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Elasticity

Elasticity is a central concept in economics that quantifies the responsiveness of one economic variable to a change in another. Rather than merely indicating the direction of change, elasticity measures the magnitude of that change in percentage terms, allowing for standardized comparison across different goods, services, and markets.

This guide covers price elasticity of demand (PED), the total revenue test, income and cross-price elasticity, price elasticity of supply, tax incidence, advanced topics like marginal revenue relationships, worked examples, and a 10-question practice quiz.

Price Elasticity: From Elastic to Inelastic

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P ($)QDemand Curve0246810020406080100ElasticUnit ElasticInelasticTR ($)QTotal Revenue Curve050100150200250020406080100Max TR
Elastic (|E| > 1)
Unit Elastic (|E| = 1)
Inelastic (|E| < 1)
Step through to see how elasticity varies along a linear demand curve and affects total revenue.
Step 0 / 6
Watch how elasticity changes along a linear demand curve: elastic at high prices, unit elastic at the midpoint, and inelastic at low prices. Total revenue is maximized at the unit elastic point.

1Introduction

Elasticity is a dimensionless measure that expresses the percentage change in a dependent variable divided by the percentage change in an independent variable. This makes it independent of the units of measurement, enabling meaningful comparisons across different goods, currencies, and markets.

While basic supply and demand analysis tells us the direction of change, elasticity provides the critical quantitative dimension. It transforms qualitative predictions into measurable impacts — moving from statements like “a price increase will hurt sales” to “a 10% price increase will lead to a 15% decrease in sales, thereby reducing total revenue.”

Why Elasticity Matters

For Firms

Setting optimal pricing strategies. Knowing PED allows firms to predict how revenue will change with price adjustments and whether to raise or lower prices.

For Governments

Designing effective tax policies, subsidies, and trade regulations. Elasticity predicts who bears the burden of a tax (tax incidence) and the revenue generated.

For Market Analysis

Understanding competitive structures and the impact of external shocks. Income elasticity predicts how demand shifts with economic growth; cross-price elasticity reveals substitutability.

In Practice

In late 2022 and throughout 2023, the OPEC+ alliance announced significant oil production cuts. Given that oil demand is relatively inelastic in the short run (limited immediate substitutes, necessity for transport and industry), OPEC+ knew the resulting percentage increase in price would likely outweigh the percentage decrease in quantity demanded, thereby increasing their total revenue from oil sales.

Linear demand curve showing elastic, unit elastic, and inelastic regions along its length

2Key Definitions

Fundamental terms for understanding elasticity at the university level.

Elasticity

A measure of the responsiveness of one variable to a change in another, expressed in percentage terms

Price Elasticity of Demand (PED)

How much quantity demanded responds to a percentage change in price

Elastic Demand

|PED| > 1: percentage change in quantity exceeds percentage change in price

Inelastic Demand

|PED| < 1: percentage change in quantity is less than percentage change in price

Unit Elastic Demand

|PED| = 1: percentage changes in quantity and price are equal

Midpoint Method

Uses averages of initial/final values as base, ensuring consistent results regardless of direction

Total Revenue Test

Method to infer PED by observing how total revenue changes with price changes

Income Elasticity (IED)

How quantity demanded responds to a percentage change in consumers' income

Cross-Price Elasticity (CPED)

How quantity demanded of one good responds to a price change of another good

Price Elasticity of Supply (PES)

How quantity supplied responds to a percentage change in price

Substitutes

Goods with positive cross-price elasticity; price increase of one raises demand for the other

Complements

Goods with negative cross-price elasticity; price increase of one lowers demand for the other

3Price Elasticity of Demand (PED)

The Price Elasticity of Demand quantifies the sensitivity of quantity demanded to changes in price. Since the Law of Demand states that price and quantity demanded move in opposite directions, PED is almost always negative. Economists often report it as an absolute value.

Mathematical Formulation

The general formula for PED is: PED = %ΔQd / %ΔP

Point Elasticity (for infinitesimal changes): PED = (dQ/dP) × (P/Q)

Arc Elasticity (Midpoint Method): PED = [(Q2−Q1) / ((Q1+Q2)/2)] / [(P2−P1) / ((P1+P2)/2)]

Graphical Interpretation

On a linear demand curve, elasticity is not constant — it changes along the curve even though the slope is constant. This is because elasticity uses percentage changes, which depend on the base price and quantity.

