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This recap covers the September 8 class, which picked up the elasticity topic where the September 3 class stopped (that opening has its own recap and transcript, labeled Part 1). Class ran from the straight-line schedule through the second law of demand and stopped there; the topic continues Thursday. Read the seven-step diagnostic first. Then use the lecture sections 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, including the long question-and-answer stretches about revenue, profit, and pricing power.

What you should be able to do

1. Work down a straight-line demand schedule with the midpoint formula, locate the unit-elastic step, and say which steps are elastic and which are inelastic.
2. Predict what a price change does to a seller’s total revenue from the elasticity, and read a revenue change backwards to say what the elasticity must have been.
3. Classify a change as a slide along the demand curve or a shift of it, separate the substitution effect from the wealth effect for someone who owns the good, and state why demand grows more elastic with time.

Opening · Practice tools and a refresher

The Canvas practice tools, and the midpoint again

Class opened with the new practice tools in the Lecture 2 and Lecture 3 modules: the slide-or-shift sorter (the price of wigs falls: a movement along the curve), the schedule-to-surplus builder (six slices of pizza at $1.50: total worth $16.25, spending $9, surplus $7.25), and the midpoint elasticity drill. They do not affect your grade. They regenerate endlessly, and the instructor asked for requests: if a tool would help you practice something, email him and he will build it.

Then a refresher on the two ideas from last week. Elasticity makes the law of demand empirical: not just “people buy more when the price falls” but how much more. Few substitutes (insulin) means a small response; many substitutes (Coke and Pepsi) means a large one. And because $10 to $9 is a 10% cut while $9 to $10 is an 11.1% rise, every percentage in this course is measured against the midpoint, the average of the two endpoints, so the direction of travel does not matter. The $6-to-$5, 5-to-6-unit step gives 18.2% against 18.2%: unit elastic. The first TopHat question asked exactly that. Unit elastic is the cutoff: quantity moving by a smaller percentage than price is inelastic, by a larger percentage is elastic.

Movement 01 · Measuring the response, continued

Elasticity changes along one straight line

Several students had asked after class whether a straight-line demand curve has one elasticity. It does not, because elasticity is not the slope. The schedule on the slide is a straight line: price $10, one unit; $9, two; $8, three; and so on. Market value (price times quantity) goes $10, $18, $24, $28, $30, $30, $28, $24, $18, $10. It rises, flattens at $30, and falls, because each $1 cut sells one more unit but also gives up a dollar on every unit already being sold. Fill in the midpoint percentages and the pattern is plain: the same $1 cut is a small percentage of a high price and a large one of a low price, and one more unit is a large share of a small quantity and a small share of a large one. So elasticity falls down the line: 6.3 on the top step, then 3.4, 2.1, 1.4, exactly 1.0 on the $6-to-$5 step where market value stops rising, and below 1 from there on. Report the number with the price interval you used.

The seller’s lesson, stated early and returned to all hour: if you can set your price, you would never want to sell in the inelastic range. At $4 you sell seven units for $28; raise the price to $5 and you sell six for $30. More money for less output, even if producing the seventh unit cost nothing. A long exchange followed. Consumers maximize total value, which works out to the same thing as maximizing consumer surplus. Producers maximize profit, not revenue, and profit needs cost, which the course has not introduced yet. With zero cost a seller is indifferent between $6 and $5 (revenue $30 either way); with positive cost the sixth unit may not be worth producing at all. The instructor promised a Canvas tool with cost included rather than working one off the top of his head.

Parallel curves, same step, different elasticities

Two exactly parallel demand curves get the same $1 cut, $4.50 to $3.50, and both respond by the same 0.57 units, because the slopes are the same. Curve 1 measures those 0.57 units against a smaller quantity, so its percentage change is larger: elasticity 1.33 against 0.67. A student supplied the reason before the TopHat question ran (“the same increase on a smaller base”), and the overwhelming majority chose it: curve 1’s quantity increase is larger relative to its starting quantity. Not a larger absolute response, not a larger percentage price cut, and not a steeper slope. The slopes are identical.

