On the distant plant called Zorx, consumers only consume one good called spice. In order to purchase the spice, a consumer will travel which will cost him $1/mile. Each consumer will pay $5 for 1 unit of spice. Each trading post that a firm sets up costs $10. The production cost of spice is $1/unit of spice. Think Zorx as a circle, and the consumers all live on its circumference. The radius of Zorx is 10/(2pie) miles. In terms of consumers, you have two modeling choices:
1. one possibility is that there is a finite number, 100, of them, so that they live at a distance of 0.1 mile from each other.
2. Another possibility is that there is a continuum mass of 100 consumers, and they are uniformly distributed over the circumference of Zorx.

Question:

1. suppose that is only one monopolist firm. How many trading spots and where would it set in order to maximize profits? what price would it charge to the consumers? What would happen if the consumers on the N half of Zorx value spice more than those on S half?

2. Suppose there are two spice-producing firms, and each can set up one trading post. Where would they set up trading posts and what prices would they charge?

3. Now suppose that there are many spice-producing firms; again each can set up one trading post, and they can set up a trading post if they find that the ensuing profit would justify their setup costs. You may suppose that they either enter sequentially or that they decide to enter simultaneously, whichever you prefer. What happens on Zorx in this case?

4. Comment on whether the solutions to this problem depend on the fact that you are dealing with a circumference rather than a line of length 10.