**Discussion**: Micro-economists are greatly intrigued by situations where the sale of one product is subsidized by the sale of another product. A classic example involves the sale of theatre tickets combined with the sale of treats to movie goers.

Typically, the profit margin is small on the movie ticket and large on the treat. Generally, movies ban outside food and drink so at least for a couple of hours the theatre has a monopoly on food services. Consumers who go to the theatre don’t have much choice because virtually all theaters set high prices on treats. Moreover, since the choice of a theatre is often determined by a group it may be difficult to go to a lower cost venue even if it existed.

Here are some links to scholarly articles on theatre tickets and popcorn:

http://www.jstor.org/discover/10.2307/2138630?uid=3739936&uid=2&uid=4&uid=3739256&sid=21103029798223

There are other real-world markets where the sale of one good impacts sales of another. It is likely that the price charged on shaving blades and printer cartridges are higher than the marginal cost of these products. Similarly, the cost of some lab services inside a doctor’s office may exceed marginal costs because patients are more likely to have their lab work done in the doctor’s lab.

There are many potential math problems involving the sale of theatre tickets, popcorn, and soda. The first questions presented below involve simple linear revenue functions.

**Problem set one:**

A theatre charges $10.00 per ticket. It sells a popcorn and soda combination for $8.00. The theatre gets 10% of the revenue from the sale of the ticket and 60% of the revenue from the sale of treats.

What is the linear equation for total revenue as a function of tickets sold to the theatre if the concession stand inside the theatre is closed for repairs? What is revenue if 50 tickets are sold?

What is the linear equation for total revenue to the theatre as a function of ticket sales if the concession stand is open and 50% of movie goers buy the treat? What is revenue if 50 tickets are sold?

**Answers**:

Revenue per ticket when the concession stand is closed is $1.00 (0.10x$10.00) Total revenue for the theatre is $1.00 x T where T is the number of tickets. At 50 tickets revenue is $50.

Revenue per ticket when the concession stand is open is $3.40 ($1.00 + 0.50 x (.60 x $8.00)) Total revenue with the concession open is $3.40 x T where T is the number of tickets. At 50 tickets we get revenue of $170.00 ($3.40 x 50).

**Notes on Todays Problem and Future Work:**The revenue lines in these problems are rays from the origin, where T=0 and Revenue=0. The slope of the ray is $1.00 for the case where the concession stand is closed and $3.40 when the concession stand is open. In subsequent posts, we will consider many other situations involving different revenue functions and costs.

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