Let a Monopolist Face Consumer Group a with Inverse Demand $P _ { A } = 100 - 2 Q _ { A }$

Multiple Choice

Let a monopolist face consumer group A with inverse demand $P _ { A } = 100 - 2 Q _ { A }$ and consumer group $B$ with inverse demand $P _ { B } = 80 - Q _ { B }$ . The monopolist can conduct third degree price discrimination, but faces a capacity constraint that $Q _ { A } + Q _ { B } \leq 100$ . What will be the amount supplied to each of the customer groups?

A) $Q _ { A } = 50 ; Q _ { B } = 50$ .
B) $Q _ { A } = 60 ; Q _ { B } = 40$ .
C) $Q _ { A } = 33.67 ; Q _ { B } = 66.33$
D) $Q _ { A } = 36.67 ; Q _ { B } = 63.33$