Five firms engage in Bertrand competition. Each firm has marginal cost of c = 3. There are no fixed costs. The demand curve in the market is is given by 135 5 =b 12 12Pmin, where q is the total quantity demanded by consumers in the market and pmin is the minimum of the price charged by the five competing firms. As usual, assume that consumers only purchase from the firm that sets the lowest price. Also, if two or more firms set the lowest price, they split the total quantity demanded evenly. 5. Suppose this game is played repeatedly for 10 times. The firms have a discount factor of &,where 0< &< 1. Denote by p the price that any of the firms would set if it was a monopolist in this market. What is the lowest level of & that would allow all five firms to set prices equal to pc in every period of an SPNE of the repeated game? (a) 0.2 (b) pC for all firms in every period cannot be part of an SPNE for any value of (c) 0.5 (d)0.8 6. Now suppose the game is repeated for infinitely many times. What is the lowest value of & that would sustain a Grim Trigger strategy as an SPNE of the repeated game? Remember that, in this context, a Grim Trigger strategy profile consists of each firm adopting the following strategy: set price pc in period 1; from period 2 onward, set price pc if no firm has ever set any price other than pC; otherwise, set price according to the Nash Equilibrium of the stage game. (a) 0.8 (b) 0.2 (c) 0.5 (d) A Grim-Trigger strategy cannot be an SPNE of this game