Q2 Duopolist firms simultaneously produce quantities q1 and q2. They jointly face a market demand that determines the price based on their quantity choices: p = 20 - q1 - 92. Firm 1's cost function is c1 (q1) = 2q1, and firm 2's cost function is c2 (q2) = 4q2. a. Construct the best response functions for firm 1 and firm 2. b. Find all NE. Now firm 1 produces first, firm 2 observes q1, and then firm 2 chooses q2. c. Find all SPNE. d. Construct a NE that isn't subgame-perfect where firm 1 produces q1 = 0, i.e., does not enter the market at all. Q3 Two firms compete on price, but because of product differentiation they do not compete Bertrand-style. Instead, they face the following demand functions: 91 = 1 - p1 + 0.5p2 92 = 1 -P2 + 0.5p1 Both firms have identical cost functions C(q) = q. a. Construct best response functions for both firms. b. Find NE prices. Now suppose firm 1 sets p1, firm 2 observes p1, and then firm 2 sets p2. c. Find all SPNE. d. Construct a NE that isn't subgame-perfect where firm 1 sets p, = 1.5