Exercise 1

A movie theater shows movies for a community of 10,000 people and shows movies on weekends. Currently, the price per ticket is $17.50. In the past, when they increased or decreased the price per ticket, they found that for every dollar (or fraction) the price increased or decreased, attendance proportionally decreased or increased by 200 people. The theater owner pays the Film Distribution Company $10 (incremental cost) in royalties per person who views the film.

Find the distribution of moviegoers' willingness to pay.

The average price they would be willing to pay.

The price per ticket that maximizes revenue.

Should the theater owner increase or decrease the price per ticket if he wants to maximize contribution?

Find the consumer surplus if the tickets are priced at the contribution-maximizing price.

Exercise 2

The theater owner in exercise 1 would like to experiment with segmenting the market into people who have a willingness to pay > $20 (evening session) and those who have a willingness to pay less than or equal to $20 (matinee session). session). The owner still pays $10 in royalties per person who watches the movie.

Find the price per ticket for the two market segments that maximize contribution. How many people would the theater owner have at each of the sessions? How much will the theater owner earn?

With segmentation, the cinema owner should increase his profits. If segmentation is fair, consumers should also increase their profit (surplus). Find the consumer's profit (surplus).

Find the prices that maximize the contribution if the cannibalization rate is 10 percent.

Find the optimal targeting level that maximizes contribution.

With the market segmented at $20, find the maximum cannibalization rate the theater owner can afford.

If the theater only has a seating capacity of 350, how much would the theater owner be willing to pay to remove that restriction?

Exercise 3

The owner of the movie theater discovered that there are two segments in the population that attend shows, older and younger, whose demand functions are the following: Minors: 700 – 10p Seniors: 500 – 25p

Find the prices that maximize the contribution for older and younger people under the capacity constraint b = 350 seats per show. The incremental cost per viewer is still $10.

What is the opportunity cost per seat? What is the marginal opportunity cost if the theater owner wants to increase the capacity by 20 seats?

The theater owner offers cheaper ticket prices to seniors as a service to the community. However, the tickets for the two towns are identical once issued. The younger ones have realized that if they get an older person to buy their tickets, they can get into the show by paying less. So, they try to cannibalize the theater. Assume there is about 10 percent cannibalization. Find the prices of the two populations that maximize the contribution under the capacity constraint b=350.