Consider a simple Hotelling Model as discussed in the class: The market is a beach of 1000 meters in length There are 1000 consumers evenly distributed along the beach, i.e., there is one consumer at every integer meter Travel is costly for consumers There are two vendors, A and B, selling ice-cream at a price P that is fixed by the ice-cream manufacture. A and B compete for larger market shares through location decisions. a) What is the Nash equilibrium of A and B's location? Why? (Hint: you can discuss by scenarios: 1) A=B; 2) A=B 500; 3) A=B=500) b) Under the Nash equilibrium, what is the total distance all consumers have to travel in order to purchase one unit of ice-cream? c) Is the above result socially optimum? What is your intuition? Now assume that the cost of setting up a vendor is F. Also assume that F 1000P, i.e., it is profitable for a monopoly to serve the whole market. d) Suppose that, currently, A is the only ice-cream firm in the market, facing NO potential entry threat from other firms. If A can only set up one vendor, what is the optimal location of this vendor? What is A's profit? e) Suppose that B is considering to enter the market and can setup one vendor as well. Facing B's potential entry, if A can operate only one vendor, what is A's optimal location? Given A's optimal location, what is B's best entry location? What is A profit in this case? f) Suppose that, facing B's potential entry, A can operate two vendors, Al and A2, and setup A1=333 and A2=666 (Assume that 2F