If a firm is operating in the elastic range of its demand curve, lowering the price will always lead to a decrease in total revenue.

When a firm is in the elastic range of its demand curve, it means that customers are very sensitive to changes in price. This sensitivity means that if the firm lowers its prices, the quantity sold will increase significantly. However, because the demand is elastic, the increase in sales is not enough to make up for the lower price, leading to a decrease in total revenue. For example, if a company sells a product for $10 and sells 100 units, its total revenue is $1,000. If it lowers the price to $8 and sells 150 units, its total revenue becomes $1,200, showing that in this case, total revenue actually increases, but if the increase in quantity sold is not enough, total revenue can still fall.