Movement 02 · Price and the seller’s revenue

The revenue grid, read from the seller’s chair

Take the middle of the schedule: $7 and 4 units ($28), $6 and 5 ($30), $5 and 6 ($30), $4 and 7 ($28), $3 and 8 ($24). Cutting the price above the bold row raised the take; below it, the same cut lowered it. The reason is the elasticity crossing one. When demand is elastic, a price cut is more than offset by the extra units sold, so revenue rises, and a price rise lowers it: go from $6 and five units to $7 and four, and the take falls from $30 to $28. When demand is inelastic, the price side wins: go from $3 and eight units to $4 and seven, and the take rises from $24 to $28. Unit elastic, the two percentages cancel and revenue is unchanged. The grid on the slide is just the elasticity table read from the seller’s chair. Market value is the buyers’ name for the same number the seller calls total revenue.

The questions kept coming, and they were good ones. Does a seller always want to cut price when demand is elastic? With zero cost, yes, because revenue is then profit; the same logic that sends a seller down from $7 toward $6 sends him up from $4 toward $5. Where does a real seller end up? That depends on cost and on market structure, neither of which the course has reached. What can be said now: a monopolist, a firm with pricing power, would never price in the inelastic range, because it could always raise revenue by restricting output and raising price, whatever its costs. A price-taking firm in a competitive market has no such choice, so a competitive market can sit on an inelastic stretch of the market demand curve. On the board: mark the unit-elastic point, and everything above it is elastic, everything below it inelastic. Find that point first and the rest follows. Can you read it off a bare curve? No. Only the numbers tell you where it is, and only a rectangular hyperbola has the same elasticity everywhere. No shortcuts: the $4-to-$3 step is (8 − 7) over 7.5 against (4 − 3) over 3.5.

Pricing power came with two examples. The only Jimmy John’s in a small town has less power than it looks, because the grocery store sells cold cuts and bread; how you define the market decides how many substitutes there are. Two gas stations at one intersection charge nearly the same price because drivers can switch, but the 7-Eleven with many pumps, a big store, and 24-hour service runs a couple of cents above the two-pump Mobil across the street, because the good is a bundle (gasoline plus convenience plus a shorter wait) and the two bundles are not perfect substitutes. The TopHat check: a seller cuts price where demand is elastic, and revenue rises because the quantity gain outweighs the price cut. The tempting wrong answer, “revenue rises because buyers are necessarily better off,” confuses two different things: consumer surplus does rise with every price cut, but that says nothing about revenue, which can be falling at the same time.

The frost, resolved

Run the frost on the schedule. Halve the crop from the $3 row: quantity 8 to 4, price $3 to $7, revenue $24 to $28. Inelastic over that interval, and the growers take in more. Halve it from the $5 row: quantity 6 to 3, price $5 to $8, revenue $30 to $24, elasticity 1.44, elastic, and the growers take in less. Same event; the only difference is where on the curve it happened. So rising revenue after a quantity cut is the signature of inelastic demand over that interval. On the board, the same point: cut quantity from Q₀ to Q₁ in the inelastic range and revenue rises; cut it again from Q₁ to Q₂, past the unit-elastic point, and revenue falls.

Less gas slides up the curve; more drivers shift it

Gas prices jumped this weekend: slide or new curve? All else equal, a slide. Think of the gasoline available in Boca this week as a fixed stock. A low stock selects a high price on the same demand curve, a high stock a low one, and elasticity says how much people cut back as the price climbs. The instructor’s own figure for the short-run price elasticity of gasoline demand is about 0.3, very inelastic, because how much you drive is set by your job and your family, and you will not change your car overnight. Given time, the room listed the margins that open up: a more efficient or electric car, public transit, walking and biking, remote work, a different job, a home closer to work. Now hold the stock fixed and add drivers: summer road trips nationwide, snowbirds in Boca every winter. The whole curve shifts right, the price rises at an unchanged quantity, and nobody slid anywhere. Keep the two apart. The TopHat check asked exactly this (a holiday adds drivers, the stock is unchanged), and the answer is a rightward shift of the demand curve with price rising as a result; a movement along the curve would need the stock to change, and the stock did not.

The gas-station owner: which effect wins?

