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4. (20 marks) Consider a team with a stadium that has a seating capacity of ('s 40, where O is measured in thousands of fans. Demand for tickets is given by P=100-0. where P is the per-game price of a ticket and O is the number of fans attending per game. For simplicity, assume that the marginal cost per fan is constant at 20 and fixed costs are 600 (in thousands of dollars) per game. a. (2 marks) Derive the team's inverse marginal revenue function. b. (2 marks) Use part (a) to calculate the team's profit-maximising price. P" , and quantity. ()' , per game. c. (2 marks) Calculate the team's maximum profit, .". Now assume that O = 40. d. (2 marks) Recalculate the profit-maximising price, P" . and quantity, Q' . per game. e. (2 marks) Recalculate the team's maximum profit, ."f (2 marks) Use parts (b) - (e) and briefly explain if the team would prefer a sellout or not. Now assume that the team can separate demand into two groups, where demand among hardcore fans is P =132-20, and demand among fairweather fans is P, = 28-0.50- (2 marks) Calculate the profit-maximising prices. P" and P, , and quantities. (" and Of h. (2 marks) Calculate the team's maximum profit, ". i. (2 marks) State the four conditions for price discrimination to exist. j. (2 marks) Use parts (c) and (h) and briefly explain how price discrimination affects its profits