Difficulty: Introductory-Intermediate | Prerequisites: understanding of demand curves, how to read and interpret graphs, basic algebra.
Price elasticity measures how sensitive quantity demanded is to a price change. It is the single most useful number in applied microeconomics: firms use it to set prices, governments use it to forecast tax revenue, and your exam will certainly test it. Consumer surplus quantifies the benefit buyers get from paying less than what they would have been willing to pay. Together, elasticity and consumer surplus let you evaluate market outcomes and policy changes in dollar terms.
Price elasticity of demand tells you the percentage change in quantity demanded per percentage change in price. If |E| > 1, demand is elastic and a price increase loses revenue; if |E| < 1, demand is inelastic and a price increase gains revenue. Consumer surplus is the area between the demand curve and the market price, representing the total "bonus" buyers enjoy from the transaction.
Price elasticity of demand (PED)
The percentage change in quantity demanded divided by the percentage change in price. Conventionally reported as a negative number (or as an absolute value). Think of it as: how dramatically buyers react when the price moves.
Elastic demand
|PED| > 1. Quantity demanded is highly responsive to price changes. A small price increase causes a proportionally larger drop in quantity. In simple terms, this means buyers are price-sensitive.
Inelastic demand
|PED| < 1. Quantity demanded is not very responsive to price changes. Think of it as: buyers keep buying even when the price goes up (necessities, addictive goods).
Unit elastic demand
|PED| = 1. The percentage change in quantity exactly matches the percentage change in price. Total revenue is unchanged by a small price change.
Total revenue test
A shortcut for determining elasticity from revenue changes. If a price increase raises total revenue, demand is inelastic. If a price increase lowers total revenue, demand is elastic.
Consumer surplus
The difference between what consumers are willing to pay (their maximum valuation, read from the demand curve) and what they actually pay (the market price). Graphically, it is the area below the demand curve and above the price line. Think of it as: the "deal" consumers get.
Market demand
The horizontal summation of all individual demand curves. At each price, add up every buyer's quantity demanded.
Inverse demand curve
The demand curve written with price as a function of quantity (P = f(Q)), rather than the standard Q = f(P). Useful for graphing (price on the vertical axis) and calculating consumer surplus.
Amazon raised its monthly Prime Student price from $7.59 to $8.99. Subscribers were projected to fall from 12.1 million to 7.8 million.
Percentage change in price: (8.99 - 7.59) / 7.59 = 1.40 / 7.59 ≈ 18.4%
Percentage change in quantity: (7.8 - 12.1) / 12.1 = -4.3 / 12.1 ≈ -35.5%
PED: -35.5% / 18.4% ≈ -1.93
The absolute value is about 1.93, meaning demand is elastic. A 1% price increase leads to roughly a 1.93% decrease in subscribers.
Revenue check:
Before: $7.59 x 12.1 million = $91.84 million/month
After: $8.99 x 7.8 million = $70.12 million/month
Revenue fell, which is consistent with elastic demand: raising the price lost more in subscribers than it gained per subscriber.
The store has two customer types:
60 teenage buyers, each with inverse demand P = 20 - 5Q (so Q = (20 - P)/5 = 4 - P/5 for P ≤ 20)
32 college-aged buyers, each with inverse demand P = 20 - 4Q (so Q = (20 - P)/4 = 5 - P/4 for P ≤ 20)
To get market demand, multiply each individual demand by the number of buyers and add horizontally:
Total teen demand: 60 x (4 - P/5) = 240 - 12P
Total college demand: 32 x (5 - P/4) = 160 - 8P
Market demand: Q = 400 - 20P (for P ≤ 20)
At P = $12:
Q = 400 - 20(12) = 400 - 240 = 160
Point elasticity: E = (dQ/dP) x (P/Q) = (-20) x (12/160) = -1.5
Since |E| = 1.5 > 1, demand is elastic at P = $12. If the owner slightly increases the price, total expenditure (revenue) will decrease. Buyers cut back by a proportionally larger amount than the price rises.
At P = $6:
Q = 400 - 20(6) = 400 - 120 = 280
E = (-20) x (6/280) = -0.43
Since |E| = 0.43 < 1, demand is inelastic at P = $6. A small price increase here would increase total revenue.
The inverse market demand is P = 20 - Q/20. At P = $6, Q = 280.
Consumer surplus is the triangle between the demand curve and the price line:
Height of the triangle: 20 - 6 = $14
Base of the triangle: 280 units
CS = 0.5 x 14 x 280 = $1,960
Streaming services, gym memberships and subscription boxes all face this calculation: if they raise prices, will elastic demand cause enough cancellations to reduce revenue? The total revenue test gives the quick answer without needing calculus.
