Question

The mesa Redbirds football team plays in a stadium with seating capacity of 80,000. However, during the past season, attendance averaged only 50,000. The average ticket price was $30. If the price elasticity is -4, what would the team have to charge in order to fill the stadium?If the price were to be decreased to $27 and the average attendance increased to 60,000, what is the price elasticity?

Answer 1

$P_1 = 30 \\ Q_1 = 50000 \\ Q_2 = 80000 \\ -4.0 = E_d = \frac{\frac{ΔQ}{\frac{Q_1+Q_2}{2}}}{\frac{ΔP}{\frac{P_1+P_2}{2}}} \\ = \frac{\frac{80000-50000}{50000-80000}}{\frac{P_2-30}{30+P_2}} \\ = \frac{30000}{13000} \times \frac{30+P_2}{P_2-30} \\ = 0.23076 \times \frac{30+P_2}{P_2-30} \\ -17.334 = \frac{30+P_2}{P_2-30} \\ -17.334P_2 + 520 = 30 +P_2 \\ 490 = 18.334P_2 \\ P_2 = 26.726$