Final answer:
The student's question involves calculating the price elasticity of demand, which measures the responsiveness of quantity demanded to a change in price. The calculation involves determining percentage changes in quantity and price, and dividing them to obtain the elasticity. In the provided example, the elasticity is 1.6, indicating that the demand is relatively elastic.
Step-by-step explanation:
The question deals with the concept of price elasticity of demand, which is a measure used in economics to show how the quantity demanded of a good responds to a change in price. The price elasticity of demand can be calculated by using the formula:
Percentage change in quantity demanded = [(Change in quantity) / (Average quantity)] × 100
Percentage change in price = [(New price - Original price) / (Average price)] × 100
Price Elasticity of Demand = (Percentage change in quantity demanded) / (Percentage change in price)
In the given scenario, as the quantity demanded increases from 40 to 60 when the price decreases from $9 to $7, we can apply the formula to find out the price elasticity:
- Change in quantity = 60 - 40 = 20
- Average quantity = (60 + 40) / 2 = 50
- Change in price = $7 - $9 = - $2
- Average price = ($9 + $7) / 2 = $8
- Percentage change in quantity demanded = (20 / 50) × 100 = 40%
- Percentage change in price = (-2 / 8) × 100 = -25%
- Price Elasticity of Demand = 40% / -25% = -1.6 (a negative sign indicates an inverse relationship)
The calculated price elasticity of demand is 1.6, which implies that the demand for Good A is relatively elastic in this price range. An elasticity greater than 1 suggests that the percentage change in quantity demanded is greater than the percentage change in price.