I came across a True/False question in my economics problem set:
Is the following statement true or false?
"A monopolist can practice third-degree price discrimination in the two markets it serves. Quantity demanded at any positive price is always higher in market 1 than in market 2. Therefore, when the monopolist profit maximizes, it will certainly charge a higher price in market 1 than in market 2."
The answer is false. However, I do not understand why it is false.
I considered two cases, case 1 where the monopolist charges both markets a uniform price. If the monopolist practices price discrimination, profits will increase for the monopolist, and price charged in market 1 will be higher than market 2.
Case 2 is where only market 1 (since it is the "strong" market) is served under uniform pricing. By price discriminating, monopolist will also serve market 2 as it generates profit, and price in market 1 is higher than in market 2.
Why then is the statement false? Am I missing out another case?
Any help is greatly appreciated! Thank you.