Final answer:
The price elasticity of demand determines how revenue is affected when price changes. If demand is elastic, lowering the price will increase total revenue. If demand is inelastic, raising the price will increase total revenue. If demand has a unitary elasticity, changing the price will not affect total revenue.
Step-by-step explanation:
The key concept in thinking about collecting the most revenue is the price elasticity of demand. Total revenue is price times the quantity of tickets sold. If demand is elastic at a certain price level, the band should lower the price. This is because the percentage drop in price will result in an even larger percentage increase in the quantity sold, thus raising total revenue. On the other hand, if demand is inelastic at a certain quantity level, the band should increase the ticket price. This is because a certain percentage increase in price will result in a smaller percentage decrease in the quantity sold, leading to an increase in total revenue. If demand has a unitary elasticity, then an equal percentage change in quantity will offset a moderate percentage change in the price, so the band will earn the same revenue whether it increases or decreases the ticket price.