Question

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

Short answer

The usual shape of a total revenue curve for a monopolist is an inverted U-shape, which is a result of the monopolist's ability to set prices and balance between the price of the product and the quantity sold. Initially, an increase in quantity sold leads to a higher total revenue, causing the curve to slope upwards. As the quantity sold continues to increase, the fall in price becomes more significant than the rise in quantity, leading to a decrease in total revenue and forming the downward-sloping part of the inverted U-shape.

Step-by-step solution

Definition of a Monopolist

A monopolist is a single seller in a market who has the power to control the supply of a particular good or service. This individual or company faces no competition and can set the prices in the market.

Definition of Total Revenue

Total Revenue (TR) is the total amount of money a firm receives from selling its products at a given quantity. It is calculated by multiplying the price (P) of the product by the quantity sold (Q), i.e., TR = P × Q.

Shape of the Total Revenue Curve for a Monopolist

The Total Revenue curve for a monopolist is generally upward-sloping and then downward-sloping, forming an inverted U-shape. This shape is attributed to the relationship between price and quantity sold as well as the monopolist's price-setting ability.

Explanation for the Inverted U-Shape

A monopolist can maximize its total revenue by finding the balance between the price of the product and the quantity sold. At low quantities, the product's price is high, and vice versa. As the monopolist increases the quantity sold, initially, the rise in quantity exceeds the fall in price. This results in an increase in total revenue, causing the curve to slope upwards. However, as the monopolist continues to increase the quantity sold, there comes a point where the fall in price becomes more significant than the rise in quantity. This means that the marginal revenue (the additional revenue earned by selling one more unit) will be less than the marginal cost (the additional cost of producing one more unit), making it unprofitable for the monopolist to expand production any further. At this point, the total revenue starts to decrease, and the curve slopes downwards, forming the downward-sloping part of the inverted U-shape. In summary, the total revenue curve of a monopolist has an inverted U-shape because the monopolist faces a trade-off between the price of the product and the quantity sold to maximize its total revenue.

Key concepts

Monopoly and Market Power

The concept of a monopoly is fundamental to understanding how certain markets operate. A monopolist is an exclusive provider of a particular good or service, with no close substitutes available to consumers. This unique position grants the monopolist significant market power, which is the ability to influence or outright set the price of the product without losing customers to competitors, simply because there are none. In contrast, firms in highly competitive markets are price takers, meaning they must accept the market price as given.

With this market power comes the responsibility of balancing the quantity supplied and the price set. An increase in the selling price can lead to higher profits per unit, but it may also decrease the quantity sold due to the law of demand. Therefore, a monopolist strategically uses its market power to generate the highest possible profits.

Price-Setting Ability

The price-setting ability of a monopolist is a unique characteristic that differentiates it from firms in competitive markets. Monopolists have the discretion to set prices above marginal costs, unlike competitors in a perfectly competitive market who must set the price equal to marginal cost. This ability to set prices gives the monopolist control over its total revenue and the potential to maximize profits.

However, even a monopolist is constrained by the demand for their product. Setting a price too high can limit the quantity they're able to sell significantly. Hence, the monopolist aims to find the optimal price point where total revenue is maximized. This is a delicate balancing act as the firm must consider how changes in price will affect the demand for its product—too high, and sales may dwindle; too low, and the potential for profits is not fully realized. Finding the sweet spot is critical for a monopolist looking to leverage its market power effectively.

Marginal Revenue

Understanding marginal revenue is crucial when discussing monopolies. Marginal revenue is the additional income that a firm earns from selling one more unit of a good or service. For a monopolist, marginal revenue is always less than the price of the product due to the negative slope of the demand curve—the monopolist must lower the price of all units sold to sell an additional unit.

When a monopolist sells an additional good, two things happen: it gains revenue from the sale of that extra unit but also loses some revenue because it had to lower the price on all the units sold to sell that one extra unit. This phenomenon is known as the output effect and the price effect, respectively. The combination of these effects leads to decreasing marginal revenue as output increases. It's important to note that the marginal revenue curve for a monopolist lies below the demand curve for its product.

Inverted U-shaped Curve

The inverted U-shaped curve demonstrates the relationship between total revenue and quantity sold for a monopolist. It is a visual representation of how total revenue varies with changes in output levels. As noted earlier, marginal revenue decreases as the monopolist produces and sells additional units. The total revenue increases at a decreasing rate until it reaches a maximum point—this is the top of the inverted 'U.' Beyond this point, increases in output lead to a drop in total revenue due to the significant reductions in price that are required to sell additional units.

The shape of the curve represents the trade-off the monopolist faces and is a graphical indication of how price elasticity of demand impacts revenue. When the demand is elastic, total revenue rises with output; when demand becomes inelastic, total revenue falls. This pivotal moment, where the total revenue curve changes from ascending to descending, is the point of maximum total revenue and is critical to the monopolist's pricing and output decisions.