What is the usual shape of a marginal revenue curve for a monopolist? Why?

Marginal revenue (MR) is the additional revenue a firm earns from selling an additional unit of output. In other words, it is the change in total revenue resulting from a one-unit increase in output. A monopolist is a single seller in a market with no close substitutes for the product they sell. Monopolists have the power to set prices and control the output in the market, unlike firms in a competitive market.

For a monopolist, the demand curve represents the willingness of consumers to buy a certain quantity of goods at various prices. It is downward sloping, which means that as the price of the good decreases, the quantity demanded increases. In a competitive market, firms are price takers, which means that they take the market price as given and cannot influence it. So, the additional revenue they earn from selling one more unit is equal to the price of that unit. In other words, the marginal revenue curve for a competitive firm is horizontal and equal to the market price. However, since monopolists are price setters, their marginal revenue is not equal to the price of their product. For a monopolist, the marginal revenue curve lies below the demand curve. This is because when a monopolist wants to sell additional units, it must lower the price of its product not only for new units but also for previous units. Thus, the marginal revenue earned from selling more units is less than the price at which they sell these units.

The usual shape of a marginal revenue curve for a monopolist is downward-sloping and steeper than the demand curve. This means that as the quantity produced and sold increases, the additional revenue earned from selling one more unit decreases at a faster rate than the decrease in price.

The marginal revenue curve for a monopolist is downward-sloping because as the monopolist lowers the price to sell more units, the additional revenue from new units is offset by the revenue loss on previously sold units due to the price reduction. The curve is steeper than the demand curve because for each additional unit sold, the monopoly has to decrease the price on all the units it sells, not just the additional unit. This price reduction causes the additional revenue to decrease faster than the decrease in price. Hence, the marginal revenue curve is downward-sloping and steeper than the demand curve for a monopolist.