Let firm A face demand curve Q_A = 100 - P_A + .5P_Band firm B face demand curve Q_B = 100 - P_B + .5P_A. Products A and B both have constant marginal cost of production of 10 per unit (and no fixed cost). Each firm acts as a Bertrand competitor. What are the Bertrand Equilibrium prices in this market? A) P_B = 72.5; P_A = 70 B) P_B = P_A = 73.33 C) P_B = 74; P_A = 87 D) P_B = P_A = 74

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Quizplus · Accepted Answer

In a Bertrand competition, firms set prices as if they were in a one-shot game, assuming that their competitors will keep their prices constant. In this case, both firms have constant marginal costs of 10, so they will set their prices just above their own marginal costs to capture as much market share as possible. To find the equilibrium prices, we need to solve for the Nash equilibrium, where neither firm has an incentive to deviate from their chosen price. For Firm A: - If Firm B charges a price of PB, then Firm A's demand curve becomes Q = 100 - PA + 0.5PB. - Firm A's profit is (PA - 10)Q = (PA - 10)(100 - PA + 0.5PB). - Taking the derivative with respect to PA, we get -90 + 1.5PA - 0.05PB = 0. For Firm B: - If Firm A charges a price of PA, then Firm B's demand curve becomes Q = 100 - PB + 0.5PA. - Firm B's profit is (PB - 10)Q = (PB - 10)(100 - PB + 0.5PA). - Taking the derivative with respect to PB, we get -90 + 1.5PB - 0.05PA = 0. Solving these two equations simultaneously, we get PA = PB = 73.33. So the equilibrium prices are P_A = P_B = 73.33.

Let Firm a Face Demand Curve QA = 100 -

Let Firm a Face Demand Curve Q_A = 100 -