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This recap covers the opening of the elasticity topic, delivered in the last 24 minutes of the September 3 class after the demand topic wrapped up (that wrap-up has its own recap and transcript). Class stopped at the midpoint formula, and the topic continues Tuesday. Read the five-step diagnostic first. Then use the two 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.

What you should be able to do

1. Define the price elasticity of demand, compute it from two percentage changes with quantity on top and the sign dropped, and classify the result as elastic, inelastic, or unit elastic.
2. Explain why elasticity is not the slope, why it changes along a straight line, and why it always describes a slide along a fixed demand curve.
3. Turn two price–quantity pairs into midpoint percentage changes and an elasticity, and predict from the substitutes available whether a good’s demand is elastic or inelastic.

Opening · Why put a number on it

The frost question is a question about a number

Everything so far has been qualitative. A frost raises the price of oranges, so people buy fewer per week — but how many fewer? “A lot” is not a prediction. Elasticity turns a direction into a magnitude, and it is worth the effort for two reasons: it does heavy lifting later in the course, and it lets an informed citizen see through a great deal of nonsense about who really pays a tax and who really gains or loses from a price control.

The puzzle from the demand wrap-up was restated as the opening question: a frost kills half the crop, yet growers take in more dollars than the full crop would have brought. Buyers lost surplus; we know that. What must be true of the demand for oranges for revenue to rise when quantity falls? The answer is a number, and the class did not reach it — it is the target for Tuesday. The roadmap: today, how big is the response and why we care; next week, gains from exchange.

Movement 01 · Measuring the response

Elasticity is a ratio of two percentages, and it is never the slope

Price rises 1% and quantity demanded falls 3%. The price elasticity of demand is the ratio of the two percentage changes, quantity over price: 3. The raw ratio is negative, always, because of the law of demand — so economists report the absolute value. A 1% price cut that raises quantity 3% has the same elasticity, 3. The number says: a 1% change in price moves quantity demanded by 3%, in the opposite direction.

A student asked whether elasticity is just the slope. No. On the board: the percentage change in quantity is ΔQ/Q and the percentage change in price is ΔP/P, so the ratio contains the slope of the demand curve — but multiplied by a price-to-quantity term that changes as you move along the curve. That is why even a straight-line demand curve does not have one elasticity; only a rectangular hyperbola holds elasticity constant. Slope matters for the calculation, but it is not the calculation.

The vocabulary. Elastic, e greater than 1: quantity responds more than proportionally — the 3-to-1 case, or a 10-to-1 case where buyers are extremely sensitive. Inelastic, e less than 1: price rises 1% and quantity falls only half a percent. Unit elastic, e equal to 1: equal proportions, the dividing line. What makes demand inelastic is a shortage of substitutes. Insulin: diabetics can adjust diet a little, but they do not slash their doses when the price rises. Yet even insulin does not have the vertical demand curve people imagine — that would mean an infinite marginal worth, and the maker could charge anything at all. Coke, by contrast, is elastic: there is Pepsi, and if the good is “sugary drinks” there is Gatorade and every energy drink too. The copper question sharpened the rule: market demand is the sum of demands by use, and copper for wiring (no substitute for the home builder) is far less elastic than copper for coins (zinc will do), so the elasticity of a good depends on how you define the good.

One more guardrail, from a student’s question: elasticity is always a slide. It holds the demand curve fixed and asks how much quantity demanded moves along it when the price moves. An increase or decrease in demand is a shift, and elasticity has nothing to say about it — it would be nonsensical to measure a response along a curve that is jumping around. The TopHat check made the definition concrete: price down 1%, quantity demanded up 3%. Elastic, 3. The tempting 0.33 is the ratio upside down — price over quantity. “Negative 3, so elastic” gets the sign of the raw ratio right but forgets the convention; “3, so inelastic” gets the classification backwards.

Then the arithmetic problem the course solves once and for all. A price cut from $10 to $9 is a 10% cut — but going back from $9 to $10 is an 11.1% rise. Same step, two percentages. The midpoint formula divides each change by the average of its two endpoints instead of by the starting point: for the price, 1 ÷ 9.5. Worked in full: price $6 → $5 and quantity 5 → 6. The quantity change is 1 over an average of 5.5, or 18.2%; the price change is also 1 over 5.5, or 18.2%. The ratio is 1 — unit elastic. The homework and the Achieve e-book use this formula, and it is the one elasticity calculation you will do by hand in this course.

What continues Tuesday

Class stopped at the midpoint formula. On Tuesday, September 8, the topic picks up there: computing an elasticity yourself, why elasticity falls as you move down a straight-line demand curve, two parallel curves with different elasticities, the rule linking elasticity to a seller’s revenue — which finally answers the frost question — the gas-station owner and the difference between less gas and more drivers, the “a 10% gas price rise won’t change my driving” objection, why the response to a price change grows over time, and what the real price of a good is (why so much of Maine’s best lobster is eaten in Chicago). TopHat questions count from Tuesday. Tuesday’s class gets its own recap and transcript page.