Upper Portion

High price, low quantity: demand is elastic (|PED| > 1)

Midpoint

Demand is unit elastic (|PED| = 1)

Lower Portion

Low price, high quantity: demand is inelastic (|PED| < 1)

Determinants of PED

1. Availability of Close Substitutes (Most Important)

The more substitutes available, the more elastic the demand. Demand for a specific brand of coffee is more elastic than demand for coffee in general.

2. Necessity vs. Luxury

Necessities (basic food, essential medicines) tend to have inelastic demand. Luxuries (designer clothes, exotic vacations) tend to have elastic demand.

3. Time Horizon

Demand tends to be more elastic in the long run. Consumers have more time to find substitutes, change patterns, or adapt to new technologies.

4. Proportion of Income

Goods representing a large portion of the budget tend to have more elastic demand. A 10% car price increase has more impact than a 10% gum price increase.

5. Market Definition

Broadly defined markets (“food”) have more inelastic demand. Narrowly defined markets (“organic Fuji apples”) have more elastic demand.

4Total Revenue & Elasticity

Total Revenue (TR = P × Q) is the total amount of money a firm receives from sales. The relationship between PED and total revenue is one of the most practical applications of elasticity.

Elastic (|PED| > 1)

P↓ → TR↑
P↑ → TR↓

Price and TR move in opposite directions

Unit Elastic (|PED| = 1)

P↓ or P↑ → TR unchanged

TR is maximized

Inelastic (|PED| < 1)

P↓ → TR↓
P↑ → TR↑

Price and TR move in the same direction

Total Revenue Test

Quick Test
  • P and TR move in opposite directions → demand is ELASTIC
  • P and TR move in the same direction → demand is INELASTIC
  • TR remains unchanged → demand is UNIT ELASTIC
Total revenue curve showing how TR rises in the elastic region, peaks at unit elasticity, and falls in the inelastic region

5Other Elasticities

Income Elasticity of Demand (IED)

IED measures how quantity demanded responds to a percentage change in income: IED = %ΔQd / %ΔIncome.

Normal Goods (IED > 0)

Demand increases as income rises.

Necessities: 0 < IED < 1 (food, utilities)

Luxuries: IED > 1 (gourmet meals, travel)

Inferior Goods (IED < 0)

Demand decreases as income rises. Consumers substitute away from these goods as they become wealthier (e.g., instant noodles, public transport for some).

Normal goods vs inferior goods: demand shifts right for normal goods and left for inferior goods when income increases

Cross-Price Elasticity of Demand (CPED)

CPED measures how quantity demanded of good X responds to a price change of good Y: CPED = %ΔQx / %ΔPy.

Substitutes (CPED > 0)

Price of Y rises → demand for X rises (e.g., coffee and tea, Coke and Pepsi)

Complements (CPED < 0)

Price of Y rises → demand for X falls (e.g., cars and gasoline, printers and ink)

Unrelated (CPED ≈ 0)

Price change of Y has no significant impact on demand for X

Substitutes vs complements: demand for X shifts right when substitute Y price rises, shifts left when complement Y price rises

Price Elasticity of Supply (PES)

PES measures how quantity supplied responds to a percentage change in price: PES = %ΔQs / %ΔP. Unlike PED, PES is typically positive because price and quantity supplied move in the same direction.

Determinants of PES

  • Flexibility of sellers: How easily producers can switch inputs or adjust production
  • Time horizon: Supply is more elastic in the long run (all inputs variable)
  • Availability of inputs: Readily available inputs make supply more elastic
  • Storage capacity: Goods that can be stored easily have more elastic supply
Different supply elasticity curves: elastic, unit elastic, and inelastic supply curves compared on the same graph

Tax Incidence

Key Principle

The burden of a tax falls more heavily on the side of the market that is less elastic. If demand is more inelastic than supply, consumers bear more of the tax. If supply is more inelastic than demand, producers bear more. Taxes on cigarettes (inelastic demand) are largely borne by consumers.

6Advanced Topics

Constant Elasticity Demand Curves

Some demand functions exhibit constant elasticity (isoelastic curves). The log-linear form is: Q = APε

Taking the natural log: ln Q = ln A + ε ln P, where ε is the constant elasticity everywhere on the curve.

Example: If Q = 100P-0.5, the PED is -0.5 at every point on this demand curve.

Elasticity and Marginal Revenue

The fundamental relationship: MR = P(1 + 1/εd) or equivalently MR = P(1 − 1/|εd|)

Elastic (|εd| > 1): MR > 0. Lowering price increases TR.

