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 1’s total production cost is given by C1(q1) = (10 −k1)q1 + k21. The demand for firm 1’s 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 2’s 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 1’s 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