Chapter 6: Elasticity – Microeconomics Study Notes

Elasticity

Price Elasticity of Demand

The price elasticity of demand quantifies how sensitive the quantity demanded of a good is to changes in its price. It is a crucial concept for understanding consumer behavior and market dynamics.

• Definition: The percentage change in quantity demanded divided by the percentage change in price.

• Formula:

$\text{Price Elasticity of Demand} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

• Interpretation: The higher the absolute value, the more responsive consumers are to price changes.

• Example: If a 10% increase in price leads to a 20% decrease in quantity demanded, elasticity = -2 (elastic demand).

Types of Price Elasticity of Demand

• Elastic Demand: Quantity demanded changes by a greater percentage than price (elasticity > 1).

• Inelastic Demand: Quantity demanded changes by a smaller percentage than price (elasticity < 1).

• Unit Elastic Demand: Quantity demanded changes by the same percentage as price (elasticity = 1).

Example: If a 5% price increase causes a 10% drop in quantity demanded, elasticity = 2 (elastic). If a 5% price increase causes a 2% drop, elasticity = 0.4 (inelastic).

Midpoint Formula for Elasticity

The midpoint formula provides a consistent method for calculating percentage changes between two points on a demand curve.

1. Find the change in quantity ($\Delta Q$) and change in price ($\Delta P$).

2. Calculate the average quantity and average price.

3. Compute percentage changes: $\frac{\Delta Q}{\text{average } Q}$ and $\frac{\Delta P}{\text{average } P}$.

4. Divide the percentage change in quantity by the percentage change in price.

$\text{Elasticity} = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}$

Example: If price rises from $10 to $12 and quantity falls from 100 to 80, use the midpoint formula to calculate elasticity.

Total Revenue Test

Total revenue is the total amount received from sales of a good, calculated as price times quantity.

$\text{Total Revenue} = \text{Price} \times \text{Quantity}$

• If price rises and total revenue rises, demand is inelastic.

• If price rises and total revenue falls, demand is elastic.

Example: If a price increase leads to higher total revenue, consumers are not very responsive to price (inelastic demand).

Cross-Price Elasticity of Demand

The cross-price elasticity of demand measures how the quantity demanded of one good responds to a price change in another good.

$\text{Cross-Price Elasticity} = \frac{\%\ \text{change in quantity demanded of Good A}}{\%\ \text{change in price of Good B}}$

• Positive value: Goods are substitutes (e.g., butter and margarine).

• Negative value: Goods are complements (e.g., coffee and sugar).

Example: If the price of tea rises and the demand for coffee increases, the cross-price elasticity is positive (substitutes).

Income Elasticity of Demand

The income elasticity of demand measures how the quantity demanded of a good changes as consumer income changes.

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

• Positive value: The good is a normal good (demand increases as income rises).

• Negative value: The good is an inferior good (demand decreases as income rises).

Example: If income rises by 10% and demand for steak rises by 15%, income elasticity = 1.5 (normal good).