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 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 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) $P _ { B } = P _ { A } = 74$