# Elasticity

> IB Economics SL · Microeconomics Unit 2
> Source: https://www.owlsprep.com/study/ib-economics-sl-u2-elasticity/

This module covers the core microeconomic concept of elasticity, including calculation, interpretation, determinants, and real-world applications of PED, YED, XED and PES for IB Economics SL.

**Prerequisites:** [Demand and Supply Fundamentals](https://www.owlsprep.com/study/ib-economics-sl-u2-demand-supply/)

## Learning objectives

- Define the four core types of elasticity in microeconomics
- Calculate elasticity values from raw price/quantity/income data
- Interpret elasticity values and classify goods and relationships
- Explain determinants of elasticity and apply to real-world policy and firm strategy

## Price Elasticity of Demand (PED)

**Price Elasticity of Demand** — A measure of the responsiveness of quantity demanded of a good to a change in its own price, holding all other variables constant.

*Notation:* PED = \frac{\% \Delta Q_d}{\% \Delta P}

*Example:* A PED of -1.2 means quantity demanded falls 1.2% for every 1% increase in price.

PED is almost always negative because of the inverse relationship between price and quantity demanded (the law of demand). IB Economics almost always uses absolute values for interpreting PED.

$$|PED| > 1 = \text{elastic}, \quad |PED| < 1 = \text{inelastic}, \quad |PED| = 1 = \text{unit elastic}$$

**Worked example:** The price of apples increases from \$2 per kg to \$2.5 per kg, leading quantity demanded to fall from 100 kg to 80 kg. Calculate PED and interpret the result.

1. Calculate percentage change in quantity demanded:

   $$\% \Delta Q_d = \frac{80 - 100}{100} \times 100 = -20\%$$
2. Calculate percentage change in price:

   $$\% \Delta P = \frac{2.5 - 2}{2} \times 100 = +25\%$$
3. Substitute into the PED formula:

   $$PED = \frac{-20\%}{+25\%} = -0.8$$
4. Interpret the result: the absolute value of PED is 0.8 < 1, so demand for apples is price inelastic.

> **Exam tip:** Always include an interpretation after calculation, 1 mark is almost always awarded for interpretation in IB exams.

*Calculator:* allowed

## Income and Cross Price Elasticity of Demand

**Income Elasticity of Demand (YED)** — Measures the responsiveness of quantity demanded to a change in consumer income, ceteris paribus. The sign of YED classifies the type of good.

*Notation:* YED = \frac{\% \Delta Q_d}{\% \Delta Y}

*Example:* Positive YED = normal good, negative YED = inferior good; YED > 1 = luxury good.

**Cross Price Elasticity of Demand (XED)** — Measures the responsiveness of quantity demanded of good X to a change in price of good Y, ceteris paribus. The sign of XED tells us the relationship between the two goods.

*Notation:* XED = \frac{\% \Delta Q_{dX}}{\% \Delta P_Y}

*Example:* Positive XED = substitutes, negative XED = complements.

**Worked example:** A 10% increase in consumer income leads to a 15% increase in demand for restaurant meals. Calculate YED and classify the good. Then, a 5% increase in the price of printers leads to a 10% decrease in demand for ink cartridges: calculate XED and state the relationship.

1. Calculate YED for restaurant meals:

   $$YED = \frac{+15\%}{+10\%} = +1.5$$
2. Interpret YED: positive value means restaurant meals are a normal good. YED > 1 means they are a luxury good.
3. Calculate XED for printers and ink:

   $$XED = \frac{-10\%}{+5\%} = -2$$
4. Interpret XED: negative value means printers and ink are strong complements.

*Calculator:* allowed

## Price Elasticity of Supply (PES)

**Price Elasticity of Supply** — Measures the responsiveness of quantity supplied of a good to a change in its own price, ceteris paribus.

*Notation:* PES = \frac{\% \Delta Q_s}{\% \Delta P}

*Example:* PES = 2 means quantity supplied increases 2% for every 1% increase in price.

PES is always positive because of the direct relationship between price and quantity supplied (the law of supply). Key factors that determine PES include time horizon (longer time = more elastic supply), factor mobility, spare production capacity, and ability to store inventory.

**Worked example:** When the price of bicycles increases from \$500 to \$600, quantity supplied increases from 1000 units to 1200 units. Calculate PES and interpret the result.

