Consider the Exclusive Territories model.

Let the upstream monopolist set sales territories for each of the retailers such that the market is split evenly between the two. Hence for R^L, the available consumers are those in the interval [0, 1/2]. We will just consider R^L (by symmetry, R^R will look exactly the same).

The value to a consumer of consumption is V + F^L + F^R. The price is P^L. Recall consumers also have to pay their transport cost. Consumers will purchase as long as their surplus from doing so is non-negative.

1. Define t as the consumer that is indifferent between purchasing and not. What is t as a function of V + F^L + F^R and P^L?
2. What is the highest price such that t = 12 (i.e. all consumers purchase)? Call this price p^

Given that R^L is a monopolist in her territory, she can set whatever price she likes. Recall that her marginal cost is zero (the upstream firm just sets a lump sum fee equal to d). Also recall that V >2 and >2.

3.Would R^L ever want to set the price greater than p^? explain.

4.Given this, how much profit does RL make if she engages in service? How much if she does not?

5.Would R^L want to engage in service?

6.Is the upstream monopolist better off with exclusive territories? Why?