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

Multiple Choice

Let firm A face demand curve $Q _ { A } = 100 - P _ { A } + .5 P _ { B }$ and firm $\mathrm { B }$ face demand curve $Q _ { B } = 100 -$ $P _ { B } + .5 P _ { A }$ . Products $\mathrm { A }$ and $\mathrm { B }$ 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) $P _ { B } = 50 + .5 P _ { A }$