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Two firms, A and B, engage in Bertrand price competition in a market with inverse demand...

Two firms, A and B, engage in Bertrand price competition in a market with inverse demand given by p = 24 - Q. Assume both firms have marginal cost: cA = cB = 0. Whenever a firm undercuts the rival’s price, it has all the market. If a firm charges the same price as the rival, it has half of the market. If a firm charge more than the rival, it has zero market share. Suppose firms have capacity constraints and KA = 5 and KB = 3. Find a Nash equilibrium of this game (pA, pB) and the quantities produced by each firm at equilibrium.

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