Please answer the question below

Consider a duopoly in which both firms produce the same good and want to maximize profits. Each firm can choose how much to produce, qi 2 0, at production cost -q2. The demand curve is given by P = max {0, 50 - 3Q }, where Q = q1 + 92. (a) Suppose firms choose their quantities simultaneously. (i) Derive each firm's best response function, showing the steps. Remember that firms must produce a non-negative quantity. (10 POINTS) (ii) Solve for the unique Nash equilibrium. Show your working. (10 POINTS) (b) Now suppose that firm 1 chooses q1 first, firm 2 observes q1, and then chooses q2. (i) Solve for the unique SPE of the game, showing the steps involved. (10 POINTS) (ii) Explain why firms producing the Nash equilibrium quantities of the simultane- ous move game is not a SPE of this game. (5 POINTS)