A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D(x) = 611-16x, where q is the quantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer parts a) through f). a) Find the elasticity. E(x) = 0 BECKH
A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D(x) = 611-16x, where q is the quantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer parts a) through f). a) Find the elasticity. E(x) = 0 BECKH
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Understanding Price Elasticity of Demand Using a Bakery's Demand Function**
A bakery works out a demand function for its chocolate chip cookies and finds it to be \( q = D(x) = 611 - 16x \), where \( q \) is the quantity of cookies sold when the price per cookie, in cents, is \( x \). Use this information to answer parts (a) through (f).
### a) Find the Elasticity
To determine the elasticity of demand, we use the formula for elasticity \( E(x) \) which is given by:
\[ E(x) = \left| \frac{dq}{dx} \cdot \frac{x}{q} \right| \]
Given the demand function:
\[ q = 611 - 16x \]
1. **Differentiate the demand function with respect to \( x \):**
\[ \frac{dq}{dx} = -16 \]
2. **Substitute \( \frac{dq}{dx} \) and the given demand function into the elasticity formula:**
\[ E(x) = \left| -16 \cdot \frac{x}{611 - 16x} \right| \]
---
### Explanatory Notes for Educational Contexts
- **Elasticity of Demand:** It measures how much the quantity demanded of a good responds to changes in price. Elasticity can indicate whether a product is elastic (sensitive to price changes) or inelastic (not sensitive to price changes).
- **Demand Function:** A mathematical function showing the quantity demanded at different price levels. Here, the demand for cookies decreases as the price increases.
Completing the rest of this problem involves applying the specific values as required for each part and understanding the final elasticity value in terms of economic behavior and pricing strategies.
---
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Transcribed Image Text:**Understanding Price Elasticity of Demand Using a Bakery's Demand Function**
A bakery works out a demand function for its chocolate chip cookies and finds it to be \( q = D(x) = 611 - 16x \), where \( q \) is the quantity of cookies sold when the price per cookie, in cents, is \( x \). Use this information to answer parts (a) through (f).
### a) Find the Elasticity
To determine the elasticity of demand, we use the formula for elasticity \( E(x) \) which is given by:
\[ E(x) = \left| \frac{dq}{dx} \cdot \frac{x}{q} \right| \]
Given the demand function:
\[ q = 611 - 16x \]
1. **Differentiate the demand function with respect to \( x \):**
\[ \frac{dq}{dx} = -16 \]
2. **Substitute \( \frac{dq}{dx} \) and the given demand function into the elasticity formula:**
\[ E(x) = \left| -16 \cdot \frac{x}{611 - 16x} \right| \]
---
### Explanatory Notes for Educational Contexts
- **Elasticity of Demand:** It measures how much the quantity demanded of a good responds to changes in price. Elasticity can indicate whether a product is elastic (sensitive to price changes) or inelastic (not sensitive to price changes).
- **Demand Function:** A mathematical function showing the quantity demanded at different price levels. Here, the demand for cookies decreases as the price increases.
Completing the rest of this problem involves applying the specific values as required for each part and understanding the final elasticity value in terms of economic behavior and pricing strategies.
---
(Control elements and navigation prompts shown in the screenshot are part of the online educational interface, aiding users in solving the problem, viewing examples, or seeking additional help.)
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