Question

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).

a) What price should you charge on weekends?

b) What price should you charge on weekdays?

Answer 1

11.25; 8.75

Step-by-step explanation:

On weekends,

Inverse demand function: P = 20 – 0.001Q

On weekdays,

Inverse demand function: P = 15 – 0.002Q

Let quantity demanded tickets on weekend be Q1 and quantity demanded tickets on weekday be Q2,

Profit function:

= [(20 - 0.001Q1) × Q1] + [(15 - 0.002Q2) × Q2] - [25,000 + 2.5(Q1 + Q2)]

For maximizing profit, Differentiating profit w.r.t Q1 and Q2,

⇒ (20 - 0.002Q1) - 2.5 = 0

⇒ (15 - 0.004Q2) - 2.5 = 0

Hence, solving for Q1 and Q2, we get

Q1 = 8,750

Q2 = 3,125

Therefore,

Price during weekends: P = 20 - (0.001 × 8,750)

= 11.25

Price during weekdays: P = 15 - (0.002 × 3,125)

= 8.75