Price Elasticity & Other Elasticities

In Section 2.1 we built two foundational ideas: when a price changes, quantity demanded moves in the opposite direction, and when a price changes, quantity supplied moves in the same direction. Those are statements about direction — they tell us "up or down," but they don't say anything about how much.

Here's the thing — direction alone isn't enough for serious analysis. Imagine you're the manager of a movie theater deciding whether to raise ticket prices by $2. You already know quantity demanded will fall (Law of Demand). But what you actually care about is: will my revenue go up or down? If your loyal customers barely react, raising the price puts more money in your pocket. If they bail at the first sign of a hike, raising the price could destroy your business.

The same question hits a senator deciding on a soda tax (will consumption really fall enough to fight obesity?), a farmer reacting to a drought (do higher prices fully offset lost crops?), and a transit authority raising bus fares (will revenue rise or fall?). All these decisions depend on the same concept: elasticity.

In this section, we'll meet four different elasticities — all built on the same percentage-change idea — and learn how to read what each one says. You'll see why elasticity is one of the most-tested concepts on the AP exam: it shows up in nearly every Unit 2 multiple-choice and appears again throughout Units 3, 4, and 6.

Let's start with the most important elasticity on the exam — the one that measures how much consumers respond to a change in the price of a good.

Why the Absolute Value?

By the Law of Demand, price and quantity demanded move in opposite directions — so technically, PED is always a negative number. A 10% rise in price brings a, say, 25% fall in quantity, giving −2.5. But that minus sign is just a leftover from the Law of Demand, not new information. To avoid the headache, economists (and the AP exam) take the absolute value. Going forward, we'll just write PED and treat it as positive.

A Quick Worked Example

Suppose a coffee shop raises the price of a latte from $4 to $5 — a 25% increase in price. Daily lattes sold fall from 200 to 150 — a 25% decrease in quantity. The PED is:

A PED of exactly 1 has a special name — "unit elastic." We'll get to what that means in a moment. For now, just notice the mechanic: compute two percentage changes, divide them, take the absolute value. That's it.

The number itself isn't the answer — what matters is what category it falls into. There are five named categories of PED, defined by where the coefficient sits relative to 1.

The Two Extreme Cases — Concrete Examples

The two extremes (perfectly inelastic and perfectly elastic) sound weird at first. Let me anchor them with real-world examples.

Visualizing the Five Cases

Why is demand for insulin nearly inelastic while demand for Cherry Coke is fairly elastic? Four factors drive a good's PED, and the College Board tests these directly on nearly every Unit 2 exam.

1. Availability of Substitutes (the biggest one)

The more close substitutes a good has, the more elastic its demand. If the price rises, consumers can easily switch — so quantity demanded falls a lot.

Examples:

• Pepsi — many substitutes (Coke, Dr Pepper, Sprite, sparkling water). Highly elastic. If Pepsi raises its price 10%, sales fall sharply as consumers switch.
• Insulin — no substitute for type 1 diabetics. Highly inelastic. Price changes barely affect quantity.
• Salt — almost no substitutes for the function it serves. Inelastic.

This single factor explains most of what you'll see on the AP exam. Whenever the question says "more close substitutes are available," elasticity rises.

2. Necessity vs. Luxury

Necessities tend to have inelastic demand — you keep buying them even when prices rise because you need them. Luxuries tend to have elastic demand — you can postpone or skip them entirely when prices rise.

Examples: Gasoline (necessity for commuters) → inelastic. A vacation cruise (luxury) → elastic. Prescription medications (necessity) → inelastic. Designer handbags (luxury) → elastic.

3. Share of Income Spent on the Good

The bigger the share of your budget a good takes up, the more elastic demand becomes. Why? Because a price change on a big-ticket item hits your budget hard, forcing you to reconsider. A price change on a tiny purchase barely registers.

Examples:

• Salt — costs pennies a year. Even if the price doubles, you won't really notice or reduce consumption. Inelastic.
• Cars — a major purchase. A 10% price increase translates to thousands of dollars, making buyers shop carefully and possibly delay. Elastic.

4. Time Horizon

The longer the time period, the more elastic demand becomes. In the short run, consumers are locked into habits and can't easily change. Given more time, they find substitutes, change behaviors, and adjust.

Classic example — gasoline:

• Short run (a week or two after price spike): You still need to drive to work, so you keep buying gas. Demand is inelastic.
• Long run (a few years): You consider buying a hybrid, moving closer to work, using public transit, or carpooling. Demand becomes much more elastic.

Summary Table

This is the single most heavily tested elasticity concept on the AP exam. The Total Revenue Test connects a producer's pricing decision to elasticity in a way you must know cold.

The Three Rules

Why? The Intuition

Suppose the seller raises the price by 10%. Two forces hit revenue:

• Price effect (positive): Each unit sold now brings in more money. This raises TR.
• Quantity effect (negative): Fewer units are sold. This lowers TR.

Which effect wins? Whichever percentage change is bigger:

The Classic AP Question Patterns

The College Board recycles this concept in three specific scenarios. Master each one:

Here's a subtle but heavily-tested point: even though a linear demand curve has a constant slope, its elasticity is NOT constant. It changes as you move down the curve — from very elastic at the top, through unit elastic in the middle, to inelastic at the bottom.

