Lecture: Consumer & Producer Surplus & Market Efficiency
Lecture script · about 15–20 minutes spoken · Week 6
Opening
Think about a deal you were glad you made. Say you'd decided a ticket to see a band was worth up to 70 dollars to you, and it cost 40. You walked away 30 dollars ahead, even though nobody handed you any money. And the person who sold it to you? If 25 dollars was the least they'd have taken, they walked away 15 dollars ahead too. Nobody got cheated. Both of you gained.
That's the feeling this week puts a number on. A used-gear shop owner sees it every time a fair price lets both sides leave happy. A city planner sees it when asking whether a market's gains are large, and whether their split is fair.
Here's where we are. In Week 1 you learned to tell a positive statement, one evidence can check, from a normative one, which rests on values. In Week 2 you saw that trade can make both sides better off. In Weeks 3 and 4 you built demand and supply and found where they cross, and in Week 5 you measured how strongly buyers respond to price.
This week we measure the gains. I'll start with the two limits on every trade, then a small market of used bicycles where you can count every gain by hand. Then we'll move to the course's running market and read the gains as areas on the diagram. After that comes the big claim, that a competitive market makes the total gain as large as it can be. And I'll end by keeping two questions apart: how big the gain is, and whether its split is fair.
1. The two limits on every trade
Every trade has a ceiling on one side and a floor on the other. The ceiling is the most you'd pay before you'd rather keep your money. The floor is the least the seller would take before they'd rather keep the good.
Those two limits have names. Willingness to pay is the most a buyer would pay for one unit of a good. Willingness to sell is the least a seller would accept for one unit, which is the seller's cost of providing it. And "cost" here is opportunity cost, from Week 1. It includes what the seller gives up, not only the cash they spent.
So a trade can help both sides only when the price sits between the two. If a buyer would pay up to 80 dollars and a seller would accept 30, any price in between leaves both of them ahead.
One honest caveat. Nobody walks around with a sign showing their willingness to pay. Economists infer it from what people do, like which prices they accept and which they turn down. The model treats it as a known number so the logic is easy to follow.
Pause and try this. A seller says, "My willingness to sell is the price I'm hoping to get." What's wrong with that?
Think about which end of the range a seller's limit sits on.
Here's the answer. Willingness to sell is the least the seller would accept, the bottom of the range, because it's the seller's cost, not the hoped-for price.
2. The bicycle ladder
Now let's make it countable. Picture a small market for used bicycles, built for this course. Five people would each like to buy one. Their willingness to pay, from highest to lowest, is 100, 80, 70, 50, and 30 dollars. Five people each have a bicycle to sell, and their costs, from lowest to highest, are 20, 30, 50, 70, and 90 dollars.
Lining them up like that is called a ladder. Buyers' values step down, and sellers' costs step up.
Suppose bicycles sell for 60 dollars. Who buys? A buyer buys only if the bicycle is worth at least the price. That's the buyers at 100, 80, and 70. The buyers at 50 and 30 sit out. Who sells? A seller sells only if the price covers their cost. That's the sellers at 20, 30, and 50. The sellers at 70 and 90 keep their bikes.
So three buyers want a bicycle, three sellers offer one, and three bicycles change hands. Nobody is left waiting in line.
Pause and try this. The buyer whose bicycle is worth 50 dollars to him doesn't buy at 60. Did that buyer lose something?
Ask whether anyone made him trade.
Here's the answer. No. He chose to sit out because the bicycle is worth less to him than the price, so his gain is zero, not a loss.
3. Adding up the gains
Each buyer who trades comes out ahead, because the bicycle was worth more than the price. That gain, added up over every buyer, is consumer surplus: each buyer's willingness to pay minus the price actually paid, added up over the units bought.
Let's add it out loud. The buyer at 100 pays 60, so gains 40. The buyer at 80 gains 20. The buyer at 70 gains 10. So 40 plus 20 plus 10 is 70 dollars of consumer surplus.
