Final answer:
To calculate the price elasticity of demand for a commodity that had a price rise from $20 to $25 and a drop in quantity demanded from 25,000 to 10,000 units, the percentage change in quantity and price are computed, leading to an elasticity of approximately -3.94, indicating that the demand is elastic.
Step-by-step explanation:
The student is asking to calculate the price elasticity of demand for a commodity that experienced a price increase from $20 to $25, which resulted in the decrease of quantity demanded from 25,000 units to 10,000 units. To calculate the elasticity, we use the formula percentage change in quantity demanded divided by the percentage change in price.
First, we find the percentage change in quantity: (10,000 - 25,000) / ((10,000 + 25,000) / 2) x 100, which equals a change of -87.5%. Next, we calculate the percentage change in price: (25 - 20) / ((25 + 20) / 2) x 100, resulting in a change of 22.22%. Then we divide the percentage change in quantity by the percentage change in price: -87.5 / 22.22, which gives us an elasticity of approximately -3.94.
This high absolute value indicates that the demand for this commodity is elastic, meaning the percent of quantity demanded decreases by a greater percentage than the increase in price. A significant change in quantity demanded due to a price change suggests that consumers are sensitive to price changes for this commodity.