Price Elasticity: Why the Same Demand Curve Can Make a Price Hike Cut Revenue

Elasticity is one of those words that sounds vague until you pin it to a number. Once you do, the same price hike that boosts revenue for one firm can quietly destroy it for another, and a piece of good news for farmers can turn into bad news for their income. This tutorial walks through Mankiw's Principles of Microeconomics (10th edition) Chapter 5 — the elasticity chapter — from definition to policy application, using the Cengage instructor slide deck as the spine. By the end, you should be able to compute the four elasticities from raw data, predict whether a price change raises or shrinks total revenue, and apply the framework to a fresh policy question on your own.

1. What Does the Elasticity Number Actually Measure?

Mankiw opens the chapter with a deliberately broad definition: elasticity is a "measure of the responsiveness of quantity demanded or quantity supplied to a change in one of its determinants." Mankiw 10e PPT The word "responsiveness" is older than the textbook — Alfred Marshall introduced it in 1890 in Principles of Economics, Book III, Chapter IV, where he wrote that demand's "elasticity (or responsiveness) is great or small according as the amount demanded increases much or little for a given fall in price." Marshall 1890 Marshall's geometric construction has since been replaced by a ratio of percentage changes, but the core idea is the same.

From definition to formula

The most common elasticity is the price elasticity of demand, which is just the percentage change in quantity demanded divided by the percentage change in price, with the minus sign dropped so the number is reported as positive:

Price elasticity of demand = |%ΔQd / %ΔP|

Two refinements matter before you compute anything. First, the percentage change is calculated with the midpoint method, dividing the change by the average of the starting and ending values rather than by the starting value alone. This makes the elasticity symmetric: going from $400 to $600 yields the same number as going from $600 to $400. Second, a negative sign from the law of demand is conventionally dropped — the elasticity is reported as a positive number, and the "direction" of the response is captured by the regime classification (elastic, inelastic, etc.) instead.

A worked example: the iPhone case

The deck's first Active Learning problem gives you the numbers to compute elasticity from scratch. iPhone quantity demanded falls from 10,600 units to 8,400 units when price rises from $400 to $600. Using the midpoint of $500 for price and the midpoint of 9,500 units for quantity:

• % change in price = ($600 − $400) / [(600 + 400) / 2] × 100 = 40%
• % change in quantity = (8,400 − 10,600) / [(8,400 + 10,600) / 2] × 100 = −23.16%
• Price elasticity = 23.16 / 40 = 0.58

An elasticity of 0.58 means the percentage drop in quantity is roughly six-tenths of the percentage rise in price — quantity is responding, but less than proportionally. This is the regime Mankiw labels inelastic.

Seeing the five regimes in one figure

Below is the first half of Figure 1 from the deck. All three panels use the same $4 → $5 price move so you can compare the quantity response across regimes.

Caption: Three-panel demand diagram on a shared price-change scaffolding. (a) A vertical demand line: price goes from $4 to $5 but quantity stays at 100 — perfectly inelastic, elasticity = 0. (b) A moderately steep demand curve: the same price move drops quantity from 100 to 90 — inelastic, elasticity < 1. (c) A flatter demand curve: the same price move drops quantity from 100 to 80 — unit elastic, elasticity = 1.

The second half of Figure 1 (panels d and e) completes the classification by showing the two regimes where quantity responds more than proportionally, or infinitely so.

Caption: Continuation of Figure 1. (d) A flatter demand curve: a 22% price rise produces a 67% quantity drop (100 to 50) — elastic, elasticity > 1. (e) A horizontal demand line at $4: any price above gives zero quantity, any price below gives infinite quantity, and exactly $4 is willing to absorb any quantity — perfectly elastic, elasticity = ∞.

Putting the two halves together, the five regimes of price elasticity of demand are:

2. Why Is the Number Different for Different Goods?

The iPhone's elasticity of 0.58 is not a fixed property of iPhones — it would change if you narrowed the market to "iPhones among teenagers with a free iPad upgrade available" or widened it to "all consumer electronics." Mankiw's slide deck lists four determinants that shift elasticity across goods:

1. Availability of close substitutes. Goods with close substitutes (one specific brand of soft drink) have elastic demand because buyers can switch. Goods with no close substitute (insulin for a diabetic) have inelastic demand.
2. Necessities versus luxuries. Necessities are inelastic; luxuries are elastic. A large price hike rarely makes a homeowner sell the house, but it can empty a luxury cruise ship.
3. Definition of the market. Narrowly defined markets are elastic; broadly defined markets are inelastic. "Food" is broadly defined and inelastic; "ice cream" is narrowly defined and elastic.
4. Time horizon. Demand is more elastic over longer horizons. Gasoline demand looks inelastic over a month (you still drive to work) but elastic over five years (you buy a hybrid, move closer to work, or switch jobs).

