In each period, the per-period inverse demand for a good is =100. The product is offered by a pair of Bertrand competitors, firms 1 and 2. Initially, each firm has a constant marginal cost of _1^=_2^=70. Also, each firm has a discount factor =0.9.

A) Determine the current (or pre-innovation) equilibrium price and quantity.

Suppose firm 1 can reduce its marginal cost from _1^=70 to _1^=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 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 _2^=70.

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.