Elasticity and Its Applications – Microeconomics Study Notes

Elasticity and Its Applications

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how much buyers and sellers respond to changes in market conditions. It is crucial for understanding how various factors affect demand, supply, and market outcomes.

• Elasticity: The responsiveness of quantity demanded (Qd) or quantity supplied (Qs) to changes in one of its determinants (such as price, income, or the price of related goods).

• Applications: Elasticity helps analyze the effects of price changes, income fluctuations, and policy interventions on market outcomes.

Price Elasticity of Demand

The price elasticity of demand measures how much the quantity demanded of a good responds to a change in its price. It is a key indicator of buyers' price sensitivity.

• Definition: 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: Along a demand curve, price and quantity move in opposite directions, making price elasticity negative. However, elasticities are typically reported as positive numbers (absolute value).

• Example: If the price of a product increases by 10% and the quantity demanded falls by 15%, the price elasticity of demand is $\frac{15}{10} = 1.5$.

Calculating Elasticity: The Midpoint Method

The midpoint method is a standard approach for calculating percentage changes and elasticity, providing consistent results regardless of the direction of change.

• Midpoint Formula for Percentage Change:

$\text{Percentage Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Average of New and Old Values}} \times 100$

• Example: If price rises from $400 to $600 and quantity falls from 10,600 to 8,400, the midpoint method gives:

$\text{Percentage Change in Price} = \frac{600 - 400}{(600 + 400)/2} \times 100 = 40\%$ $\text{Percentage Change in Quantity} = \frac{8,400 - 10,600}{(8,400 + 10,600)/2} \times 100 = -23.16\%$ $\text{Elasticity} = \frac{23.16}{40} = 0.58$

Determinants of Price Elasticity of Demand

Several factors influence the price elasticity of demand for a good:

• Availability of Close Substitutes: Demand is more elastic when substitutes are available (e.g., Cheerios vs. Airfare).

• Narrowly vs. Broadly Defined Goods: Narrowly defined goods (e.g., Mountain Dew) have higher elasticity than broadly defined ones (e.g., soda).

• Necessities vs. Luxuries: Luxuries (e.g., Rolex watches) have higher elasticity than necessities (e.g., insulin).

• Time Horizon: Demand is more elastic in the long run than in the short run (e.g., gasoline).

Varieties of Demand Curves

The elasticity of demand can vary along different demand curves:

• Elastic Demand: Elasticity > 1

• Inelastic Demand: Elasticity < 1

• Unit Elastic Demand: Elasticity = 1

• Perfectly Inelastic Demand: Elasticity = 0 (vertical curve)

• Perfectly Elastic Demand: Elasticity = ∞ (horizontal curve)

Total Revenue and Elasticity

Total revenue (TR) is the product of price and quantity sold. The effect of a price change on total revenue depends on the elasticity of demand:

• Formula:

$\text{Total Revenue} = P \times Q$

• Elastic Demand: Price increase leads to a decrease in total revenue.

• Inelastic Demand: Price increase leads to an increase in total revenue.

• Example: If demand is elastic ($E = 1.8$), raising price from $2,000 to $2,500$ reduces quantity from 12 to 8, and total revenue falls. If demand is inelastic ($E = 0.8$), raising price increases total revenue.

Income Elasticity of Demand

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

• Formula:

$\text{Income Elasticity of Demand} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}}$

• Normal Goods: Income elasticity > 0

• Inferior Goods: Income elasticity < 0

Cross-Price Elasticity of Demand

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

• Formula:

$\text{Cross-Price Elasticity of Demand} = \frac{\%\ \text{change in quantity demanded of Good 1}}{\%\ \text{change in price of Good 2}}$

• Substitutes: Cross-price elasticity > 0

• Complements: Cross-price elasticity < 0

Price Elasticity of Supply

The price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price.

• Formula:

$\text{Price Elasticity of Supply} = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}$

• Elastic Supply: Quantity supplied responds substantially to price changes.

• Inelastic Supply: Quantity supplied responds only slightly to price changes.

Varieties of Supply Curves

• Elastic Supply: Elasticity > 1

• Inelastic Supply: Elasticity < 1

• Unit Elastic Supply: Elasticity = 1

• Perfectly Inelastic Supply: Elasticity = 0 (vertical curve)

• Perfectly Elastic Supply: Elasticity = ∞ (horizontal curve)

Determinants of Supply Elasticity

The price elasticity of supply depends on how easily sellers can change the quantity produced. Supply is generally more elastic in the long run, as firms can adjust production capacity and new firms can enter the market.

Applications of Elasticity

• Policy Analysis: Elasticity helps evaluate the effects of taxes, subsidies, and regulations (e.g., drug interdiction vs. drug education).

• Market Outcomes: Elasticity determines how changes in demand or supply affect equilibrium price and quantity (e.g., wheat market, oil market).

Summary Table: Types of Elasticity

Type of Elasticity	Formula	Interpretation
Price Elasticity of Demand	$\frac{\%\ \text{change in Qd}}{\%\ \text{change in P}}$	Responsiveness of quantity demanded to price changes
Income Elasticity of Demand	$\frac{\%\ \text{change in Qd}}{\%\ \text{change in income}}$	Responsiveness of quantity demanded to income changes
Cross-Price Elasticity of Demand	$\frac{\%\ \text{change in Qd of Good 1}}{\%\ \text{change in price of Good 2}}$	Responsiveness of quantity demanded of one good to price changes of another
Price Elasticity of Supply	$\frac{\%\ \text{change in Qs}}{\%\ \text{change in P}}$	Responsiveness of quantity supplied to price changes

Key Takeaways

• Elasticity quantifies how much quantity demanded or supplied responds to changes in price, income, or related goods' prices.

• Understanding elasticity is essential for predicting market reactions and designing effective policies.

• Elasticity varies by product, market definition, time horizon, and availability of substitutes.