Question

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

Short answer

The total revenue curve for a monopolist typically has the shape of an inverted parabola, which can be attributed to the relationship between price, quantity, and demand in a monopoly. As a monopolist increases the quantity sold, it earns more total revenue even if it must reduce the price slightly. However, at a certain point, lowering the price too much will result in a decrease in total revenue despite selling more units. This relationship between price-setting power and demand curve is what causes the total revenue curve to rise steeply initially, peak, and then gradually fall back down.

Step-by-step solution

1. Defining Total Revenue for a Monopolist

Total revenue is the amount of money a firm receives by selling a certain quantity of its product. In the case of a monopolist, it is the sole seller of a unique product in the market. The total revenue can be calculated by multiplying the price of the product by the quantity sold (Total Revenue = Price × Quantity).

2. Understanding Price, Quantity, and Demand in a Monopoly

In a monopoly, the firm has the ability to set the price of its product, as it is the only seller in the market. However, this price-setting power is not limitless – it is constrained by the demand for the product. As the price of the product goes up, the quantity demanded decreases, and vice versa. This relationship is represented by the downward-sloping demand curve.

3. The Shape of the Total Revenue Curve

In a monopoly, the total revenue curve (TR) is shaped somewhat like an inverted parabola. It starts from the origin (zero revenue when no product is sold) and then rises steeply, reaches a peak, and then gradually falls back down. This shape of the TR curve is determined by the relationship between price, quantity, and demand discussed earlier.

4. Reasoning Behind the Shape of the Total Revenue Curve

The initial upward slope of the TR curve is due to the fact that, as a monopolist increases the quantity sold, it earns more total revenue even if it has to lower the price a little to sell more units. However, after a certain point, further increasing the quantity will lead to lower price reductions that are so substantial that the total revenue will decrease despite selling more units. This is the reason for the downward slope of the TR curve after its peak. In summary, the total revenue curve for a monopolist is usually shaped like an inverted parabola due to the relationship between price, quantity, and demand in a monopoly. An understanding of how a monopolist's price-setting power interacts with the demand curve helps explain why the total revenue curve has this shape.