Microeconomics Essentials: Price Elasticity of Demand—Responsiveness and Revenue

What Price Elasticity of Demand Measures

Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its price. It is defined as the percentage change in quantity demanded divided by the percentage change in price:

PED = (%ΔQd) / (%ΔP)

Because price and quantity demanded typically move in opposite directions, PED is usually negative. In practice, economists often discuss the absolute value of elasticity (how large the response is), focusing on responsiveness rather than the sign.

Responsiveness is Not the Same as Slope

It is tempting to think elasticity is “the slope of the demand curve,” but they are different:

• Slope uses levels: ΔQ/ΔP (units of quantity per dollar).
• Elasticity uses percent changes: (%ΔQ)/(%ΔP) (unit-free).

That unit-free feature is why elasticity is better for comparing responsiveness across different goods (e.g., movie tickets vs gasoline) or across different price ranges.

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Elastic vs Inelastic: Categories and Limiting Cases

Using the absolute value |PED|:

• Elastic demand: |PED| > 1 (quantity responds more than proportionally to price).
• Inelastic demand: |PED| < 1 (quantity responds less than proportionally).
• Unit elastic demand: |PED| = 1 (proportional response).

Two limiting cases help anchor intuition:

• Perfectly inelastic demand: |PED| = 0. Quantity demanded does not change when price changes (a vertical demand curve).
• Perfectly elastic demand: |PED| → ∞. Even a tiny price increase causes quantity demanded to drop to zero (a horizontal demand curve).

How to Compute Elasticity with Percentage Changes

The Basic Percentage-Change Approach

The basic idea is:

• Compute % change in quantity demanded.
• Compute % change in price.
• Divide the first by the second.

However, a common problem appears: if you compute percentage changes using the starting value as the base, the result depends on which direction you move (from A to B vs B to A). To avoid that, economists often use the midpoint method.

The Midpoint Method (Recommended)

The midpoint method uses the average of the two values as the base for percentage changes:

%ΔQ = (Q2 − Q1) / ((Q1 + Q2)/2)

%ΔP = (P2 − P1) / ((P1 + P2)/2)

PED = (%ΔQ) / (%ΔP)

Computation Walkthroughs (Simple Numbers)

Walkthrough 1: Demand is Elastic

Suppose price rises from $10 to $12, and quantity demanded falls from 100 to 70.

Step 1: Compute %ΔQ using midpoint

Q1 = 100, Q2 = 70

ΔQ = 70 − 100 = −30

Average Q = (100 + 70)/2 = 85

%ΔQ = −30 / 85 = −0.3529 = −35.29%

Step 2: Compute %ΔP using midpoint

P1 = 10, P2 = 12

ΔP = 12 − 10 = 2

Average P = (10 + 12)/2 = 11

%ΔP = 2 / 11 = 0.1818 = 18.18%

Step 3: Compute PED

PED = (−35.29%) / (18.18%) = −1.94

In absolute value, |PED| = 1.94 > 1, so demand is elastic.

Walkthrough 2: Demand is Inelastic

Suppose price rises from $10 to $11, and quantity demanded falls from 100 to 95.

Step 1: %ΔQ

ΔQ = 95 − 100 = −5

Average Q = (100 + 95)/2 = 97.5

%ΔQ = −5 / 97.5 = −0.0513 = −5.13%

Step 2: %ΔP

ΔP = 11 − 10 = 1

Average P = (10 + 11)/2 = 10.5

%ΔP = 1 / 10.5 = 0.0952 = 9.52%

Step 3: PED

PED = (−5.13%) / (9.52%) = −0.54

|PED| = 0.54 < 1, so demand is inelastic.

Walkthrough 3: Unit Elastic (Revenue-Neutral at the Margin)

Suppose price rises from $10 to $11, and quantity demanded falls from 100 to 90.

ΔQ = −10, Average Q = 95 ⇒ %ΔQ = −10/95 = −10.53%

ΔP = 1, Average P = 10.5 ⇒ %ΔP = 1/10.5 = 9.52%

PED ≈ (−10.53%) / (9.52%) ≈ −1.11

This is slightly elastic. To get exactly unit elastic with midpoint, you would need the percentage drop in Q to match the percentage rise in P in absolute value. The key idea: unit elastic means proportional changes.

