1)Show that there is no Nash Equilibrium in the three-player Hotelling game. (HINT: consider the three possible spatial arrangements, each firm at a different point, two firms at the same point, and all three firms at the same point and show that none is an equilibrium.) (20 possible points)

2)Explain briefly why a monopolistically competitive industry is inefficient (relative to a perfectly competitive industry). What happens to the degree of inefficiency as new firms enter? Do existing firms become more efficient or less efficient? Does consumer surplus increase or decrease? (10 possible points)

3)It is argued by some that product differentiation can be viewed as a barrier to entry. Give an example of a situation where product differentiation is a barrier to entry. Alternatively, also give an example of a situation where product differentiation may encourage entry. (10 possible points)