Unit Elastic (|εd| = 1): MR = 0. TR is maximized.

Inelastic (|εd| < 1): MR < 0. Lowering price decreases TR.

Profit Maximization

A profit-maximizing firm will always operate in the elastic portion of its demand curve. In the inelastic region, the firm could increase revenue by raising price while also reducing costs (fewer units produced), so it would never maximize profit there.

7Worked Examples

Introductory

Calculating PED for a Local Brewery

A brewery sells IPA at $6/pint (500 pints/week). Raising to $8/pint drops sales to 300 pints/week. Calculate PED using the midpoint method.

Step 1: Qavg = (500+300)/2 = 400. %ΔQ = (300−500)/400 = −50%

Step 2: Pavg = ($6+$8)/2 = $7. %ΔP = ($8−$6)/$7 ≈ 28.57%

Step 3: PED = −50% / 28.57% ≈ −1.75

Result: |−1.75| > 1 → Demand is elastic

Key insight: Since demand is elastic, the brewery would increase total revenue by lowering its price. Raising price reduced TR from $3,000 to

,400.

Intermediate

Total Revenue Test for a Gaming Console

Console launched at $500 (100,000 units sold). Price reduced to $450, sales jump to 120,000 units. Is demand elastic or inelastic?

TR1 = $500 × 100,000 = $50,000,000

TR2 = $450 × 120,000 = $54,000,000

Test: P↓ and TR↑ → demand is elastic

Key insight: When price and total revenue move in opposite directions, demand is elastic. The price reduction was revenue-increasing.

Intermediate

Income Elasticity for Organic Produce

Income rises from $50,000 to $55,000. Organic produce demand rises from 10,000 to 11,500 units/month.

Step 1: %ΔQ = (11,500−10,000) / 10,750 ≈ 13.95%

Step 2: %ΔI = (55,000−50,000) / 52,500 ≈ 9.52%

Step 3: IED = 13.95% / 9.52% ≈ 1.465

Result: IED > 1 → Normal good (luxury)

Key insight: For every 1% increase in income, demand for organic produce increases by about 1.465%, characteristic of a luxury good.

Intermediate

Cross-Price Elasticity for Streaming Services

Netflix price increases by 10%. Hulu demand increases by 15%.

CPED = %ΔQHulu / %ΔPNetflix = 15% / 10% = 1.5

Result: CPED > 0 → Netflix and Hulu are substitutes

Key insight: A positive cross-price elasticity indicates substitutes. Consumers readily switch from the more expensive to the cheaper service.

Introductory

Price Elasticity of Supply for Custom Furniture

Custom dining table: at

,000, supply is 10/month. At
,500, supply is 15/month.

Step 1: %ΔQs = (15−10) / 12.5 = 40%

Step 2: %ΔP = (

,500−
,000) /
,250 ≈ 22.22%

Step 3: PES = 40% / 22.22% ≈ 1.80

Result: PES > 1 → Supply is elastic

Key insight: The furniture maker is quite responsive to price changes, likely due to flexibility in production or ability to reallocate resources.

8Memory Aids

Elastic = Earn More by Lowering Price

“If demand is Elastic, a price drop makes you Earn more revenue.”

Inelastic = Insensitive to Price Changes

“If demand is Inelastic, consumers are Insensitive to price changes, so raising price increases revenue.”

Midpoint Method

“Average it out! Divide by the average of the two values to get a consistent result.”

Substitutes: Same Sign

“Substitutes have a Same Sign (positive cross-price elasticity). Complements have a Contrary sign (negative).”

Tax Incidence

“Less Elastic Pays More! The side of the market with the less elastic curve bears the greater burden of a tax.”

PED Chain

“Price change leads to Quantity change, which affects Total Revenue. Understanding the magnitude of Q's response is the key.”

9Common Mistakes

Confusing Slope with Elasticity

Thinking a steeper curve always means more inelastic

Slope is absolute change (ΔP/ΔQ), while elasticity is proportional change (%ΔQ/%ΔP). Elasticity changes along a linear demand curve even though the slope does not.

Forgetting Percentage Changes

Using absolute changes instead of percentage changes

Elasticity always uses percentage changes. Using absolute changes (just ΔQ/ΔP) gives a unit-dependent measure that is not elasticity.

Wrong Sign Interpretation

Misinterpreting the sign of elasticity

PED is typically negative (law of demand). Income and cross-price elasticity signs have specific meanings: positive IED = normal good, negative IED = inferior good; positive CPED = substitutes, negative CPED = complements.