OpenStax's open-textbook mirror adds one further refinement: goods that take a large share of the household budget — housing, cars, vacations — tend to have more elastic demand because a given percentage price change hits total spending harder. OpenStax 3e Ch. 5 Think of it as a fifth lens sitting beside Mankiw's four.

So elasticity is not a property of the good itself but a joint output of (substitutability, necessity vs. luxury, market breadth, time horizon, budget share). Two goods with identical price-quantity data can sit in different regimes if they sit in different markets.

3. How Does the Number Decide Whether a Price Hike Raises or Shrinks Revenue?

The payoff of the elasticity concept is what it does to total revenue (TR), the amount paid by buyers and received by sellers, computed simply as price times quantity: TR = P × Q.

The revenue rectangle

Geometrically, TR is the rectangle under the demand curve at the current price-quantity point. The deck's Figure 2 makes this concrete.

Caption: A single-panel demand diagram. At a price of $4 and quantity of 100, the rectangle formed by P × Q under the demand curve equals $400 — that is, total revenue. The orange-filled area is the literal "area under the demand curve" Mankiw refers to when he says TR is the box under the curve.

Now the punchline: when price changes, TR changes too, but which way depends entirely on the elasticity regime.

Three regimes, three revenue outcomes

Elastic demand (|E| > 1): price and total revenue move in opposite directions. A price hike loses more revenue from the quantity drop than it gains from the higher price per unit. Inelastic demand (|E| < 1): price and total revenue move in the same direction. The quantity drop is proportionally smaller, so the higher price wins. Unit-elastic demand (|E| = 1): TR is unchanged when price changes. The deck's Figure 3 puts two of these regimes side by side.

Caption: Side-by-side comparison of revenue outcomes under the same $4 → $5 price move. (a) Inelastic demand: quantity falls from 100 to 90, and TR rises from $400 to $450 — the orange "extra revenue from selling at a higher price" rectangle is larger than the blue "lost revenue from selling fewer units" rectangle. (b) Elastic demand: quantity falls from 100 to 70, and TR falls from $400 to $350 — the blue lost-revenue rectangle dominates.

The intuition check: insulin is a necessity with no close substitute, so its demand is inelastic, and a 10% price hike pushes TR up (quantity falls less than 10%, so revenue rises). Luxury cruises have close substitutes and are luxuries, so demand is elastic, and a 20% fare cut pushes TR up (quantity rises more than 20%). Both answers come from the same rule, just applied to opposite regimes.

Slope is not elasticity

A subtle but common mistake is to read elasticity off the slope of the demand curve. A linear demand curve has a constant slope, but its elasticity changes along its length. The deck's Figure 4 and the accompanying elasticity schedule make this visible.

Caption: A linear demand curve from (0, $7) to (14, 0), with eight marked data points. The upper half (high price, low quantity) is bracketed as "Elasticity is larger than 1"; the lower half (low price, high quantity) is bracketed as "Elasticity is smaller than 1." A linear demand curve has constant slope but changing elasticity.

The eight-row elasticity schedule ties this to arithmetic. Reading along the line, elasticity moves through 13.0, 3.7, 1.8, 1.0, 0.6, 0.3, and 0.1 as we descend the curve. Total revenue reaches its maximum of $24 at exactly the unit-elastic point (P = $3, Q = 8). Above that point, a price cut increases revenue; below it, a price cut decreases revenue.

So a single linear demand curve can be elastic at the top, unit-elastic in the middle, and inelastic at the bottom — and revenue is maximized at the unit-elastic point. Slope tells you nothing about elasticity without knowing where on the curve you are.

4. What About Supply? And the Other Two Demand Elasticities?

Elasticity is not unique to demand. The deck defines three siblings.

Price elasticity of supply

Price elasticity of supply is defined the same way as on the demand side: percentage change in quantity supplied divided by percentage change in price. The same five regimes apply — perfectly inelastic (vertical supply), inelastic, unit elastic, elastic, perfectly elastic (horizontal supply) — and the same P $4 → $5 scaffolding makes the mirror image obvious.

Caption: First half of the supply-side Figure 5. (a) Perfectly inelastic supply: a vertical line at Q = 100, P moves $4 → $5 with zero quantity response. (b) Inelastic supply: a moderately steep upward-sloping line; the same price move raises quantity from 100 to 110 (a 22% price rise produces a 10% quantity rise, so Es < 1).

