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 is the equation of firm B's (price) reaction function? A) $P _ { B } = 50 - .5 P _ { A }$ B) $P _ { B } = 55 - .25 P _ { A }$ C) $P _ { B } = 55 + .25 P _ { A }$ D) $P _ { B } = 50 + .5 P _ { A }$

Question

Quizplus · Accepted Answer

In Bertrand competition, each firm sets its price to maximize profit given the price of the other firm. Firm B's profit is maximized when marginal revenue equals marginal cost. Solving for P_B in terms of P_A, we get the reaction function P_B = 55 + 0.25P_A.

Let Firm a Face Demand Curve QA = 100 - PB=50−.5PAP _ { B } = 50 - .5 P _ { A }PB​=50−.5PA​

Let Firm a Face Demand Curve Q_A = 100 - $P _ { B } = 50 - .5 P _ { A }$