Does a monopoly choose output, price, or both?

In a monopoly, even though monopolist is a sole producer in the market, he/she can only choose either price or output. Since monopolist faces the downward market demand curve, if he/she sets the high price, it will demotivate customers to purchase a greater quantity of products. This results in the lower output production. Inversely, if he/she chooses to set a higher output, the price will be lower. When monopolist determines the quantity of output, it also implicitly settle the market price.

Thus, a monopoly can either choose price or output. It cannot have both high price and high output simultaneously.