7. Suppose that a market has the demand function Qd = 20 - 0.5P. Using the midpoint method, what is the price elasticity of demand between $30 and $40?
7. Suppose that a market has the demand function Qd = 20 - 0.5P. Using the midpoint method, what is the price elasticity of demand between $30 and $40?
Chapter1: Making Economics Decisions
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![**Question 7:**
Suppose that a market has the demand function \( Q_d = 20 - 0.5P \). Using the midpoint method, what is the price elasticity of demand between $30 and $40?
---
**Explanation:**
To find the price elasticity of demand using the midpoint method, we use the following formula:
\[
\text{Price Elasticity of Demand (E_d)} = \frac{\left(\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}\right)}{\left(\frac{P_2 - P_1}{(P_2 + P_1)/2}\right)}
\]
Where:
- \(Q_1\) and \(Q_2\) are the quantities demanded at prices \(P_1\) and \(P_2\), respectively.
- \(P_1\) and \(P_2\) are the two different prices.
Given the demand function \( Q_d = 20 - 0.5P \):
1. Calculate \(Q_1\) when \(P_1 = 30\):
\[
Q_1 = 20 - 0.5 \times 30 = 5
\]
2. Calculate \(Q_2\) when \(P_2 = 40\):
\[
Q_2 = 20 - 0.5 \times 40 = 0
\]
3. Substitute the values into the midpoint formula to find \(E_d\):
\[
E_d = \frac{\left(\frac{0 - 5}{(0 + 5)/2}\right)}{\left(\frac{40 - 30}{(40 + 30)/2}\right)} = \frac{\left(\frac{-5}{2.5}\right)}{\left(\frac{10}{35}\right)}
\]
\[
E_d = \frac{-2}{0.2857} \approx -7
\]
The price elasticity of demand between $30 and $40 is approximately \(-7\), indicating that the demand is elastic in this price range.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52525dde-f306-4ac1-a4d1-dd42ba5f8956%2F9d580344-0bc7-4df6-8397-ddb5f73ab4f0%2Frw49l2m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7:**
Suppose that a market has the demand function \( Q_d = 20 - 0.5P \). Using the midpoint method, what is the price elasticity of demand between $30 and $40?
---
**Explanation:**
To find the price elasticity of demand using the midpoint method, we use the following formula:
\[
\text{Price Elasticity of Demand (E_d)} = \frac{\left(\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}\right)}{\left(\frac{P_2 - P_1}{(P_2 + P_1)/2}\right)}
\]
Where:
- \(Q_1\) and \(Q_2\) are the quantities demanded at prices \(P_1\) and \(P_2\), respectively.
- \(P_1\) and \(P_2\) are the two different prices.
Given the demand function \( Q_d = 20 - 0.5P \):
1. Calculate \(Q_1\) when \(P_1 = 30\):
\[
Q_1 = 20 - 0.5 \times 30 = 5
\]
2. Calculate \(Q_2\) when \(P_2 = 40\):
\[
Q_2 = 20 - 0.5 \times 40 = 0
\]
3. Substitute the values into the midpoint formula to find \(E_d\):
\[
E_d = \frac{\left(\frac{0 - 5}{(0 + 5)/2}\right)}{\left(\frac{40 - 30}{(40 + 30)/2}\right)} = \frac{\left(\frac{-5}{2.5}\right)}{\left(\frac{10}{35}\right)}
\]
\[
E_d = \frac{-2}{0.2857} \approx -7
\]
The price elasticity of demand between $30 and $40 is approximately \(-7\), indicating that the demand is elastic in this price range.
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