Study Guide: Demand and Supply Elasticity in Microeconomics

Demand and Supply Elasticity

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how responsive the quantity demanded or supplied of a good is to changes in price, income, or the price of related goods. Understanding elasticity helps businesses and policymakers predict the effects of price changes, taxes, and subsidies on market outcomes.

19.1 Price Elasticity of Demand

The price elasticity of demand quantifies the responsiveness of the quantity demanded to changes in the price of a commodity. It is defined as the percentage change in quantity demanded divided by the percentage change in price.

• Formula: $\text{Price Elasticity of Demand} = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Price}}$

• Interpretation: An elasticity of -0.1 means a 10% increase in price leads to a 1% decrease in quantity demanded.

• Convention: Elasticity is usually reported as a positive number, ignoring the negative sign due to the law of demand.

Example: If the price of oil increases by 10% and quantity demanded decreases by 2%, the price elasticity is 0.2.

Types of Price Elasticity

• Elastic Demand: Percentage change in quantity demanded is greater than percentage change in price. Total revenue falls when price rises.

• Inelastic Demand: Percentage change in quantity demanded is less than percentage change in price. Total revenue rises when price rises.

• Unit Elastic Demand: Percentage change in quantity demanded equals percentage change in price. Total revenue remains unchanged when price changes.

• Perfectly Inelastic Demand: Quantity demanded does not change regardless of price (vertical demand curve).

• Perfectly Elastic Demand: Quantity demanded drops to zero with any price increase (horizontal demand curve).

19.2 Elasticity and Total Revenues

The relationship between price elasticity of demand and total revenue is crucial for business pricing decisions.

• Elastic Demand: Price and total revenue are inversely related.

• Inelastic Demand: Price and total revenue are positively related.

• Unit Elastic Demand: Total revenue does not change with price changes.

• Formula for Total Revenue: $\text{Total Revenue} = \text{Price} \times \text{Quantity Sold}$

Example: Ride-sharing services lowered prices by 10-50%, increasing quantity demanded and total revenue, illustrating elastic demand.

19.3 Determinants of Price Elasticity of Demand

Several factors influence the price elasticity of demand:

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

• Share of Budget: Goods that take up a larger share of a consumer's budget have more elastic demand.

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

Short Run vs. Long Run: In the short run, consumers cannot fully adjust to price changes; in the long run, they can.

19.4 Cross Price and Income Elasticities of Demand

Elasticity concepts extend beyond price changes to include related goods and income changes.

• Cross Price Elasticity of Demand: Measures the responsiveness of demand for one good to changes in the price of another good.

• Formula: $\text{Cross Price Elasticity} = \frac{\%\ \text{Change in Quantity Demanded of Good Y}}{\%\ \text{Change in Price of Good X}}$

• Substitutes: Positive cross price elasticity (increase in price of X increases demand for Y).

• Complements: Negative cross price elasticity (increase in price of X decreases demand for Y).

• Income Elasticity of Demand: Measures responsiveness of demand to changes in income.

• Formula: $\text{Income Elasticity} = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Income}}$

• Normal Goods: Positive income elasticity.

• Inferior Goods: Negative income elasticity.

19.5 Price Elasticity of Supply

The price elasticity of supply measures the responsiveness of the quantity supplied to changes in price.

• Formula: $\text{Price Elasticity of Supply} = \frac{\%\ \text{Change in Quantity Supplied}}{\%\ \text{Change in Price}}$

• Elastic Supply: Elasticity greater than 1.

• Inelastic Supply: Elasticity less than 1.

• Unit Elastic Supply: Elasticity equal to 1.

• Perfectly Elastic Supply: Quantity supplied falls to zero with any price decrease (horizontal supply curve).

• Perfectly Inelastic Supply: Quantity supplied does not change regardless of price (vertical supply curve).

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

Example: Behavioral economists found that a 1% increase in payments for gym workouts increased supply by 0.15%.

Applications and Policy Examples

• Taxation: When demand is highly elastic, consumers bear less of the tax burden; firms bear more.

• Philadelphia Soft Drinks Tax: A 35% price increase led to a 45% decrease in purchases, indicating elastic demand.

• Airline Ticket Taxes: A 1% price increase reduced quantity demanded by 8%, showing highly elastic demand.

Summary Table: Relationship Between Price Elasticity and Total Revenue

Elasticity Type	Price Change	Total Revenue Change
Elastic (>1)	Increase	Decrease
Inelastic (<1)	Increase	Increase
Unit Elastic (=1)	Increase	No Change

Summary of Key Learning Objectives

• Calculate price elasticity of demand and supply using percentage changes.

• Explain the relationship between elasticity and total revenues.

• Describe determinants of elasticity: substitutes, budget share, time horizon.

• Classify goods as substitutes or complements using cross price elasticity.

• Classify goods as normal or inferior using income elasticity.

• Explain how time affects elasticity of supply.