Elasticity: Measuring Responsiveness in Microeconomics

Chapter 5: Elasticity – Measuring Responsiveness

Overview

This chapter explores the concept of elasticity in microeconomics, focusing on how buyers and sellers respond to changes in prices and other economic factors. Elasticity is a crucial tool for understanding market behavior and for making informed business decisions.

• Price Elasticity of Demand

• How Businesses Use Demand Elasticity

• Other Demand Elasticities

• Price Elasticity of Supply

Price Elasticity of Demand

Definition and Interpretation

Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

• Formula:

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

• If the price of a good falls, the quantity demanded will rise. Elasticity tells us how much it will rise.

• If a price change leads to a small change in sales, demand is inelastic.

• If a price change leads to a large change in sales, demand is elastic.

Example: If cutting the price of t-shirts by 15% leads to a 25% increase in quantity demanded, the price elasticity of demand is:

$\text{Price Elasticity of Demand} = \frac{+25\%}{-15\%} = -1.67$

Economists often use the absolute value of elasticity for interpretation.

Elastic vs. Inelastic Demand

• Elastic Demand: The absolute value of elasticity is greater than 1 ($|\text{Elasticity}| > 1$). Buyers are very responsive to price changes.

• Inelastic Demand: The absolute value of elasticity is less than 1 ($|\text{Elasticity}| < 1$). Buyers are not very responsive to price changes.

Examples:

• If $|\Delta Q| = 35\%$ and $|\Delta P| = 20\%$, then $|\text{Elasticity}| = 1.75$ (elastic).

• If $|\Delta Q| = 8\%$ and $|\Delta P| = 3\%$, then $|\text{Elasticity}| = 2.67$ (elastic).

• If $|\Delta Q| = 3\%$ and $|\Delta P| = 10\%$, then $|\text{Elasticity}| = 0.3$ (inelastic).

Visualizing Elasticity

• Elastic demand curves are relatively flat.

• Inelastic demand curves are relatively steep.

Perfectly Elastic Demand: A horizontal demand curve ($\text{Elasticity} = \infty$). Any price increase causes quantity demanded to drop to zero.

Perfectly Inelastic Demand: A vertical demand curve ($\text{Elasticity} = 0$). Quantity demanded does not change with price.

Determinants of Price Elasticity of Demand

Key Factors

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

• Necessities vs. Luxuries: Necessities tend to have inelastic demand; luxuries are more elastic.

• Definition of the Market: Narrowly defined markets (e.g., specific brands) have more elastic demand than broadly defined markets (e.g., food).

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

• Proportion of Income: Goods that take up a larger share of income tend to have more elastic demand.

Example: Airline tickets for a weekend trip are more elastic for someone who can drive as an alternative, and more inelastic for someone who must fly due to distance or time constraints.

Calculating Price Elasticity of Demand

Midpoint Formula

To avoid discrepancies depending on the direction of change, economists use the midpoint formula:

$\text{Elasticity} = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}$

• Step 1: Calculate the percent change in price using the midpoint.

• Step 2: Calculate the percent change in quantity demanded using the midpoint.

• Step 3: Divide the percent change in quantity by the percent change in price.

Example: If the price of brownies increases from $1.50 to $2.25 and quantity demanded falls from 72 to 60:

• Percent change in price: $\frac{2.25 - 1.50}{(2.25 + 1.50)/2} = 42.8\%$

• Percent change in quantity: $\frac{60 - 72}{(60 + 72)/2} = -18.2\%$

• Elasticity: $\frac{-18.2\%}{42.8\%} = -0.43$ (inelastic)

Elasticity and Total Revenue

Relationship Between Price, Quantity, and Revenue

Total Revenue (TR) is the total amount received by sellers, calculated as:

$\text{Total Revenue} = \text{Price} \times \text{Quantity}$

• If demand is elastic, lowering price increases total revenue.

• If demand is inelastic, raising price increases total revenue.

