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Three firms compete in Cournot competition in a market where the inverse demand function is P(q1, q2, q3) = 50 - q1- q2- q3. Each has per-unit cost 10 and zero fixed cost. They simultaneously choose quantities. What is the Nash equilibrium quantity for firm 3? Round your answer to three decimal places.
Let A = firm 3's profit in the Cournot equilibrium.
Now suppose that the firms form a cartel, i.e., they act as a monopoly and split the profit evenly. If the total quantity produced by the cartel is Q, then the inverse demand is P(Q) = 50 - Q.
Let B = firm 3's profit in the cartel.
Calculate C = B - A. Round your answer to 3 decimal places.
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