How to use this page

This recap covers the second half of the demand topic, delivered in the first 42 minutes of the September 3 class. The elasticity topic began in the same period and has its own recap and transcript. Read the five-step diagnostic first. Then use the two movements to reconnect each idea to an example from class. Finish with the application checks. The separate complete transcript is available when you want the full explanation or the exact sequence of the lecture.

Housekeeping from class. TopHat questions were a freebie again on Thursday; from Tuesday, September 8, they count, so fix any Wi-Fi or TopHat problem with OIT before then. The problem-set due dates have been extended. Slide access through TopHat is being sorted out with the company.

What you should be able to do

1. Take a demand schedule and compute marginal worth, total worth, spending, and consumer surplus at any price — and locate spending and surplus on the demand diagram.
2. Say what a higher price does to buyers’ surplus, distinguish that from what it does to sellers’ revenue, and explain why a steep demand curve loses less surplus than a flat one.
3. Resolve the diamond–water paradox and its modern cousins (teachers and quarterbacks, nurses and doctors), state a price as an exchange rate without dollars, and rewrite any “need” claim as how much, at what price.

Movement 03, continued · What one more unit is worth

Two columns become a full accounting, and the gap is the buyer’s gain

Class picked up at the table. The law of demand, restated: a buyer keeps buying until the marginal value of the last unit equals the price. Offered a 60-cent unit for 50 cents, she takes it and is 10 cents better off; she stops at the unit that is worth exactly the price. That is why a demand schedule alone tells you the marginal worth of every unit — at $1.00 she buys one, so the first quart is worth $1.00; at 50 cents she buys six, so the sixth is worth 50 cents. Add the marginals and you have total worth: $1.00 + $0.90 + $0.80 + $0.70 + $0.60 + $0.50 = $4.50. Multiply price by quantity and you have spending: $3.00. The difference, $1.50, is consumer surplus — 50 cents of gain on the first quart, 40 on the second, down to nothing on the sixth. She does not buy a seventh because it is worth 40 cents and costs 50, and that 50 cents buys something else.

The same accounting draws. Each quart is a bar as tall as its worth; the bar tops trace the demand curve. Spending is the rectangle under the price line — six times 50 cents. Surplus is what sits above the price line and below the curve; smooth the steps and it is a triangle, one-half base times height, as long as the curve is drawn up to the vertical axis. The TopHat question tested the point directly: $3.00 buys five quarts at 60 cents or six at 50 cents, so what is the sixth quart worth? Ten students said “nothing, because spending did not change.” But total spending never tells you value. At 50 cents she takes six units, so the sixth is worth 50 cents. Value is at the margin.

Then the frost. Half the orange crop dies, the price rises, and growers may take in more dollars than before. Is anyone harmed? Buyers are: the spending rectangle may have grown, but the surplus triangle shrank. Growers may or may not gain — revenue can rise or fall, and which one depends on the next topic, elasticity. A student asked whether the slope of the demand curve matters. It does: on the board, surplus before the frost was regions A + B + C and after it only A; with a steeper curve, buyers cut back far less and lose far less surplus. But slope and elasticity are not the same thing — elasticity is the percentage change in quantity over the percentage change in price, it changes along a straight line, and only a rectangular hyperbola holds it constant. That was a preview; the number came in the next deck.

Finally, Adam Smith’s paradox. In 1776 Smith could not explain why diamonds cost more than water, which people “need” — and his failure gave economics a century of the labor theory of value. Consumer surplus dissolves it. Total value is surplus plus spending. For diamonds that is a $9 rectangle and a sliver; for water it is an enormous trapezoid. Smith was right that water is worth more in total. He missed that the price is set at the margin, where the next diamond is scarce and the next gallon of water is not. The paradox is still with us: teachers “are underpaid and NFL quarterbacks overpaid,” nurses versus doctors. Add up every teacher’s salary and it swamps the 32 starting quarterbacks; importance shows in the total. A salary, like a price, is set at the margin — and a lot of people can be a K-12 teacher, while about 32 can start at quarterback.

