As a manager if a chain of movie theaters that are monopolies in their respectiv

Question

As a manager if a chain of movie theaters that are monopolies in their respective markets, you have noticed much higher demand on weekends than during the week. You therefore conducted a study that has revealed two different demand curves at your movie theaters. On weekends, the inverse demand function is: P=15-0.001Q; on weekdays, it is P=10-0.001Q. You acquire legal rights from movie producers to show their films at a cost of $20,000 per movie, plus a $2 royalty for each moviegoer entering your theaters (the average moviegoer in your market watches a movie only once). Devise a pricing strategy to maximize your firm’s profits.

Explanation / Answer

On weekends, the inverse demand function is P = 15 – 0.001Q On weekdays, the inverse demand function is P = 10 – 0.001Q Total cost = 20,000 + 2Q MC = dTC/dQ = 2 Let the price charged by movie Theatre Company to movie goers during the weekends as P1 and number of movie goers as Q1. Therefore, P1 = 15 – 0.001Q TR = P1Q1 = 15Q1 – 0.001Q12 MR = dTR/dQ = 15 – 0.002Q1 Profit will be maximized when MR = MC 15 – 0.002Q1 = 2 0.002Q1 = 13 Q1 = 1500 Substituting in demand equation, we get P1 = 15 – 0.001*1500 = $13.5 They can charge $13.5 in weekends. Total revenue = 1500*13.5 = $20,250 Let the price charged by movie Theatre Company to movie goers during the weekdays as P2 and number of movie goers as Q2. Therefore, P2 = 10 – 0.001Q TR = P2Q2 = 10Q2 – 0.001Q22 MR = dTR/dQ = 10 – 0.002Q2 Profit will be maximized when MR = MC 10 – 0.002Q2 = 2 0.002Q2 = 8 Q2 = 4000 Substituting in demand equation, we get P1 = 10 – 0.001*4000 = $6 They can charge $6 in weekdays. Total revenue = 4000*6 = $24,000

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