What is the current equilibrium price and quantity in the industry?

Two firms compete in a Cournot-type duopoly. The industry demand is given by P = 100 − 2Q. Each firm has a constant average and marginal cost of $60.

a. What is the current equilibrium price and quantity in the industry?

b. Suppose that one firm discovers a procedure that lowers its average and marginal cost to $50.

i. If the innovator does not license its product but simply competes as the low-cost firm in a Cournot duopoly, what will be the innovator’s profit?

ii. What will be the innovator’s profit if it licenses the technology to its competitor at a royalty rate of $10?

iii. Suppose instead that the innovator licenses the technology for a fixed fee. What is the highest fee that the non-innovator will be willing to pay? What will the innovator’s profits be if it can charge the highest possible such fee?