Summary of Economic Elasticity Concepts and Applications

Economic Elasticity: Concepts, Applications & Calculations

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Introduction

Related demand elasticities measure how the demand for one good responds to changes in another variable (another good's price or consumers' income). These concepts help us classify goods (substitutes, complements, normal, inferior) and predict how consumers will react to price or income changes.

Definition: Cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good.

Definition: Income elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in consumers' income.

Cross-price Elasticity of Demand (CPED)

What it measures

  • CPED tells us whether two goods are substitutes, complements, or unrelated.

Formula

  • The cross-price elasticity of demand is calculated as

$$\text{CPED} = \frac{%\text{ change in quantity demanded of Good A}}{%\text{ change in price of Good B}}$$

Interpretation

  • CPED > 0: goods are substitutes (an increase in the price of Good B raises demand for Good A).
  • CPED < 0: goods are complements (an increase in the price of Good B lowers demand for Good A).
  • CPED = 0: goods are unrelated/independent.

Definition: Substitute goods are goods that can replace each other; complementary goods are used together; unrelated goods have no effect on each other.

Strength of substitution or complementarity

  • If |CPED| > 1: demand is relatively elastic with respect to the other good’s price (close/strong substitutes or strong complements).
  • If |CPED| < 1: demand is relatively inelastic (weak substitutes or weak complements).

Example: Parmalat and Clover milk

  1. Price of Parmalat rises from R10 to R12 per litre. Quantity demanded of Clover rises from 500 L to 800 L.

Step 1: Percentage change in quantity demanded of Clover

$$%\Delta Q = \frac{800 - 500}{500} \times 100% = 60%$$

Step 2: Percentage change in price of Parmalat

$$%\Delta P = \frac{12 - 10}{10} \times 100% = 20%$$

Step 3: CPED

$$\text{CPED} = \frac{60%}{20%} = 3$$

  • CPED = 3 (positive and > 1) so Parmalat and Clover are close/strong substitutes.

Real-world applications

  • Firms use CPED to set prices: if a competitor raises price and CPED is high, a firm can expect higher demand.
  • Policy makers consider CPED when taxing related goods (e.g., tax on petrol affects demand for public transport if they are substitutes).
💡 Did you know?Fun fact: Strong substitutes often belong to the same brand category (for example, two popular soft drink brands) and have high positive CPED values which makes competition intense.

Income Elasticity of Demand (IED)

What it measures

  • IED shows how quantity demanded changes as consumer income changes and helps classify goods as normal, inferior, or luxury/necessity.

Formula

  • The income elasticity of demand is

$$\text{IED} = \frac{%\text{ change in quantity demanded}}{%\text{ change in income}}$$

Interpretation

  • IED > 0: normal good (demand rises when income rises).
  • IED < 0: inferior good (demand falls when income rises).
  • IED = 0: demand is unaffected by income (perfectly income-inelastic)

Definition: Normal goods are goods whose demand increases as income increases. Inferior goods are goods whose demand decreases as income increases.

Strength of income responsiveness

  • IED > 1: income-elastic — demand changes proportionally more than income (often luxury goods).
  • 0 < IED < 1: income-inelastic — demand changes less than income (necessities).
  • IED < 0: inferior — demand falls as income rises.

Example: Beef

  1. Income rises from R4,000 to R6,000. Quantity demanded of beef rises from 2 kg to 3.5 kg.

Step 1: Percentage change in quantity demanded

$$%\Delta Q = \frac{3.5 - 2}{2} \times 100% = 75%$$

Step 2: Percentage change in income

$$%\Delta Y = \frac{6000 - 4000}{4000} \times 100% = 50%$$

Step 3: IED

$$\text{IED} = \frac{75%}{50%} = 1.

