[26] Cinema Barn is a rustic looking movie house in a medium-sized college town. To operate, the cinema owners must pay a fixed nightly amount of $100 for films, ushers, and so on, regardless of how many people come to watch a movie. For simplicity, assume that if the cinema is closed, its costs are zero. The nightly demand for Cinema Barn screenings by students is Q5 = 200 4011, where Q5 is the number of movie tickets demanded by students at price PS. The nightly demand for non-student moviegoers is QN = 140 10PN. a. [4] If Cinema Barn charges a single price, PT, to everybody, what is the aggregate demand for movies? (Hint: Consider reservation prices for viewing films.) b. [8] What is the profit-maximizing number of tickets for the cinema to sell if it charges one price to everybody? What would its profit be? c. [10] If Cinema Barn could perfectly sort moviegoers into the two groups by requiring that they show student IDs (assume no ticket reselling by students and no fake student IDs for non-students), would Cinema Barn want to price discriminate? Why is it important that ticket reselling is not occurring? d. [4] Suppose that nonstudents find a way to obtain fake student-IDs at a negligible cost (treat it as zero) and this opens up a secondary market of cinema tickets. What will happen to price(s) of cinema tickets? Answer concisely