1. Calculate percentage change in quantity supplied:

   $$\% \Delta Q_s = \frac{1200 - 1000}{1000} \times 100 = 20\%$$
2. Calculate percentage change in price:

   $$\% \Delta P = \frac{600 - 500}{500} \times 100 = 20\%$$
3. Calculate PES:

   $$PES = \frac{20\%}{20\%} = 1$$
4. Interpretation: supply of bicycles is unit price elastic.

*Calculator:* allowed

## Determinants and Applications

Elasticity values have critical practical implications for government policy and firm pricing strategy. Key determinants of PED include the number of close substitutes, proportion of income spent on the good, time horizon, and whether the good is a necessity or luxury:

1. Fewer close substitutes = more inelastic demand
2. Smaller proportion of income spent = more inelastic demand
3. Shorter time horizon = more inelastic demand
4. Necessities have more inelastic demand than luxuries

Common applications include: governments set indirect taxes based on PED: inelastic demand for cigarettes means a tax will raise more revenue than it reduces consumption, while elastic demand for polluting goods means a tax will significantly cut consumption. Firms use PED to set pricing to maximize total revenue.

**Worked example:** A coffee shop faces PED of -0.5 for its coffee. If it increases price by 10%, what happens to total revenue?

1. First, note |PED| = 0.5 < 1, so demand is inelastic.
2. For inelastic demand, price and total revenue move in the same direction.
3. Calculate the change in quantity demanded:

   $$\% \Delta Q_d = PED \times \% \Delta P = -0.5 \times 10\% = -5\%$$
4. Calculate new total revenue:

   $$\text{New } TR = (1.1P) \times (0.95Q) = 1.045PQ = 1.045 \times \text{Original } TR$$
5. Conclusion: total revenue increases by 4.5%.

*Calculator:* allowed

## Common pitfalls

- **Wrong:** Interpreting a PED of -0.8 as elastic directly from the negative value
  - Why it fails: PED is always negative due to the law of demand; interpretation depends on absolute value
  - Correct: Take the absolute value of PED: |-0.8| = 0.8 < 1, so demand is inelastic
- **Wrong:** Classifying a good with negative YED as a normal good
  - Why it fails: The sign of YED directly indicates the type of good based on how demand changes with income
  - Correct: Negative YED means demand falls as income rises, so the good is inferior
- **Wrong:** Confusing XED signs: calling positive XED complements
  - Why it fails: The direction of change for related goods is often mixed up by students
  - Correct: Positive XED = substitutes (price of Y up, demand for X up), negative XED = complements
- **Wrong:** Forgetting to interpret elasticity values after calculation
  - Why it fails: Many students only write the numerical value and miss the interpretation mark
  - Correct: Always add one sentence to state what the value means (e.g. 'demand is inelastic')

## Cheatsheet

| Elasticity Type | Formula | Key Interpretation | Common Use Case |
| --- | --- | --- | --- |
| PED | $\frac{\% \Delta Q_d}{\% \Delta P}$ | \|PED\| > 1 = elastic, <1 = inelastic | Firm pricing, tax incidence |
| YED | $\frac{\% \Delta Q_d}{\% \Delta Y}$ | + = normal, - = inferior; >1 = luxury | Good classification, forecasting |
| XED | $\frac{\% \Delta Q_X}{\% \Delta P_Y}$ | + = substitutes, - = complements | Related goods pricing |
| PES | $\frac{\% \Delta Q_s}{\% \Delta P}$ | >1 = elastic supply, <1 = inelastic | Supply response analysis |

## What's next

Elasticity is a foundational concept that underpins almost all further microeconomic analysis in IB Economics SL. You will use elasticity to analyze the incidence of indirect taxes and subsidies, the impact of price controls, and how changes in aggregate income affect demand for different types of goods. Mastery of elasticity calculations and interpretation is essential for full marks on both Paper 1 and Paper 2 exam questions, and it appears in almost every exam session.

- [Government intervention in markets](https://www.owlsprep.com/study/ib-economics-sl-u2-government-intervention-in-markets/)
- [Types of market failure](https://www.owlsprep.com/study/ib-economics-sl-u2-types-of-market-failure/)

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