Imagine that the previous Lowe's-Home Depot price war layed over and over again every week and that contrary to the prediction for the one- hrms will try to engage in tacit collusion and attempt to charge a high price every time To mutually enforce this unspoken agreement and make sure neither store suddenly and unilaterally lowers their price, both stores are engaged in a "grim trigger" strategy (and both stores know the other store's strategy, perhaps from past experience), Grim trigger means the following: "if you lower your price today, I will never trust you again to cooperate/collude. I will therefore forever abandon any attempt to collude and, starting in the next round (next week), will always charge a low price in the future." The question you need to solve is this: What is the threshold (weekly) discount rate g above which it does not pay to engage in a price war? Let me explain: Intuitively, since the firms are weighing this week's profits to those in the future, we need to know how much weight they place on future income. Put differently, firms are maximizing the present value of a stream of profits. Next week's profit is discounted by (1-g); the profit in two weeks is discounted by (1-g)" and so forth. So proceed as follows: (1) For the first player (say Lowe's), what is the stream of profits if both players always collude? What is the present value of that stream? (FYI: the infinite geometric series "1 + (1-g) + (1-g)? + (1-8) +." is simply equal to 1/g.) (2) Again for the first player, what is the stream of payments if the first player fails to collude today? (Remember that this will trigger Nash-reversion starting in the second period.) (3) Compare the two present values to find the threshold value. Show your work