Final answer:
The band should consider the concept of price elasticity of demand to set ticket prices and generate the most total revenue. If demand is elastic, lowering ticket prices can lead to higher total revenue by selling more tickets. If demand is inelastic, selling fewer tickets at a higher price may be more profitable.
Step-by-step explanation:
The band should set the ticket price to generate the most total revenue by considering the concept of price elasticity of demand. When demand is elastic, a decrease in price leads to an increase in quantity demanded, resulting in higher total revenue. On the other hand, when demand is inelastic, an increase in price leads to a decrease in quantity demanded and lower total revenue.
In this scenario, if the band faces elastic demand and wants to maximize total revenue, it should consider lowering ticket prices to sell more tickets. By doing so, the band can fill the stadium to its capacity of 15,000 seats and still generate more revenue compared to selling fewer tickets at a higher price.
However, if the band faces inelastic demand, where lowering prices does not significantly increase the quantity demanded, it may be more profitable for the band to sell fewer tickets at a higher price. This is because the increase in price outweighs the decrease in quantity demanded, resulting in higher total revenue.