Lecture: Monopoly
Lecture script · about 15–20 minutes spoken · Week 11
Opening
Picture a small town on an island. One ferry runs to the mainland. There's no bridge and no second boat. If you need a doctor, a part for your shop, or a shift at a job across the water, you ride that ferry at whatever fare it posts. And if the fare goes up, you can't walk to the next dock, because there isn't one.
A family filling a prescription for a patented medicine is in a similar spot. There's one seller, and no close substitute. This lecture is about sellers like that.
Here's where we are. In Week 6 you measured consumer surplus as a triangle and saw that a competitive market makes total surplus as large as it can be. In Week 7 the surplus a market loses got a name, the deadweight loss. And in Week 10 you met marginal revenue and the rule every firm follows: produce where marginal revenue equals marginal cost. For the chair workshop, a price taker, that rule read as price equals marginal cost.
In this lecture that rule meets a seller with no rivals. I'll start with what makes a monopoly. Then we'll build the ferry's revenue, choose how many tickets it sells, and read its fare. We'll measure what riders lose, put a number on market power, and finish with discounts and the antitrust laws. Next week, in Week 12, the course turns to markets with a few rivals instead of none.
1. What makes a monopoly
Why would a town have only one ferry? Maybe the company owns the only dock. Maybe the town hands out a single license. Maybe one boat can carry everyone more cheaply than two boats splitting the riders. Each reason keeps a second seller out.
Economists have names for this. A monopoly is a market with a single seller of a product that has no close substitutes, protected by barriers that keep rivals from entering. And barriers to entry are obstacles that stop new firms from starting to sell in a market, such as control of a key resource, patents and licenses, or economies of scale that let one firm serve the market most cheaply.
That last one deserves a closer look. Economies of scale means a firm's average cost per unit falls as it produces more. When those savings are so large that one firm can serve all buyers more cheaply than two could, you have a natural monopoly. A town's water system is the classic case. One set of pipes under every street is enough, and a rival digging up the same streets would only double the cost.
One honest word about the ferry. It's a classroom model built for this course, not a real company, and its numbers are illustrative.
Pause and try this. A huge company sells a product that dozens of rivals also sell. Is it a monopoly?
Think about what the word monopoly requires.
Here's the answer. No, because a monopoly is the only seller of a product with no close substitutes, and size alone doesn't make a firm the only seller.
2. The ferry's demand
Last week the chair workshop could sell as many chairs as it liked at the market price. The ferry is different. It is the whole market, so it faces the whole market's demand, and that demand slopes down.
Here's the ferry's demand in words. The fare, in dollars a ticket, is 20 minus the number of tickets it sells, counted in hundreds a day. At a fare of 20 dollars, nobody rides. Each 1-dollar cut in the fare draws more riders, so at 19 dollars it sells 1, measured in hundreds, and at 12 dollars it sells 8, which is 800 tickets a day.
This gives the ferry market power: a seller's ability to raise its price above marginal cost without losing all of its buyers. A price taker has none. The ferry has plenty.
Now picture a graph with tickets, in hundreds, along the bottom and dollars a ticket up the side. Demand is a straight line starting at 20 dollars on the side and sloping down to the right, falling 1 dollar each time the quantity rises by 1.
Pause and try this. Can the ferry post a fare of 20 dollars and still fill its boat?
Picture the top end of that demand line.
Here's the answer. No, because at 20 dollars riders buy no tickets at all, so demand limits even a seller with no rivals.
3. Marginal revenue falls below the price
This is the idea the whole week turns on. To sell more tickets, the ferry has to cut the fare, and the cut applies to every rider, not only the new ones.
Let's build the revenue. Total revenue is the fare times the quantity, in hundreds of dollars a day. At 1 it's 19. At 2 the fare is 18, so revenue is 36. Keep going and revenue climbs to 51, 64, 75, 84, 91, 96, 99, and finally 100 at a quantity of 10.
Marginal revenue is the change in total revenue from one more unit, here one more step on the quantity scale. Subtract each total from the next and you get 19, 17, 15, 13, 11, 9, 7, 5, 3, and 1.
Look closely at the second step. The fare drops from 19 to 18. The new riders bring in 18. But the first group of riders now pays 1 dollar less each. So the second step adds 18 minus 1, which is 17, below the fare of 18. That's why marginal revenue sits below the price at every quantity after the first. On the graph it's a second straight line, starting at 20 dollars like demand but falling twice as steeply.