Confusing Substitutes with Complements

Getting the sign of cross-price elasticity backwards

Substitutes have positive CPED (price of Y up, demand for X up). Complements have negative CPED (price of Y up, demand for X down).

Ignoring Time Period

Not specifying short-run vs. long-run context

Elasticity is highly dependent on the time horizon. Both demand and supply tend to be more elastic in the long run as consumers and producers have more time to adjust.

Not Using the Midpoint Method

Using the initial point as the base for arc elasticity

When calculating elasticity between two distinct points, the midpoint method is crucial to ensure the result is consistent regardless of the direction of the price change.

Confusing Total Revenue with Profit

Assuming higher total revenue means higher profit

Total Revenue (P × Q) is not the same as Profit (TR − TC). A firm might increase TR by lowering price (elastic demand), but costs might rise faster than revenue.

Frequently Asked Questions

Why do economists use percentage changes to calculate elasticity instead of absolute changes?
Economists use percentage changes to make elasticity a dimensionless measure, independent of the units in which price and quantity are measured. If absolute changes were used, the elasticity value would change if prices were measured in dollars instead of cents, or quantities in tons instead of pounds. Percentage changes allow for meaningful comparisons of responsiveness across different goods and different currencies or units.
Why is the Midpoint Method preferred for calculating arc elasticity?
The Midpoint Method addresses the problem of inconsistent elasticity values when moving between two points on a demand or supply curve. If you use the initial price and quantity as the base for percentage changes, the elasticity calculated from a price increase will differ from the elasticity calculated from an equivalent price decrease. The Midpoint Method uses the average of the initial and final quantities and prices as the base, providing a single, consistent elasticity value regardless of the direction of the change.
Can elasticity change along a demand curve?
Yes, for a linear demand curve, elasticity is not constant; it changes along its length. Demand is typically elastic at higher prices and lower quantities (the upper portion of the curve), unit elastic at the midpoint, and inelastic at lower prices and higher quantities (the lower portion of the curve). Only specific non-linear demand curves, such as log-linear demand functions, have a constant elasticity across all points.
How does elasticity relate to a firm's market power?
A firm's market power is inversely related to the price elasticity of demand for its product. If a firm faces highly elastic demand, consumers have many substitutes and are very responsive to price changes, so the firm has little power to raise prices. Conversely, if a firm faces inelastic demand (e.g., due to unique products, strong brand loyalty, or lack of substitutes), it has greater market power, allowing it to raise prices with a relatively small impact on quantity demanded.
What is the difference between short-run and long-run elasticity?
Short-run elasticity refers to responsiveness over a period where some factors are fixed (e.g., consumers cannot immediately change their car for a more fuel-efficient one). Demand and supply tend to be less elastic in the short run. Long-run elasticity refers to responsiveness over a period long enough for all factors to be variable. Demand and supply tend to be more elastic in the long run because consumers have more time to find substitutes and change habits, and producers have more time to adjust production capacity.
How do firms estimate the elasticity of demand for their products?
Firms employ various methods: market experiments (varying prices across regions), statistical analysis using historical sales data and econometric regression models, consumer surveys about hypothetical purchasing behavior, observing competitor behavior and resulting market shifts, and consulting published industry-specific elasticity estimates from economists and market research firms.

Practice Quiz

Test your understanding of elasticity in economics — select the correct answer for each question.

1.What does it mean if the price elasticity of demand for a good is -0.7?

2.If a 5% increase in the price of good A leads to a 10% decrease in the quantity demanded of good A, the price elasticity of demand is:

3.Which of the following goods is most likely to have an inelastic price elasticity of demand?

4.If the cross-price elasticity of demand between coffee and tea is +0.8, what can we conclude?

5.A firm observes that when it increases the price of its product by 10%, its total revenue decreases. This implies that the demand for its product is:

6.If the income elasticity of demand for a good is -0.3, it is classified as a(n):

7.Which of the following statements about the price elasticity of supply (PES) is generally true?

8.If a government imposes a new tax on a good with perfectly inelastic demand, who will bear the entire burden of the tax?

9.The relationship between marginal revenue (MR), price (P), and the price elasticity of demand (εd) is given by MR = P(1 + 1/εd). If a firm is operating where |εd| = 0.5, what can we say about its marginal revenue?

10.Which of the following factors would make the demand for a good more elastic?

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