Two firms compete by setting prices of identical p…

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Two firms compete by setting prices of identical products. Consumer purchase from whichever firm offers the lowest price. Market demand is given by P = 300 – Q.
(a) If MCA = 100 and MCB = 100, briefly explain why the Nash equilibrium is where both firms set price equal to marginal cost.
(b) Suppose the firms have different marginal costs (e.g., MCA = 90, MCB = 100). What is the Nash equilibrium in this situation?
(c) Return to case (a) in which both firms have identical marginal cost, but the firms compete again and again. The firms’ discount factors are 0.75.
Explain whether it would be possible for the firms to tacitly collude such that they both charged the monopoly price. If so, how would they collude. If not, why not?
(d) Would your answer to part (c) change if a firm could deviate for three periods before it was detected?

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