A student’s question from last week, answered with a picture. The owner buys gas at P₁ and, as a driver, uses Q₁. The price rises to P₂. Holding his demand curve fixed, he slides up it to Q′ and buys less: the substitution effect, biking to work one day a week, working from home. But the higher price raises the owner’s income, and if gasoline is a normal good for him, his whole demand curve shifts right: the wealth effect (the instructor uses “income effect” and “wealth effect” interchangeably). If the shift is large, he ends up buying more gas than before the price rose. That is not a violation of the law of demand, because the law says all else equal, and all else was not equal: his income changed. If the shift is small, substitution wins and he buys less, though less than a non-owner would cut. For the population as a whole the ownership channel is tiny, since almost nobody owns a gas station, so for the market the substitution effect is what matters.

Movement 03 · Time

“A 10% gas price rise won’t change my driving”

The usual objection, and nothing in economics says it is wrong about tomorrow. Wake up to gas at double today’s price and you will drive about as much tomorrow as you planned to, because tomorrow is already locked in. Your extreme short-run demand curve is nearly vertical, and the measured short-run elasticity of about 0.3 says a 1% price change moves quantity only about a third of a percent. But over time more options become viable, all the ones the room had already listed, and people get far more sensitive to price. On the board: from the steep curve D₀, the operative curve flattens through D₁, D₂, D₃, and at the same higher price the cut in gasoline bought grows and grows. This is the second law of demand: the longer a price change is expected to remain in effect, the more elastic demand becomes. A last question, why gas stations do not simply raise prices if demand is so inelastic: because a station in Boca is one of many, and the one across the intersection is a near-perfect substitute; a lone station in a small town might get away with it.

What continues Thursday

Class stopped at the second law of demand. Still to come from this topic: the real price of a good is its relative price (candy goes from $4 to $5 while ice cream goes from $2 to $3: did candy get more expensive?), why so much of Maine’s best lobster is eaten in Chicago, and the four-tools recap that turns “how much” into a prediction. Thursday’s class gets its own recap and transcript page. The instructor also promised a Canvas practice tool that adds cost to the revenue table, in answer to Tuesday’s questions.

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

Example from class	Economic lesson
Market value $10, $18, $24, $28, $30, $30, $28 …	Along one straight line, revenue rises, flattens, and falls; the flat step is unit elastic, and elasticity falls from 6.3 to 0.16 as you move down.
Selling the first unit for $9 instead of $10	A price cut sells one more unit but gives up a dollar on every unit already sold; eventually the give-up wins and revenue falls.
Two parallel curves, 0.57 units each, 1.33 versus 0.67	Elasticity is not slope: the same unit response is a larger percentage of a smaller base.
$6 and five units to $7 and four; $3 and eight to $4 and seven	A price rise lowers revenue where demand is elastic ($30 to $28) and raises it where demand is inelastic ($24 to $28).
“Why not sell at $4, or even give it away?”	Sellers maximize profit, not revenue; without cost the question cannot be settled, and with zero cost the seller is indifferent between $6 and $5.
A monopolist and the inelastic range	A firm with pricing power never prices where demand is inelastic; it could always restrict output, raise price, and collect more.
The only Jimmy John’s in town	Pricing power depends on substitutes, and substitutes depend on how you define the market; the grocery store sells cold cuts too.
The 7-Eleven and the Mobil across the street	Near-perfect substitutes sell at nearly the same price; a couple of cents of difference prices the rest of the bundle (pumps, store, hours, wait).
“Revenue rises because buyers are better off”	Consumer surplus rises with every price cut; revenue can be falling at the same time. Two different questions.
Half the oranges from the $3 row versus from the $5 row	Rising revenue after a quantity cut is the signature of inelastic demand over that interval; the same halving higher up the line lowers revenue.
Low, mid, and high gasoline stocks in Boca	A change in the amount on hand selects a different price on the same curve: a slide, which elasticity describes.
Snowbirds in winter, road trips in summer	More buyers shift the whole demand curve; the price rises at an unchanged quantity, and no elasticity of demand describes it.
The gas-station owner who buys more after the price rises	Substitution slides him up his curve; the wealth effect shifts the curve right; when the shift is big enough he buys more, and the law of demand still holds because all else was not equal.
Short-run gasoline elasticity of about 0.3	Tomorrow’s plans are locked in, so the very-short-run curve is nearly vertical; inelastic is not the same as unresponsive.
D0, D1, D2, D3 fanning out on the board	The second law of demand: the longer a price change is expected to hold, the more elastic demand becomes, as cars, commutes, jobs, and homes change.

