Chapter 6: Elasticity – Microeconomics Study Notes

Elasticity in Microeconomics

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures the responsiveness of one variable to changes in another. It is most commonly used to analyze how quantity demanded or supplied responds to changes in price, income, or the price of related goods.

• Elasticity quantifies the sensitivity of economic variables, providing insight into consumer and producer behavior.

• Understanding elasticity helps firms and policymakers predict the effects of pricing, taxation, and income changes.

Percentage Change (Midpoint Method)

The midpoint method is used to calculate percentage changes to avoid bias depending on the direction of change.

• Formula:

$\text{Percentage Change} = \frac{\text{New Value} - \text{Old Value}}{\left(\frac{\text{New Value} + \text{Old Value}}{2}\right)}$

• This method is preferred for elasticity calculations because it gives consistent results regardless of the direction of change.

• Example: If the price of a good increases from $10 to $12, the percentage change is$\frac{12-10}{(12+10)/2} = \frac{2}{11} \approx 18.18\%$.

Price Elasticity of Demand (Ed)

Price elasticity of demand measures how much the quantity demanded of a good responds to a change in its price.

• Formula:

$E_d = \left| \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \right|$

• Interpretation: A higher absolute value indicates greater sensitivity to price changes.

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

Total Revenue (TR)

Total revenue is the total amount of money a firm receives from selling its product.

• Formula:

$TR = \text{Price} \times \text{Quantity}$

• Relationship with Elasticity: When demand is elastic, lowering price increases total revenue; when inelastic, raising price increases total revenue.

Cross-Price Elasticity of Demand (Exy)

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

• Formula:

$E_{xy} = \frac{\% \text{ change in quantity demanded of good X}}{\% \text{ change in price of good Y}}$

• Interpretation:

  • Positive value: Goods X and Y are substitutes.

  • Negative value: Goods X and Y are complements.

  • Zero: Goods are unrelated.

• Example: If the price of tea increases and the demand for coffee rises, the cross-price elasticity is positive, indicating they are substitutes.

Income Elasticity of Demand (Ei)

Income elasticity of demand measures how the quantity demanded of a good responds to changes in consumer income.

• Formula:

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

• Interpretation:

  • $E_i > 0$: The good is a normal good (demand increases as income rises).

  • $E_i < 0$: The good is an inferior good (demand decreases as income rises).

• Example: If income rises by 10% and demand for restaurant meals increases by 15%, $E_i = 1.5$ (normal good).

Price Elasticity of Supply (Es)

Price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price.

• Formula:

$E_s = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}}$

• Example: If a 5% increase in price leads to a 10% increase in quantity supplied, $E_s = 2$ (elastic supply).

Elasticity Classifications

Elasticity values are classified to describe the degree of responsiveness.

Elasticity Value	Classification
> 1	Elastic
< 1	Inelastic
= 1	Unit elastic

• Elastic: Quantity responds strongly to price changes.

• Inelastic: Quantity responds weakly to price changes.

• Unit elastic: Proportional response.

Summary Table: Types and Interpretations of Elasticity

Elasticity Type	Formula	Interpretation
Price Elasticity of Demand	$E_d = \left| \frac{\% \Delta Q_d}{\% \Delta P} \right|$	Responsiveness of quantity demanded to price changes
Price Elasticity of Supply	$E_s = \frac{\% \Delta Q_s}{\% \Delta P}$	Responsiveness of quantity supplied to price changes
Cross-Price Elasticity	$E_{xy} = \frac{\% \Delta Q_x}{\% \Delta P_y}$	Substitutes (>0), Complements (<0), Unrelated (=0)
Income Elasticity	$E_i = \frac{\% \Delta Q_d}{\% \Delta I}$	Normal good (>0), Inferior good (<0)