Price elasticity of demand (arc/midpoint method):
E = (%ΔQ) / (%ΔP) = [(Q2 - Q1)/Q1] / [(P2 - P1)/P1]
Point elasticity (using calculus):
E = (dQ/dP) x (P/Q)
Total revenue:
TR = P x Q
Total revenue test:
If |E| > 1 (elastic): price increase causes TR to fall.
If |E| < 1 (inelastic): price increase causes TR to rise.
If |E| = 1 (unit elastic): TR does not change.
Consumer surplus (linear demand):
CS = 0.5 x (P_max - P_market) x Q_market
where P_max is the vertical intercept of the demand curve (the maximum willingness to pay for the first unit).
Horizontal aggregation of demand:
Q_market(P) = n1 x q1(P) + n2 x q2(P) + ...
where n_i is the number of consumers of type i, and q_i(P) is each individual's demand at price P.
"Elasticity and slope are the same thing." They are not. Slope is dP/dQ (constant along a linear demand curve). Elasticity is (dQ/dP) x (P/Q), which changes at every point along a straight-line demand curve because the P/Q ratio changes.
"If demand is inelastic, raising prices always makes the firm better off." This is true only for small price increases near the current point. Large price changes can push you into the elastic region of the curve.
"Consumer surplus is the area under the entire demand curve." No. It is the area between the demand curve and the price line, only above the market price. The area below the price line represents what consumers actually spend.
"You add demand curves vertically to get market demand." You add them horizontally. At each price, sum the quantities each individual demands. Vertical addition is used for public goods, not private goods.
⚠️ Computing price elasticity from given data (percentage changes, not just absolute changes) is a near-certain exam question.
⚠️ The total revenue test is a fast way to check your elasticity calculation: if your number says elastic but revenue rises after a price increase, something is wrong.
⚠️ Consumer surplus as a triangle calculation appears frequently. Know the formula CS = 0.5 x base x height, and be able to identify the correct base and height from a graph.
⚠️ Be able to aggregate individual demand curves into a market demand curve by horizontal summation. This often involves working with inverse demand (P as a function of Q) and converting back and forth.
True or False: If |PED| = 2, demand is inelastic. (False, it is elastic)
Fill in the blank: Consumer surplus is the area below the ______ curve and above the ______ line. (demand; price)
True or False: If a firm raises its price and total revenue rises, demand must be inelastic at that point. (True)
Fill in the blank: To find market demand from individual demands, you sum quantities ______ at each price. (horizontally)
True or False: Elasticity is constant along a straight-line demand curve. (False)
Q: Amazon raises its Prime Student monthly fee from $7.59 to $8.99, and subscribers drop from 12.1 million to 7.8 million. What is the price elasticity of demand?
A: %ΔP = (8.99 - 7.59)/7.59 ≈ 18.4%. %ΔQ = (7.8 - 12.1)/12.1 ≈ -35.5%. PED = -35.5/18.4 ≈ -1.93. Demand is elastic.
Q: A comic book store faces market demand Q = 400 - 20P. At P = $12, what is the elasticity, and will a price increase raise or lower revenue?
A: At P = 12, Q = 160. E = (-20)(12/160) = -1.5. |E| > 1, so demand is elastic. A price increase will lower total revenue.
Q: Using Q = 400 - 20P, calculate consumer surplus at P = $6.
A: At P = 6, Q = 280. The demand curve's price intercept is P = 20. CS = 0.5 x (20 - 6) x 280 = 0.5 x 14 x 280 = $1,960.
Q: There are 60 consumers each with demand q = 4 - P/5 and 32 consumers each with demand q = 5 - P/4. What is the total market demand?
A: Total Q = 60(4 - P/5) + 32(5 - P/4) = 240 - 12P + 160 - 8P = 400 - 20P, for P ≤ 20.
Elasticity connects to consumer choice and income/substitution effects (Document 1): goods with many close substitutes tend to have elastic demand because the substitution effect is large. It also connects to utility maximisation and optimal bundles (Document 3): the marginal utility per dollar condition ensures that the consumer's choices are consistent with the demand curves from which elasticity is derived.
Price elasticity of demand, PED, elastic, inelastic, unit elastic, total revenue test, consumer surplus, producer surplus, deadweight loss, market demand, horizontal summation, inverse demand curve, demand aggregation, willingness to pay, reservation price, Amazon Prime Student, arc elasticity, point elasticity, midpoint method, microeconomics problem set 3, NYU intro micro