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Handout on Stackelberg Duopoly

# Handout on Stackelberg Duopoly - The 2-Firm Stackelberg...

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The 2-Firm Stackelberg Market Introduction Suppose two firms each produce a homogeneous product with no costs of production. Let market price be linear in the combined output of both firms in the market and of the form P = a - b ( q 1 + q 2 ) , where q i is the output of the i -th individual firm. Sequential Moves In the Stackelberg model, Firm 1—the Leader—is able to move first, while Firm 2—the Follower—moves subsequently. If the Leader is “forward-looking,” she can anticipate how the Follower will pick his output in response to any prior choice of output she herself makes. Specifically, it is easy to see that if Firm 1 produces output q 1 , then the relation between Firm 2’s output, q 2 , and the market price he receives is of the form P = a - bq 1 - bq 2 . where a - bq 1 is constant from Firm 2’s perspective 1 . Marginal revenue for Firm 2 is thus of the form MR 2 = ( a - bq 1 ) - 2 bq 2 . Firm 2 will choose an output, q * 2 , to equate MR 2 to Firm 2’s marginal cost, here assumed to be zero. This gives q * 2 = a 2 b - q 1

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Handout on Stackelberg Duopoly - The 2-Firm Stackelberg...

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