Problem
The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p1 cents, the number of movie tickets that domestic students are willing to buy per year is given by: q1=157-0.9p1. At a price of p2 cents, the number of movie tickets that international students are willing to buy per year is given by: q2=103-0.34p2. The total costs for the movie theater depend on the total number of tickets sold, q1+q2, and are given by the following total cost function C(q1+q2)=(q1+q2)2.
Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students.
I. If this is the case, then how much will the movie theater charge to domestic students (p1)?
Note: You should round all of your answers below to the second decimal point.
II. How much will the movie theater charge to international students (p2)?
III. How many movie tickets will domestic students buy (q1)?
IV. How many movie tickets will international students buy (q2)?
V. The movie theater's management receives too many complaints from students about the fact that they charge different prices to domestic vs international students, so they are forced to charge the same price to everybody. With this new pricing strategy, what will be the cost of a movie ticket?
VI. How many movie tickets does the theater now sell in total?
VII. How do the cinema's profits change with this new pricing strategy? In other words, how much are the profits with uniform pricing, minus the profits with differentiated pricing?