4 Alessandra wants to sell vegetable pasty for 6$ and she achieved to sells 50 pasties. Then she decides the earn more. Price rise up to 8$ and she sells 40 pasties. Find the elasticity and explain?
4 Alessandra wants to sell vegetable pasty for 6$ and she achieved to sells 50 pasties. Then she decides the earn more. Price rise up to 8$ and she sells 40 pasties. Find the elasticity and explain?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![**Understanding Price Elasticity of Demand through a Practical Example**
In this exercise, we will analyze a situation where Alessandra is selling vegetable pasties and determine the price elasticity of demand for her product.
---
### Scenario:
Alessandra initially sets the price of her vegetable pasties at $6 and manages to sell 50 pasties. Seeking to increase her revenues, she decides to raise the price to $8. Following the price increase, she sells 40 pasties. Our task is to find the price elasticity of demand and explain what this means.
### Steps to Calculate Price Elasticity of Demand:
1. **Identify the initial and new prices and quantities:**
- Initial Price (P1) = $6
- New Price (P2) = $8
- Initial Quantity (Q1) = 50 pasties
- New Quantity (Q2) = 40 pasties
2. **Calculate the percentage change in quantity demanded:**
\[
\text{Percentage change in quantity demanded} = \frac{Q2 - Q1}{\left(\frac{Q2 + Q1}{2}\right)} \times 100
\]
\[
\text{Percentage change in quantity demanded} = \frac{40 - 50}{\left(\frac{40 + 50}{2}\right)} \times 100 = \frac{-10}{45} \times 100 \approx -22.22\%
\]
3. **Calculate the percentage change in price:**
\[
\text{Percentage change in price} = \frac{P2 - P1}{\left(\frac{P2 + P1}{2}\right)} \times 100
\]
\[
\text{Percentage change in price} = \frac{8 - 6}{\left(\frac{8 + 6}{2}\right)} \times 100 = \frac{2}{7} \times 100 \approx 28.57\%
\]
4. **Calculate the price elasticity of demand (Ed):**
\[
E_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
\]
\[
E_d = \frac{-22.22\%}{28.57\%} \approx -0.78
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Transcribed Image Text:**Understanding Price Elasticity of Demand through a Practical Example**
In this exercise, we will analyze a situation where Alessandra is selling vegetable pasties and determine the price elasticity of demand for her product.
---
### Scenario:
Alessandra initially sets the price of her vegetable pasties at $6 and manages to sell 50 pasties. Seeking to increase her revenues, she decides to raise the price to $8. Following the price increase, she sells 40 pasties. Our task is to find the price elasticity of demand and explain what this means.
### Steps to Calculate Price Elasticity of Demand:
1. **Identify the initial and new prices and quantities:**
- Initial Price (P1) = $6
- New Price (P2) = $8
- Initial Quantity (Q1) = 50 pasties
- New Quantity (Q2) = 40 pasties
2. **Calculate the percentage change in quantity demanded:**
\[
\text{Percentage change in quantity demanded} = \frac{Q2 - Q1}{\left(\frac{Q2 + Q1}{2}\right)} \times 100
\]
\[
\text{Percentage change in quantity demanded} = \frac{40 - 50}{\left(\frac{40 + 50}{2}\right)} \times 100 = \frac{-10}{45} \times 100 \approx -22.22\%
\]
3. **Calculate the percentage change in price:**
\[
\text{Percentage change in price} = \frac{P2 - P1}{\left(\frac{P2 + P1}{2}\right)} \times 100
\]
\[
\text{Percentage change in price} = \frac{8 - 6}{\left(\frac{8 + 6}{2}\right)} \times 100 = \frac{2}{7} \times 100 \approx 28.57\%
\]
4. **Calculate the price elasticity of demand (Ed):**
\[
E_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
\]
\[
E_d = \frac{-22.22\%}{28.57\%} \approx -0.78
\]
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