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Related Demand Elasticities

Klíčové pojmy: CPED formula: $\text{CPED} = \dfrac{\%\Delta Q_A}{\%\Delta P_B}$, CPED > 0 => goods are substitutes, CPED < 0 => goods are complements, CPED = 0 => goods are unrelated, IED formula: $\text{IED} = \dfrac{\%\Delta Q}{\%\Delta Y}$, IED > 0 => normal good; IED < 0 => inferior good, If |elasticity| > 1 => relatively elastic response; if |elasticity| < 1 => relatively inelastic, Compute % changes using $\%\Delta X = \dfrac{\text{new}-\text{old}}{\text{old}}\times100\%$, Use sign and magnitude together to classify relationships, When solving, calculate % changes first, then divide to find elasticity

## Introduction Related demand elasticities measure how the demand for one good responds to changes in another variable (another good's price or consumers' income). These concepts help us classify goods (substitutes, complements, normal, inferior) and predict how consumers will react to price or income changes. > **Definition:** Cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. > **Definition:** Income elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in consumers' income. ## Cross-price Elasticity of Demand (CPED) ### What it measures - CPED tells us whether two goods are **substitutes**, **complements**, or **unrelated**. ### Formula - The cross-price elasticity of demand is calculated as $$\text{CPED} = \frac{\%\text{ change in quantity demanded of Good A}}{\%\text{ change in price of Good B}}$$ ### Interpretation - CPED > 0: goods are **substitutes** (an increase in the price of Good B raises demand for Good A). - CPED < 0: goods are **complements** (an increase in the price of Good B lowers demand for Good A). - CPED = 0: goods are **unrelated/independent**. > **Definition:** Substitute goods are goods that can replace each other; complementary goods are used together; unrelated goods have no effect on each other. ### Strength of substitution or complementarity - If |CPED| > 1: demand is **relatively elastic** with respect to the other good’s price (close/strong substitutes or strong complements). - If |CPED| < 1: demand is **relatively inelastic** (weak substitutes or weak complements). ### Example: Parmalat and Clover milk 1. Price of Parmalat rises from R10 to R12 per litre. Quantity demanded of Clover rises from 500 L to 800 L. Step 1: Percentage change in quantity demanded of Clover $$\%\Delta Q = \frac{800 - 500}{500} \times 100\% = 60\%$$ Step 2: Percentage change in price of Parmalat $$\%\Delta P = \frac{12 - 10}{10} \times 100\% = 20\%$$ Step 3: CPED $$\text{CPED} = \frac{60\%}{20\%} = 3$$ - CPED = 3 (positive and > 1) so Parmalat and Clover are close/strong substitutes. ### Real-world applications - Firms use CPED to set prices: if a competitor raises price and CPED is high, a firm can expect higher demand. - Policy makers consider CPED when taxing related goods (e.g., tax on petrol affects demand for public transport if they are substitutes). Fun fact: Strong substitutes often belong to the same brand category (for example, two popular soft drink brands) and have high positive CPED values which makes competition intense. ## Income Elasticity of Demand (IED) ### What it measures - IED shows how quantity demanded changes as consumer income changes and helps classify goods as **normal**, **inferior**, or **luxury/necessity**. ### Formula - The income elasticity of demand is $$\text{IED} = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in income}}$$ ### Interpretation - IED > 0: **normal good** (demand rises when income rises). - IED < 0: **inferior good** (demand falls when income rises). - IED = 0: demand is unaffected by income (perfectly income-inelastic) > **Definition:** Normal goods are goods whose demand increases as income increases. Inferior goods are goods whose demand decreases as income increases. ### Strength of income responsiveness - IED > 1: **income-elastic** — demand changes proportionally more than income (often luxury goods). - 0 < IED < 1: **income-inelastic** — demand changes less than income (necessities). - IED < 0: **inferior** — demand falls as income rises. ### Example: Beef 1. Income rises from R4,000 to R6,000. Quantity demanded of beef rises from 2 kg to 3.5 kg. Step 1: Percentage change in quantity demanded $$\%\Delta Q = \frac{3.5 - 2}{2} \times 100\% = 75\%$$ Step 2: Percentage change in income $$\%\Delta Y = \frac{6000 - 4000}{4000} \times 100\% = 50\%$$ Step 3: IED $$\text{IED} = \frac{75\%}{50\%} = 1.