Question 1 — On the class schedule, the price is cut from $8 to $7 and quantity demanded rises from 3 to 4. Compute the midpoint elasticity of that step and classify it. What happens to market value?

Quantity: 1 ÷ 3.5 = 28.6%. Price: 1 ÷ 7.5 = 13.3%. Elasticity = 28.6 ÷ 13.3 ≈ 2.1, elastic. Market value rises from $24 to $28: the quantity side won, as it always does above the unit-elastic step.

Question 2 — Now the step from $4 to $3, with quantity going 7 to 8. Same $1 cut, same one extra unit. Is this step elastic too?

No. Quantity: 1 ÷ 7.5 = 13.3%. Price: 1 ÷ 3.5 = 28.6%. Elasticity = 0.47, inelastic. The dollar step and the unit step are the same as in Question 1; only the bases changed. That is the whole point of the table: a straight line does not have one elasticity. Market value falls from $28 to $24.

Question 3 — Two demand curves are parallel. Does the steeper-looking one on your sketch have the lower elasticity?

Parallel curves have the same slope, so neither is steeper. The one farther from the origin measures the same quantity response against a larger quantity, so its percentage change, and its elasticity, is smaller over the same price interval: 0.67 against 1.33 in class. Read the percentages, not the tilt.

Question 4 — A transit agency finds that riders barely change their trips when the fare moves. To collect more revenue, should it raise or cut the fare?

Raise it. “Barely change” means inelastic, and with inelastic demand the price side of the ratio wins: quantity falls proportionally less than the fare rises, so total revenue goes up. (Whether that is the agency’s goal, and what it does to riders, are separate questions.)

Question 5 — A frost halves an orange crop from 6 units to 3 and the growers’ revenue falls from $30 to $24. What must have been true of the demand for oranges over that interval?

Elastic. Quantity fell and revenue fell with it, so the quantity side won; in class the elasticity of that halving was 1.44. Rising revenue after a quantity cut is the signature of inelastic demand, and this is the opposite case.

Question 6 — A classmate says: “When a seller cuts the price, buyers gain surplus, so revenue must rise.” Where is the error?

The first half is true and the second does not follow. Consumer surplus rises with every price cut along a fixed demand curve. Revenue rises only if demand is elastic over that step; past the unit-elastic point revenue falls while surplus keeps rising. Buyers’ gains and the seller’s take are two different questions.

Question 7 — A cold snap in the north sends snowbirds to Boca and gasoline sales jump at a higher price. Does the higher price show that demand is inelastic?

No. More buyers shifted the whole demand curve to the right; the price rose because demand rose, not because the stock of gasoline fell. Elasticity describes a slide along a fixed curve when the amount on hand changes. A shift tells you nothing about elasticity.

Question 8 — Gas prices rise and the owner of a gas station ends up driving more than before. Is his demand curve upward sloping?

No. Two things happened. The higher price slid him up his old curve (substitution: less gas), and the higher price made him richer, which shifted his whole curve to the right (wealth effect). The shift was large enough to outweigh the slide. Both curves slope down, and the law of demand still holds, because “all else equal” was violated: his income changed.

Question 9 — Would a monopolist ever price where demand for its product is inelastic?

Not if it wants to maximize profit. In the inelastic range it could restrict output, raise the price, and collect more revenue while producing less, whatever its costs. So it prices at the unit-elastic point or in the elastic range. A price-taking firm in a competitive market cannot move the price, so a competitive market can sit on an inelastic stretch of the market demand curve.

Question 10 — Gasoline doubles in price overnight and stays there. When is the cut in gasoline consumption larger: after one year, or after three?

After three years. In the first days almost nothing changes; over a year people carpool, ride transit, and sell the truck; over several years cars, commutes, jobs, and homes are chosen around the new price. The operative demand curve flattens from D₀ out to D₃. That is the second law of demand.

Bottom line

Elasticity is a property of a price interval, not of a curve: it falls as you move down a straight line and it is never the slope. It tells a seller whether quantity or price wins when the price moves, which is why a frost that halves the crop can raise the growers’ take, and why a firm with pricing power never sits in the inelastic range. It describes a slide along one demand curve, never a shift of it, so more drivers, or an owner made richer by the price rise, are different pictures. And it grows with time, because the cheap adjustments come first and the expensive ones later. Thursday finishes the topic with the real price of a good.