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

Example from class	Economic lesson
Half the oranges, more dollars	Whether revenue rises when quantity falls depends on a number — the elasticity of demand. (Resolved Tuesday.)
Price up 1%, quantity down 3%	Elasticity is the ratio of the two percentages, quantity on top, reported as a magnitude: 3, elastic.
Who pays taxes; who gains from price controls	Elasticity is the tool for judging policy claims about burdens and benefits, not just a textbook ratio.
ΔQ/Q over ΔP/P on the board	The slope is inside the formula but is not the formula; elasticity changes along a straight line, and only a rectangular hyperbola holds it constant.
Insulin	Few substitutes make demand inelastic — but not vertical; a vertical curve would mean infinite marginal worth.
Coke, Pepsi, Gatorade, energy drinks	More substitutes, and a narrower definition of the good, make demand more elastic.
Copper for wiring versus copper for pennies	Market demand sums the demands by use; each use has its own elasticity, set by the substitutes available in that use.
“Is elasticity a slide or a shift?”	Always a slide: elasticity measures quantity demanded moving along a fixed demand curve.
The 0.33 answer on the TopHat question	The ratio upside down — price over quantity. Quantity goes on top.
$10 to $9 is 10%; $9 to $10 is 11.1%	Percent changes depend on the base; the midpoint (the average of the two endpoints) removes the ambiguity.
$6 to $5, 5 units to 6	Midpoint changes of 18.2% on both sides give an elasticity of exactly 1: unit elastic.

Question 1 — The price of a good falls 2% and quantity demanded rises 1%. What is the elasticity, and how do you classify it?

0.5, inelastic. Quantity over price: 1% ÷ 2% = 0.5. Quantity responded less than proportionally to the price change. Note that inelastic does not mean nobody responded — quantity did rise, just by less than the price fell.

Question 2 — A classmate divides 1% by 3% and reports an elasticity of 0.33 for the TopHat question. What went wrong?

The ratio is upside down. Elasticity is the percentage change in quantity divided by the percentage change in price: 3% ÷ 1% = 3, elastic. Dividing price by quantity measures nothing the course uses.

Question 3 — Why is the demand for insulin inelastic, and why is it still not a vertical line?

Inelastic because there are few substitutes: a diabetic can adjust diet somewhat, but cannot switch to a rival product the way a Coke drinker switches to Pepsi. Not vertical because a vertical demand curve would mean the marginal unit is worth an infinite amount — and then the maker could charge any price at all. No real good looks like that.

Question 4 — The price of copper doubles. Which falls more, the quantity of copper demanded for house wiring or for coins? Why?

Coins. A mint can substitute zinc; a home builder has no substitute for copper wire. Each use has its own elasticity, set by the substitutes available in that use, and the market demand for copper sums the two. The elasticity of “copper” depends on which copper you mean.

Question 5 — Is a steeper demand curve always a less elastic one?

Not as a rule. Slope is part of the elasticity calculation but not all of it: elasticity is ΔQ/Q over ΔP/P, so the price-to-quantity ratio at the point you are measuring matters too. That is why elasticity changes along a single straight line. Steeper is a useful rough guide, not a definition.

Question 6 — Using the midpoint formula, what is the percentage change in price when a price falls from $10 to $9?

The change is $1; the midpoint is ($10 + $9) ÷ 2 = $9.50. So the percentage change is 1 ÷ 9.5 = 10.5% — the same whether you go from $10 down to $9 or from $9 up to $10, which is the point of using the midpoint.

Question 7 — Price falls from $6 to $5 and quantity rises from 5 units to 6. Compute the elasticity with the midpoint formula.

Quantity: 1 ÷ 5.5 = 18.2%. Price: 1 ÷ 5.5 = 18.2%. Elasticity = 18.2 ÷ 18.2 = 1, unit elastic — a price fall of 18.2% raised quantity demanded by 18.2%.

Question 8 — A new highway brings more drivers to town and gasoline sales jump 20% at an unchanged price. Does that show the demand for gas is elastic?

No. The price did not change; the demand curve shifted because a held-constant condition (the number of buyers) changed. Elasticity describes a slide along a fixed demand curve when the good’s own price moves. A shift tells you nothing about elasticity.

Bottom line

Elasticity puts a number on the law of demand: the percentage change in quantity demanded over the percentage change in price, quantity on top, sign dropped. Above 1 the quantity side wins and demand is elastic; below 1 the price side wins and demand is inelastic; at 1 they tie. Substitutes drive the number, it always describes a slide along a fixed curve, it is not the slope, and it is computed against the midpoint so the answer does not depend on which way you travel. Tuesday turns that number into a prediction about revenue — and answers the frost.