Consider the Cournot duopoly with linear inverse demand function P = aQ where P is the market price and Q = q1 + q2 is the total quantity supplied. Two firms have asymmetric constant marginal costs: c1 for Firm 1 and c2 for Firm 2. What is the Nash equilibrium if 0 < ci < a/2; i = {1, 2}. What if c1 < c2 < a but 2c2 > a + c1?
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The profit function for Firm 1 is: π1 = (P - c1)q1 π1 = (aQ - c1)q1 π1 = (a(q1 + q2) - c1)q1 π1 = (a(q1 + q2) - c1)q1 The profit function for Firm 2 is: π2 = (P - c2)q2 π2 = (aQ - c2)q2 π2 = (a(q1 + q2) - c2)q2 Show more…
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