Elasticity in Microeconomics: Chapter 4 Study Notes

Elasticity in Microeconomics

Introduction

Elasticity is a central concept in microeconomics, measuring how responsive one variable is to changes in another. In this chapter, we focus on price elasticity of demand and supply, as well as related elasticities such as income elasticity and cross-price elasticity. Understanding elasticity helps explain consumer and producer behavior, market outcomes, and the effects of government policies like taxation.

Price Elasticity of Demand

Definition and Importance

• Price elasticity of demand measures how much the quantity demanded of a good responds to changes 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 resulting from a shift in the supply curve.

Graphical Illustration

Figure 4-1 demonstrates the effects of a supply shift with two different demand curves:

• With elastic demand, a supply shift leads to a larger change in quantity and a smaller change in price.

• With inelastic demand, a supply shift leads to a larger change in price and a smaller change in quantity.

Measurement of Price Elasticity

• 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, percentage changes in price and quantity have opposite signs. By convention, elasticity is reported as a positive number.

Numerical Example

Product	Original Price	New Price	Average Price	Original Quantity	New Quantity	Average Quantity
-	$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 not constant elasticity.

• Elasticity varies along the curve: it is higher at higher prices and lower quantities, and lower at lower prices and higher quantities.

Types of Demand Elasticity

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

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

• Unit elastic demand: $\eta = 1$

Determinants of Elasticity of Demand

• Availability of Substitutes: More substitutes make demand more elastic.

• Definition of the Market: Narrowly defined products have more elastic demand than broadly defined ones.

• Importance in Budget: Goods that take up a large fraction of the consumer's budget have more elastic demand.

• Time Horizon: Demand is more elastic in the long run than in the short run.

Elasticity and Total Expenditure

Relationship Between Price Changes 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 how much the quantity supplied of a good responds to changes in its 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, the more elastic the supply.

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

Elasticity and Excise Taxes

Tax Incidence and Elasticity

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

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

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

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

  • If demand is inelastic and supply is elastic, consumers bear more of the tax burden.

  • If supply is inelastic and demand is elastic, producers bear more 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 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.

Normal Goods

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

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

• The more necessary an item, the lower its income elasticity.

Inferior Goods

• Inferior goods have negative income elasticity; as income rises, quantity demanded falls.

• Examples are more common at the individual level than for the market as a whole.

Cross-Price Elasticity of Demand

• Measures the responsiveness of quantity demanded 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 $\eta_{XY} > 0$, X and Y are substitutes.

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

• A change in the price of Y shifts the demand curve for X:

  • If substitutes, an increase in the price of Y increases demand for X (demand curve for X shifts right).

  • If complements, an increase in the price of Y decreases demand for X (demand curve for X shifts left).

Additional info: Some tables and figures were inferred and expanded for clarity. All equations are provided in LaTeX format as required.