A monopolist faces two consumer groups: old and young. The inverse demand of old clients for the output of the monopolist is $P _ { 0 } = 100 - 2 Q _ { 0 }$. The inverse demand of young clients for the output of the monopolist is $P _ { y } = 80 - Q _ { y }$. The marginal cost of supplying any type of client is $M C = 10$. If the monopolist can price discriminate between the two groups (i.e., charge a different uniform price to each group), what price will old and young clients be charged?
A) $P _ { 0 } = \$ 45 ; P _ { y } = \$ 55$
B) $P _ { o } = \$ 55 ; P _ { y } = \$ 45$
C) $P _ { 0 } = \$ 50 ; P _ { y } = \$ 50$
D) $P _ { o } = \$ 40 ; P _ { y } = \$ 60$

Question

Quizplus · Accepted Answer

To find the profit-maximizing price for each group, we first derive the marginal revenue (MR) for each group and set it equal to the marginal cost (MC). For the old clients, $MR_0 = 100 - 4Q_0$, and for the young clients, $MR_y = 80 - 2Q_y$. Setting these equal to the MC of 10 and solving for $Q_0$ and $Q_y$ gives us the quantities that maximize profit for each group. Substituting these quantities back into the inverse demand functions gives us $P_o = \$55$ and $P_y = \$45$.

A Monopolist Faces Two Consumer Groups: Old and Young P0=100−2Q0P _ { 0 } = 100 - 2 Q _ { 0 }P0​=100−2Q0​

A Monopolist Faces Two Consumer Groups: Old and Young $P _ { 0 } = 100 - 2 Q _ { 0 }$