To calculate the price elasticity of demand (Ed), we use the formula:

$E_d = \left| \frac{\text{percentage change in quantity}}{\text{percentage change in price}} \right|$

Where:

• Percentage change in quantity is calculated as: $\frac{Q_2 - Q_1}{Q_1} \times 100$
• Percentage change in price is calculated as: $\frac{P_2 - P_1}{P_1} \times 100$

Given:

• Price 1 (P₁) = $3
• Quantity 1 (Q₁) = 120 cones
• Price 2 (P₂) = $2.75
• Quantity 2 (Q₂) = 142 cones

Step 1: Calculate the percentage change in quantity

$\text{Percentage change in quantity} = \frac{142 - 120}{120} \times 100 = \frac{22}{120} \times 100 = 18.33\%$

Step 2: Calculate the percentage change in price

$\text{Percentage change in price} = \frac{2.75 - 3}{3} \times 100 = \frac{-0.25}{3} \times 100 = -8.33\%$

Step 3: Calculate the price elasticity of demand (Ed)

$E_d = \left| \frac{18.33}{-8.33} \right| = 2.2$

Interpretation:

The price elasticity of demand for your ice cream is 2.2. This means the demand for your ice cream is elastic. A 1% decrease in price leads to a 2.2% increase in the quantity sold.

Would you like further details or have any other questions? Here are some related questions for you:

1. How does the elasticity value change if the price decrease is smaller (e.g., $2.90)?
2. How would you interpret an elasticity value of less than 1 for this scenario?
3. What are the implications of elastic demand for pricing strategy in your ice cream store?
4. How would you estimate the revenue change if you increased the price from $2.75 to $3?
5. How does the concept of price elasticity relate to the law of demand?

Tip: Elasticity is a crucial concept in business and economics for understanding how changes in price affect overall revenue.