Movement 04 · Rates, prices, and “need”

A demand claim needs a quantity per period and a relative price

Quantity can mean three things, and all three are per unit of time. Usually it is a flow — gallons of gas per week. It can be a stock on hand — how many eggs you keep in the fridge, which grows as eggs get cheaper. Or it can be the addition to a stock — how many more you add when the price falls. That is why every quantity in this course carries a “per week” or “per month.”

And a price is an exchange rate, with or without money. In R. A. Radford’s Allied POW camp, cigarettes from the monthly Red Cross parcels became money — complete with lending markets and interest rates. As the month’s cigarettes were smoked, their value in everything else rose (mild deflation); when the next pallet arrived, it fell (inflation). Prices never needed dollars. If one bottle of water trades for three granola bars, that ratio is the relative price, and relative prices are what micro cares about — a trillion dollars on an alien planet tells you nothing until you know what it buys. If the rate moves to two bottles for three bars, granola bars got dearer and water got cheaper; the same fact, read from either side. Dollar prices, when they appear on the board, stand in for everything else money could buy — do not smuggle them back in as the “real” price.

Which settles the golf courses. “Many people do not play as often as they would like because of a lack of courses” is missing its units: at what price? At a low enough price that sentence is true of everything — swap in filet mignon, or cigars. The wrap-up put six moves together: name the buyer, the good, and the quantity per period; state the price as a relative price; sort a change in price (a slide) from a change in conditions (a shift); read the curve’s height as worth; read the gap above the price as the buyer’s gain; and answer every “needs more” with “at what price?”

A closing question reached ahead to supply. Producer surplus is the seller’s cousin of consumer surplus — closely related to profit, so think of consumer surplus as psychic profit. Drawn with an upward-sloping supply curve (the seller’s marginal cost), producer surplus is the area below the price and above supply. Redraw the frost as a leftward shift of supply and the higher price shrinks buyers’ surplus to a small triangle — and, as drawn, cuts producers’ surplus too. A higher price is never good for a buyer and is not always good for a seller: orange growers do not root for frosts.

Where Part 1 left off, and what came next

Tuesday, September 1, built the law of demand, the slide-versus-shift distinction, and the worth–spending–surplus table through consumer surplus; its recap and transcript are separate pages. This page finishes the topic. About 42 minutes into Thursday’s class the elasticity topic began, picking up the student’s question about the slope of the demand curve; that material is on the T3b Lecture Recap and its transcript, and continues on Tuesday, September 8.

Examples are memory cues; the right column is the principle each example should help you recover.

Example from class	Economic lesson
A 50-cent can of green beans	A market price reveals what the marginal unit is worth to somebody.
Gains of 50, 40, 30, 20, 10, and 0 cents	Consumer surplus is the gap between worth and price on every unit before the last; the marginal unit earns none.
Why not a seventh quart at 50 cents?	It is worth 40 cents; the 50 cents buys something better. Price is what you give up in all other goods.
$3.00 either way: five quarts or six	Total spending does not measure value; the sixth quart is worth its price, 50 cents.
One-half base times height	Smoothed, consumer surplus is the triangle above the price line and below the demand curve; spending is the rectangle beneath the price.
A frost kills half the oranges	Revenue is not welfare: a higher price can raise growers’ dollars while buyers lose surplus — and growers may lose too.
Regions A, B, C and the steeper curve D′	Buyers on a steep curve cut back little and lose less surplus; slope is related to elasticity but is not elasticity.
Adam Smith’s diamonds and water	Price is set at the margin; total value (surplus plus spending) can be huge for a cheap good. There is no paradox.
Teachers and quarterbacks; nurses and doctors	Importance shows in the total; a salary is a marginal price, and scarce skills command high margins.
Eggs in the fridge	Quantity can be a flow, a stock on hand, or an addition to a stock — all per unit of time, and all respond to price.
Cigarettes in the POW camp	Prices exist without cash; a money’s value in other goods rises as it gets scarce and falls when a new supply arrives.
A trillion dollars on an alien planet	Dollar figures mean nothing until you know what they buy; micro runs on relative prices.
Water bottles for granola bars	A price is an exchange rate; when one side gets dearer the other gets cheaper by the same fact.
Golf courses, filet mignon, and cigars	“People would do more of it if there were more of it” is true of everything at a low enough price; ask at what price.
Producer surplus: the seller’s side of the gap	Sellers gain the gap between price and marginal cost; drawn with supply, a frost can hurt sellers as well as buyers.

