3. [30] Suppose that two firms are competing in a heterogeneous market where the demand functions of firm I and firm 2 are given by q, = A - 3p, + 2p2 and 92 = A - 3p2 + 2p. Both firms have a marginal cost equal to 1. (a) [10] Calculate the optimal profits for the two firms when they compete in prices. (b) [10] If firm 1 spends an amount F to reduce its marginal cost to 0, what is the maximum value of F that it would be willing to pay? For the rest of the problem, suppose, instead, that firm I sets the quantity (q) while simultan neously firm 2 sets the price (p2). (c) [5] Draw the two best response functions in a graph and indicate the Nash equilibrium. Be as detailed as possible in giving intuition. Note: the graphs will be in the (p2, q1) space, but remember that you are not drawing any demand curves. (d) [5] Compute both of the firms' equilibrium prices, quantities, and profits. Which firm makes a higher profit? Explain the intuition of this