Show proof by way of computing when demand is elastic marginal revenue is positive but less than price?

Answer 1

When demand is elastic, the price elasticity of demand is greater than one (|E| > 1). In this scenario, a decrease in price leads to a proportionally larger increase in quantity demanded, resulting in an increase in total revenue. Marginal revenue (MR) can be calculated as the change in total revenue divided by the change in quantity; since total revenue increases with a price decrease, MR remains positive but is less than the price. Mathematically, if the price (P) is $10 and the quantity demanded increases significantly due to a price drop, MR would be positive but less than $10, confirming that demand is elastic.