Quick Classification Table

Determinants of Price Elasticity of Demand

1) Availability of Close Substitutes

The more and closer the substitutes, the easier it is for consumers to switch away when price rises, making demand more elastic.

• More elastic: one brand of breakfast cereal among many similar cereals.
• More inelastic: a medication with no close alternative for a specific condition.

2) Necessity vs Luxury

Necessities tend to have more inelastic demand because consumers feel they must buy them even when price rises. Luxuries tend to be more elastic because consumers can postpone or avoid them.

• More inelastic: basic utilities for many households.
• More elastic: premium add-ons or high-end discretionary purchases.

3) Time Horizon

Demand is often more elastic in the long run than in the short run because consumers have more time to adjust behavior, find alternatives, or change habits.

• Short run: if gasoline prices rise this week, commuting patterns may not change much immediately.
• Long run: over months/years, people may move closer to work, carpool, buy a more fuel-efficient car, or use public transit.

4) Share of Budget (Importance in Spending)

If a good takes a large share of a consumer’s budget, a price change has a bigger impact on their finances, so they are more likely to adjust quantity demanded (more elastic). If it is a tiny share, consumers may not bother changing behavior (more inelastic).

• More elastic: a major monthly expense like rent (for many people, within constraints).
• More inelastic: a small item like a single spice purchase.

Elasticity and Total Revenue

Total revenue (TR) is:

TR = P × Q

When price changes, total revenue changes depend on which effect dominates:

• Price effect: higher price tends to raise revenue per unit.
• Quantity effect: higher price tends to reduce units sold.

Elasticity tells you which effect is stronger.

Revenue Rule of Thumb

• If demand is elastic (|PED| > 1): a price increase decreases TR; a price decrease increases TR.
• If demand is inelastic (|PED| < 1): a price increase increases TR; a price decrease decreases TR.
• If demand is unit elastic (|PED| = 1): TR is approximately unchanged when price changes (the two effects offset).

Revenue Walkthrough Using Numbers

Revisit Walkthrough 1 (elastic): price rises from $10 to $12, quantity falls from 100 to 70.

• Initial TR = 10 × 100 = 1000
• New TR = 12 × 70 = 840

Even though price is higher, the quantity drop is large enough that total revenue falls. That matches elastic demand.

Revisit Walkthrough 2 (inelastic): price rises from $10 to $11, quantity falls from 100 to 95.

• Initial TR = 10 × 100 = 1000
• New TR = 11 × 95 = 1045

Here the quantity drop is small, so total revenue rises. That matches inelastic demand.

Application Questions (Check Your Understanding)

Classify Elasticity and Predict Revenue

• Q1. Demand is elastic. If price rises, what happens to total revenue? Explain using the price effect vs quantity effect.
• Q2. Demand is inelastic. If price falls, what happens to total revenue? Why?
• Q3. Demand is unit elastic. If price rises by 10%, what must happen (approximately) to quantity demanded in percentage terms? What happens to total revenue?

Compute Elasticity (Midpoint Method)

• Q4. Price falls from $20 to $18 and quantity demanded rises from 50 to 60. Compute PED using midpoint steps: average values, % changes, then the ratio. Is demand elastic or inelastic?
• Q5. Price rises from $5 to $6 and quantity demanded falls from 200 to 190. Compute PED and classify it.

Determinants: Reasoning Scenarios

• Q6. Which is likely more price elastic: a specific brand of bottled water or “water” as a broad category? Use substitutes to justify.
• Q7. A streaming service raises its monthly price. Over the next week, cancellations are small, but over the next year, cancellations grow. Which determinant is driving the change in elasticity over time?
• Q8. Two goods experience the same 10% price increase. For which good is quantity demanded more likely to change: a $2 item bought occasionally or a $1,200 annual expense that most households pay? Use share of budget reasoning.