Pause and try this. At 8 on the quantity scale the fare is 12 dollars. Is marginal revenue there above or below 12?
Think about what the fare cut does to the earlier riders.
Here's the answer. It's below, because the 8th step adds only 5: the new riders' fares minus what the fare cut takes from everyone else.
4. The output rule, MR equals MC
The ferry knows what each step adds to revenue. Now it needs what each step adds to cost. In this model the marginal cost is a constant 4 dollars a ticket, for fuel, crew time, and wear.
The rule hasn't changed from Week 10. Every profit-maximizing firm produces where marginal revenue equals marginal cost. It sells each step that adds at least as much to revenue as to cost.
So walk the list. Marginal revenue is 19, 17, 15, and on down to 5 at the 8th step. Each of those is at least 4, so each one adds to profit. The 9th step adds only 3, and 3 is less than 4. So the ferry stops at 8, which is 800 tickets a day.
You can find the same answer from the marginal-revenue line. Set 20 minus twice the quantity equal to 4. Twice the quantity is 16, so the quantity is 8.
Pause and try this. Should the ferry sell the 9th step of tickets, where marginal revenue is 3?
Compare that 3 with the cost of carrying the riders.
Here's the answer. No, because those riders add 3 dollars a ticket to revenue but 4 dollars a ticket to cost, so profit would fall.
5. Reading the price from demand
The rule picked a quantity, 8. It didn't pick a price. For that, the ferry goes back to its demand curve and asks: what's the highest fare at which riders buy exactly 8?
Demand says 20 minus 8, which is 12 dollars. So the fare is 12, not 4. The 4 is where marginal revenue met marginal cost, and that crossing only sets the quantity.
Now the profit. Each ticket earns 12 minus 4, which is 8 dollars over its cost. Multiply by 8 and the profit is 64, in hundreds of dollars a day. Check it another way: revenue of 96 minus the cost of 32 is 64. And at 7 or at 9 the profit would be 63, so 8 really is the best choice.
On the graph, picture the profit as a rectangle. Its height runs from the 4-dollar cost line up to the 12-dollar fare. Its width runs from zero out to 8.
Pause and try this. After finding the quantity of 8, a classmate posts a fare of 4 dollars. What did they read wrong?
Think about which line the fare comes from.
Here's the answer. They read the price off the crossing of marginal revenue and marginal cost, when the fare comes from the demand curve, which gives 12 dollars at that quantity.
6. The competitive benchmark
To judge the ferry, compare it with a crossing served by many small boats. Each boat is a price taker with the same 4-dollar cost, so the market runs where price equals marginal cost.
Set the fare from demand equal to 4. Then 20 minus the quantity is 4, so the quantity is 16. A competitive crossing would carry 16 at a fare of 4 dollars.
Put the two side by side. The monopoly sells 8 instead of 16, half as many tickets. It charges 12 instead of 4, three times the fare. And the costs are the same in both cases. The monopoly sells less because its marginal revenue falls below the fare, not because carrying riders costs it more.
Pause and try this. Does the monopoly sell fewer tickets because its cost per rider is higher than the small boats' cost?
Recall the marginal cost in both versions.
Here's the answer. No, because both face the same 4-dollar cost per rider, and the monopoly stops early only because its marginal revenue drops below the fare.
7. The deadweight loss of monopoly
Now we bring back Week 6. Consumer surplus is the area below the demand curve and above the price, a triangle.
Under competition, that triangle has a base of 16 and a height from 20 down to 4, which is 16. Half of 16 times 16 is 128, in hundreds of dollars a day. Under the monopoly, the triangle shrinks to a base of 8 and a height from 20 down to 12, which is 8. Half of 8 times 8 is 32.
So riders lose 96. Where does it go? The ferry's profit of 64 moves from riders to the owner. That's a transfer. The other 32 goes to no one. It's the deadweight loss, the surplus lost on the tickets that are no longer sold: half of the 8 missing tickets times the 8-dollar gap between fare and cost. And the pieces add up: 32 plus 64 plus 32 is 128.
Whether the owner deserves that profit is a question about fairness, a normative question. The size of the loss is a positive result of the model.
Pause and try this. Is the ferry's profit of 64 part of the deadweight loss?
Ask whether anyone receives it.
