Chapter 4, Review Exercises, Question 061 The demand for a product is q = 2000 – 4p where 4 is units sold at a price of p dollars. Find the elasticity E if the price is $40 . Round your answer to two decimal places. The demand i v elastic. the absolute t inelastic. neither elastic nor inelastic.
Chapter 4, Review Exercises, Question 061 The demand for a product is q = 2000 – 4p where 4 is units sold at a price of p dollars. Find the elasticity E if the price is $40 . Round your answer to two decimal places. The demand i v elastic. the absolute t inelastic. neither elastic nor inelastic.
Transcribed Image Text:### Chapter 4, Review Exercises, Question 061
#### Problem Statement:
The demand for a product is given by the equation \( q = 2000 - 4p \), where \( q \) is the number of units sold at a price of \( p \) dollars. Find the elasticity \( E \) if the price is $40.
Round your answer to two decimal places.
\[ E \approx \, \_\_\_\_\_ \]
#### Elasticity Calculation:
To determine whether the demand is elastic, inelastic, or neither (absolute thresholds), you can use the following multiple-choice options provided:
1. elastic.
2. inelastic.
3. neither elastic nor inelastic.
Please select the appropriate option by considering the calculated elasticity value.
---
#### Detailed Explanation of Graphs/Diagrams (If present):
There are no specific graphs or diagrams included in this question. However, the interface indicates that a dropdown menu with the choices mentioned above is available for selection.
### Steps for Solving the Problem:
1. **Find the Derivative of the Demand Function**: The demand function is \( q = 2000 - 4p \).
\[ \frac{dq}{dp} = -4 \]
2. **Calculate the quantity demanded at \( p = $40 \)**:
\[ q = 2000 - 4(40) = 2000 - 160 = 1840 \]
3. **Use the elasticity formula**:
\[ E = \left| \frac{p}{q} \frac{dq}{dp} \right| \]
Substituting the values:
\[ E = \left| \frac{40}{1840} \cdot (-4) \right| = \left| \frac{40 \cdot -4}{1840} \right| = \left| \frac{-160}{1840} \right| \approx 0.09 \]
4. **Compare the calculated elasticity**:
- If \( E > 1 \), the demand is elastic.
- If \( E < 1 \), the demand is inelastic.
- If \( E = 1 \), the demand is unit elastic.
Finally, based on the calculated elasticity value, select the appropriate option from the dropdown menu.
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![### Chapter 4, Review Exercises, Question 061
#### Problem Statement:
The demand for a product is given by the equation \( q = 2000 - 4p \), where \( q \) is the number of units sold at a price of \( p \) dollars. Find the elasticity \( E \) if the price is $40.
Round your answer to two decimal places.
\[ E \approx \, \_\_\_\_\_ \]
#### Elasticity Calculation:
To determine whether the demand is elastic, inelastic, or neither (absolute thresholds), you can use the following multiple-choice options provided:
1. elastic.
2. inelastic.
3. neither elastic nor inelastic.
Please select the appropriate option by considering the calculated elasticity value.
---
#### Detailed Explanation of Graphs/Diagrams (If present):
There are no specific graphs or diagrams included in this question. However, the interface indicates that a dropdown menu with the choices mentioned above is available for selection.
### Steps for Solving the Problem:
1. **Find the Derivative of the Demand Function**: The demand function is \( q = 2000 - 4p \).
\[ \frac{dq}{dp} = -4 \]
2. **Calculate the quantity demanded at \( p = $40 \)**:
\[ q = 2000 - 4(40) = 2000 - 160 = 1840 \]
3. **Use the elasticity formula**:
\[ E = \left| \frac{p}{q} \frac{dq}{dp} \right| \]
Substituting the values:
\[ E = \left| \frac{40}{1840} \cdot (-4) \right| = \left| \frac{40 \cdot -4}{1840} \right| = \left| \frac{-160}{1840} \right| \approx 0.09 \]
4. **Compare the calculated elasticity**:
- If \( E > 1 \), the demand is elastic.
- If \( E < 1 \), the demand is inelastic.
- If \( E = 1 \), the demand is unit elastic.
Finally, based on the calculated elasticity value, select the appropriate option from the dropdown menu.](https://content.bartleby.com/qna-images/question/92ac4bd1-ce2e-4c9a-a27a-d1c524faff08/f709a16a-0e65-4b1b-aceb-b54a5d1e5fbd/vekq28q.png)
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