Strategic investment in Bertrand competition with differentiated goods In the market for electric cars, firm 1 is a pioneer who invests k in R&D for efficient production. Firm l's total production cost is given by Ci(q) = (10 k)q+k. The demand for firm l's electric cars is given by q 20 2p1 +P2. On the other hand, firm 2 is a latecomer whose total production cost is given by C2(92) = 1022. The demand for firm 2's electric cars is given by q2 = 20 2p2 + P1. Assume the two firms compete by setting prices after firm 1 invests k. + = 1. What are the equilibrium prices, (P1, P2), in terms of k? (Hint: find the best response functions.) 2. What is firm l's optimal level of investment, ki? 3. Use your answers to questions 1 and 2 to compute the equilibrium profits. Does firm 1 have an advantage over firm 2? P1. 4. Suppose firm 2 charges P2 = 12.60 regardless of Note that p2 = 12.60 is roughly how much firm 2 would charge in equilibrium in question 2. What is firm l's optimal level of investment, ki, in this case? 5. Compare firm l's optimal investment level in questions 2 and 4. Explain whether firm 1 has a strategic incentive to overinvest or underinvest using Fudenberg and Tirole (1984)'s taxonomy