Consider a Cournot duopoly in which inverse demand is given by P = 120 − Q. Marginal cost of each firm is currently $60.

a. What is the Cournot equilibrium quantity for each firm, product price, and profit of each firm? Now assume that one of the firms develops a new technology that reduces marginal cost to $30.

b. If it keeps control of this innovation itself, what will be the new Cournot equilibrium outputs, product price, and profits of the two firms?

c. If it licenses the innovation to its rival at some per unit fee r, calculate the innovator’s profit as a function of r. What is the profit-maximizing value of r for the licensor?