Final answer:
Demand is classified as relatively elastic when price and total revenue vary in opposite directions because it shows a high responsiveness to changes in price.
Step-by-step explanation:
If price and total revenue vary in opposite directions, it means that as the price increases, the total revenue decreases, and vice versa. This scenario indicates that the demand is relatively elastic. As price increases, buyers decrease their quantity demanded significantly, and revenue from sales falls, which reflects a high responsiveness to price changes. On the other hand, price changes in a relatively inelastic demand situation would not significantly affect the total revenue.
It's important to understand that the elasticity of demand measures the sensitivity of consumers' quantity demanded to a change in price. When demand is elastic, a price increase causes a disproportionately large drop in quantity demanded, reducing total revenue. Conversely, when demand is inelastic, a price increase does not cause a significant decrease in quantity demanded, so total revenue may still increase.