $4.40) ÷ $4.40] × 100

= 0.2273 × 100

= 22.73%

6. Price elasticity of demand for cereal:

= Percentage change in quantity demanded ÷ Percentage change in price

= 4.55 ÷ 22.73

= 0.2

7. The price elasticity of demand is comes out to be 0.2 which is less than 1, indicates that quantity demanded is less responsive to changes in the price level.

8 & 9. Given that,

Initial quantity demanded = 210

New quantity demanded = 230

Initial price = $4.10

New price = $3.50

Using the mid point method,

Average price:

= (Initial price + New price ) ÷ 2

= ($4.10 + $3.50 ) ÷ 2

= $3.8

Percentage change in price:

= (New price - Initial price) ÷ Average price

= ($3.50 - $4.10) ÷ $3.8

= 0.1579 or 15.79%

Average quantity demanded:

= (Initial quantity demanded + New quantity demanded ) ÷ 2

= (210 + 230) ÷ 2

= 220

Percentage change in quantity demanded:

= (New quantity demanded - Initial quantity demanded) ÷ Average quantity demanded

= (230 - 210) ÷ 220

= 0.0909 or 9.09%

Price elasticity of demand:

= Percentage change in quantity demanded ÷ Percentage change in price

= 9.09 ÷ 15.79

= 0.56