If all other things are equal, the monopolist will charge a higher price in the market where demand is higher. The monopolist will do this is as long as these markets are truly separate enough to allow for price discrimination.
A monopolist will always produce the quantity of its product where its marginal revenue and its marginal costs are equal to one another. This is known as the profit maximizing quantity of output. The price that the monopolist charges is found by determining the price that consumers in a given market will pay for that amount of output.
However, this price discrimination can only occur if the two markets are truly segmented. Markets that are not truly segmented would allow those in the cheaper market to engage in arbitrage. They could buy at the lower price and resell to those who are charged the higher price. But if the markets really are separate, this will not be possible and the monopolist will be able to charge a higher price in one market.
Thus, as long as the markets are separate, the monopolist will charge a different price in each so as to maximize profits.