Question: Stackelberg Theory of Duopoly. Stackelberg suggested that one firm might increase its profits if it were able to observe its competitors reaction function. Such a firm would then use its competitor's reaction function as its estimate of its competitor's output.
(a) Show that if the first firm substitutes the second firms reaction function of part (a) of the previous problem into its profit equation and maximizes With respect to q1(k + 1), then the equilibrium is unchanged.
(b) In a Stakelberg strategy the two firms are designated leader and follower. The leader, knowing the followers reaction function, reveals its actual planned output to the follower. The follower then uses the value supplied by the leader in its reaction function to determine its output level. The leaders original plan anticipates the follower's response to it. Show that if the first firm is the leader, its equilibrium profit is higher than in the Cournot equilibrium.