Students and Adults both like going to the football games. The demand for football tickets by students is given by qS = 60 - pS , while the demand by adults is given by the equation qA = 100 - pA. Suppose the marginal cost of of a seat is 0 and that there are no fixed costs.
(a) Suppose that the monopolist must charge a single price to students and adults. What price P M will be charged and what is the total number of tickets QM that are sold? Calculate the monopolist's overall profit, πM
(b) How many tickets are sold to students, qS ? How many tickets are sold to adults,
qA? Calculate the students' surplus and the adults' surplus.
(c) Now suppose the monopolist is allowed to charge a different price to each group. What price pS will the monopolist charge to students and how many tickets qS will the monopolist sell to students. What price pA will the monopolist charge to adults and how many tickets qA will the monopolist sell to adults?
(d) Calculate the students' surplus, the adults' surplus, and the overall monopoly profits.
(e) What happened to overall societal welfare as a result of the monopolist charging two prices?