. Serenity Spa increased its total monthly revenue from $11,250 to $12,350 when it raised the price of a
massage from $75 to $95. What is the price elasticity of demand for Harry's Haircuts?

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

\[
\text{PED} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}
\]

**Step 1: Calculate the percentage change in price.**

\[
\%\ \text{change in price} = \frac{\text{new price} - \text{old price}}{\text{old price}} \times 100
\]

Substitute the values:

\[
\%\ \text{change in price} = \frac{95 - 75}{75} \times 100 = \frac{20}{75} \times 100 = 26.67\%
\]

**Step 2: Calculate the percentage change in quantity demanded.**

The total revenue is the product of the price and the quantity demanded. Therefore, the quantity demanded before and after the price change can be estimated using the revenue figures.

Before the price increase:
\[
\text{Revenue} = \text{Price} \times \text{Quantity}
\]
\[
11,250 = 75 \times Q_1
\]
\[
Q_1 = \frac{11,250}{75} = 150
\]

After the price increase:
\[
12,350 = 95 \times Q_2
\]
\[
Q_2 = \frac{12,350}{95} \approx 130
\]

Now calculate the percentage change in quantity demanded:
\[
\%\ \text{change in quantity} = \frac{Q_2 - Q_1}{Q_1} \times 100 = \frac{130 - 150}{150} \times 100 = \frac{-20}{150} \times 100 = -13.33\%
\]

**Step 3: Calculate the price elasticity of demand (PED).**

\[
\text{PED} = \frac{-13.33\%}{26.67\%} = -0.5
\]

### Conclusion:
The price elasticity of demand for Serenity Spa's massages is $-0.5$, indicating inelastic demand. This means that the percentage decrease in quantity demanded is less than the percentage increase in price.

Would you like further clarification or details on any part of this process?

### Related Questions:
1. What does a price elasticity of demand of $-0.5$ imply for the business?
2. How would the total revenue change if the price was further increased?
3. What factors influence the elasticity of demand for massages at Serenity Spa?
4. How could the spa maintain demand despite the price increase?
5. Can you compare this result with the elasticity of a more essential service or product?

### Tip:
For inelastic goods, increasing the price tends to increase total revenue, as the decrease in quantity demanded is relatively smaller than the increase in price.

Serenity Spa increased its total monthly revenue from $11,250 to $12,350 when it raised the price of a massage from $75 to $95. What is the price elasticity of demand for Harry's Haircuts?

Discover how to calculate the price elasticity of demand for Serenity Spa, where a price increase from $75 to $95 changed monthly revenue from $11,250 to $12,350. This detailed step-by-step solution covers key economic concepts like percentage change, revenue calculation, and price elasticity. Ideal for high school economics or business studies students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation