9.2 How a Profit-Maximizing Monopoly Chooses Output and Price

Monopoly Output, Price, and Efficiency

A profit-maximizing monopoly chooses how much to produce and what price to charge using the same core logic as any firm: produce where the additional revenue from one more unit equals the additional cost. But because a monopolist is the only seller, it faces the entire market demand curve, which changes how revenue behaves and leads to higher prices, lower output, and efficiency losses compared to competitive markets.

Profit-Maximizing Output and Price

A monopoly maximizes profit by producing the quantity where marginal revenue (MR) equals marginal cost (MC).

$MR = MC$

• Marginal revenue is the change in total revenue from selling one additional unit.
• Marginal cost is the change in total cost from producing one additional unit.

Once the monopolist finds the quantity where $MR = MC$, it doesn't charge a price equal to MR or MC. Instead, it goes up to the demand curve at that quantity and charges the highest price consumers are willing to pay. This is a critical step that trips up a lot of students.

How to find the profit-maximizing price and quantity on a graph:

1. Locate where the MR curve intersects the MC curve. Read the quantity off the horizontal axis. That's $Q_m$, the profit-maximizing quantity.
2. From $Q_m$, draw a vertical line up to the demand curve (not the MR curve).
3. Read the price off the vertical axis at that point on the demand curve. That's $P_m$, the monopoly price.

Because $P_m$ is above MC at the profit-maximizing quantity, the monopolist earns economic profit on each unit sold. Total economic profit equals $(P_m - ATC) \times Q_m$, where ATC is the average total cost at that quantity.

Unlike in perfect competition, these economic profits can persist in the long run. No new firms can enter to compete them away because barriers to entry block the market. These barriers can be legal (patents, licenses), technological (control of a key resource), or natural (economies of scale that make one firm the lowest-cost producer).

Monopoly vs. Perfect Competition

The key difference comes down to the shape of the demand curve each firm faces.

• A perfectly competitive firm faces a horizontal (perfectly elastic) demand curve at the market price. It's a price taker: it can sell as many units as it wants at that price without affecting it. Because of this, $P = MR$ for a competitive firm.
• A monopolist faces a downward-sloping demand curve, which is the entire market demand. To sell one more unit, the monopolist must lower the price on all units it sells, not just the extra one.

This is why the MR curve lies below the demand curve for a monopolist. When the firm drops its price to sell an additional unit, it gains revenue on that new unit but loses revenue on every unit it was already selling at the higher price. The net effect (MR) is less than the price received.

In perfect competition, the firm produces where $P = MC$, which gives both the efficient quantity and zero long-run economic profit. A monopolist produces where $MR = MC$, then charges a price above MC, resulting in a smaller quantity and a higher price than a competitive market would deliver.

Economic Inefficiencies

Monopoly creates two types of inefficiency and redistributes surplus away from consumers.

Allocative inefficiency: A market is allocatively efficient when $P = MC$, meaning the value consumers place on the last unit equals the cost of producing it. A monopolist charges $P > MC$, so some units that consumers value more than they cost to produce never get made. Resources are misallocated.

Productive inefficiency: A firm is productively efficient when it produces at the minimum of its average total cost curve. Because monopolists face no competitive pressure, they may have less incentive to cut costs or innovate. They don't have to produce at the lowest possible ATC to survive.

Deadweight loss: The combination of lower output and higher price means some mutually beneficial trades between buyers and sellers never happen. This lost surplus is called deadweight loss, and it represents a net loss to society, not just a transfer from one group to another. On a graph, deadweight loss is the triangular area between the demand curve and the MC curve, from $Q_m$ to the competitive quantity $Q_c$.

Surplus redistribution: Some of what would have been consumer surplus in a competitive market gets captured by the monopolist as economic profit. Consumers pay more and get less.

Price discrimination is one way monopolists try to capture even more surplus. By charging different prices to different consumers based on their willingness to pay, a monopolist can increase its profits beyond what a single-price strategy allows. There are three degrees:

• First-degree: Charge each consumer their maximum willingness to pay. Captures all consumer surplus. Rare in practice.
• Second-degree: Charge different prices based on quantity purchased (e.g., bulk discounts).
• Third-degree: Charge different prices to different groups (e.g., student discounts, senior pricing). This is the most common form.

Price discrimination can actually reduce deadweight loss in some cases (especially first-degree), since more units get sold, but it transfers surplus from consumers to the monopolist.