Final answer:
The percentage change in ticket sales is -22.22%, indicating that the demand is elastic. Since the demand is elastic, the band may increase revenue by lowering ticket prices, as a smaller percentage drop in price could lead to a larger percentage increase in the quantity sold.
Step-by-step explanation:
The student's question involves calculating the percentage change in demand and interpreting the elasticity of demand. Tickets to a Beyonce concert increase from $90 to $110, which is a change in price. Consequently, ticket sales decrease from 100,000 to 80,000, which is a change in quantity. To assess the elasticity, we can use the midpoint formula for percentage change.
To calculate the percentage change in price using the midpoint formula: ((New Price - Old Price) / ((New Price + Old Price)/2)) x 100. That is ((110 - 90) / ((110 + 90) / 2)) x 100 = (20 / 100) x 100 = 20%. For quantity, it would be: ((New Quantity - Old Quantity) / ((New Quantity + Old Quantity)/2)) x 100. That is ((80,000 - 100,000) / ((80,000 + 100,000) / 2)) x 100 = (-20,000 / 90,000) x 100 ≈ -22.22%.
The price elasticity of demand is, therefore, the percentage change in quantity divided by the percentage change in price: -22.22% / 20% = -1.11. The negative sign indicates that the relationship between price and quantity demanded is inverse, but for elasticity we consider absolute value, which is 1.11. This number tells us that the demand is elastic; changes in price lead to larger percentage changes in quantity demanded.
So the percentage change in ticket sales is approximately -22.22%, which means that the elasticity of demand is elastic. In this case, considering the principles of elasticity, Beyonce could potentially maximize revenue by reducing ticket prices, as the percentage drop in price would potentially result in a larger percentage increase in quantity sold.