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Consider the following sequential duopoly (Stackelberg) game between two firms.

Firm 1 chooses a quantity q₁ between 0 and 80, which firm 2 observes, after which firm 2 chooses a quantity q₂ between 0 and 80. The demand curve for the market is given by p space equals space 80 minus q₁ minus q₂. There is a unique subgame perfect equilibrium. Which of the following occurs in it?
a. Firm 1 produces 60 and Firm 2 produces 20 after Firm 1 produces 60
b. Firm 1 produces 30 and Firm 2 produces 30 after Firm 1 produces 30
c. Firm 1 produces 70 and Firm 2 produces 10 after Firm 1 produces 70
d. Firm 1 produces 40 and Firm 2 produces 20 after Firm 1 produces 40

1 Answer

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In the subgame perfect equilibrium of the sequential duopoly game, Firm 1 produces 70, and Firm 2 produces 10 after Firm 1's production of 70, reflecting Stackelberg competition dynamics. Option c) is correct.

In the sequential duopoly game described, where Firm 1 chooses a quantity q₁ first, followed by Firm 2 choosing quantity q₂, the subgame perfect equilibrium involves Firm 1 anticipating the reaction of Firm 2 and choosing a quantity that maximizes its profit given this anticipation.

In this case, the equilibrium would likely involve Firm 1 producing a quantity that accounts for the response of Firm 2, aiming to maximize its profit. Looking at the given options:

The answer that aligns with the concept of Stackelberg competition is option (c): Firm 1 produces 70, and Firm 2 produces 10 after Firm 1 produces 70. This scenario is consistent with the leader-follower dynamic in a Stackelberg game, where Firm 1, as the leader, produces a larger quantity, and Firm 2, the follower, responds with a smaller quantity. This strategic interaction allows Firm 1 to capture a significant portion of the market share, as reflected in the equilibrium outcome.

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