Question: Mou Team and Pep Team are two rival teams that have their stadiums placed at the two extremes of an avenue of 1 km in length. Mou Team has its stadium at the extreme A and Pep Team at the extreme B. There are 10,000 people (which you can normalize to 1) living along the avenue, that are uniformly distributed. In addition, 1,000 people (which you can normalize to 0.1) live at the extreme A and 3,000 people (which you can normalize to 0.3) live at the other extreme B. The entire population is so fond of football that on Sundays everybody goes to one of the stadiums. The choice of stadium depends on the ticket prices set by the teams and the distance to each stadium. Transportation costs are such that a person at a distance of x km to stadium A has a transportation cost of x. The marginal cost is zero for both stadiums. Answer the following questions:
(a) Find the indifferent consumer and demand of each stadium.
(b) Calculate the prices, the demand and the profits of each stadium in equilibrium. Do the stadiums obtain the same profits? Why?
(c) Suppose that the Football League requires the two teams to set the same prices but the teams can freely choose the location of their stadiums. Would the teams change the location of the stadiums (if they could relocate at no cost)? Where would the teams locate their stadiums? Explain your answer.