Question 2 128 marks) Consider a firm {e.g. a local movie theatre) that could supply services to consumers at both peak time [e.g. weekend and public holidays), and off- peak time (e.g. weekday). The firm offers peak and off-peak prices to the consumers depending on when they use the service - the price for peak service is p1 and for off- peak service it is Fig. The quantity of services sold in peak and off-peak time is denoted as '11 and q2, respectively. The firm starts with a capacity of I5. in which at both peak and off-peak times, the number of customers it serves (i.e. ql or oz] cannot be greater than t? [e.g. Q is the number of total seats available in the movie theatre). 1:11 The firm faces a demand function for peak service as (31 = hip\" and a 1 b1 demand function for off-peak service as q; = 3 $322, with 111,612,111, iiz :- 2 0. For each customer served, it costs the firm c to provide the services, regardless of whether it is a peak time or off-peak period customer. The firm cannot produce negative quantity in either of the peak and off-peak services. to) Express the total profit of the firm in terms of q1.q2, H1,a2,b1, b2, and c [2 marks) (b) If a1 = 400,5:2 = 400.111 = 1, is: = 1 and c = 20.6 = 200, what is the profit maximizing quantity of peak and off-peak services for the firm? {Consider all constraints faced by the firm) (4 marks) 455W903 (c) If a, = 400,:12 = 400,111 = 115,52 = 1 and c = EILQ = 201], what is the profit maximizing quantity of peak and off-peak services for the firm? (4 marks} (d) In the long run, the firm could choose the capacity [0} by paying :1 for each unit of capacity, with d :2 . {e.g. the movie theatre could adjust the seating and it costs Ed for each unit of capacity to be installed and maintained for service.) Assumes that the firm has no pre-existing capacity, so it has to pa},r for all units of capacity it chooses. What would be the quantity of services provided for peak and off-peak service, and the capacity, that the firm chooses to maximise profit? Assumes that :11 :> r: + d and a; c c. [10 marks) (e) For the demand functions given for the peak and off-peak services, what implicit economic assumptionis} did we make? Are they reasonable assumptionis), why or why not? (Answer must be typed). {8 marks)