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In the Stackelberg duopoly model, two firms operate in a market with homogeneous goods. The key feature distinguishing this model from the Cournot duopoly is the sequential nature of decisions: one firm (the leader) chooses its output level first, and the other firm (the follower) chooses its output level after observing the leader's choice. This timing gives the leader a strategic advantage, as it can anticipate the follower's best response and incorporate it into its own decision-making process. This setup is a classic example of a game with a first-mover advantage and is analyzed using backward induction. Let us consider a simple Stackelberg model with the following assumptions: * Two firms, Firm 1 (leader) and Firm 2 (follower), produce a homogeneous product. * Market demand is linear and given by the inverse demand function: P(Q) = a - bQ, where Q = q₁ + q₂ is the total market output, and a, b > 0. * Both firms have identical constant marginal and average costs: C(q) = c · q, where c < a. ### Step 1: Derive the follower’s (Firm 2's) reaction function Firm 2 observes the quantity q₁ chosen by Firm 1 and then chooses its quantity q₂ to maximize its own profit, taking q₁ as given. Firm 2’s profit function is: π₂ = P(Q)·q₂ - C(q₂) = (a ________ ____ ________ ________ __________ __________ _________ ______ ___ __________.
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