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

Multiple Choice

Let firm A face demand curve Q_A = 100 - P_A + .5P_B and 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) $P _ { B } = 50 + .5 P _ { A }$