Final answer:
The quantity demanded will decrease by 55.55% when the price of a good with a price elasticity of demand of 2.5 rises from 18 to 22. This percentage change is found by calculating the percentage change in price and multiplying it by the price elasticity of demand.
Step-by-step explanation:
If the price elasticity of demand for a good is 2.5, and the price of the good rises from 18 to 22, we can calculate the expected percentage change in the quantity demanded by using the formula for price elasticity of demand, which is:
Price Elasticity of Demand (PED) = (Percentage change in quantity demanded) / (Percentage change in price)
First, we calculate the percentage change in price:
Percentage change in price = [(New Price - Original Price) / Original Price] × 100
Percentage change in price = [(22 - 18) / 18] × 100 = 22.22%
Now, knowing that the PED is 2.5, we can rearrange the formula to solve for the percentage change in quantity demanded:
Percentage change in quantity demanded = PED × Percentage change in price
Percentage change in quantity demanded = 2.5 × 22.22%
Percentage change in quantity demanded = 55.55%
Since the demand is elastic, the percentage change in quantity demanded is more than the percentage change in price. Therefore, the quantity demanded will decrease by 55.55%, which isn't one of the options provided.