Chapter 4: Elasticity – Microeconomics Study Notes

Chapter 4: Elasticity

Chapter Outline and Learning Objectives

• Explain and calculate price elasticity of demand and supply.

• Understand the relationship between total expenditure and price elasticity of demand.

• Analyze the effects of excise taxes using elasticity concepts.

• Calculate income and cross elasticities of demand and distinguish between types of goods.

4.1 Price Elasticity of Demand

Definition and Key Concepts

• Elastic demand: Quantity demanded is very responsive to a change in the product's own price.

• Inelastic demand: Quantity demanded is very unresponsive to changes in its price.

• Elasticity is related to the slope of the demand curve, but is not the same as slope.

Visualizing Elastic and Inelastic Demand

• Elastic demand curves are flatter; a small price change leads to a large change in quantity demanded.

• Inelastic demand curves are steeper; a price change leads to a small change in quantity demanded.

• Visual comparisons are only valid if graphs are on the same scale and start from the same equilibrium.

Table: Price Reductions and Quantity Demanded

Commodity	Reduction in Price	Increase in Quantity Demanded (per month)
Cheese	$2 per kilogram	7,500 kilograms
T-shirts	$2 per shirt	25,000 shirts
iPhones	$2 per iPhone	500 iPhones

Measuring Price Elasticity of Demand

• Elasticity (Greek letter eta: η) is defined as:

$\eta = \frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}$

$\eta = \frac{\Delta Q / \overline{Q}}{\Delta p / \overline{p}}$

• Elasticity is usually negative, but the absolute value is used for interpretation.

• Elasticity is measured using average (base) values of price and quantity.

Calculating Elasticity Between Two Points

$\eta = \frac{(Q_1 - Q_0)/\overline{Q}}{(p_1 - p_0)/\overline{p}}$

Where $\overline{p} = (p_1 + p_0)/2$ and $\overline{Q} = (Q_1 + Q_0)/2$

$\eta = \frac{(Q_1 - Q_0)/(Q_1 + Q_0)}{(p_1 - p_0)/(p_1 + p_0)}$

Numerical Example

• Suppose the price of a 6-pack of Corona Beer drops from $9.00 to $8.00, and quantity demanded rises from 2,000 to 3,000.

$\eta = \frac{(3000 - 2000)/2500}{(8 - 9)/8.5} = \frac{0.4}{-0.1176} = -3.40$

• Absolute value: 3.40 (highly elastic demand)

Elasticity Along a Linear Demand Curve

• Elasticity falls as you move down a linear demand curve.

• At the top, demand is perfectly elastic ($\eta = \infty$); at the midpoint, unit elastic ($\eta = 1$); at the bottom, perfectly inelastic ($\eta = 0$).

Constant Elasticity Demand Curves

• Perfectly inelastic: $\eta = 0$ (vertical line)

• Perfectly elastic: $\eta = \infty$ (horizontal line)

• Unit elastic: $\eta = 1$ (special curve where % change in price = % change in quantity at all points)

Elasticity vs. Slope

• Slope measures absolute changes; elasticity measures percentage changes.

• Elasticity can vary along the curve even if the slope is constant.

Determinants of Elasticity of Demand

• Availability of close substitutes (more substitutes = higher elasticity)

• Length of time interval considered (longer time = higher elasticity)

• Necessity vs. luxury (necessities = lower elasticity; luxuries = higher elasticity)

• Specificity of product definition (narrower definition = higher elasticity)

Short-Run vs. Long-Run Elasticity

• Demand is more elastic in the long run as consumers have more time to adjust.

Examples

• Food (broad category): inelastic

• Leafy vegetables sold at a specific supermarket on Wednesdays: highly elastic

4.1.1 Total Expenditure and Elasticity

Definition

• Total Expenditure (TE) = Price × Quantity

• The effect of a price change on TE depends on elasticity:

  • If demand is elastic ($\eta > 1$), TE increases when price falls.

  • If demand is inelastic ($\eta < 1$), TE decreases when price falls.

  • If demand is unit elastic ($\eta = 1$), TE remains unchanged when price changes.

4.2 Price Elasticity of Supply

Definition and Formula

• Measures the responsiveness of quantity supplied to a change in the product's own price.

• Denoted by $\eta_s$:

$\eta_s = \frac{\text{percentage change in quantity supplied}}{\text{percentage change in price}}$

$\eta_s = \frac{\Delta Q_s / \overline{Q}}{\Delta p / \overline{p}}$

Determinants of Supply Elasticity

• Technical ease of substitution in production

• Nature of production costs

• Time span under consideration

• Availability of resource inputs

• Mobility of factors (e.g., labor)

• Ability to store finished products

• Production capacity utilization

• Length and complexity of production cycle

Example Calculation

• If quantity supplied increases from 20 to 40 as price rises from $1.50 to $2.50:

$\eta_s = \frac{20/40}{1.50/4.25} = 1.42$

4.3 Elasticity Matters for Excise Taxes

Tax Incidence

• Excise tax: A tax on the sale of a specific commodity (e.g., cigarettes, alcohol, gasoline).

• Tax incidence: Refers to who bears the burden of the tax (consumers or producers).

• The division of the tax burden depends on the relative elasticities of supply and demand.

• More inelastic demand means consumers bear more of the tax burden; more elastic demand means producers bear more.

Algebra of Tax Incidence

• When a tax is imposed, the price received by sellers is less than the price paid by buyers by the amount of the tax.

• Government revenue from the tax: $GR = Q_t \times t$

• Consumer burden: $(p_c - p_0) \times q_t$

• Producer burden: $(p_0 - p_s) \times q_t$

Application: Payroll Taxes

• Similar analysis applies to payroll taxes, where workers supply labor and firms demand labor.

• Instead of price and quantity, the variables are wage and employment.

4.4 Other Demand Elasticities

Income Elasticity of Demand

• Measures the responsiveness of quantity demanded to a change in income.

$\eta_Y = \frac{\text{percentage change in quantity demanded}}{\text{percentage change in income}}$

• If $\eta_Y > 0$, the good is normal.

• If $\eta_Y < 0$, the good is inferior.

Luxuries vs. Necessities

• Necessities have lower income elasticity; luxuries have higher income elasticity.

• Income elasticity can vary with consumer income levels and between countries.

Economic Effects of Income Changes

• Increased income can shift demand from agriculture to manufacturing, and later to services.

Cross Elasticity of Demand

• Measures the responsiveness of quantity demanded for one good to a change in the price of another good.

$\eta_{XY} = \frac{\text{percentage change in quantity demanded of good X}}{\text{percentage change in price of good Y}}$

• If $\eta_{XY} > 0$, X and Y are substitutes.

• If $\eta_{XY} < 0$, X and Y are complements.

Table: Terminology of Elasticity

Price Elasticity of Demand (Supply)	Income Elasticity of Demand	Cross Elasticity of Demand
Perfectly inelastic: 0	Inferior good: (-)	Substitute: (+)
Inelastic: 0-1	Normal good: (+)	Complement: (-)
Unit elastic: 1	Income-inelastic: <1
Elastic: >1 < infinite	Income-elastic: >1
Perfectly elastic: infinite

Summary

• Elasticity is a central concept in microeconomics, measuring responsiveness of demand and supply to changes in price, income, and prices of related goods.

• Understanding elasticity helps predict changes in total expenditure, tax incidence, and market outcomes.