Strategic investment in Bertrand competition with differentiated goods In the market for electric cars, firm 1 is a pioneer who invests k1 in R&D for efficient production. Firm 1s total production cost is given by C1(q1) = (10 k1)q1 + k21. The demand for firm 1s electric cars is given by q1 = 20 2p1 + p2. On the other hand, firm 2 is a latecomer whose total production cost is given by C2(q2) = 10q2. The demand for firm 2s electric cars is given by q2 = 20 2p2 + p1. Assume the two firms compete by setting prices after firm 1 invests k1.

1. What are the equilibrium prices, (p1, p2), in terms of k1? (Hint: find the best response functions.) What is firm 1s optimal level of investment, k1?

2. Use your answers to question 1 to compute the equilibrium profits. Does firm 1 have an advantage over firm 2?

3. Suppose firm 2 charges p2 = 12.60 regardless of p1. Note that p2 = 12.60 is roughly how much firm 2 would charge in equilibrium in question 1. What is firm 1s optimal level of investment, k1, in this case? Compare firm 1s optimal investment level in question 2. Explain whether firm 1 has a strategic incentive to overinvest or underinvest using Fudenberg and Tirole (1984)s taxonomy.