Q. No 3 Consider the standard Hotelling location model in which two firms first simultaneously choose locations in [0.1], then simultaneously choose prices. Each firm must, set a single delivered price, and must absorb the transport cost itself. That is, every customer of a firm pays the same price; the firm makes less profit on more distant consumers. Each firm can refuse to sell to consumers who are very far away from it (in order to avoid making a loss on those consumers). Call the set of consumers to whom firm i is willing to sell the "market area of firm i'. As in Hotelling's model, each consumer buys from the firm with the lowest price (although no transport cost has to be added to the prices in this model); if both firms charge the same price, then half of the consumers in the intersection of the firms' market areas (if this intersection is nonempty) buy from each firm. a) Find Nash Equilibrium in case of number of firms changes from 1 to 6. b) Prove the efficiency of these equilibriums c) Fix the locations of the two firms, and examine the possibility of a pure strategy Nash equilibrium (p1, p2) in prices as follows: d) Is there an equilibrium with pi