# Elasticities of demand and supply

> IB Economics HL · IB Economics 2023 Syllabus (HL)
> Source: https://www.owlsprep.com/study/ib-economics-hl-u2-elasticities-of-demand-and-supply/

This module covers all four core elasticity metrics for IB HL Economics, including their formulas, determinants, real-world applications, and exam-standard calculation and evaluation frameworks for Paper 1, 2 and 3 questions.

**Prerequisites:** [Law of demand, supply and market equilibrium](https://www.owlsprep.com/study/ib-economics-hl-u2-market-equilibrium/); [Indirect taxes and government subsidies](https://www.owlsprep.com/study/ib-economics-hl-u2-taxes-subsidies/)

## Learning objectives

- Calculate PED, YED, XED and PES using raw market data for Paper 3 quantitative questions
- Explain core determinants of each elasticity type and their real-world market implications
- Analyze how elasticity values shape tax incidence, subsidy outcomes and firm total revenue
- Evaluate context-dependent elasticity differences for 15-mark Paper 1 extended response questions

## Price Elasticity of Demand (PED) Core Concepts

PED measures how sensitive consumer purchasing decisions are to price changes, and is the most frequently tested elasticity metric across all IB Economics exam papers.

**Price Elasticity of Demand** — The percentage change in quantity demanded of a good following a 1% change in its own price

*Notation:* $E_d$

*Example:* A 10% price rise leading to a 5% quantity fall gives an absolute PED value of 0.5, classified as inelastic.

$$E_d = \frac{\% \Delta Q_d}{\% \Delta P}$$

**Worked example:** A bakery reduces the price of sourdough from \$5 to \$4, and weekly quantity demanded rises from 100 loaves to 130 loaves. Calculate PED.

1. Step 1: Calculate percentage change in quantity demanded

   $$\% \Delta Q_d = \frac{130 - 100}{100} \times 100 = +30\%$$
2. Step 2: Calculate percentage change in price

   $$\% \Delta P = \frac{4 - 5}{5} \times 100 = -20\%$$
3. Step 3: Divide and take absolute value

   $$E_d = \left| \frac{30\%}{-20\%} \right| = 1.5, classified as elastic demand$$

> **tip**
>
> Total revenue rises when price increases for inelastic demand, and falls when price increases for elastic demand.

**Check your understanding**

Test your understanding of PED classification:

1. If PED = 0.3, what happens to total revenue when price rises by 20%?

   - Revenue falls
   - Revenue rises
   - Revenue stays the same
   - Revenue falls to zero

   *Why:* Inelastic demand means price and total revenue move in the same direction.

> **Exam tip:** IB mark schemes always award 1 mark for stating the formula explicitly, even if you calculate the value mentally, so never skip this step for full points.

## Income and Cross-Price Elasticity of Demand

YED and XED are used to classify goods by their relationship to consumer income and other related goods, and are heavily tested in Paper 2 data response questions.

**Income Elasticity of Demand** — The percentage change in quantity demanded following a 1% change in disposable consumer income

*Notation:* $E_y$

$$E_y = \frac{\% \Delta Q_d}{\% \Delta Y}$$

**Cross-Price Elasticity of Demand** — The percentage change in quantity demanded of Good A following a 1% change in price of Good B

*Notation:* $E_{xy}$

$$E_{xy} = \frac{\% \Delta Q_{d,A}}{\% \Delta P_B}$$

**Worked example:** Average consumer income rises 8%, and demand for bus travel falls 3%. Calculate YED and classify the good.

1. Step 1: Substitute values into YED formula

   $$E_y = \frac{-3\%}{+8\%} = -0.375$$
2. Step 2: Interpret the negative sign

   $$E_y < 0, so bus travel is classified as an inferior good in this market$$

> **mnemonic**
>
> YED > 0 = Normal Good, YED < 0 = Inferior Good; XED > 0 = Substitutes, XED < 0 = Complements

> **Exam tip:** For 15 mark essays, you must distinguish between necessity (YED 0-1) and luxury (YED >1) normal goods to access top evaluation marks.

## Price Elasticity of Supply (PES)

PES measures how quickly firms can adjust production levels in response to price changes, and is particularly relevant for agricultural and primary commodity market analysis.

**Price Elasticity of Supply** — The percentage change in quantity supplied of a good following a 1% change in its own market price

*Notation:* $E_s$

$$E_s = \frac{\% \Delta Q_s}{\% \Delta P}$$

**Worked example:** The price of coffee beans rises 20%, and global coffee supply increases 8% in the same harvest year. Calculate short-run PES.