Question 1 — At 60 cents a buyer takes five quarts and spends $3.00. At 50 cents she takes six and still spends $3.00. What is the sixth quart worth to her?

50 cents. Total spending tells you nothing about value. The law of demand says she buys until the marginal unit is worth just what it costs; at 50 cents she takes six, so the sixth is worth 50 cents. “Nothing, because spending did not change” reads a total where a margin belongs.

Question 2 — Marginal worths run $1.00, $0.90, $0.80, $0.70, $0.60, $0.50, $0.40. At a price of 50 cents, give total worth, spending, and consumer surplus, and say where each sits on the diagram.

She stops at six (the seventh is worth 40 cents). Total worth = $4.50, the sum of the six marginals. Spending = $0.50 × 6 = $3.00, the rectangle under the price line. Consumer surplus = $4.50 − $3.00 = $1.50, the area above the price line and below the demand curve — on a smooth curve, one-half base times height.

Question 3 — A frost kills half the orange crop and growers take in more dollars than before. Was anyone harmed?

Yes — the buyers. The higher price moves them up their demand curve; the spending rectangle may grow, but the surplus above the price line shrinks. Revenue is not welfare. Whether growers gain depends on how much quantity fell relative to the price rise — the elasticity question — and with the supply side drawn in, growers can lose surplus too.

Question 4 — Two demand curves pass through the same point. When the price rises by the same amount, which curve’s buyers lose more consumer surplus — the steep one or the flat one? Does that make slope the same thing as elasticity?

The flat one: those buyers cut back a lot, and the lost surplus (regions B and C on the board) is large; buyers on the steep curve barely cut back and lose only a sliver. Slope is related to elasticity but is not elasticity: elasticity is the percentage change in quantity over the percentage change in price, and it changes along even a straight-line demand curve.

Question 5 — Water keeps people alive and diamonds are jewelry, yet diamonds cost far more. Where did Adam Smith go wrong?

He compared total value with price. Price is set at the margin: the next diamond is scarce and worth a lot, the next gallon of water is plentiful and worth little. Total value — surplus plus spending — is enormous for water and small for diamonds, exactly as Smith sensed. Confusing the two led him to the labor theory of value.

Question 6 — “Teachers are underpaid and NFL quarterbacks are overpaid.” What does the diamond–water logic say about this claim?

The claim confuses total value with marginal value. Teaching as a whole is far more valuable than quarterbacking — add up every teacher’s salary and it swamps 32 quarterbacks’ pay. But a salary is a price, set at the margin, and a lot of people can be a K-12 teacher while about 32 can start at quarterback. What people should be paid is a question for philosophers; what they are paid is set where the next worker is scarce.

Question 7 — After a disaster, cash stops circulating. One bottle of water used to trade for three granola bars; now two bottles trade for three bars. Does water still have a price, and what happened to it?

Yes. A price is an exchange rate, and three granola bars per bottle is one. Water got cheaper — three bars now buy two bottles instead of one — and by the same fact granola bars got dearer, from one-third of a bottle each to two-thirds. Micro works in relative prices; the POW camp ran a whole economy on cigarettes.

Question 8 — A report says the city needs more golf courses because “many people do not play as often as they would like because of a lack of courses.” What is missing?

The price. At a low enough price, nearly everyone would do nearly everything more often — swap in filet mignon or cigars and the sentence still reads. A demand claim must say how much, per what period, at what relative price. Without the price, “need” is not a claim at all.

Bottom line

Value is determined at the margin. The demand schedule tells you what each unit is worth; summing gives total worth, multiplying gives spending, and the gap between them — the area above the price line — is why the buyer trades. Total spending never measures value, which is why the sixth quart is worth 50 cents, why a revenue-raising frost still harms buyers, and why cheap water is worth more in total than expensive diamonds. And every demand claim needs its units: a quantity per period and a relative price. “Needs more” has no meaning until you ask, at what price?