Elasticity in Microeconomics: Concepts, Measurement, and Applications

Elasticity in Microeconomics

Introduction

Elasticity is a central concept in microeconomics that measures the responsiveness of one variable to changes in another. In this chapter, we focus on the elasticity of demand and supply, their determinants, and their implications for market outcomes and policy.

Price Elasticity of Demand

Definition and Importance

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

• Demand is elastic when quantity demanded is highly responsive to price changes.

• Demand is inelastic when quantity demanded is relatively unresponsive to price changes.

• The more elastic the demand, the less the change in equilibrium price and the greater the change in equilibrium quantity for a given shift in the supply curve.

Measurement of Price Elasticity of Demand

• Price elasticity of demand (Greek letter eta: η) is defined as:

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

$\eta = \frac{\Delta Q_d / \overline{Q}_d}{\Delta P / \overline{P}}$

• Where $\overline{P}$ is the average price and $\overline{Q}_d$ is the average quantity demanded.

• Because the demand curve has a negative slope, the percentage changes in price and quantity have opposite signs. However, elasticity is usually reported as a positive number (absolute value).

Numerical Example

Product	Original Price	New Price	Average Price	Original Quantity	New Quantity	Average Quantity
Example Good	$5.00	$3.00	$4.00	116,250	123,750	120,000

$\eta = \frac{123,750 - 116,250}{120,000} \div \frac{5.00 - 3.00}{4.00} = \frac{7,500/120,000}{2.0/4.0} = \frac{0.0625}{0.5} = 0.125$

Elasticity Along a Linear Demand Curve

• A negatively sloped linear demand curve has a constant slope but does not have constant elasticity.

• Elasticity varies along the curve: it is higher (more elastic) at higher prices and lower quantities, and lower (more inelastic) at lower prices and higher quantities.

Types of Demand Elasticity

• Perfectly inelastic demand: $\eta = 0$ (vertical demand curve; quantity does not change with price).

• Perfectly elastic demand: $\eta = \infty$ (horizontal demand curve; price does not change with quantity).

• Unit elastic demand: $\eta = 1$ (percentage change in quantity equals percentage change in price).

Determinants of Price Elasticity of Demand

Availability of Substitutes

• Goods with close substitutes tend to have more elastic demand.

• Narrowly defined goods (e.g., specific brands) are more elastic than broadly defined goods (e.g., food).

Importance in Consumer Budgets

• Goods that take up a small fraction of the consumer's budget tend to have inelastic demand.

• Goods that take up a large fraction of the budget tend to have elastic demand.

Time Horizon

• Demand is more elastic in the long run than in the short run, as consumers have more time to adjust their behavior and find substitutes.

Elasticity and Total Expenditure

Relationship Between Price, Quantity, and Total Expenditure

• Total expenditure = Price × Quantity

• When price falls:

  • If demand is elastic, total expenditure rises.

  • If demand is inelastic, total expenditure falls.

  • If demand is unit elastic, total expenditure remains unchanged.

• When price rises:

  • If demand is elastic, total expenditure falls.

  • If demand is inelastic, total expenditure rises.

  • If demand is unit elastic, total expenditure remains unchanged.

Price Elasticity of Supply

Definition and Measurement

• Price elasticity of supply measures the responsiveness of quantity supplied to a change in the product's own price.

• Supply is elastic when quantity supplied is highly responsive to price changes.

• Supply is inelastic when quantity supplied is relatively unresponsive to price changes.

• Formula:

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

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

• Where $\overline{P}$ is the average price and $\overline{Q}_s$ is the average quantity supplied.

Determinants of Supply Elasticity

• Ease of Substitution: The easier it is for producers to shift resources from other products to the one whose price has risen, the more elastic the supply.

• Time Horizon: Supply is more elastic in the long run, as producers can adjust their productive capacity.

Elasticity and Tax Incidence

Excise Taxes and Market Outcomes

• An excise tax is a tax on the sale of a particular product.

• Excise taxes raise the price paid by consumers and lower the price received by producers.

• The incidence of a tax refers to who actually bears the burden of the tax.

• The burden of an excise tax depends on the relative elasticities of supply and demand:

  • If demand is more inelastic than supply, consumers bear a greater share of the tax burden.

  • If supply is more inelastic than demand, producers bear a greater share of the tax burden.

Application: Payroll Taxes

• Payroll taxes (e.g., Employment Insurance, Canada Pension Plan) are shared between workers and firms.

• The allocation of the tax burden depends on the elasticities of labor demand and supply.

• The more inelastic the labor supply, the higher the burden on workers.

Other Demand Elasticities

Income Elasticity of Demand

• Measures the responsiveness of quantity demanded to changes in income.

• Formula:

$\eta_I = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in income}}$

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

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

• For normal goods:

  • If $0 < \eta_I < 1$, demand is income inelastic (necessities).

  • If $\eta_I > 1$, demand is income elastic (luxuries).

• Inferior goods have negative income elasticity because an increase in income leads to a reduction in quantity demanded.

Cross Price Elasticity of Demand

• Measures the responsiveness of demand for one good to changes in the price of another good.

• Formula:

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

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

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

• An increase in the price of Y increases demand for X if they are substitutes, and decreases demand for X if they are complements.