It never pays a monopolist to sell at a low price in one market when he or she can get a higher price in another market

The statement 'It never pays a monopolist to sell at a low price in one market when he or she can get a higher in another market' is absolutely true. It is because monopolist has full control over the market and there is no reason for the monopolist to lower down the prices. The monopolist can easily increase the prices of goods if the good is price inelastic. In other words, if the rise in the prices does not affect the demand for the goods, the monopolist has an advantage in increasing the prices.

However, if the good is price elastic, the monopolist can increase the prices to a certain limit. Once the limit is crossed, the demand for the good would start declining. Hence, one can conclude that the monopolist can sell the good at higher prices in another market but such actions are subject to certain conditions like price elasticity of goods.