Sellers come out ahead too. Their gain is producer surplus: the price received minus each seller's cost, added up over the units sold. The seller at 20 gets 60, so gains 40. The seller at 30 gains 30. The seller at 50 gains 10. That adds to 80 dollars.
Put them together and you get total surplus, consumer surplus plus producer surplus, the whole gain from the trades. Here that's 70 plus 80, or 150 dollars. Nobody printed that money. It's the value of moving three bicycles to people who want them more than their old owners did.
Pause and try this. A classmate writes consumer surplus as "price minus value." Which way round should it be?
Ask whose gain it is.
Here's the answer. Value minus price, because a buyer gains when the bicycle is worth more to them than they pay.
4. The efficient number of trades
Now forget the price for a moment. Suppose you could choose which bicycles change hands. How many trades would make the biggest total gain?
Pair the buyer who values a bike most with the seller whose cost is lowest, then keep going down the ladder. The first pair gains 100 minus 20, which is 80. The second gains 80 minus 30, or 50. The third gains 70 minus 50, or 20. And the fourth? It's 50 minus 70, which is negative 20. The fifth is worse, negative 60.
So the best you can do is three trades. Add 80, 50, and 20 and you get 150 dollars. A fourth trade would bring the total down to 130, because it moves a bike from someone who values it at 70 to someone who values it at 50.
That's the efficient number of trades: the number that makes total surplus as large as possible. Every trade worth more than it costs happens, and no trade that costs more than it's worth happens.
Here's the part I find striking. Nobody organized that bicycle market. Each person looked only at the price of 60 and their own number. And the market landed on exactly three trades and exactly 150 dollars, the same as the best pairing.
Pause and try this. Someone says more trades is always better, so five trades must beat three. How would you answer?
Look at the sign of the fourth pair's gain.
Here's the answer. The fourth and fifth pairs lose value, negative 20 and negative 60, so forcing them to trade makes the total smaller, not larger.
5. Reading the curves as values and costs
The ladder had ten people. The course's running market has far more, so instead of a list of people, we read the curves.
Here's the trick. A demand curve, read straight up from any quantity, tells you what that unit is worth to the buyer who buys it. A supply curve, read straight up from any quantity, tells you what that unit costs the seller who sells it.
On the running market, the demand curve starts at a price of 9 dollars when quantity is zero and falls by 1 dollar for every 10 units. The supply curve starts at 3 dollars and rises by 1 dollar for every 10 units. Price is up the side, quantity is across the bottom, and the two lines cross at 30 units and 6 dollars.
So take the 10th unit. On demand, 9 minus 1 is 8, so some buyer values it at 8 dollars. On supply, 3 plus 1 is 4, so some seller can provide it for 4. That one unit could create 4 dollars of gain.
Pause and try this. At the 10th unit, which curve sits higher, demand or supply?
Compare 8 dollars with 4 dollars.
Here's the answer. Demand sits higher, at 8 dollars against 4, which is why trading that unit creates a gain.
6. The two triangles
On the ladder, you added gains one person at a time. With a straight line and many units, those little gains stack into a shape, and the shape is a triangle. A triangle's area is one half times its base times its height.
At the running market's equilibrium, the price is 6 dollars and 30 units trade each day. Consumer surplus is the triangle below the demand curve and above the price line. Its base runs from zero to 30 units, and its height runs from 6 dollars up to 9. One half times 30 times 3 is 45 dollars a day.
Producer surplus is the triangle above the supply curve and below the price line. Same base, 30 units, and its height runs from 3 dollars up to 6. One half times 30 times 3 is again 45 dollars a day. Together that's 90 dollars a day of total surplus.
The two triangles match here only because the two lines are equally steep. On the ladder, remember, buyers got 70 and sellers got 80.
Pause and try this. Someone computes consumer surplus as 30 times 3, which is 90. What went wrong?
Picture the shape of the gains.
Here's the answer. They used the full rectangle, which is twice the triangle, so consumer surplus is 45, not 90.
7. Why the equilibrium is efficient
The bicycle market found its best number of trades. The running market does the same thing, and here's how to see it. Compare each unit's value to its cost.