Caption: Single-panel unit-elastic supply. A 22% price rise from $4 to $5 produces a 22% quantity rise from 100 to 125. Es = 1.

Caption: Second half of the supply-side Figure 5. (d) Elastic supply: a flatter upward-sloping line; the same price move raises quantity from 100 to 200 (a 22% price rise produces a 67% quantity rise, so Es > 1). (e) Perfectly elastic supply: a horizontal line at P = $4; at exactly $4 producers will supply any quantity, above $4 supply is infinite, below $4 supply is zero.

Two determinants govern supply elasticity. First, the flexibility of sellers: can they switch inputs, use existing stocks, or hire new workers quickly? Second, the time horizon: supply is typically inelastic in the short run (capacity is fixed, contracts are signed) and elastic in the long run (new factories, new suppliers, new substitutes).

As a second worked example for the supply side, OpenStax's apartment-supply case gives a clean midpoint calculation: rent rises from $650 to $700 and quantity supplied rises from 10,000 to 13,000 units. The midpoint yields %ΔP = 7.4% and %ΔQ = 26.1%, so Es = 3.53 — clearly elastic, since a 1% rent rise brings a 3.5% quantity response. OpenStax 3e Ch. 5

Capacity-driven variation in supply elasticity

Just as elasticity changes along a linear demand curve, it can change along a single supply curve when firms hit a capacity ceiling. The deck's Figure 6 illustrates.

Caption: A convex upward-sloping supply curve with two labeled ranges. At low output (P $3 → $4, Q 100 → 200) the supply curve is elastic — a 29% price rise pulls a 67% quantity increase. At high output near capacity (P $12 → $15, Q 500 → 525) the same curve is inelastic — a 22% price rise pulls only a 5% quantity increase.

Income elasticity and cross-price elasticity

The deck also defines two more demand elasticities that fall outside the price-quantity framework but follow the same percentage-change ratio logic.

Income elasticity of demand = %ΔQd / %ΔIncome. A positive number means a normal good (demand rises with income); a negative number means an inferior good (demand falls with income).

Cross-price elasticity of demand = %ΔQd of good 1 / %ΔP of good 2. A positive number means substitutes (price of tea up → demand for coffee up); a negative number means complements (price of printers up → demand for ink cartridges down). OpenStax gives coffee/tea as the textbook substitute pair and coffee/sugar as the textbook complement pair.

5. Three Policy Stories Where the Number Decides the Outcome

The elasticity framework is not just an exercise in computing ratios. Mankiw's chapter closes with three applications where a single number — the elasticity of one side of the market — decides the qualitative outcome.

Application 1: Farming — good news can be bad news

A new wheat hybrid raises yield per acre by 20%. Supply shifts right from S₁ to S₂, price falls from $3 to $2, quantity rises from 100 to 110. Because wheat demand is inelastic, the price drop is proportionally larger than the quantity rise, and total revenue falls from $300 ($3 × 100) to $220 ($2 × 110). This is the so-called paradox of public policy: productivity gains that should make farmers better off can actually make them worse off.

Caption: A single-panel supply-and-demand diagram. Downward-sloping Demand crosses upward-sloping S₁ at ($3, 100) and the rightward-shifted S₂ at ($2, 110). The labeled sequence of annotation boxes walks through the inelastic-demand paradox: an increase in supply leads to a large fall in price, a smaller proportional rise in quantity, and a net fall in revenue from $300 to $220.

Application 2: OPEC — short-run vs. long-run price spikes

OPEC's 1973–1974 and 1979–1981 supply cuts produced large oil price spikes. Mankiw's framework says the size of the spike depends on the time horizon: in the short run, both supply and demand are inelastic, so a leftward supply shift pushes price up sharply; in the long run, both are elastic, so the same shift pushes price up only a little.

Caption: Two-panel oil-market diagram. (a) Short run: steep supply curves (S₁ and S₂) and a steep demand curve; the same leftward supply shift opens a large P₁-to-P₂ price gap. (b) Long run: flatter supply curves and a flatter demand curve; the same shift opens only a small P₁-to-P₂ gap.

