Final answer:
A monopolist must decrease the price it charges for each additional unit it sells because it faces a downward-sloping demand curve and to sell more, the price must be lowered for all units, resulting in decreasing marginal revenue.
Step-by-step explanation:
The statement "A monopoly must decrease the price it charges for each additional unit it sells" is true. A monopolist is not a price taker; it is a price maker which means it decides the quantity to produce and consequently determines the market price. However, due to the downward-sloping demand curve that the monopolist faces, to sell more units, the monopolist must lower the price not just of the additional units, but of all units sold, which results in decreasing marginal revenue. Therefore, if a monopoly wants to increase sales, it must reduce the price, causing the marginal revenue to be less than the price.