Question

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

Short answer

The usual shape of a marginal revenue curve for a monopolist is downward sloping and lies below the demand curve. This occurs because the monopolist has to lower the price for all units, including previous ones, in order to sell additional units. The market power that the monopolist possesses, being the sole producer of a product, enables it to control the supply and price. As a result, the additional revenue generated from selling each subsequent unit decreases, leading to the downward-sloping marginal revenue curve.

Step-by-step solution

Define Marginal Revenue

Marginal Revenue (MR) is defined as the change in total revenue as a result of producing one more unit of output. In other words, it is the additional revenue generated from selling one more unit of a product.

Monopolistic Market Structure

A monopolist is a firm that is the sole producer of a unique good or service with no close substitutes. The monopolist has complete control over the supply and price of the product. Due to the lack of competition, a monopolist can adjust the quantity it produces, and hence the price it charges for its product, to maximize its profits.

Demand Curve for a Monopolist

The demand curve for a monopolist is downward sloping, which means that as the price of a product increases, the quantity demanded decreases, and vice versa. To sell additional units, the monopolist has to lower the price. This feature sets the monopolist apart from firms in competitive markets, where the demand curve is flat, and each firm is a price taker.

Calculate Marginal Revenue for a Monopolist

To derive the marginal revenue curve for a monopolist, we can use the following formula: \( MR = P + Q \cdot \frac{dP}{dQ} \) where \(P\) and \(Q\) are the price and quantity, respectively, and \(\frac{dP}{dQ}\) is the slope of the demand curve.

Shape of the Marginal Revenue Curve for a Monopolist

The marginal revenue curve for a monopolist is usually downward sloping and lies below the demand curve. This is because as the monopolist lowers the price to sell more units, the additional revenue generated from selling each additional unit declines. Due to the downward-sloping demand curve, the monopolist has to reduce the price not only for the additional unit it wants to sell, but also for all the previous units sold. This causes the marginal revenue curve to be more steeply sloped than the demand curve.

Reason for the Shape of the Marginal Revenue Curve

The reason behind the shape of the marginal revenue curve for a monopolist is the market power that the monopolist possesses. Since the monopolist is the sole producer of the product, it has the ability to control the supply and price at which it sells the product. As a result, the monopolist needs to lower the price to sell more units. This behavior leads to the downward-sloping marginal revenue curve, as the additional revenue generated from selling each subsequent unit of output decreases.