Demand in a duopoly is given by p = 100 – Q. Both firms have marginal cost c.
a. Find the Cournot equilibrium quantities, price and profits.
b. Suppose Firm 1’s marginal cost decreases to c – d (while Firm 2’s marginal cost is still c). Find the new Cournot equilibrium quantities, price and profits.
c. An inventor has developed a technique which will reduce the marginal cost of either (or both) firms to c-d. If the inventor commits to selling to one firm only (and both firms know this), how much are firms willing to pay for the invention?
d. If the inventor sells to both firms, how much is each firm willing to pay for the invention?
e. Should the inventor commit to sell to one firm or should he sell to both?
Sample Solution
