Q. 1. Clients to Live Theaters, Inc. can be partitioned into 2 groups: seniors and everyone else. The converse demand curves for every of the two groups are given below. The marginal cost (which equals the average variable cost) of serving an additional patron, either senior or everyone else, is equal to $4. Fixed costs are equal to $1000.

Ps = 80 - Qs
Pe = 100 - 2Qe

Where Ps and Pe denote, respectively, the prices charged to seniors and everyone else and Qs and Qe denote the number of seniors and the number of all other customers served.

a. Illustrate Live Theaters with total revenue function? Illustrate its total cost function? Its total profits occupation?

b. What are the profit maximizing levels of price and output if Live Theaters, Inc. engages in 3rd degree price discrimination? Show that MRe = MRs = MC

c. Illustrate the profits associated with this option?

d. If Live Theaters charges one price to all patrons, what would it be? Illustrate how many customers would it serve? Explain what would be its profits?