Economic question

Suppose that, just as in the previous problem, two firms compete in a market in which demand is described by P = 180 - Q. Each firm incurs no fixed cost and has marginal cost of 10. However, instead of competing in quantities, they compete in price.~ (a) What is the one period Nash equilibrium output, price and profits? (b) What is the output of each firm if they collude to produce the monopoly output? What profit does each firm make with such collusion? (c) If one firm decides to cheat on the collusion, assuming the other firm will continue to produce half of the monopoly output, how much will the cheating firm produce? What will be the industry price and profits of the two firms? ~ (d) Suppose the market game described above is now repeated indefinitely. What discount rate is necessary in order to maintain the collusive agreement? Why is it different than in part d) of the previous question? ~