Question

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

Short answer

The usual shape of the marginal revenue curve for a monopolist is downward-sloping and steeper than the demand curve. This is because a monopolist needs to lower the price to sell more units of its product, resulting in a decrease in total revenue from the initial units as the price falls. Consequently, the marginal revenue declines at a faster rate compared to the demand curve, making the marginal revenue curve's slope steeper than the demand curve.

Step-by-step solution

A monopolist faces a downward-sloping demand curve, which means that it can sell more of its product only by lowering the price. The demand curve shows the relationship between the price and the quantity demanded of a product in a market. Since there are no close substitutes, the monopolist sets the price according to the demand curve. #Step 2: Relationship between Demand Curve and Revenue Curve#

To determine the shape of the marginal revenue curve, we first need to examine the relationship between the demand curve and a monopolist's revenue. Total revenue (TR) is calculated as the price (P) multiplied by the quantity of the product sold (Q): \(TR = P \times Q\). Since the demand curve is downward-sloping, the price usually needs to decrease for the quantity sold to increase. #Step 3: Deriving the Marginal Revenue Curve#

Marginal revenue (MR) is the additional revenue generated by selling one more unit of a product. Mathematically, MR is the change in total revenue (∆TR) divided by the change in the quantity produced (∆Q). So, \(MR = \frac{\Delta TR}{\Delta Q}\). As a monopolist increases the quantity sold (Q), the price (P) has to be lowered, and this leads to two opposing effects on total revenue – the increase in revenue from selling more products and the decrease in revenue from lowering the price. As a result, the marginal revenue curve will be downward-sloping but will decrease at a faster rate compared to the demand curve. #Step 4: Explaining the Shape of the Marginal Revenue Curve#

The usual shape of the marginal revenue curve for a monopolist is downward-sloping and steeper than the demand curve. The reason for this shape is that the monopolist needs to lower the price to sell more units of its product. This results in a decrease in total revenue from the initial units as the price falls, causing the marginal revenue to decline at a faster rate compared to the demand curve. As a result, the marginal revenue curve's slope is steeper than the demand curve, reflecting the need for the monopolist to lower prices to increase sales quantity.