Here's the answer. No, because the owner receives the 64, so it's a transfer, while the deadweight loss is the 32 that no one gets.
8. The Lerner index
Some sellers have a little market power and some have a lot. In 1934 the economist Abba Lerner proposed one way to measure it. The Lerner index is the markup of price over marginal cost as a share of the price. It's zero for a price taker and grows as market power grows.
For the ferry, the markup is 12 minus 4, which is 8 dollars. As a share of the 12-dollar fare, that's 8 out of 12, or two-thirds. In words, two-thirds of every fare is markup over the cost of carrying one more rider.
Last week's chair workshop sold at a price equal to its marginal cost, so its markup was zero, and so was its index.
Pause and try this. Does a bigger Lerner index mean the seller has more market power or less?
Think about what a zero index meant for the workshop.
Here's the answer. More, because the index grows as a larger share of the price is markup over marginal cost, and a price taker's index is zero.
9. Price discrimination
Think about a movie theater that charges students less than other adults for the same seat at the same show. Or an airline that charges different fares for the same flight depending on when you book. The seat costs the seller the same either way.
That's price discrimination: selling the same good at different prices to different buyers for reasons unrelated to cost. It needs three things. The seller needs market power, since a price taker must charge the going price. It needs a way to sort buyers by willingness to pay, like a student ID. And it needs a way to stop resale, like checking that ID at the door.
The ferry meets the first condition already. A resident pass with a name on it could do the other two jobs, sorting daily riders from visitors and stopping resale.
Pause and try this. A delivery company charges more to send a package to a far-off town. Is that price discrimination?
Ask what drives the higher price.
Here's the answer. No, because the higher price reflects a higher cost of delivering, and price discrimination means different prices for reasons unrelated to cost.
10. Natural monopoly and antitrust
Go back to the water system. In a natural monopoly, breaking the seller into rivals would raise cost, so governments often regulate its price or run it themselves instead.
For other monopolies, the United States has antitrust law. The antitrust laws are the federal laws that police competition, chiefly the Sherman Act of 1890 and the Federal Trade Commission Act and Clayton Act of 1914. Section 7 of the Clayton Act bars mergers whose effect "may be substantially to lessen competition, or to tend to create a monopoly."
How hard to enforce those laws is a contested question, and I'll give you both sides at full strength. The case for vigorous enforcement starts from the positive result you've seen: a monopoly sells less at a higher price and leaves a deadweight loss, so blocking mergers that create market power protects buyers. The case for restraint says some firms are large because they produce cheaply, and patents grant temporary market power on purpose, to reward invention. Heavy enforcement, on this view, can slow new products. Each side's last step is a normative weighing, and this course gives no verdict.
Pause and try this. Is the claim that a monopoly sells less than a competitive market positive or normative?
Ask whether evidence could test it.
Here's the answer. It's positive, because it describes what the model predicts and can be checked, while how hard to enforce antitrust law rests on values.
11. The classic wrong turns
Most slips this week come from carrying last week's shortcuts into a market with one seller. Here's one to catch. A classmate says the ferry charges whatever it wants, sets price equal to marginal cost, and has a deadweight loss equal to its profit.
Take those one at a time. Demand limits the ferry, since 20 dollars sells nothing. Price equals marginal cost is the price taker's rule, while the ferry uses marginal revenue equals marginal cost and reads its fare from demand. And the profit of 64 is a transfer, while the deadweight loss is 32.
Pause and try this. Which rule picks the ferry's quantity, and which curve picks its price?
Go back to the carry-along sentence from the chapter.
Here's the answer. Marginal revenue equals marginal cost picks the quantity, 8, and the demand curve picks the price, 12 dollars, because riders pay what demand says they will pay for that quantity.
Closing
Let's pull it together in the order we went. A monopoly is the only seller of a product with no close substitutes, protected by barriers to entry. Because it must cut its fare for everyone to sell more, its marginal revenue falls below the price. It still follows marginal revenue equals marginal cost, which gave the ferry 8, and it reads its price from demand, 12 dollars. Against the competitive 16 at 4 dollars, riders lose surplus, the owner gains 64, and 32 is lost to everyone. Two-thirds of each fare is markup. Discounts by group need market power, sorting, and no resale. And antitrust enforcement is a debate where values do the final weighing.
Next in this module come the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. Next week, in Week 12, we meet monopolistic competition and oligopoly, where a seller faces a few rivals or many close ones.
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