Example: If a company raises the price of its product by 15% and demand is elastic, total revenue will decrease. If demand is inelastic, total revenue will increase.

Other Demand Elasticities

Cross-Price Elasticity of Demand

Cross-price elasticity measures how the quantity demanded of one good responds to a change in the price of another good.

$\text{Cross-Price Elasticity} = \frac{\%\,\text{Change in Quantity Demanded of Good X}}{\%\,\text{Change in Price of Good Y}}$

• Positive sign: Goods are substitutes.

• Negative sign: Goods are complements.

Example: If the price of raspberries rises by 8% and the demand for blueberries increases by 12%, the cross-price elasticity is $\frac{12\%}{8\%} = 1.5$ (substitutes).

Income Elasticity of Demand

Income elasticity measures how the quantity demanded of a good responds to a change in consumer income.

$\text{Income Elasticity} = \frac{\%\,\text{Change in Quantity Demanded}}{\%\,\text{Change in Income}}$

• Positive sign: The good is a normal good (demand increases as income rises).

• Negative sign: The good is an inferior good (demand decreases as income rises).

Example: If income rises by 4% and demand for box Mac & Cheese falls by 3%, the income elasticity is $\frac{-3\%}{4\%} = -0.75$ (inferior good).

Price Elasticity of Supply

Definition and Calculation

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Price elasticity of supply measures how responsive the quantity supplied is to a change in price.

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

Elastic supply: $|\text{Elasticity}| > 1$ (suppliers are very responsive to price changes).

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"""stic supply: $|\text{Elasticity}| < 1$ (suppliers are not very responsive to price changes).

Example: If raising the price of donuts by 12% leads to a 16% increase in quantity supplied, the price elasticity of supply is $\frac{16\%}{12\%} = 1.33$ (elastic).

Determinants of Price Elasticity of Supply

• Flexibility of Production: If producers can easily change the quantity produced, supply is more elastic.

• Availability of Inputs: If inputs are readily available, supply is more elastic.

• Capacity Constraints: If firms have unused capacity, supply is more elastic.

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

• Ability to Store Goods: Storable goods have more elastic supply.

Example: Landscaping companies can quickly hire more workers and buy more equipment, making supply elastic. Airlines, which require expensive planes and skilled pilots, have inelastic supply.

Calculating Price Elasticity of Supply

Use the midpoint formula for consistency:

$\text{Elasticity} = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}$

Example: If the price for tutoring rises from $15 to $20 per hour and the number of hours supplied increases from 5 to 8:

• Percent change in price: $\frac{20 - 15}{(20 + 15)/2} = 28.57\%$

• Percent change in quantity: $\frac{8 - 5}{(8 + 5)/2} = 46.15\%$

• Elasticity: $\frac{46.15\%}{28.57\%} = 1.61$ (elastic)

Summary Table: Types of Elasticity

Elasticity Type	Formula	Interpretation	Significance
Price Elasticity of Demand	$\frac{\%\,\text{Change in Qd}}{\%\,\text{Change in P}}$	How buyers respond to price changes	Elastic ($>1$), Inelastic ($<1$)
Cross-Price Elasticity	$\frac{\%\,\text{Change in Qd of X}}{\%\,\text{Change in P of Y}}$	How demand for one good responds to price changes in another	Positive: Substitutes; Negative: Complements
Income Elasticity	$\frac{\%\,\text{Change in Qd}}{\%\,\text{Change in Income}}$	How demand responds to income changes	Positive: Normal good; Negative: Inferior good
Price Elasticity of Supply	$\frac{\%\,\text{Change in Qs}}{\%\,\text{Change in P}}$	How sellers respond to price changes	Elastic ($>1$), Inelastic ($<1$)

Key Takeaways

• Elasticity measures responsiveness in economic variables.

• Price elasticity of demand and supply are central for predicting market outcomes.

• Other elasticities (cross-price, income) help classify goods and understand market relationships.

• Businesses use elasticity to set prices and forecast revenue changes.