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Question: consider a duopoly in which inverse demand is given by...

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Consider a duopoly in which inverse demand is given by P = 120 – Q. The marginal cost of each firm is currently 60 and the firms compete by simultaneously setting quantities.

(a) What is the equilibrium quantity for each firm, the equilibrium price and the profit of each firm? Now assume that one of the firms, firm 1, develops a new technology that reduces its own marginal cost to 30.

(b) If firm 1 keeps this innovation for itself (so that the marginal cost of firm 2 is still 60), what will be the new equilibrium levels of output, price and profits of the two firms?

(c) If firm 1 licences the innovation to its rival at some unit fee r (so that the marginal cost of firm 2 becomes 30 + r), calculate firm 1’s profit as a function of r. What is the profitmaximising value of r for firm 1?

(d) Assume instead that firm 1 licenses the innovation to its rival for a fixed fee of L (so that the marginal cost of firm 2 becomes 30). What is the maximum fee that firm 1 can charge?

(e) Will firm 1 prefer to set a per unit license fee or a fixed license fee? What kind of licensing arrangement would consumers prefer?

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