Is the following statement accurate: "A monopolist always charges the highest possible price?"
No, this statement is not accurate. Monopolists cannot simply raise prices as high as they like. The demand for their goods or services may be less elastic than the demand for most other products, but the demand curve is still downward sloping. Monopolists cannot raise their prices indiscriminately if they wish to maximize their profits.
It is true that consumers cannot buy a competitor’s products if a monopolist raises its prices. However, this does not mean that they have no option but to buy. For example, let us think about a small town whose airport is only served by one airline. People from that town cannot choose a competing airline. However, if the airline that serves the town raises its prices too high, some people will likely choose not to fly at all. This means that the airline cannot just raise its prices as high as it wishes.
In all market structures, firms maximize their profits by producing the quantity of goods where their marginal costs are equal to their marginal revenue. A monopolist is no different. It finds this point and charges the price at which people demand that quantity of the goods.
Monopolists, then, can raise their prices more than most firms, but they cannot raise them as high as they wish.