Why? Because elasticity depends on percentage changes, not absolute changes. Near the top of the curve, price is high and quantity is low. A $1 price drop is a small percentage of the high price, but the resulting quantity gain is a huge percentage of the tiny quantity. Result: %ΔQ >> %ΔP, so PED is large (elastic). At the bottom, the math reverses.

The Total Revenue Connection

Combine this with the Total Revenue Test, and you get a key insight: total revenue is maximized at the midpoint of a linear demand curve, where PED = 1. To the left of the midpoint (high prices, elastic region), lowering prices raises TR. To the right (low prices, inelastic region), raising prices raises TR. Both directions push you toward the midpoint.

Now flip to the producer side. Just like PED measures how responsive buyers are, PES measures how responsive sellers are to a price change.

Interpreting PES (Same Categories as PED)

The five categories work exactly the same way:

Quick Worked Example

If a 10% price increase causes quantity supplied to rise by 20%, then:

What Makes Supply Elastic vs. Inelastic?

Three factors drive PES:

• Time horizon — same logic as demand. Producers need time to expand capacity, build new factories, hire workers. Short run = inelastic. Long run = more elastic.
• Availability of inputs & ease of production — if a firm can quickly grab more raw materials and ramp up production, supply is elastic. If inputs are scarce or production is technically complex, supply is inelastic. Example: an oil refinery can't easily double output overnight, even if the price spikes — supply of oil is inelastic in the short run.
• Spare capacity — if firms have idle equipment and unused labor, they can quickly scale up production in response to a price rise. Supply is elastic. If they're already at maximum capacity, they can't easily produce more — supply is inelastic.

So far, both elasticities we've studied measured responsiveness to a price change. Now we shift to measuring responsiveness to an income change.

The Sign Tells You the Type of Good

This is where YED gets exam-worthy. The number's value tells you how strong the response is, but the sign tells you what kind of good you're looking at.

For Normal Goods: Necessity vs. Luxury (a Second Layer)

Within the category of normal goods (YED > 0), the magnitude of YED tells you whether the good is a necessity or a luxury:

• 0 < YED < 1 → income-inelastic normal good = necessity. Income rises but consumption rises by less. Examples: bread, milk, gasoline.
• YED > 1 → income-elastic normal good = luxury. Income rises and consumption rises by even more. Examples: yachts, designer clothing, fine dining.

Worked Example

When Tom's income rises by 10%, his quantity of golf balls purchased rises by 25%. Compute YED:

YED is positive (so golf balls are a normal good for Tom) AND greater than 1 (so they're an income-elastic normal good — a luxury for him). Both pieces of info come from a single coefficient.

The last of our four elasticities measures how the demand for ONE good responds to a price change in a DIFFERENT good. This is the formal way to identify whether two goods are substitutes, complements, or unrelated.

The Sign Tells You the Relationship

A Worked Example

When the price of butter rises by 10%, the quantity of margarine demanded rises by 15%. Compute XED:

XED is positive → butter and margarine are substitutes. The magnitude (1.5) tells you they're fairly close substitutes — consumers switch readily between them.

Here's a one-stop reference for all four elasticities. Before the exam, you should be able to fill this in from memory.

• "Slope and elasticity are the same thing." Wrong. Slope measures absolute changes; elasticity measures percentage changes. A linear demand curve has constant slope but changing elasticity along its length. They're related but not identical.
• "If demand is elastic, raising the price will raise revenue." Backwards. Elastic demand means quantity falls MORE than price rises, so revenue falls. The "I'll raise prices and make more money" reasoning only works when demand is inelastic.
• "A vertical demand curve is perfectly elastic." Backwards. Vertical = no response to price = perfectly inelastic. Horizontal = infinite response = perfectly elastic. Easy way to remember: a horizontal line is "flat as a pancake" — flat = elastic.
• "PED, YED, and XED are all positive." Only PED (in absolute value) is always positive. YED is positive for normal goods, negative for inferior. XED is positive for substitutes, negative for complements. Stripping the sign loses critical information.
• "All necessities have low PED, and all luxuries have high PED." Usually true, but not always. The four determinants (substitutes, necessity, share of income, time) sometimes pull in different directions. Coffee is "non-essential" for many but has few substitutes for daily caffeine drinkers — making it less elastic than the luxury label suggests.
• "In the long run, demand becomes less elastic because people get used to higher prices." Opposite. In the long run, consumers find substitutes, change habits, and adapt — making demand more elastic over time. The short run is when people are stuck in their patterns.
• "Income elasticity of zero means demand is constant." It means demand doesn't respond to income, but it could still respond to price changes (PED ≠ 0) or to other goods' prices (XED ≠ 0). Each elasticity is independent.
• "If the price elasticity of supply is 0.5, the supply curve is elastic." No. PES = 0.5 means quantity supplied changes by HALF the percentage that price changes — that's inelastic. PES > 1 is elastic; PES < 1 is inelastic; PES = 1 is unit elastic. The same thresholds apply as for PED.