Please solve both problem 1 and problem 2 and show all work. Thanks.

Problem 1 Let's assume our market has two identical firms (Firm A and Firm B). For simplicity, assume both have a marginal cost of 30, and both face the same demand curve: P = 150 - qA - qB (a) Assume these firms are currently in a Bertrand model. How much would each firm produce? What price would they charge? What profit would each make? (b) Now, let's assume these firms are in a Cournot model. How much would each firm produce? What price would they charge? What profit would each make? (c) Now, let's assume these firms are in a Stackelberg model. If Firm A is the leader, how much would each firm produce? What price would they charge? What profit would each make? (d) Finally, assume these firms decided to collude. If that was true, how much would firm each produce? What price would they charge? What profit would each make? Problem 2 Assume we are currently in the market from part d above, and the firms are using a tit-for-tat strategy. If the interest rate (r) is 3%, what does each firm choose to do? Explain your reasoning. For simplicity, only solve for Firm A