Exercises . . Exercise #4. In each period, the per-period inverse demand for a good is p = 100 Q. The product is offered by a pair of Bertrand competitors, firms 1 and 2. Initially, each firm has a constant marginal cost of c; care = 70. Also, each firm has a discount factor 8 = 0.9. A) Determine the current (or pre-innovation) equilibrium price and quantity. Suppose firm 1 can reduce its marginal cost from care = 70 to cpost = 70 by incurring a R&D investment cost of 1000. Suppose also that firm 1's R&D investment leads to = 10. This innovation is protected by a patent of T years. If there were no patent, there would be no innovation. B) Determine firm 1's profit (ignoring the R&D investment cost) in each period during which its innovation is protected by the patent. Once the patent expires, the innovating firm's rival can have access to the cost- reducing innovation, i.e., firm 2's marginal cost becomes cpost = 70 E. C) Determine the equilibrium price and quantity in each period after the patent expires. D) Determine the minimal length of the patent, i.e., the minimal value of T, so the R&D investment is undertaken assuming the smallest unit of time is 1 year. E) Determine the total surplus pre-innovation and post-innovation after the patent of T years expires. . 28