3. (3.5 p.) Firms A and B face the following demand functions QA = 9-2PA + Pg and QB = 92P8 + PA, correspondingly. They have identical cost functions with MC=AC=3. (a) Suppose that both firms set their prices simultaneously. Find Nash equilibrium. (b) Suppose that firms A and B form a cartel. Find the prices charged by the cartel. (c) Suppose that firms A and B compete by setting prices simultaneously and they reset prices every month. (i) Specify the grim-trigger strategies that will sustain cartel's prices found in (b) under high enough value of discount factor. (ii) Find optimal deviation and verify credibility of the punishment specified in (i). Note: You are not asked to derive the value of discount factor under which cooperation can be sustained as SPNE! (d) Now, suppose they interact only once. (i) Assume that firm B moves first, then firm A observes the price chosen by B and decides on its own price. Find the resulting subgame perfect Nash equilibrium. (ii) Compare profits of firm B in case of sequential and simultaneous games. Is it a general result (is it true for arbitrary demand functions and technologies? 3. (3.5 p.) Firms A and B face the following demand functions QA = 9-2PA + Pg and QB = 92P8 + PA, correspondingly. They have identical cost functions with MC=AC=3. (a) Suppose that both firms set their prices simultaneously. Find Nash equilibrium. (b) Suppose that firms A and B form a cartel. Find the prices charged by the cartel. (c) Suppose that firms A and B compete by setting prices simultaneously and they reset prices every month. (i) Specify the grim-trigger strategies that will sustain cartel's prices found in (b) under high enough value of discount factor. (ii) Find optimal deviation and verify credibility of the punishment specified in (i). Note: You are not asked to derive the value of discount factor under which cooperation can be sustained as SPNE! (d) Now, suppose they interact only once. (i) Assume that firm B moves first, then firm A observes the price chosen by B and decides on its own price. Find the resulting subgame perfect Nash equilibrium. (ii) Compare profits of firm B in case of sequential and simultaneous games. Is it a general result (is it true for arbitrary demand functions and technologies