Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![**Q.13.** Price elasticity of demand of a good is -0.75. Calculate the percentage fall in its price that will result in a 15 percent rise in its demand.
**Explanation:**
The question involves calculating the price change using the concept of price elasticity of demand, which is a measure of how much the quantity demanded of a good responds to a change in price.
The formula for price elasticity of demand is:
\[
\text{Elasticity} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}
\]
Given:
- Price elasticity = -0.75
- \% change in quantity demanded = +15%
To find the \% change in price, rearrange the formula:
\[
\% \text{ change in price} = \frac{\% \text{ change in quantity demanded}}{\text{Elasticity}}
\]
Substitute the given values:
\[
\% \text{ change in price} = \frac{15}{-0.75} = -20
\]
Therefore, the price must decrease by 20% to result in a 15% increase in demand.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88488e2c-0a47-4922-a6ba-876fd3432f18%2F4268049e-be21-4862-87dd-b94dffedf1dc%2Fa4e3uvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Q.13.** Price elasticity of demand of a good is -0.75. Calculate the percentage fall in its price that will result in a 15 percent rise in its demand.
**Explanation:**
The question involves calculating the price change using the concept of price elasticity of demand, which is a measure of how much the quantity demanded of a good responds to a change in price.
The formula for price elasticity of demand is:
\[
\text{Elasticity} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}
\]
Given:
- Price elasticity = -0.75
- \% change in quantity demanded = +15%
To find the \% change in price, rearrange the formula:
\[
\% \text{ change in price} = \frac{\% \text{ change in quantity demanded}}{\text{Elasticity}}
\]
Substitute the given values:
\[
\% \text{ change in price} = \frac{15}{-0.75} = -20
\]
Therefore, the price must decrease by 20% to result in a 15% increase in demand.
Expert Solution
Basic concept
# the ratio of the percentage change in the quantity demanded by the percentage change in price gives us the elasticity of demand full stop the value of elasticity of demand is always negative because this shows that there exist negative relationship between price and quantity.
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