SOLUTIONS-1697610823048

Solution 4: To find the optimal ticket price using the variable ticket price technique, we need to maximize total revenue, which is given by the product of price (P) and quantity (Q) sold. For the Clippers game: Inverse Demand: P = 210 - 3Q Total Capacity (C): 20,000 To find the quantity, we set P = MC (since MC is zero until full capacity): MR = 210-6Q-Q = 210-7Q = 0 Q = 210/7 = 30 P = 210-3(30) = 150 For Total Revenue (TR) = P * Q TR = 150*30 =$4500. For the Mavericks game: Inverse Demand: P = 140 - 7Q = 0 Q = 20 TR = PQ = 7020 = $1400 Setting P = MC: 140 - 3.5Q = 0 Price for the Mavericks game: P == 140- 3.5*(20) = $70 Total Revenue: TR = 70 * 20 ≈ $1,400 For the Pistons game: Inverse Demand: P = 60 – 10 Q Q = 6 Price for the Pistons game:

MR = 60 – 5*(6) =$30 Total Revenue: TR = PQ = 30 * 6 = $180 Consequently, setting ticket prices at $150 for the Clippers matchup, $70 for the Mavericks encounter, and $30 for the Pistons game would result in a total revenue of $6080, comprising $4500 from the Clippers game, $1400 from the Mavericks game, and $180 from the Pistons game. b) If the Lakers cannot charge different prices, they need to set a uniform price that maximizes total revenue across all three games. To do this, they need to consider the combined demand for all games. The combined demand is the sum of the individual demands: P combined = P Clippers + P Mavericks + P Pistons = 210 - 3Q + 140 - 3.5Q + 60 - 5Q = 30+20+6 =56 If the Lakers are unable to implement varied pricing, they must maintain a uniform ticket price across all games. In order to determine the average ticket price, we must identify the cost per ticket that results in a total revenue of $6080 for 56 seats. P = 6080/56 = 108.57 Revenue lost compared to VTP: Lost Revenue = TR_combined - (TR_Clippers + TR_Mavericks + TR_Pistons) = 6080 – (4500+1400+180) =$ 100 c) To boost attendance against less desirable teams like the Pistons, the Lakers can employ a price discrimination technique called third-degree price discrimination. This involves charging different prices to different groups based on their price elasticity of demand.

Price for the Pistons game: P = 60 - 5(20000/3) = 10 Total Revenue: TR_Pistons = 10 * (20,000/3) = $66,667 Total Revenue for all games: TR Total = TR Clippers + TR Mavericks + TR Pistons = $ 6080 - $3,000,000 - $ 1,40,000 - $66,667 =$ 5253 = $5,052,951. This strategy can be more profitable if the Lakers make it to the playoffs because playoff games often command higher ticket prices due to increased demand and the higher stakes associated with playoff matches. This can offset the revenue lost during the regular season, making the playoff run more lucrative overall. Additionally, playoff games generate additional revenue from merchandise sales, concessions, and increased fan engagement, further boosting profitability. Solution 5: a) To maximize revenue, UT needs to find the optimal quantity (Q) of tickets to sell to both alumni and students. For Alumni: Inverse Demand: P = 150 - 4Q Total Capacity (C): 16,300 Setting P = MC (which is zero until full capacity): 150 - 4Q = 0 4Q = 150 Q Alumni = 37.5 (round down to 37 for a whole number) Price for Alumni: P = 150 - 4(37) = $14

Total Revenue from Alumni: TR Alumni = P * Q Alumni = 14 * 37 = $518 For Students: Inverse Demand: P = 70 - 2.3Q Setting P = MC (which is zero until full capacity): 70 - 2.3Q = 0 2.3Q = 70 Q Students = 30.43 Price for Students: P = 70 - 2.3(30) = $38 Total Revenue from Students: TR Students = P * Q Students = 38 * 30 = $1,140 Total Revenue: TR Total = TR Alumni + TR Students = $518 + $1,140 = $1,658 b) With the introduction of Student Sections, UT can now sell an additional 4,000 tickets to current students at a price of $10 each. For Students (including Student Section): Q Students = 30 (from previous calculation) + 4,000 (Student Section) = 4,030

(0.471 - 0.448) ² + (0.471 - 0.448) ² + ... + (0.471 - 0.448) ² = 6.58 The within-season variation for the 1972 Dolphins is 6.58. For the 1972 Dolphins, this calculation results in a within-season variation of 6.58. 2007 Patriot: who secured victories in all 16 regular-season games before losing in the Super Bowl, faced opponents with a combined record of 111 wins, 142 losses, and 3 ties. This translates to an average winning percentage of 0.439. (0.625 - 0.439) ² + (0.563 - 0.439) ² + ... + (0.344 - 0.439) ² = 15.36 The within-season variation is then calculated using the squared differences between each opponent's winning percentage and the mean, which yields a value of 15.36 for the 2007 Patriots. In conclusion, the higher within-season variation for the 2007 Patriots compared to the 1972 Dolphins suggests that the Patriots encountered tougher competition in terms of their opponents' winning percentages. Based on this analysis, it can be argued that the 2007 Patriots faced the most competitive Division, Conference, and Overall, League during their respective season. Solution 7: The Herfindahl-Hirschman Index (HHI) for Formula 1 Drivers and Constructor Championships over the specified period (2009-2019). For Formula 1, we have two categories: Driver Champion and Constructor Champion. HHI for Formula 1 Drivers (2009-2019): The HHI for the Driver Championship is calculated based on the number of times each driver won the championship during this period. Year Driver Champion Number of Wins 2009 Jenson Button 1 2010 Sebastian Vettel 1 2011 Sebastian Vettel 1 2012 Sebastian Vettel 1 2013 Sebastian Vettel 1 2014 Lewis Hamilton 1 2015 Lewis Hamilton 1 2016 Nico Rosberg 1 2017 Lewis Hamilton 1

2018 Lewis Hamilton 1 2019 Lewis Hamilton 1 The HHI calculation is as follows: HHI Drivers= (1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) =11 HHI for Formula 1 Constructors (2009-2019): The HHI for the Constructor Championship is calculated based on the number of times each constructor (team) won the championship during this period. Year Constructor Champion Number of Wins 2009 Brawn GP 1 2010 Red Bull Racing (RBR) 1 2011 Red Bull Racing (RBR) 1 2012 Red Bull Racing (RBR) 1 2013 Red Bull Racing (RBR) 1 2014 Mercedes 1 2015 Mercedes 1 2016 Mercedes 1 2017 Mercedes 1 2018 Mercedes 1 2019 Mercedes 1 The HHI calculation is as follows: HHI Constructors= (1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) +(1 2 ) =11 In both cases, the HHI is 11, which indicates a high level of dominance in both the Driver and Constructor Championships in Formula 1 over this period. This suggests that certain drivers and teams were consistently dominant, potentially leading to a perception of less competitiveness in the sport during these years.