Final answer:
A 10 percent increase in price with a price elasticity of demand of 2.0 leads to a 20 percent decrease in quantity demanded, demonstrating that the good is highly responsive to price changes, or elastic.
Step-by-step explanation:
If the price elasticity of demand for a good is 2.0, then a 10 percent increase in price results in a 20 percent decrease in quantity demanded. This is because the price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of that good. The formula for calculating the elasticity is the percentage change in quantity demanded divided by the percentage change in price.
The elasticity is given as a positive number, even though demand curves are downward sloping and hence would produce a negative elasticity. We read elasticity values as absolute values, ignoring the negative sign. In this case, an elasticity of 2.0 means that for every 1% increase in price, there is a corresponding 2% decrease in quantity demanded.
Thus, a 10% increase in price, when multiplied by the elasticity of 2.0, results in a 20% decrease in quantity demanded. This relationship highlights that the good in question is elastic, meaning consumers are quite sensitive to price changes.