Two firms, A and B, compete à la Bertrand when selling a homogeneous good whose demand equals P = 400 − Q. Each firm’s constant marginal and average cost of producing the good equals 60. Suppose that it is possible for firm A to costly develop a new technology that lowers both the marginal and average cost to 40. If there isn’t a patent system, firm A can do costly research to find the new technology, but will see its invention copied immediately after discovery (a process called "reverse engineering"). With a patent system, this is rendered illegal.

a. What is the equilibrium without a patent system?

b. And with a patent system? Note that the equilibrium depends on the cost of developing the new technology. So, you need to state the equilibrium for all potential values of the cost of developing the new technology. In particular, you should assume that the cost of developing the new technology can be any positive value.

c. Is the patent system socially desirable?