Stackelberg Duopoly Question

zrypur
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Consider a leader-follower quantity competition game between two rival firms (i.e. Stackelberg Duopoly). Suppose firm 1 is the leader (so firm 1 chooses its level of output first) and firm 2 is the follower (so firm 2 observes the level of output that firm 1 produces, then decides how much to produce in response). Unlike the example from class, the two firms may have differing cost functions. Assume the following general form:

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2. Consider a leader-follower quantity competition game between two rival firms (i.e. Stackelberg Duopoly). Suppose firm 1 is the leader (so firm 1 chooses its level of output first) and firm 2 is the follower (so firm 2 observes the level of output that firm 1 produces, then decides how much to produce in response). Unlike the example from class, the two firms may have differing cost functions. Assume the following general form: TC1 = f1 + 0191 TC2 = f2 + C292 Firm 1's Cost Function Firm 2's Cost Function Here, the parameters fi and Cį refer to firm i’s fixed cost and constant marginal cost respectively. Finally, assume that the demand relation has the following generic form: p = A - bQ, where Q = 91 +92- a) Find the equilibrium values for the amount of output of the two firms (qi and q2). b) Show that if the firms have the same marginal cost, the leader will produce twice as much as the follower in equilibrium. To do this, simply set C1 = C2 = c in your answer to part a) and show that, after simplification, 91 = 2qž -
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