Elasticity and Total Revenue

Total revenue is just price multiplied by quantity sold. Raise the price and you gain money on every unit still sold, but you lose units because quantity demanded falls as price rises. Which effect wins depends entirely on elasticity. If demand is elastic, quantity is sensitive to price, so the percentage drop in quantity is bigger than the percentage rise in price, and revenue falls. If demand is inelastic, quantity barely budges, so the price increase dominates and revenue rises. At unit elastic demand, the two effects exactly cancel and revenue is at its maximum.

This gives total revenue a predictable shape as you slide down a demand curve from high price to low price. Starting at a very high price where quantity is tiny, demand is elastic, so lowering price raises revenue. Revenue keeps climbing as price falls, peaks right where demand is unit elastic, then starts falling once demand becomes inelastic, because now quantity gains are too small to offset the lower price per unit. The total revenue curve is shaped like a hill sitting above the demand curve.

This connects directly to why sellers care about elasticity when setting prices, and it sets up later work on tax incidence and deadweight loss, where the same elastic-versus-inelastic logic determines who bears a tax and how much surplus is lost.