(18 marks) Suppose that there are two firms that are both producing the same good. Their production levels are q and 2 respectively. If they produce at these levels, the price that they will be able to charge is 100-6(91 +92). Each firm can produce at a marginal cost of 1 (their total costs are equal to the quantity that they produce). a) (3 marks) Write down the profit maximization problem for firm 1, assuming that they take the production levels of firm 2 as a given. In other words, write down firm 1's problem as if it were treating 92 as a constant. b) (6 marks) Find the level of production q which solves the problem in part a) in terms of 92. Be sure to show that this level of production satisfies both the first order and second 1 2 order conditions. This is a single variable optimisation problem. c) (6 marks) Complete the same exercise for firm 2, solving for the optimal level 92 that maximises profits for firm 2 while treating q as a constant. This is a single variable optimisation problem. d) (3 marks) Find the levels of q and q2 which satisfy the conditions you found in parts b) and c).