As a manager of 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 = 20 - 0.001Q; on weekdays, it is P = 15 - 0.002Q. You acquire legal rights from movie producers to show their films at a cost of $25,000 per movie, plus a $2.50 "royalty" for each moviegoer entering your theaters (the average moviegoer in your market watches a movie only once). What type of pricing strategy should you consider in this case?

The best strategy will be to do price distrimination and charge

weekends: $ 11.25 per ticket

weekdays: $ 8.75 per ticket

Explanation:

we should look up for the price for each type of demand considering

Marginal Revenue = Marginal Cost

weekends

P = 20 - 0.001Q

revenue P x Q = (20-0.001Q) xQ

revenue = 20q-0.001q^2

marginal revenue is the derivate of the revenue function

it represent the revenue generate for an adidtional unit:

dR/dQ = - 0.002q + 20

Cost 25,000 + 2.5Q

Marginal cost: cost for an additional unit

dC/dQ = 2.5

We equalize:

2.5 = 20 - 0.002q

q = 17.5/0.002 = 8,750

price = 20-0.001Q = 20 - 0.001 (8,750) = 20 - 8.75 = 11,25

weekdays

we do the same procedure:

revenue = (15-0.002Q) xQ = 15Q-0.002Q^2

marginal revenue = 15-0.004Q

the cost function is the same so the marginal cost too.

now MR = MC

2.5 = 15-0.004Q

Q = 12.5/0.004 = 3,125

P = 15-0.002 (3,125) = 15 - 6.25 = 8.75