# 3rd Degree Price Discrimination

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.

• The cost of producing each unit of the good is \$1. • All consumers are exactly identical, with each consumer willing to pay up to \$10 for one unit of the good. (Also, each consumer is willing to pay at most \$0 for a second unit of the good.) • Market 1 has 200 consumers, while Market 2 has 100. (And so, it is true that "quantity demanded at any positive price is always higher in market 1 than in market 2."†) Since all the consumers are exactly identical, the profit-maximizing price in both markets is simply the maximum each consumer is willing to pay, namely \$10 (and the producer will produce 300 units of the good). Thus, it is false that the monopolist "will certainly charge a higher price in market 1 than in market 2".