Please answer all parts of this question

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Please answer all parts of this question.

(a) Consider two identical firms with no fixed costs and constant marginal cost c which compete in quantities in each of an infinite number of periods. The quantities chosen are observed by both firms before the next round of play begins. The inverse demand is given by p = 1 − q1 − q2, where q1 is the quantity produced by firm 1 and q2 is the quantity produced by firm 2. The firms use 'trigger strategies' and they revert to static Cournot behaviour if cooperation breaks down. Derive the lowest value of the discount factor such that the firms can sustain the monopoly output level and discuss the economic reasoning behind your result.

 

(b) An incumbent firm operates a store in a local market and faces the potential entry of a single rival. The entrant's choices are to enter or to stay out of the market. If the entrant stays out, it earns 1 (the return from the best alternative investment); the incumbent earns 5. If the entrant comes in, then the incumbent must decide whether to cooperate with the entrant (in which case both earn a return of 2) or to fight entry (in which case both earn a zero return). What is the subgame perfect equilibrium of this game? Would your answer change if the incumbent operated 20 stores in 20 separate markets, and faced 20 potential entrants, one in each market, who must make their entry decisions sequentially? Provide a brief discussion of your results in the context of empirical evidence on entry deterrence.