The structural-VAR evidence in Kilian (2009) backs the short-run side of this story. Kilian identifies oil supply shocks using the assumption that "crude oil supply is assumed not to respond to innovations to the demand for oil within the same month" — the formal statement of a near-vertical short-run supply curve. His impulse-response grid shows that after a one-standard-deviation negative oil supply shock, production stays depressed for months and the price response is small and transitory. Kilian 2009

Caption: A 3×3 impulse-response grid from Kilian's structural-VAR analysis. Rows correspond to identified structural shocks (oil supply, aggregate demand, oil-specific demand); columns to response variables (oil production, real activity, real oil price). The relevant panel for the OPEC story is the top-left: an oil supply shock causes an immediate, sharp drop in oil production that only partially reverts within a year — confirming the textbook "vertical short-run supply" picture. Kilian 2009

Kilian's decomposition also delivers a harder lesson: most of the historical oil-price variability traces to demand shocks (global activity surges, precautionary demand around geopolitical events), not to OPEC supply cuts. The textbook "OPEC controls the price" story is qualitatively correct in the short run and quantitatively weaker than it sounds.

Application 3: Drug interdiction — inelastic demand and crime

Increase the number of federal drug-enforcement agents, and the drug supply curve shifts left. Equilibrium price rises, quantity falls, and — because short-run drug demand is inelastic (addicts keep using despite higher prices) — total revenue going to drug dealers rises. Higher dealer revenue means more competition for territory and more drug-related crime in the short run.

The long run flips this: as higher prices persist, they discourage experimentation and shrink the pool of new addicts, so demand becomes more elastic, interdiction revenue eventually falls, and drug-related crime decreases. Mankiw's text summarizes it as: drug interdiction increases drug-related crime in the short run but decreases it in the long run. Miron (2003) is the empirical anchor: prohibition raises cocaine and heroin prices substantially (though less than earlier estimates suggested), grounding the assumption that interdiction actually shifts the supply curve left in a measurable way. Miron 2003

6. Can You Use It on Something You Have Not Seen Before?

The whole point of the framework is that it transfers to new questions. Two exercises from the deck's closing slides test this.

Teen-smoking tax: a market-level vs. firm-level distinction

The government puts a $2 per pack tax on cigarettes; after one month, quantity demanded falls only slightly. Three conclusions follow. (A) Demand is inelastic in the short run — small quantity response to a substantial price hike. (B) If the industry colludes to raise the price further, TR will rise, because inelastic demand means price and TR move in the same direction. (C) But if only your firm raises its price while competitors hold theirs, that firm loses many customers and its revenue falls; the collusive outcome only works if all firms move together.

The (B) vs. (C) split is the lesson: the TR direction is a market-level prediction, not a firm-level one. Elasticity predicts how the industry moves, not how a single firm can exploit the situation.

Orange-crop storm: the inelastic-side test

A storm destroys half the orange crop. Is this more likely to hurt growers if demand is very elastic or very inelastic? Walk through the TR rule: if demand is very inelastic, quantity barely falls, so price rises proportionally more, and TR rises — growers are helped by the shortage. If demand is very elastic, price does not rise enough to offset the quantity loss, and TR falls — growers are hurt. So growers are more likely to be hurt when demand is elastic, and more likely to be helped when demand is inelastic.

Synthesis

The elasticity number is the lens. Once you know which side of the market is inelastic, you can predict the direction of price, quantity, and revenue for almost any supply-or-demand shift the textbook will throw at you. A technology shock that shifts supply right hurts producers if demand is inelastic (farming); it helps consumers either way. A supply restriction that shifts supply left helps producers if demand is inelastic (drug interdiction, short run); the same restriction is largely absorbed by consumers if demand is elastic (long-run OPEC). The elasticity number decides which story you are in.

References

1. Mankiw, N. G., Principles of Microeconomics (10th Edition), Chapter 5: Elasticity and Its Application — Cengage product page
2. Mankiw, N. G., Principles of Microeconomics (10th Edition), Cengage Instructor Slide Deck, Chapter 5 (uploaded PDF) — local file: parsed/content.md / Mankiw_PrinciplesofMicroeconomics_10e_PPT_week4.pdf
3. OpenStax, Principles of Microeconomics 3e, Chapter 5: Elasticity (Shapiro, MacDonald, Greenlaw; CC BY-NC-SA 4.0) — OpenStax Chapter 5
4. Marshall, A., Principles of Economics (1890), Book III, Chapter IV: "The Elasticity of Wants" — Marxists.org HTML
5. Kilian, L., "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," American Economic Review 99(3): 1053–69 (June 2009) — Working-paper PDF (June 2008)
6. Miron, J. A., "The Effect of Drug Prohibition on Drug Prices: Evidence from the Markets for Cocaine and Heroin," NBER Working Paper 9689 (May 2003); published in Review of Economics and Statistics 85(3): 522–530 — NBER WP 9689 PDF