Elasticity in Microeconomics: Concepts, Measurement, and Applications

Elasticity in Microeconomics

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how responsive one variable is to changes in another variable. Most commonly, it refers to how the quantity demanded or supplied of a good responds to changes in price, income, or the price of related goods. Understanding elasticity helps explain consumer and producer behavior, and informs policy decisions.

Price Elasticity of Demand

Definition and Interpretation

• Price Elasticity of Demand (PED): The percentage change in quantity demanded resulting from a one percent change in price, holding all else constant.

• Formula:

$e = \frac{\%\Delta Q}{\%\Delta P}$

• Usually negative due to the Law of Demand (as price increases, quantity demanded decreases).

• Elasticity is a unit-free measure, allowing comparison across goods and markets.

Calculating Percentage Changes

• Change: $\Delta x = x_{new} - x_{old}$

• Average Value: $\bar{x} = \frac{x_{new} + x_{old}}{2}$

• Percentage Change: $\%\Delta x = \frac{\Delta x}{\bar{x}} \times 100$

Example: If quantity increases from 100 to 200, $\Delta Q = 100$, $\bar{Q} = 150$, so $\%\Delta Q = \frac{100}{150} \times 100 = 66.7\%$.

Elasticity and Slope

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

• For a linear demand curve $Q = a - bP$:

$e = \frac{dQ}{dP} \cdot \frac{P}{Q}$

• Elasticity varies along a linear demand curve, even though the slope is constant.

Classification of Price Elasticity of Demand

Elasticity Value	Classification	Description
$|e| = 0$	Perfectly Inelastic	Quantity demanded does not change with price
$0 < |e| < 1$	Inelastic	Quantity demanded changes less than price
$|e| = 1$	Unit Elastic	Quantity demanded changes exactly as price
$|e| > 1$	Elastic	Quantity demanded changes more than price
$|e| = \infty$	Perfectly Elastic	Buyers only purchase at one price

Determinants of Demand Elasticity

• Availability of Substitutes: More substitutes make demand more elastic (e.g., medicine vs. collectibles).

• Proportion of Income: Goods that take a larger share of income tend to have more elastic demand (e.g., cars vs. transit fares).

• Time Horizon: Demand is more elastic in the long run as consumers adjust their behavior.

Examples of Elasticities for Various Goods

Good or Service	Elasticity
Furniture	1.26
Motor Vehicles	1.14
Gas, Electricity, Water	0.92
Food	0.12
Cigarettes	0.40

Elasticity and Revenue

Total Revenue and Expenditure

• Total Revenue (TR): $TR = P \times Q$

• Total Expenditure: $TE = P \times Q$ (from the buyer's perspective)

• How revenue/expenditure changes with price depends on elasticity:

Type of Demand	Effect of Price Increase on Quantity	Effect on Revenue/Expenditure
Elastic ($|e| > 1$)	Quantity decreases more than 1%	Revenue decreases
Inelastic ($|e| < 1$)	Quantity decreases less than 1%	Revenue increases
Unit Elastic ($|e| = 1$)	Quantity decreases exactly 1%	Revenue unchanged

Other Demand Elasticities

Income Elasticity of Demand

• Definition: The percentage change in quantity demanded per percentage change in income.

• Formula:

$e_{I} = \frac{\%\Delta Q}{\%\Delta I}$

• Normal Goods: Positive income elasticity (demand increases as income rises).

• Inferior Goods: Negative income elasticity (demand decreases as income rises).

• Income-Elastic: $e_{I} > 1$ (luxury goods).

• Income-Inelastic: $0 < e_{I} < 1$ (necessities).

Cross-Price Elasticity of Demand

• Definition: The percentage change in quantity demanded of good A per percentage change in the price of good B.

• Formula:

$e_{AB} = \frac{\%\Delta Q_A}{\%\Delta P_B}$

• Substitutes: Positive cross-price elasticity.

• Complements: Negative cross-price elasticity.

Price Elasticity of Supply

Definition and Classification

• Price Elasticity of Supply (PES): The percentage change in quantity supplied per percentage change in price.

• Formula:

$e_s = \frac{\%\Delta Q_s}{\%\Delta P}$

• Usually positive (Law of Supply).

Elasticity Value	Classification	Description
$|e_s| = 0$	Perfectly Inelastic	Quantity supplied does not change with price
$0 < |e_s| < 1$	Inelastic	Quantity supplied changes less than price
$|e_s| = 1$	Unit Elastic	Quantity supplied changes exactly as price
$|e_s| > 1$	Elastic	Quantity supplied changes more than price
$|e_s| = \infty$	Perfectly Elastic	Only sell at a given price

Determinants of Supply Elasticity

• Availability of Production Substitutes: More substitutes make supply more elastic (e.g., cornfields vs. oil refineries).

• Financial Flexibility: Firms with more resources or insurance can adjust supply more easily.

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

Estimating Elasticities

Empirical Measurement

• Elasticities are estimated using observed data on prices and quantities over time.

• Random or natural experiments (e.g., supply shocks) can help identify demand or supply elasticities.

• Econometric methods are used in advanced courses to estimate elasticities from real-world data.

Shifts in Supply and Demand

Key Shifters

Demand Shifters	Supply Shifters
Price of substitutes	Price of production substitutes
Price of complements	Price of factors of production
Consumption preferences	Production technologies
Population	Number of producers
Income	Interest rates

Summary

• Elasticity measures responsiveness of demand or supply to changes in price, income, or related goods' prices.

• Understanding elasticity is crucial for predicting the effects of market changes and policy interventions.

• Elasticity affects total revenue, expenditure, and market outcomes.

Additional info: Some context and examples were expanded for clarity and completeness, as the original notes were fragmented and included shorthand or incomplete tables.