Please pay careful attention to the questions. You must answer exactly as asked. Please insert the answers in this document. Screenshots of computer programs solutions can be inserted in the document, but you must provide the exercise completed in the computer program used to get the solution.

Exercise 1

A movie theater shows films for a community of 700 people shows films during weekends. Right now, the price per ticket is $17.50. In the past, when they increased or decreased the price per ticket, they discovered that for every dollar (or fraction) that the price was increased or decreased, the attendance decreased or increased proportionally by 20 people. The theater owner pays the Film Distribution Company $10 (incremental cost) in royalties per person who views the film. Find

1. The willingness-to-pay distribution of the movie goers.
2. The average price they would be willing to pay.
3. The price per ticket that maximizes revenue.
4. Should the theater owner increase or decrease the price per ticket if she wants to maximize contribution?
5. Find the consumer surplus if the tickets are priced at the price that maximizes contribution.

Exercise 2

The owner of the theater in Exercise 1 would like to experiment with segmenting the market into people who have a willingness-to-pay >$17(evening session) and those who have a willingness-to-pay less than or equal to $17(matinee session). The owner still pays $10 in royalties per person who views the film.

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

2. With segmentation, the theater owner should increase her profit. If the segmentation is fair the consumers should also increase their benefit (surplus). Find the consumer benefit (surplus).

3. If the theater only has a capacity of 300 seats, how much would the theater owner be willing to pay to eliminate that constraint?

4. Find the optimal segmentation level that maximizes contribution, the prices to be charged to both segments,

Exercise 3

The movie theater owner discovered that there are two segments in the population that attend the shows, older and younger people, whose demand functions are as follows:

Older: 700 20p

Younger: 700 - 50p

1. Find the prices that maximize revenue for the older and younger individuals under the capacity constraint b=300 seats per show.

2. What is the opportunity cost per seat?

3. The theater owner offers the cheaper price tickets to the older individuals as a service to the community. However, the tickets for the two populations are identical once they are issued. Younger people have realized that if they could get an older person to buy them tickets, they could get into the show paying less. So, they try to cannibalize the theater. Assume that there is a cannibalization of about 10 percent. Find the prices of the two populations that maximizes revenue under the capacity constraint b=300.