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To calculate and compare the profits earned by each firm under both the Cournot and Stackelberg models, we consider a standard duopoly setup with linear demand and cost functions. Let the inverse demand function be: P = a - bQ, where Q = q₁ + q₂ (total output by Firm 1 and Firm 2), and P is the price in the market. Let both firms have identical cost functions: C(q) = c·q, where c is the marginal cost (constant), and q is the output of the firm. --- ### 1. Cournot Model In the Cournot model, both firms choose quantities simultaneously. Step 1: Profit Function for Each Firm Profit for Firm 1: π₁ = (P - c)·q₁ = (a - b(q₁ + q₂) - c)·q₁ Profit for Firm 2: π₂ = (a - b(q₁ + q₂) - c)·q₂ Step 2: Best Response Functions Differentiate π₁ with respect to q₁ and set it equal _________ ___ _____ ________ __________ __________.
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