Question 4: Competing firms with different objectives In a market there are two firms, labeled 1 and 2. The firms sell a homogeneous good and compete in quantities. They have the same cost function, given by C(g;) = 20q;, where g; > 0 is firm i's output level. There is a single price in the market, P(q; + 32), where 100 g1 g2 if 1 + 42 100. The objective of Firm 1 is to maximize its profits, and the objective of Firm 2 is to maximize its revenues. The two firms choose their quantities simultaneously with each other, and they interact only once. (a) Write up the normal-form representation of the game, using formal mathematics notation. (b) State the best-response correspondence of each firm. Moreover, plot the graphs of the two correspondences in a diagram with g; on the horizontal axis and g, on the vertical axis. Finally, solve for all (pure strategy) Nash equilibria of the game. (c) Consider the following claim: In the game described above, any strategy q2 > 50 is strictly dominated for Firm 2. Either prove this claim or show that it is false (e.g., by providing a counter example)