**Price Elasticity of Demand Calculation**(a) The problem states: "If the price of a good increases from $3.50 to $4.25, leading to a fall in quantity demanded from 25 to 15 units, what is the price elasticity of demand for the good at this price range? Interpret the value."**Explanation:**Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in the price of that good. It is calculated using the formula:\[ \text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \]1. **Calculate the percentage change in quantity demanded:** \[ \% \text{ change in quantity demanded} = \frac{\text{New quantity - Original quantity}}{\text{Original quantity}} \times 100 = \frac{15 - 25}{25} \times 100 = -40\% \]2. **Calculate the percentage change in price:** \[ \% \text{ change in price} = \frac{\text{New price - Original price}}{\text{Original price}} \times 100 = \frac{4.25 - 3.50}{3.50} \times 100 \approx 21.43\% \]3. **Calculate the price elasticity of demand:** \[ \text{PED} = \frac{-40\%}{21.43\%} \approx -1.87 \]**Interpretation:**The price elasticity of demand for this good at the given price range is approximately -1.87, indicating that the demand is elastic. This means the percentage change in quantity demanded is greater than the percentage change in price. A 1% increase in price results in a 1.87% decrease in quantity demanded, showing consumers are quite responsive to price changes.

A good's price elasticity of demand is a measure of how sensitive the quantity demanded is to its…

Answered: $4.25, leading to a fall in quantity…

$4.25, leading to a fall in quantity demanded fr 25 to 15 units, what is the price elasticity of demand for the good at this price range?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Price Elasticity of Demand Calculation**

(a) The problem states: "If the price of a good increases from $3.50 to $4.25, leading to a fall in quantity demanded from 25 to 15 units, what is the price elasticity of demand for the good at this price range? Interpret the value."

**Explanation:**

Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in the price of that good. It is calculated using the formula:

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

1. **Calculate the percentage change in quantity demanded:**

\[
\% \text{ change in quantity demanded} = \frac{\text{New quantity - Original quantity}}{\text{Original quantity}} \times 100 = \frac{15 - 25}{25} \times 100 = -40\%
\]

2. **Calculate the percentage change in price:**

\[
\% \text{ change in price} = \frac{\text{New price - Original price}}{\text{Original price}} \times 100 = \frac{4.25 - 3.50}{3.50} \times 100 \approx 21.43\%
\]

3. **Calculate the price elasticity of demand:**

\[
\text{PED} = \frac{-40\%}{21.43\%} \approx -1.87
\]

**Interpretation:**

The price elasticity of demand for this good at the given price range is approximately -1.87, indicating that the demand is elastic. This means the percentage change in quantity demanded is greater than the percentage change in price. A 1% increase in price results in a 1.87% decrease in quantity demanded, showing consumers are quite responsive to price changes.

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