Take the 20th unit. Buyers value it at 7 dollars, and it costs sellers 5. Trading it gains 2 dollars, so leaving it untraded would throw that away. Now take the 40th unit. Buyers value it at 5 dollars, and it costs sellers 7. Trading it destroys 2 dollars.
So every unit up to the 30th is worth more than it costs, and every unit past the 30th costs more than it's worth. If the market stopped at 20 units, total surplus would be 80 dollars a day. If it pushed on to 40, total surplus would also fall to 80. Stopping at 30 units gives the most, 90 dollars a day, and that's exactly where the market lands.
That's allocative efficiency: an outcome in which goods are produced and traded up to the point where total surplus is as large as it can be. In the competitive model, the equilibrium quantity reaches it. And it's a positive result. It's arithmetic you can check.
But I want to be honest about the fine print. That result holds under the model's assumptions: a competitive market, people who know what they're trading, and nobody outside the trade getting hit with a cost. Later weeks test every one of those.
Pause and try this. Should the market trade the 40th unit?
Compare what buyers would pay for it with what it costs to make.
Here's the answer. No, because it costs sellers 7 dollars and is worth only 5 to buyers, so trading it lowers total surplus.
8. Efficiency versus equity
So far we've asked how big the gain is. There's a second question hiding in the same numbers: is the split fair? On the ladder, buyers got 70 dollars and sellers got 80. Is that fair? Was it fair that the buyer at 50 went home without a bike?
That second question is about equity, which means fairness in how the gains from a market are divided among buyers, sellers, and others. Judging it rests on values, so it's a normative question, not a result the model can prove.
Here's an analogy. Think of the total surplus as a pizza. Efficiency asks whether the pizza is as big as it can be. Equity asks how the slices are shared. You can measure the pizza with a ruler. You can't measure fairness with one. Two people who agree on every number on the ladder can still disagree about the slices, because they hold different values.
So when someone says, "The market is efficient, so the outcome is good," watch for the word "so." Everything before it is positive. Everything after it is a value judgment that slipped in.
Pause and try this. Is this positive or normative: "At a price of 60, three bicycles sell and total surplus is 150 dollars"?
Ask whether the ladder's numbers could check it.
Here's the answer. It's positive, because you can check every part of it against the ladder.
9. The classic wrong turns
Most slips this week aren't deep confusions. They're a swapped label, a missing one half, or a value judgment sneaking in. So here's a three-step routine.
First, say whose gain it is. Buyers gain value minus price, so consumer surplus sits below demand and above the price. Sellers gain price minus cost, so producer surplus sits above supply and below the price. Second, find the shape. With straight lines each surplus is a triangle, so don't forget the one half. Third, separate size from split. Efficiency is about the size; fairness is a separate, normative question.
And one more. The word "surplus" did double duty in this course. In Week 4, a surplus meant unsold units piling up at a price above equilibrium. This week, consumer surplus is a gain to buyers. When you say "surplus" now, say whose.
Pause and try this. A classmate writes, "Producer surplus is the area below demand and above the price." Which surplus did they actually describe?
Think about which side of the market sits on the demand curve.
Here's the answer. That's consumer surplus, because the demand curve carries the buyers' values.
Closing
Let's pull it together. Willingness to pay is the most a buyer would pay, and willingness to sell is a seller's cost. On the bicycle ladder at 60 dollars, three bikes sold, buyers gained 70, sellers gained 80, and the total was 150. Pairing values with costs showed that three trades is efficient, and the market found it.
On the running market, consumer surplus and producer surplus are triangles, 45 dollars a day each, for a total of 90. Every unit up to 30 is worth more than it costs, and none past 30 is, so the equilibrium is efficient in the model. And efficiency is about the size of the gain, while equity, the fairness of its split, is a normative question.
Next in this module, read through the slide deck, then the Readings and Resources page, and then work the lecture tutorial, the practice set, and the quiz. Next week, in Week 7, Government Intervention: Price Controls, Taxes & Subsidies, these triangles become the tool for measuring what a price ceiling, a price floor, or a tax does to a market.
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