
Monopoly Questions
A monopoly sells in 2 separate markets. The demand functions are $\displaystyle Q_1=100P_1$and $\displaystyle Q_2=1402P_2 $with a constant variable cost of $10.
1. Suppose the monopoly were forced to charge 1 single price. What is the optimal price?
2. Suppose the monopoly can perfectly discriminate in both markets, calculate the profit for both market.
1. Should i combine both demand functions into one? So Q=2403P?
2. For each market, should i set price = mc? so $\displaystyle 100Q_1=10 $ and $\displaystyle 70Q_2/2=10 $?
Thanks in advance

Be careful how you combine the demand functions in the first question. $\displaystyle Q_2=1402P_2 $ only when $\displaystyle P<70 $, otherwise $\displaystyle Q_2=0 $. Therefore, your combined demand function is only valid for $\displaystyle P<70 $.
Remember you don't want to set price equal to marginal cost, you want to set marginal revenue equal to marginal cost.