1. Step 1: Substitute values into PES formula

   $$E_s = \frac{+8\%}{+20\%} = 0.4$$
2. Step 2: Classify the value

   $$E_s < 1, so short-run coffee supply is inelastic$$

> **note**
>
> PES is almost always more elastic in the long run, as firms can build new factories or plant new harvests to respond to price signals.

## Determinants of All Elasticity Types

Each elasticity type has distinct, exam-testable determinants that explain why elasticity values vary widely across different goods and market contexts.

| Elasticity Type | Key Determinants |
| --- | --- |
| PED | Number of close substitutes, proportion of income spent on good, time horizon, luxury vs necessity classification |
| YED | Consumer income bracket, good classification as necessity/luxury/inferior |
| XED | Degree of similarity between two goods, strength of complementary use cases |
| PES | Production spare capacity, inventory storage ability, time horizon, factor mobility |

**Exam command terms**

IB exam command terms for elasticity questions have strict mark scheme expectations:

- **Calculate** — Show full formula, substitution and final value to earn all 3 marks

- **Explain** — Link a determinant directly to the resulting elasticity magnitude

- **Evaluate** — Discuss how elasticity values may change in the long run vs short run

## Elasticity Applications: Tax Incidence

The most high-stakes application of elasticities in IB exams is calculating the distribution of indirect tax burden between consumers and producers.

**Comparing methods**

Tax incidence splits are determined by relative elasticity values:

- **Inelastic Demand, Elastic Supply** — Consumers bear the majority of the tax burden, as they cannot easily reduce quantity demanded when price rises

- **Elastic Demand, Inelastic Supply** — Producers bear the majority of the tax burden, as they cannot easily reduce production levels when after-tax revenue falls

**Worked example:** A \$2 per unit tax is placed on cigarettes, where PED = 0.2 and PES = 2.8. What share of the tax burden falls on consumers?

1. Step 1: Use the relative elasticity tax incidence rule

   $$Consumer burden = \frac{PES}{PES + |E_d|} = \frac{2.8}{2.8 + 0.2} = 0.933$$
2. Step 2: Calculate final burden

   $$Consumers pay 93% of the \$2 tax, or \$1.86 per unit$$

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Forgetting to take absolute value of PED values
  - Why it fails: PED is always negative due to the inverse law of demand, so the sign carries no useful information for classification
  - Correct: Explicitly state you are using the absolute value of PED before classifying it as elastic or inelastic
- **Wrong:** Mixing up sign conventions for YED and XED
  - Why it fails: Confusing positive XED for substitutes with positive YED for normal goods leads to wrong classification
  - Correct: Label the elasticity type clearly before interpreting the sign of your calculated value
- **Wrong:** Stating agricultural PES is elastic in the short run
  - Why it fails: Crops take months to grow, so supply cannot be adjusted immediately after a price change
  - Correct: Only classify PES as elastic for agricultural goods in the multi-year long run time horizon
- **Wrong:** Claiming elastic demand leads to higher total revenue when price rises
  - Why it fails: Mixing up the inverse relationship between price and revenue for elastic vs inelastic demand curves
  - Correct: Use the rule that total revenue moves in the same direction as price for inelastic demand, and opposite for elastic demand
- **Wrong:** Assigning 100% of tax burden to consumers for all goods
  - Why it fails: Failing to compare relative PED and PES values to split the tax incidence fairly
  - Correct: Always reference both elasticity values when explaining the distribution of tax burden in your exam response

## Cheatsheet

| Elasticity Type | Formula | Value Thresholds | Core Interpretation |
| --- | --- | --- | --- |
| PED | %ΔQd / %ΔP | <1 = Inelastic, >1 = Elastic | Determines revenue change from price shifts |
| YED | %ΔQd / %ΔY | <0 = Inferior, 0-1 = Necessity, >1 = Luxury | Classifies goods by income responsiveness |
| XED | %ΔQd of A / %ΔP of B | <0 = Complements, >0 = Substitutes | Measures cross-market good linkages |
| PES | %ΔQs / %ΔP | <1 = Inelastic, >1 = Elastic | Determines firm supply response to price changes |

## What's next

Mastering elasticities is the foundational skill for scoring full marks on IB HL Microeconomics data response and extended essay questions, as this concept underpins analysis of government intervention, market failure, and firm pricing strategy. You will now apply these elasticity frameworks to calculate tax and subsidy welfare impacts, evaluate the effectiveness of government price controls, and analyze how elasticity values shape outcomes for primary commodity markets that are a frequent case study in IB exams. This module also directly prepares you for the Paper 3 quantitative section where 6-8 marks are routinely allocated to elasticity calculation and interpretation tasks.

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